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In the case of the BigFish and Jumper environments, no simple policy exists common to every level that allows for a good performance, thus almost no agent is able to succeed without retraining on new levels. We note, however, that the small number of levels (50) used to train the experts contributes to the lack of generalization; in {{cite:f29c585a69c84d572d9422302546273501ec2d89}}, individual networks trained on 100, 300, and even 1000 levels had similar performance on test levels for BigFish and Jumper.
However, the performance of the student network on CoinRun is interesting as the simple policy of running right while jumping as soon as possible is often enough to finish many levels.
In fact, Figure REF shows that the student is able to solve more than half of the 100 unseen levels we tested it on.
On the other hand, the fail cases are in a large majority due to the presence of enemies in the path of the agent when following this simple policy.
This confirms that, although simple, the policy extracted by the distillation process is quite general and can transfer as is to multiple new levels.
{{figure:95994dcd-c781-4c34-bfc5-a0c0588e83dd}} | r | 1c8af11d16cb7e9b8f721aa878b5ff5b |
We show qualitative results on AFHQ dog and wild (Figure REF ), FFHQ faces (Figure REF ), and StyleGAN2 {{cite:f1e9223b47ba31f8addce10c2667be8ac1a294cc}} (Figure REF ). All models are trained with ten user edits.
| r | 8a30bc5c27d6234da8030d38635905d2 |
The small fraction of time that the radio pulsations are detectable is notable. There are several possible explanations that are difficult to differentiate between with only one relatively low signal-to-noise detection. One reason could be simply interstellar scintillation. High frequency observations of nearby MSPs are particularly susceptible to scintillation. For some of the MSPs found in LAT-directed surveys at Parkes, the observed flux density varies by a factor of 20 from observation to observation and some of the pulsars are detectable in only about one third of the observations (Camilo et al. 2012, in preparation). Alternatively, the pulsations could be eclipsed by material local to the system itself. There are several possible mechanisms for such eclipses {{cite:71e90aa4ea278c2cdea289bc91d9a09de4496225}} and which mechanism is operative may be different for different systems. In this case, the continuum detections of a radio point source suggest that the pulsations may be scattered out of existence (e.g. scattering by plasma turbulence) rather than the radio waves being actually absorbed. Variations in the scattering medium may be responsible for the non-detections at other times and frequencies. The presence of a red, flaring optical component, likely from the pulsar flux reprocessed in the companion wind {{cite:3f5be7d2de772177ef5ac101bd8411c4c9d64210}} gives additional evidence for a wind of variable density and covering fraction. The timescale and magnitude of dispersion measure variations can be a useful diagnostic of these processes. We see some evidence for DM growing to just over 38.0 pc cm{{formula:b04600ce-a746-4c45-8298-4b2730e40cbe}} in the later part of our observation but the significance is too limited to draw any firm conclusions. Also, it is difficult to constrain the presence of a scattering tail in the pulse profile for the same reasons.
| d | ac8361b7ea42267effdb3dd6e5649b94 |
Inspired by previous works {{cite:4ce920ebc9792d1efe3d7263fe35a70642d70da3}}, {{cite:08fe441e8cae6b8fddfeb0eb04e10895e09e43b5}}, {{cite:00ad09977dcb5436e6f349a551cca104da009cf9}},
we introduce a novel pseudo multi-labeling strategy.
Concretely, we extract pseudo-attributes from product titles and optimize a multi-label classification objective.
This forms a weakly-supervised representation learning problem.
The advantage of our formulation is two-folds:
(a)
Our pseudo-attributes instance-dependent and thus more fine-grained than category labels, despite being noisy by nature;
(b)
Our pseudo-attributes retain the majority of information from the text modality, whilst the visual feature learning is conducted in an intra-modal manner.
This decoupling design well mitigates the challenges as discussed earlier.
Further, we build a strong baseline model
with ImageNet-pretrained backbones {{cite:3c927530003d54fc0a43f332b267a8f7e4c71db8}}, {{cite:9e6d1de0e2e8a10f14f3420800c77588e2080969}}, advanced training recipes (, TrivalAugment {{cite:2692b1de3a268cb739c7664e682df7f1a5277c33}} and random erasing {{cite:9d0afaaa32f849b9405e2f2a7bfaa030eb7bd849}}) and post-processing (feature whitening {{cite:df33868401b932b01a58dc7978a652b41f15bb54}}, {{cite:0d70cf1379c2182412dbfc167b0ad181f90fa0e7}}, k-reciprocal reranking {{cite:e45a561c034e6d770922a22aa6202ff02b4cc0b7}} and model ensemble).
Empirically, we show that our method outperforms all competing methods by a large margin, getting hold of the second position out of about twenty teams on the leaderboard.
| i | 63db7b741ff163685752155f56c2ee0f |
Notwithstanding these limitations we have shown that ideal networks
designed to be maximally navigable at minimal cost share basic
structural properties with real networks. Compared to existing works
on navigation-optimal distributions of shortcut edges in Euclidean
grids
{{cite:3d05444dc79e69b9354702e24a63e7be0d7af760}}, {{cite:4a229c00792c76b8c00724531547328b59384737}}, {{cite:608cf9cbf12fe70a82bf77976c94a73911147df2}}, {{cite:d957af5f96f6aaa3574f8ccff253549261cc656a}}
which do not yield realistic network topologies, this result is quite
unexpected because there is absolutely nothing in the definition of
these ideal networks that would enforce or even welcome a formation of
any particular network structure. The networks are defined purely in
terms of navigation optimality. The surprising finding that the
structure of these ideal networks is similar to the structure of real
networks should not be misinterpreted as if these idealisations are
generative models for real navigable networks. Instead the former are
skeletons or subgraphs of the latter. Since these skeletons consist of
the minimum number edges required for {{formula:1987bd5c-6311-479c-bd6e-595e06fa1df1}} navigability,
there is no even a parameter to control the most basic structural
network property—the average degree, which is always controllable in
generative models. On the contrary, as follows from
Eq. (REF ), the average degree in these skeletons is
uncontrollable and lies between 1 and 4.
| d | 862ba9b358123dbecf73689e4e18b89b |
From Andrzejak et al. {{cite:679219f58a4afe9b829b1e90079bfe77e3a88236}}, 10 Participants (5 Healthy and 5 Epileptic Patients)
| d | 2738538329bb83c72ba3845b34fc442f |
M3 SMOTE ENN {{cite:f7527b03d9bfd2d58b7a7c8186fdebfefda7f158}} 13 Binary C4.5 AUC
| m | e440531b851471064076c266b2ee0cd8 |
More generally, the phylogenetic networks that we have
considered in this paper did not have arc weights. It would
be interesting to understand how arc weights might affect
our results, especially when we want to make
a straight-line drawing where the length of an
arc is proportional to its weights. A special case that could be
considered first are
temporal phylogenetic networks which incorporate a
natural vertical time axis which provides timings for
past evolutionary events (see e.g. {{cite:62613848eb39938118ff60031a76bec6bce633e5}}). This
concept appears to be related to upward planarity, and it
would be interesting to further investigate this relationship. Moreover, in
general as the theory of phylogenetic networks continues to
grow it could be worthwhile to develop new algorithms
to produce planar phylogenetic networks from biological data.
| d | d07d3ec8735034a433ed8764c2eca662 |
Perhaps one of the most interesting findings is that our PAC-Bayes bound is able to capture the power law scaling of the learning curve of DNNs. This scaling has been the subject of recent important work in deep learning theory {{cite:bca9778c4465fe5bcb75069d0ad06a2880e4173b}}, {{cite:10d35739b990d6c45547676d654349d30e978a3d}}. However, the work of {{cite:10d35739b990d6c45547676d654349d30e978a3d}} also highlights the importance of predicting the error as a function of data size, model size (number of parameters) and training iterations, for the purposes of optimizing the loss for a given compute budget. Our theory works in the limit of infinitely large models, trained to convergence (0 training error) so it can only capture the scaling when data is the bottleneck. Extending our theory to finite-sized models and non-zero training error is an important direction for future work.
| d | 33b51d14585cbeba910a055a48d6e9ad |
The systems confined in quantum dots weakly coupled to electron reservoirs are studied with the transport spectroscopy using the Coulomb blockade phenomenon {{cite:0327b25f72406e26b5781f261ea0c9c4cfca509a}}, {{cite:09e2dbfb7ae1418465cf79ff2d0c1284e077ec7b}}.
In the Coulomb blockade regime, the flow of the current across the dot is stopped
when the chemical potential of the confined {{formula:6392e55d-97c2-4e3f-aaea-7256d7551241}} -electron is outside the transport window
defined by the Fermi levels of the source and drain. For a small voltage drop between the reservoirs,
the position of the chemical potential can be very precisely determined.
The chemical potential {{formula:e9943768-e13e-4bb0-bd7c-f4e398eff252}} is defined by the ground state energies of systems with {{formula:2518394c-15eb-4ba2-8e9a-e616fb648fd8}} and {{formula:f8856162-4da8-4dea-8cc8-568681db6ab5}} electrons {{cite:0327b25f72406e26b5781f261ea0c9c4cfca509a}}, {{cite:09e2dbfb7ae1418465cf79ff2d0c1284e077ec7b}}. The ground-state energy crossing in the {{formula:ffa0afc9-ca3b-41e7-9c31-2070b94a0ae1}} electron system produces {{formula:2d1354ab-bea8-4a52-9beb-6eccf65b23a8}} -shaped cusps
in the charging line as a function of the external magnetic field for the {{formula:64e1088b-6054-4770-9d9a-761154302aee}} -th electron added to the confined system, while the ground-state transitions for the {{formula:ee9b34b2-f44b-42e5-892b-a930c0073a9f}} system produces {{formula:0cdab97f-67db-4428-a9ae-750fee5865d8}} -shaped cusps.
Transport spectroscopy allows reconstruction of the energy spectra with
a precision of the order of a few {{formula:3ff29a05-04ea-4923-907f-a9aba4faa823}} eV {{cite:f63cd21d0b7216d1fc6a52df8c76f23ba31ac76c}}.
The results presented above indicate that the formation of the Wigner molecule in the laboratory frame
leads to a near degeneracy of the ground state near {{formula:7f7c3e3e-6708-4e21-b7b5-e6cec61669d2}} . The larger the electron separation
in the single-electron charge islands, the closer the degeneracy at {{formula:f11fc0f0-820d-4f29-b645-a8e9b909fea3}} .
The ground state becomes spin-polarized
at low magnetic field and no further ground-state transitions are observed.
The systems without the Wigner molecular charge density undergo a number
of ground-state transitions that also appear at higher magnetic field.
The transport spectroscopy technique can also be used for detection of the
excited part of the spectra when the corresponding energy level enters the transport window {{cite:0327b25f72406e26b5781f261ea0c9c4cfca509a}}, {{cite:f63cd21d0b7216d1fc6a52df8c76f23ba31ac76c}}.
Detection of a dense set of levels near the ground state can be used as a signature of Wigner molecule formation {{cite:c7ad50b59c989a986b04df3504604541cdeb37e5}}, {{cite:863d3c65e79bf35b85eb1454fb4dff197f64255c}}.
| d | 55e545152be1cfc685d295459bfa4d09 |
The large-scale fading of the BS-RIS and RIS-user channels are modelled as {{formula:3d94a7e3-2b28-4e08-9750-9234462425be}} , {{formula:3e12aea2-bf7a-406a-a49c-a10401bdcc3e}} , {{formula:ec2c48b3-7d81-4c83-87b8-996ceb2f5725}} , {{formula:2f0ab48a-cc3f-4e09-a571-aae8698258dd}} , where {{formula:7e1227a8-aa59-4419-9656-b7822605dd17}} and {{formula:889441cc-9c7f-497e-9698-d1192d8e9abb}} are the path loss exponents {{cite:be417c9340b2d9a5fd22ec188d332c0d72741f91}}, {{formula:364203cf-8c5a-4448-b264-ad2de0768c98}} ({{formula:c48028bd-ec17-45ea-9a39-d74b6cc965f2}} ) denotes distance between the BS ({{formula:74ce1224-ba1c-49d8-931e-d626cdf67e0e}} -th RIS) and the {{formula:37741ae3-f065-4aca-9775-b28bed7e9434}} -th RIS ({{formula:ee0ad7ca-1004-48bd-b9cb-745c66b14216}} -th user). The default simulation parameters are listed in Table I.
{{figure:7a1cd9ba-e68f-4f53-b181-157fff6a596e}}{{figure:035f8b48-4f04-4a71-8ad0-6885662c68b9}} | r | 8cad452e4c7c2abd411d8ea146ebf973 |
We view the proposed model as a simple first step towards addressing pitfalls of Bayesian approaches to high-dimensional clustering. There are several important aspects that we have not been able to address in this initial paper. The first is the issue of fast computation in very large {{formula:c63fb7b9-8d4d-4509-8de3-a35736cd30f7}} clustering problems. We have taken a relatively simple MCMC approach that works adequately well in our motivating application in which one has the luxury of running the analysis for many hours for each new dataset. However, there is certainly a need for much faster algorithms that can exploit parallel and distributed processing; for example, running MCMC for different subsets of the variables in parallel and combining the results. Potentially building on the algorithms of {{cite:de18d6adda6e0ccba62eac1da55090de779d8cd6}} and {{cite:cf94b6565979e76be9d06af10eb72c18ace261c9}} may be promising in this regard.
| d | 2c6e1255025e9b7a1f676c5fa81e6acb |
Sometimes authors even refer to the quantity {{formula:9a7b4ec8-bb09-4f75-8840-542e95b7c408}} (expressed in terms of the HHZ variables {{formula:7183b9c9-ddac-4917-9686-5067a5a3d795}} and {{formula:d2afe977-962e-4f4e-904a-0a3b25040ebb}} ) as the free energy {{formula:a13c4013-bd67-4dc0-b679-9b25266701e6}} , rather than the full complex expression {{cite:f4f1c4d3ee9bec4acf5afacbf73c4d75111a6d49}}, {{cite:7a3dade90a2c88531351e829e1f55a8fe0f8f5ad}}, {{cite:3653430e25375cd8fe9dd8357f157cf4035ed7da}}, {{cite:6a1eb480fa69a0a088c74f69bdf3945d3468bad4}}. The analogous comparison between the real part of the complex chemical potentials is also successful:
{{formula:66f5f8a9-ca9c-4e48-8a03-2b5e165f09ff}}
| r | 8dad3a21751046ba2643549c0e7bbdc9 |
Since the continuous Newton flow (REF ) is intrinsically
a nonlinear diminishing system for the energy function {{formula:392a640f-a54a-469d-a71e-fe6c3bccfff2}} ,
it can be integrated by the strong stability preserving methods {{cite:17b9f6b704e6a0f01b00685eb88cb266f147acfc}}, {{cite:f7acc410777cc55529098e143b0110e5b0758929}}
and the steady-state solution {{formula:d8ab6121-5279-4175-9a1d-ab0768dd93f3}} can be obtained after the long time
integration. Here, we consider another approach based on the traditional optimization
methods for problem (REF ). We expect that the new method has the global
convergence as the homotopy continuation method and the fast convergence rate near
the steady-state solution {{formula:03e9fee5-0f8b-4453-bebe-bccc16a79805}} as the merit-function method. In order to
achieve these two aims, we construct the special continuation Newton method with the
new step size {{formula:5c1e8cc5-7657-43ab-be55-de5aea2a1d52}} and the time step size
{{formula:38c87cc1-c8e1-4e70-87e1-1363eb433520}} is adaptively adjusted by the trust-region updating strategy for
problem (REF ).
| m | a45b0b58f67d6e0b982325d023c02974 |
In this section, we present the results for two trained hierarchic decomposition models. We use the ShapeNet dataset {{cite:ab6f06daedbb2743e748446bec4128be4a2d4242}} for training along with the NVIDIA Kaolin v0.1 library {{cite:ca0a75b6ebdbb93ef9016f0f0845de95ffcaa9af}}, which is used to compute signed distance function values of the 3D objects and to infer the ground truth inside-outside space. The first model (abbreviated ModelP) is trained on the Pistol subset of ShapeNet with the maximum depth of the superquadric pair tree set to 3 levels. The second model (ModelS) is trained on the full ShapeNet dataset with the maximum depth set to 2 levels. Training with more levels proved challenging, and resulted in degenerated SQs, often small and out of bounds.
| r | a6ec0546281167b44ba55420a490f3a3 |
We also compare with other methods on Colored MNIST in a single-bias setting. There are two variants of Colored MNIST datasets in previous works—(1) adding colors to the foreground (i.e., digit) {{cite:15b50e2db9cdbdf13258e7e0ad0a8ed1e525d1bc}}, {{cite:9ab8b29aa900625f44b5514de6eb94179620ce83}}, {{cite:268fdff4db223ac727cf5ba4823c9c5de2c1cd0b}}; (2) adding colors to the background {{cite:85e6ea135ffad63a91874f0880a7f92ef8649b1a}}, {{cite:76718197c38b5491b9b7f3a5b6fcd5dd4f4795ad}}. Therefore, we conduct experiment on both variants of Colored MNIST dataset. We denote the Colored MNIST with foreground color as “Colored MNIST (foreground)” and the Colored MNIST with background color as “Colored MNIST (background).” Same with the experiment setting on Multi-Color MNIST, we follow the setting used in LfF {{cite:c65aa0507a204956e58b402ed42229afde2a29fe}}, including using MLP as the network architecture, training with 100 epochs, etc. Same with LfF, we report the results under four ratios of bias-aligned samples in the training set—0.995, 0.99, 0.98, and 0.95. In terms of evaluation metrics, we follow LfF to report the accuracy results on bias-conflicting samples and unbiased accuracy. We additionally report the accuracy results on bias-aligned samples.
| r | cba469eae63d17893b76e42df8677b98 |
“God used beautiful mathematics in creating the world.” During the 20th century physicists constructed many beautiful theories that would describe the Universe at all scales even though some of the theories were not so simple. However up to date no theory was able to give a decisive answer regarding the fate of our universe. Physicists started from quantization of fields to construct the fundamental theory of physics. Despite the success of quantum theory, gravity can be considered classical for most of the observed phenomenons in nature except some extreme cases such as the black holes and the beginning of universe moment where gravity is quantized. The main problem of quantum theory is the probabilistic nature associated with it. Our observed reality in contrast seems to be so deterministic despite the fact that at atomic level, particles are described by wavefunctions that have probabilistic behavior. These facts were under serious investigations during the past century and many approaches were developed to solve this issue. Probably the most famous approaches are the Copenhagen and many-worlds interpretations. Before we can give a final answer about which interpretation is correct we have to answer the following important question ” What makes quantum world so different from our intuitive daily life thinking {{formula:ff16d89f-7003-4d4a-bcef-c73b8eed1ab2}} “ The uncertainty principle of Heisenberg and consequently the vacuum fluctuations play important rule behind the scenes in making the quantum world different from classical world. The Heisenberg uncertainty principle is a collection of mathematical inequalities which bound the accuracy of the measurement of two physical quantities such as the momentum (energy) and the position (time) of a quantum particle. In quantum theory, local energy densities can be negative for a short period of time {{cite:ef120dc2dad38102fc2e448af67b6e63c8a4d170}}. This fact violates the classical energy conditions in General Relativity {{cite:fcf80e26bf1761087c7b23f7d8a67ee263e88fd7}}, {{cite:6c47ba008823aec2c9b212372aadb2494d001943}}. In {{cite:db6f86f19b94c55ecb5e4f8f209f89ac684f24d0}} the author of this manuscript proposed a mechanism for restoring energy conditions at quantized level. The cost was introducing particles with negative energies localized at quantum gravity scale ( very curved spacetime) with reversed arrow of time. These particles are the missing anti-particles in quantum field theory but with larger masses, opposite charge, time reversed and negative energies. Note that in quantum field theory, ordinary anti-particles have the same masses, opposite charges, same time direction and with positive energies. Using quantum interest conjecture we consider the trapped anti-particles with negative energies as the loan amount and the evolving positive energy particles ( our observed universe) as an attempt to pay that loan with interest {{cite:2eb7ff4cbb429821dc085abb0ef7a3053471224f}}. Following this direction we succeeded to solve many problems in physics such as the arrow of time problem, hierarchy problem, particle-antiparticle asymmetry {{cite:db6f86f19b94c55ecb5e4f8f209f89ac684f24d0}}. It is important to note that the concept of increasing entropy( the second law of thermodynamics) and quantum interest conjecture are interchangeably related to each others. Due to the simplicity of our approach plus its ability to give logical answers to the aforementioned longstanding questions suggest the possibility for this approach to fill the gap in fundamental physics .
| i | 41685a55f7cae58dffff232767fd65c0 |
One could arguably compute mfc on the basis of human-annotated semantic similarity ratings.
Datasets of such ratings exist {{cite:dc4124a06c6d9ef51f22e2dc68b15c562eaf2aaf}}, {{cite:907fd0010fdb3bff2cdf142d25c5c9607c882674}}, but they do not provide a (dis)similarity between every pair of items as is required to perform a Mantel test.
Instead, as mentioned above, we use distributional semantics models as proxy for meaning representations and use a distance between word vectors.
We consider four sets of pre-trained word embeddings:
fastText {{cite:f9f568f9ac5275e12465b7a847442722832465c4}}, glove 6b and glove 840b {{cite:92dad8c685cf3f0e1989ee7052093d538bbaddac}},
and word2vec {{cite:57ac9e944af22c1e2492af594a279437e002c51a}}.
| m | 37e225112fa8dcd846fd59d9c23c88d3 |
Unconditional Generation of SkeGAN:
The effect of temperature {{formula:8f73b41f-53cd-45bc-91cc-bd5b7f85faaa}} for unconditional generation is similar to its effect in conditional generation in the case of VASkeGAN. As {{formula:f1217027-88cb-45e5-8319-9ecc6a2cca99}} increases the randomness of the generated sketches also increases. Since we are investigating its effect on unconditional generation, there is no ground-truth to compare the randomness. Instead, a group of sketches generated with a particular {{formula:579f1087-984e-49c1-99bb-233d3506af92}} must be compared with those generated with a different value of {{formula:b8163f5a-babb-4ad3-b3ab-3bcda8818693}} . The influence of {{formula:4a978841-9c44-4039-a71e-c6488be0205c}} on {{formula:35e79d6c-873d-4a02-b515-e48bd095cf62}} , {{formula:b83bac3f-999a-4ea7-803d-0b0a3c78954b}} and {{formula:fd08ef5a-6f96-4bba-8b70-cdf4231107c7}} is same for those in conditional generation of VSkeGAN. In addition to this, it influences the mixing weights of GMM by acting as its inverse multiplier as in {{cite:f7771232c7344a84d3303070ac563d93df5dc7ed}}. In Figure REF , there are 5 rows each depicting the sketches generated by SkeGAN at {{formula:983f50f6-6297-445a-968b-45146b143f18}} values of 0.2, 0.4, 0.6, 0.8 and 1.0. We find here that {{formula:b77ca6d1-4d20-423e-9532-6fb910303cba}} value of 0.4 is ideal for sketch generation based on visual appeal.
{{figure:5e49cd39-ff81-4619-aeef-f4349ead0403}} | d | e603d93526613deaf5d263431e78800d |
Pseudo-LiDAR {{cite:3be251c152ae090c5ca6ff0301c7ecc3e1770259}} + segmentation: Uses Pseudo-lidar with PSMNet to generate a 3D point cloud from the input stereo images which is used to project the semantic segmentation of the front view to the bird's eye view. The PSMNet is trained separately on the respective datasets for better performance.
Pseudo-LiDAR {{cite:3be251c152ae090c5ca6ff0301c7ecc3e1770259}} + BEV U-Net: The RGB 3D point projected in the BEV aligned with the ground truth layout is used to train a U-Net segmentation network.
IPM + BEV U-Net: Inverse perspective mapping is applied to the input image to project it to the BEV space which is used to train a U-Net segmentation network.
MonoLayout {{cite:26a1e9b4c4588df19acfb7f580de54d66d22424b}}: This baseline uses MonoLayout to generate BEV semantic map from a single image.
Rather than using OpenStreetMap data for adversarial training, we used random samples from the training set itself.
MonoLayout {{cite:26a1e9b4c4588df19acfb7f580de54d66d22424b}} + depth: The input RGB image concatenated with the depth is used as an input to the MonoLayout Model.
MonoOccupancy {{cite:734392a7c9f76507f6e03a3f0e2d2e1c0aad1978}} + depth: The input RGB image concatenated with the depth is used as an input to the MonoOccupancy Model.
| m | 33693a3d790b643a07161220c6245139 |
As argued in {{cite:8facfd99ee2c23df7552c61b32a04347ab8ba081}} the norm of weights does not necessary captures good generalization. They show in particular that generalization in ReLu networks is invariant along hyper planes corresponding to reciprocal rescaling in and out side of a nonlinearity by some constant {{formula:d50247d4-3876-4562-9ab5-76c25bb30457}} and {{formula:5e2f284f-a3ab-4703-a383-b2a822860bfd}} respectively. If {{formula:e992e547-9980-4bb3-94e1-cc3404bb68fb}} is absorbed into weights a norm along such hyperplane gets arbitrarily large despite it represents the same function and thus has the same generalization properties. As can be seen such a rescaling has no effect on a bound (REF ) of Corollary REF because {{formula:1ffe759e-7a01-4300-87cd-cdca4a5833ce}} 's would cancel out along the path products involved. Regularizing a path products as in our method is more subtle than regularizing norms as follows from geometric vs. arithmetic mean or more general Jensen's inequality. More over {{formula:1f425449-00b4-412b-bce9-b18d00e42c0e}} with regularized spectral products as in Proposition (REF ) share many properties with low spectral rank used to characterize simple functions in {{cite:ba5423dedd93d2115138b4765b2aec9fa9a52994}}.
| d | 415da03a883d9da286ac08d8b5b20371 |
We use OpenFace 2.0 {{cite:4c015ba6bca25aa53354dacfce423bd4a256fbe2}} to compute the head position, head pose, gaze, facial AU presence, and facial AU intensity from individual frames in each video segment.
| m | 795590736a58cf529f36f134c847540b |
The above theorem for {{formula:01692196-0461-4f20-8dea-9dbd7ce1e938}} -{{formula:03381ef3-d89b-4804-abdc-b1c24c2beb6f}} in {{formula:fb7a5985-710f-424b-9106-1f4c51e9d81e}} -metric is obtained through an intermediate hardness of approximation
proof for {{formula:b7b05d0e-e3b5-4b7e-93d2-c8b28d8c1054}} -{{formula:d5f4bdb5-75da-4358-95a2-c95b1cb9c3fc}} in the Hamming metric (see Theorem REF ).
Additionally, the fact that medians and means have nice algebraic definitions in {{formula:48d4dcc3-9158-4b8c-a9d5-0857c61b3b37}} and {{formula:533c143c-68e9-4b08-8455-6ad9ddcfa241}} respectively
allow us to transfer the hardness from Hamming metrics without much loss.
Furthermore, thanks to a technical result of Rubinstein {{cite:0e40eb44398192ceb4388a621638a1147e07f252}} on near isometric embedding from Hamming metric in {{formula:0486e79d-a284-4b40-bda6-f02e7ed879f4}} dimensions to Edit metric in {{formula:61ab34dc-f34a-49de-bbd1-2adff9d4dc31}} dimensions, we can translate all our (discrete case) results in the Hamming metric to the Edit metric
(see Appendix A in {{cite:1c2b4e150f976a4fd15bd853b6b069d4a3be9195}} for details).
| r | c977a3e46ce468024e0a704d52fe72b3 |
From the Lemma of Douglas-Dupont (see in {{cite:cddc47a1afe52ec22d1dabcfbba05ed0eaf6871b}}), it follows that, given a function
{{formula:fd47f5dd-731e-49eb-95b4-18c465310e2c}} , there is an interpolator {{formula:daa4c4f4-be5f-44af-9abb-179696fb2ddb}} such that
{{formula:cda7f55b-f3d4-4560-a5ff-a82bcf99142a}}
| m | 2ec5a65fd8957433adedef3a86be1540 |
Compared with the previous theoretical works that used the plane wave expansion method on the {{formula:301c797c-29bb-49a5-94d7-bc4bf2b61f46}} model {{cite:43a3c16d4eb683e68620727477459a8a054ff85b}}, {{cite:b15333b3ccea93279a0e188ffaa4c318e04c1c18}}, our results show the following differences: (i) the inverted bands are related to the renormalized Dirac cones; (ii) the Chern number may get increased even when the thickness of the middle magnetic-doped TI layer decreases; (iii) the gaps are well opened in the Chern insulator phase in another two TI multilayer structures. The differences are attributed to the fact that the surface states of each TI layer in the multilayer structures are well captured by the Dirac cone model, but may not be correctly described by the plane-wave expansion method. We hope that these conclusions, especially (ii) and (iii), would be demonstrated in the future TI multilayer experiments.
| d | d086e8a061faa53d5289edccacd79c96 |
We show the quantitative results on Matterport3D dataset {{cite:c8c8f0325058e18a56f8bee82312df755f6a013a}}.
The sampling strategies are the same as our experiments on PROX dataset.
We first perform K-Means ({{formula:ec0e4bf5-6b4e-43de-9c59-2323113e37ea}} ) and evaluate the obtained human-scene interaction anchors on Matterport3D with the entropy of cluster sizes and the average distance between the cluster center and the samples belong to it.
| r | 7b8f65f41b1bf499f2e52eb820862072 |
We perform a series of tests to show the physical accuracy, robustness, and generalizability of our method compared to other baseline methods.
We primarily use data from a high-fidelity SPH solver with adaptive time stepping {{cite:d6ee9fcde0fa48ffd8f46506203ad34005988b64}}. The resulting, two-dimensional dataset "WBC-SPH" consists of randomly generated obstacle geometries and fluid regions. Gravity direction and strength are additionally varied across simulations. In addition to this primary dataset, we also use the MPM-based fluid dataset "WaterRamps" from Sanchez-Gonzalez et al. {{cite:fd1886ba87a5a990e4b8cf1c763301747df66545}}, and the three-dimensional liquid dataset "Liquid3d" from Ummenhofer et al. {{cite:7acf56eeac49a54cb7224c3437c3d540929d4b10}} for additional evaluations. Both consist of randomized fluid regions with constant gravity. A more detailed description of the datasets is provided in App. REF .
| r | 0b82490a4148f63ec32163084882abc9 |
6.2. In the homological mirror symmetry due to Kontsevich {{cite:6fe984f989c14dd1da6fa8e1b6c6233e7fcb0bbf}}, monodromy transformations in B-structures are interpreted as the corresponding transformations in the derived category of coherent sheaves {{formula:8fc881dd-7c2e-4420-9e4d-43cfce398f40}} . From this viewpoint, the gluing of nilpotent cones in {{formula:53fb6877-f769-4a0c-add4-446e11f55f44}} suggests the corresponding gluing of Kähler cones in {{formula:c7706cbe-945a-4823-a20a-a8980f9298ed}} as a homological extension of the movable cones. The resulting wall structures of the gluing in {{formula:7b5b724f-1536-4bf4-be4f-090d792acee3}} should be regarded as the wall structures in the stability space {{cite:5f8b9962faa57c037b1dca61db2684a1c5572c7f}} of the objects in {{formula:fedb2c59-a133-451e-9817-fca0db921c2c}} .
| d | 83a332d21681e232df22d378625909d9 |
It is well-known that for {{formula:a9b45444-b5fb-4ab8-82fe-d04af8a0c94b}} (cf. {{cite:57601bbcc49a634e1af43dc3f7b5d0974438fd1e}}, {{cite:d0454dfba4cc6000e9f7b7feba7d4d6989ba2064}})
{{formula:4b8d0276-f76b-4bed-ab71-c0f3aa20f6c1}}
| m | 808335b37f49ed6c35043526c5d25314 |
Moreover, UAVs flight duration is bounded by the on-board battery lifetime. To improve the energy performance, solutions can optimize for energy efficiency such as in {{cite:7aa99394b0f4e1c279a15196dc4e9a783dbc7897}} where the authors derived a model for the propulsion energy consumption taking the trajectory into consideration, and then they utilized it to optimize the trajectory of a UAV communicating with a ground terminal such that the energy efficiency is maximized. Alternatively, to cope with the limited on-board energy that DBSs have, the authors in {{cite:4c9050025098d1f0d9d7bf6ae5f2da003c17ac6f}} demonstrated a UAV prototype with solar panels. Also, the authors in {{cite:84abebbed1d3c6e4eac940b1a795a1feb2e32dd6}} study the use of renewable energy sources by UAVs and formulate a signal-to-noise ratio (SNR) outage minimization problem which optimizes the transmit power and flight time of the UAV. Similarly in {{cite:103266bc8c061f100a166eaf6bfec8b3c4ed84cc}}, the authors formulate a joint trajectory and resource allocation optimization problem in which a UAV can increase its altitude in the presence of clouds in order to harvest more energy. An algorithm is proposed to determine the UAV's trajectory in each time slot which takes into consideration the aerodynamic power consumption, on-board energy, and users' quality of service (QoS) requirements. However, in this work we consider the presence of high buildings that can obstruct both the light from the sun and the FSO link, and therefore the placement of DRSs should avoid both types of obstructions.
| i | c9a8f7c076eb6633ed20c709057af60b |
Based only on the experimental data reported by {{cite:efc0785029fee2b7aa5afee270aaa933965ea06d}}, W. D. Langer & T. Velusamy (cited as private communication in {{cite:efc0785029fee2b7aa5afee270aaa933965ea06d}}) searched for ortho-CH{{formula:8d6a2da7-9ed7-47c5-b327-e07df9ff9839}} C{{formula:d1c1e278-0a0a-426d-97aa-fa35a38c4b65}} N in TMC-1. An upper limit of {{formula:b1781c0c-2f9b-435c-adb4-a9999b1735fb}} {{formula:2331492a-ed90-40f1-a691-4661e9ec5f22}} 5 mK for the {{formula:a1ab01f2-630a-409f-a64a-10a20a76ed55}} = 5-4 transition at 21,864 MHz, averaged over the 0.20 km s{{formula:7c17aed6-8868-44ae-ac24-feb6a0a4e4c9}} spectral resolution, was obtained using the position switching observing mode with an on-source integration time of 6 hr. From these observations, W. D. Langer & T. Velusamy estimate that the column density of CH{{formula:07225ed8-cc66-419f-a95d-c913289159c6}} C{{formula:d9798347-5e3e-41ac-adc2-4bb50eb4ea80}} N in TMC-1 is {{formula:ae40cab0-c354-4720-9414-b4481d8cc9b1}} 2{{formula:354e94ae-366d-4d72-898b-194d91d31a9d}} 10{{formula:b4463e6c-d794-403c-81ad-84a43fce9eac}} cm{{formula:f8381d62-2ad3-49ce-9bfc-4b2ccdc109dd}} for an assumed dipole moment of 4.42 D, a rotational temperature of 10 K, a line width of 0.5 km s{{formula:7c5b39e2-2400-4580-a95c-1ab7804e1d4c}} , and under the assumption that the source fills the telescope beam, 45{{formula:ed897ffd-2a9a-4109-b668-9a22fbe3ffd9}} . Our QUIJOTE survey has an excellent sensitivity, with a {{formula:abb02ecd-cbfd-4bbb-9819-a4bac3192d9f}} rms noise level of 0.30 mK per 38.15 kHz channel, which has allowed the detection of the 3-cyano propargyl radical.
| r | 00caa77dbb91b85bfd303feb5178e275 |
Weighted Boxes Fusion. Typically, detectors generate multiple bounding box predictions (with confidence scores) of a lesion's location. Predictions become clustered together when an ensemble is created from multiple selected epochs of a single detector or over different object detection networks. Weighted boxes fusion {{cite:8d27cd4c8dfac8ca618756a01905706918460265}} was used to combine the clustered predictions and yield precise detections.
| m | 7dfc676dc663e9697f97706a4726babd |
We compare the performance of our proposed method to competing approaches on
the MultiWOZ benchmark {{cite:13349286a20e6be98aef5a8ade78999d8c15a66c}}.
Our experimental results show that we are able to improve
the state-of-the-art performance across different benchmark metrics.
Apart from MultiWOZ's context-to-text metrics, we demonstrate the benefits of
TCUP's learned latent representations quantitatively using a clustering analysis following {{cite:a8148f63db45728e6bbcd80606cdd70011732935}}.
| i | 6d727a66bb589e177b3eaaddc4923bc8 |
Our model-fitting results reveal
that the acceleration zones could extend
to spatial distances of {{formula:6bb2e5a6-14bb-4710-abc0-154caf3850c2}} 300–400 pc from the cores
(for knots C4, C5, C9,
C17 and B6, see Table 1 and 2). This result is consistent with MHD
theories for jet formation. For example, Vlahakis & Königl ({{cite:c871bac22977fd41ce98b63e4bb3bd00d87ff2ac}})
suggested that relativistic MHD models of jet formation could provide
extended acceleration on kilo-parsec scales and proposed a specific
MHD model for
the jet in 3C345 and predicted an acceleration to {{formula:b5ce0058-ed60-4791-8bf0-04a198eddd94}} 10 at
a radial distance Z{{formula:2f91b750-0e4b-4a27-a930-2c1ced846893}} 20 pc. Interestingly, this model also predicted
an acceleration to {{formula:9685f600-16c0-451f-b2c2-e39da8f97f62}} 20 at a radial distance Z{{formula:d7f5d457-cd3e-4cef-ab2e-2380fc9fcc51}} 300 pc.
Thus the Vlahakis/Königl's radial self-similar solution of MHD
jet-formation mechanism with their specifically selected parameters
may be already a successful theory. Similar intrinsic acceleration
observed in other blazars may also be understood within this framework.
Moreover stronger and more extended bulk acceleration could be expected
if magnetic collimation occur in cylindrical-type magnetic surface
structures.
Radial scales of {{formula:69eb1fce-79ec-43ca-aa02-6dc71c5de617}} 300 pc approximately
correspond to {{formula:08b56c15-a624-4382-aac5-570564f0003f}} ,
if the mass of central supermassive black hole is
{{formula:a5e6d964-516b-4bd4-9fb9-7686e433c228}}
(Woo & Urry {{cite:465ca442e70b8c34ff0c745a871c273f75b28717}}; {{formula:27ad9c82-1e76-4ff7-8169-0fd95d6c4465}} –Schwarzschild radius).
The long-extended acceleration/collimation of relativistic jets
might also be helpful to explain why jets in giant radio galaxies
could extend to Mpc-scales
(e.g. in giant radio galaxy DA240, see Tsien ({{cite:0e6a7988bf51225b762c8395612b3d4e7a840277}}),
Tsien & Saunders ({{cite:b238610353867a4d33d03b1f4a4d9f11e5da7262}}),
Willis et al.({{cite:e79e3b0f031ec238a13b4ff4bfca72fa4d5502a8}})). As Qian et al.
({{cite:c9f895e80ee8e93dafe0c68da5b8e5817b6d3079}}) suggested that except precession of jet-nozzles, other
mechanisms may also cause jet precession on different time scales,
e.g., geodetic precession, Newtonian-driven precession, Lense-Thirring
effect (Begelman et al. {{cite:c6a55b5ca6191ad7caf67745bb821025b8b73e7e}}, Katz {{cite:847ed94d5ed0101cff72d05d9dca9ff2b5bc0fbb}}, Lense & Thirring
{{cite:817552900890c43bec09888dcdbafff7f3010e01}}). Especially, geodetic precession may occur on timescales
of {{formula:ad42fe2b-ca8b-46a1-b342-274bd63530c1}} years. This kind of jet precession has been observed
in the inverse symmetric distribution of lobes and hotspots in FRII
radio galaxies (e.g., in Cygnus A and NGC326, see Ekers et al.
{{cite:39c7a720677eefb6297c42819f4b6b68898f9f54}} and Ekers {{cite:38c9dae43ace6c0582dd1ffcb4918bdaa64fcd00}}; also referring to
Hargrave & Ryle {{cite:d3ff038b33ef7a9f8167b689551fa96bb835efdc}}; Perley et al. {{cite:e86dc988db9c359734952401699942e395d2d7a5}}; Oort {{cite:1f114fbaccf106024c8f90fbcefa189fa2fe18f6}};
Fanaroff & Riley {{cite:7d56a7fcffb64592361234490b276837a66c4d44}}; Tsien {{cite:0e6a7988bf51225b762c8395612b3d4e7a840277}}, Tsien & Saunders
{{cite:b238610353867a4d33d03b1f4a4d9f11e5da7262}}, Tsien & Duffet-Smith {{cite:befbc0aba3c49b1c4b5fccaf1a9438e59e5f9044}}). In blazars different
jet-precession mechanisms may cause different periodicities in their
optical/radio light-curves.
Previously through model-fitting of the kinematics of
superluminal components
in blazars in terms of the precessing nozzle scenario we have tentatively
found three blazars, where double-jet systems might exist in their nucleus:
3C279 (Qian et al. {{cite:707e39dd1fbc78e3b760b02c6c31a7a7b219fa33}}), OJ287 (Qian {{cite:05272523a1b6905d2f6d303b8ad4a0229bc2a0a4}}), 3C454.3
(Qian et al. {{cite:2a617192433e1a7258442121cb34b3d11810776e}}). Here we add a new one: 3C345.
These double-jet systems may be produced by binary
supermassive black hole systems and thus our precessing nozzle scenario
would be useful to investigate the characteristics of binary black holes,
e.g., determining orbital period, mass of black holes, precession of
jet-nozzle, mechanism of precession, etc.
It might be expected that more blazars could be found to possibly house
binary supermassive black hole systems, if observational data are plenty
enough to make model-simulation of their VLBI-kinematics.
As previously suggested, in our precessing nozzle scenario for
3C345 and other blazars we assumed that precessing nozzles not only
eject superlumianl knots (relativistic shocks or plasmons), but also eject
rotating magnetized plasmas. Thus the whole jets (or jet-bodies) comprise
multiple superluminal knots (ejected at different times, distributing
at different positions and moving along different helical trajectories)
plus the rotating plasmas associated with the superluminal knots. The
accelerated motion and the increase in Lorentz factors along helical
trajectories are one of the most important features of these knots, which
can well be interpreted in terms of MHD theories for
jet-formation/collimation/acceleration mechanisms (e.g., Vlahakis &
Königl {{cite:2ec7f7f7c473a4382bfd37af1fc6e7847d565a69}}, {{cite:c871bac22977fd41ce98b63e4bb3bd00d87ff2ac}}; Blandford & Znajek {{cite:4ef290cc006750415303316bb7bedd6c4e550073}};
Meier & Nakamura {{cite:a1837b77c7b367e0b65ab109b8584637c3856f38}}). The apparently superluminal components
can be interpreted as relativistic shocks traveling along helical
trajectories toward us in the work-frame of electromagnetic mechanisms.
The results obtained in this work for 3C345, especially those for its
knot C9, firmly support these viewpoints on the nature of superluminal
components (Jorstad et al. {{cite:295301e6b9d951a90e2099b0422036817b12e94e}}, {{cite:d96e27216b3dd826af69e8cdceb56b09b519c4d9}}).
In contrast, some authors suggested that the apparent trajectories of
superluminal components could result from the underlying jet
structure pattern (formed by Kelvin-Helmholtz instabilities) lit up
by passages of plasma condensations ejected during nuclear flares.
The close correlation between flux evolution and Doppler boosting effect
(found for knot C9 in this paper)
Such kind of close correlation between flux evolution and
Doppler boosting will be presented elsewhere for more superluminal
components in 3C345 (Qian, in preparation). obviously do not support such interpretations.
Since 3-dimensional models were used for simulating the trajectory
and kinematic behavior of knots in 3C345, we could separate their intrinsic
bulk acceleration from the effects of trajectory curvature.
Thus their kinematic parameters (ejection
time; bulk Lorentz factor, viewing angle, Doppler factor and apparent
velocity vs time) and the location of bulk acceleration zone could be
consistently modeled. Generally, the modeled parameters are
consistent with those derived in other works by using different methods
(e.g., Jorstad et al.{{cite:295301e6b9d951a90e2099b0422036817b12e94e}}, {{cite:d96e27216b3dd826af69e8cdceb56b09b519c4d9}}, {{cite:23f95c5f0391872851b03c14b8297bdf664ebe26}}; Klare
{{cite:ff5dd54b47ea09e48f88b59cacdeec981543d6af}}; Schinzel {{cite:a0ed0cea478280751f8c0a5649564b234399f9e1}}): for example, our modeled Doppler
factors could be compared with those
derived from variability time scales of optical/radio outbursts.
Our model-fitting results for 3C345 demonstrate that within the
collimation/acceleration zone its superluminal knots ejected from the
precessing nozzle could have a common inner trajectory pattern, which
precesses to produce the observed inner trajectories of the knots.
However, beyond this zone their outer motion would follow different
individual trajectories. This precessing common inner trajectory could
extend to different distances for different knots (see Table 1 and
Table 2). We have made use of the precessing nozzle scenario
to model fitting
of the inner-jet kinematics of superluminal knots in 3C345. The concept
of precessing common trajectory may be essential for doing this study.
Obviously, the strong magnetic fields of the magnetosphere in its nucleus
may play determinative role to form the steady common trajectory pattern,
which precesses to produce the trajectories of the knots ejected at
different times. The model-fitting of the inner trajectories of the knots
in terms of the precessing nozzle scenario naturally explain
the position angle swings observed in 3C345. In other blazars and QSOs
(e.g., 3C279, OJ287, 3C454.3, B1308+326, PG1302-102, NRAO 150) similar
phenomena were discovered and model-fitted (Qian et al. {{cite:707e39dd1fbc78e3b760b02c6c31a7a7b219fa33}},
Qian {{cite:05272523a1b6905d2f6d303b8ad4a0229bc2a0a4}} and references therein). We would like to point out that
the precessing nozzle scenarios for these blazars and QSOs are not only
based on the model-fittings of the available observational data-sets, but
also are confirmed by other observations. For example, Hodgson et al.
({{cite:a5b2d4e7aa63916fb5d27dd2a43b4aa70d8bbb20}}) have found some evidence for the possible presence of double
ejection directions. Particularly, in the case of 3C279 one of the double
jet (jet B) which was predicted and searched for quite a long time
had already been observed in much earlier years (Pauliny-Toth et al.
{{cite:263e4f34fe768e52c454203b80c010a309f0121a}}, Pauliny-Toth {{cite:6aa34190079eedfc2140bd8b1f697e415248b46c}}; de Pater & Perley {{cite:e343ec37a46c59dcfd3807bbe65e0bed85a8a633}};
Cheung {{cite:2456b71d1ea4af4e878f06740cd410e0151843e2}}). For blazar OJ287 the possibility of double jet
structure has been suggested (Villata et al. {{cite:0365c617382465b4de8dcbe20b40eac5b7739bab}},
Qian {{cite:394434f8662aab31fba421d0bdf3ba46a7888ff8}}). Thus the assumptions in our precessing nozzle
scenarios seem valid for some blazars.
In the process of model-simulations bulk Lorentz factor {{formula:0edbd061-1f6e-4b5d-a88c-fb7319482a6a}}
as function of time was derived for each superlumianl components.
Interestingly, most of the components (for both jet-A and jet-B) are
modeled as accelerated and their Lorentz factors
varied over quite large ranges, e.g. knot C10 (jet-A) in [4.5,29] (Table 1).
These intrinsic acceleration should be produced by the strong
torsion of toroidal magnetic fields in the collimation/acceleration
zones (e.g., Vlahakis & Königl {{cite:c871bac22977fd41ce98b63e4bb3bd00d87ff2ac}}), which could extend as far
as {{formula:ca49be6e-610d-42bb-af79-6681a9ffaa07}} 400 pc from the radio core (e.g. for knot C9; Table 1).
Generally, when
the Doppler factor versus time of a knot was derived as in this paper, one
can investigate the intrinsic radio light-curves of the knot and
model-simulating the intrinsic evolution of its electron density/magnetic
field (e.g., Qian et al. {{cite:69e90681c1f7fab4567fd0fd7594633ad6490bf2}}). However,
the 15GHz and 43GHz light-curves of knot C9 could almost completely be
interpreted in terms of its Doppler boosting effect during the main flare
(during {{formula:34a3cbf6-017d-49bd-ba40-d6f58de90a66}} 1997.50–2000.25), implying that the
intrinsic radio emission of
this superluminal knot was very stable or the relativistic shock
responsible for producing the knot having very stable physical properties
(see Sec.4.4.6). This result is important, because it is for the first
time to find the radio light-curves at both 15GHz and 43GHz being
closely coincident with the Doppler boosting profile and strongly
justify our precessing nozzle scenario. The common viewpoint (or scenario)
for superluminal knots participating relativistic motion and
magnetohydrodynamic acceleration mechanisms are firmly supported.
Only within our
precessing nozzle scenario, where Doppler factor curve {{formula:7706dc60-9e69-4d71-892c-5839ffef1349}} (and
Doppler boosting profile {{formula:de6d9183-3352-4b45-9ab6-669dfc585e38}} ) can be obtained for
interpreting flux evolution of superluminal knots. Usual analysis of
VLBI-observations obtains only averaged values for bulk Lorentz
factor or Doppler factor, which could not be used to study flux evolution of
superluminal knots.
{{table:f8798c8b-831c-40b3-b9ee-04578628cdb8}}{{table:37604e64-acdc-4814-b1a4-c77be4906645}}{{table:42e59b38-af9d-4b71-81f3-ca40001a9f5e}}
Due to both jet nozzles (nozzle-A and nozzle-B of 3C345) precessing
with the same period (4.6 yr in source frame), the precession of the
nozzles could be caused by the orbital motion of the binary holes,
rather than other mechanisms of precession (for example, geodetic
precession and Newtonian-driven precession; referring to
Qian et al. {{cite:c9f895e80ee8e93dafe0c68da5b8e5817b6d3079}}, {{cite:05272523a1b6905d2f6d303b8ad4a0229bc2a0a4}}; Britzen et al. {{cite:e569621d618b5655163622dd7df31881297012b0}})
Our works have shown
that the double-jet structures revealed in the four blazars (3C279,
3C454.3, 3C345 and OJ287) have similar (common) features: both jets
precess in the same direction with the same period. Such kind of jet
precession could not be caused by hydrodynamical instabilities induced
by the interactions between the jets and the surrounding media..
If this interpretation is
valid, the mass-ratio q=m/M between the primary and secondary
holes could be approximately estimated to be equal to the ratio
between the jet apertures: q{{formula:e3e101c7-67af-4428-8b9e-64b35f617d8c}} 0.87 This value is estimated
at core separation {{formula:7401f968-2fe3-4776-b17a-c1effda6d812}} 0.5 mas. In the case of knots moving along
curved trajectories the jet-cone apertures critically depend on core
separations and thus the value q=0.87 is only a rough estimation..
The orbital period and mass ratio obtained for 3C345 here could
tentatively provide
some useful constraints on the total mass and gravitational radiation
lifetime of the putative supermassive black hole binary in 3C345.
Some results are presented in Table 3 to show the relation between
the mass of the primary black hole and the parameters of the binary
(total mass, orbital separation, post-Newtonian parameter and
gravitational radiation lifetime), showing that the total mass
should be less than 9.5{{formula:683d8079-35c8-42b2-8478-182a73dbd435}} if its gravitational
radiation lifetime {{formula:d68c0172-f1f2-44ff-9a5e-a8e39379d033}} yr.
Interestingly and
to our own surprise, the VLBI-kinematics of the four blazars (3C345,
3C454.3, 3C279 and OJ287) could have been interpreted in terms of the
precessing jet-nozzle scenario with binary black hole systems,
and their precession periods and mass ratios could have been
tentatively derived
(Qian {{cite:394434f8662aab31fba421d0bdf3ba46a7888ff8}}, Qian et al. {{cite:05272523a1b6905d2f6d303b8ad4a0229bc2a0a4}}, {{cite:2a617192433e1a7258442121cb34b3d11810776e}} and this paper).
Thus we would have to investigate whether there are physically reasonable
parameters to describe these binary black hole systems which have
the orbital period {{formula:5da3562d-db09-4ebf-927c-a33101387200}} and mass ratio q as listed in Table 4.
For the four blazars (or the four putative binary black hole systems),
their parameters (mass {{formula:4dbea365-95c4-4e43-989c-ce93a3f0e105}} and {{formula:5d26911e-e73c-47d2-b010-fc5e3a68e35d}} , post-Newtonian parameter
{{formula:fcfa5682-8e99-4551-8e98-f9be5bc510fa}} , gravitational radiation lifetime {{formula:c254c58a-e6f6-42b9-8d3e-c333fcad53fb}} , ratios {{formula:a99e9ef5-09f0-4b66-bde3-90edf1ee827e}}
and {{formula:1eca3d14-b854-4010-b436-99acd0531125}} between orbital separation and gravitational radius
calculated for different orbital separations {{formula:7b94b883-8385-4963-842b-abfa8ef097d6}} (0.01 pc–
0.05 pc) are given in Table 5, taking the {{formula:573d2bd6-a644-4caf-92f7-0f5b5b75593b}} and q listed in
Table 4 into accountFormulas for calculating these parameters
can be found in Qian et al. ({{cite:c9f895e80ee8e93dafe0c68da5b8e5817b6d3079}}).
Values for {{formula:b9407306-4e7e-48b6-863b-1b8d68e50542}} =0.014 and 0.015 pc
were also used , but not listed in Table 5. For the four blazars 0.01 pc
corresponds to angular distance of {{formula:fe4ea61d-2fcc-445d-af34-7aaaa365ce37}} 1-2 {{formula:c90df955-c462-4475-893a-d29376b159a7}} as.. Based on Table 5,
we can search for appropriate
ranges for the masses and separations {{formula:51dbe8e5-622c-4d62-9b93-56d9b8debbbd}} for the four binary systems,
if requiring their gravitational radiation lifetime limited in the range
{{formula:d83dc3c5-2cf8-4787-9043-00f120407753}} –{{formula:403915a1-c7ba-4cf1-855a-516ce116ddf6}} yr.
It was found that: (a) For 3C279, the ranges [{{formula:62873bec-5117-44a7-9ebb-3627a6d41c08}} =0.03–0.04 pc] and
[{{formula:627f1a97-2e64-4bec-a0e5-785a49690cd0}} =5.21 {{formula:68c1fe1d-71e5-4d84-be07-599bb7703f1f}} –1.24 {{formula:341cf1db-0900-4671-b7a5-7065d352dd09}} ] yr correspond to mass ranges
[{{formula:25e09c43-1521-4b5f-aebb-0c1ff4ae6987}} =4.91, {{formula:f25a32ab-cc04-4183-81f7-e706834ab931}} =2.45] and [{{formula:7ef97094-736b-40cb-b9b8-6a5fff4b2c17}} =11.6, {{formula:e99f807e-a1b7-4d25-8458-d608a089d075}} =5.80], respectively.
These masses are well consistent with the values
(3–8 {{formula:f903549c-fe06-4763-8e41-cfbeb28dc187}} ) given in Woo & Urry ({{cite:465ca442e70b8c34ff0c745a871c273f75b28717}}),
Wang et al.
({{cite:f35cd4974bf907441666571c03f20454307508d4}}), Gu et al. ({{cite:1ccc7232de7c0cb3e645c3bb084c7c262b5b6fb4}}) and Nilsson et al. ({{cite:774481bdd22dbe638bfe7fae500c4a3c028276d4}}).
This is a very good case, indicating that the related parameters of the
binary system derived for 3C279 by our precessing jet-nozzle scenario
seem to be physically sound;
(b) For 3C454.3, the ranges [{{formula:0c664ecd-fb7e-4680-bc3a-f8b4843e569e}} =0.015–0.02 pc] and
[{{formula:f9ab6805-483a-4c63-9007-60784a0692df}} =3.41 {{formula:674327ec-155d-418d-aba1-ecc1f6e4e67c}} –8.22 {{formula:8ac7c5f2-de30-4096-a385-547ec6002261}} ] yr correspond to the mass ranges
[{{formula:b30602c0-1728-4ded-827a-59157bd08608}} =6.01, {{formula:b547a642-d45f-4172-b3f6-93f7059862c1}} =1.80] and [{{formula:cedbe6d6-22b6-4b1e-a2c2-4ff5ec82524a}} 14.2, {{formula:fc706765-7eac-44ee-8745-51f8f1d339c9}} =4.26]. These masses
are well consistent with the values of 1.3–1.5 {{formula:ddd999f1-ec9d-413f-acc8-15724de760be}}
given in Woo & Urry ({{cite:465ca442e70b8c34ff0c745a871c273f75b28717}}) and Wang et al. ({{cite:f35cd4974bf907441666571c03f20454307508d4}});
(c) For 3C345, as mentioned in the previous item, its total mass should be
less than 9.5 {{formula:be77b5fe-0362-434b-84c8-07a57172ab26}} if requiring {{formula:c162effa-95c1-4553-8883-5c4a9220f4a5}}{{formula:e0b1d778-6f80-4614-a411-b544b44271ab}} yr.
According to Woo & Urry its black hole mass=2.63 {{formula:aba43e29-03f8-45cb-b35f-be46db259211}} ,
but Lobanov & Roland ({{cite:0a665a3eec9e58f3f28b6d3d93e2b9a8785d8ea9}}) adopted a mass
1.42 {{formula:ecd1519a-8cd8-4609-89c5-afaa4ade1d1c}} for their binary black hole model. Here
we found that the ranges [{{formula:f9b95eed-c632-47c4-be30-cc95665671a3}} =0.01–0.014 pc] and
[{{formula:7f3800ec-1123-4400-a277-350765e62bea}} =5.73 {{formula:eb3bbf8a-2ef1-4f8a-80be-83175926dadb}} –1.06 {{formula:08293ee7-2fd9-4fff-a0b1-94a3ec729f8f}} ] yr correspond to the mass ranges
of [{{formula:ba41373f-c85c-4c31-a58b-0252777d7fe7}} =1.83–5.02] and [{{formula:3db4f1e3-7e36-4983-8638-228268ea35d6}} =1.59–4.37], which seem to be
reasonable values. According to Wang et al. ({{cite:f35cd4974bf907441666571c03f20454307508d4}}), 3C345 is
distinctly different from 3C279 and 3C454.3 in the
relation between its kinematic luminosity ({{formula:09d1e62f-a020-40cb-9f0a-ab57a939b0a7}} ) and broad-line
region luminosity ({{formula:c9e1b6b5-0173-49c8-93c4-2eadc7d62b3c}} ), possibly implying some jet-disk
connection which could result in its measured mass higher than that
of the black hole itself. In addition, Xie et al. ({{cite:ff92343efa3fed658fac7c717032003d9cc5c2ae}}) measured
a mass of 2.57 {{formula:1af4fe8f-350e-4438-a6fb-3437ab06b6ac}} , similar to that we derived;
(d) For OJ287, the ranges [{{formula:938bc8c9-a9ed-4da6-814c-71c55b3e485f}} =0.02–0.03] pc and [{{formula:83e7555f-72dd-40c1-ac41-55017cc4299d}} =
1.60 {{formula:7096bd29-09d8-4292-9e41-256fc651a05a}} –2.10 {{formula:396144d6-72ea-42cf-a180-00a6e1d60204}} ] yr correspond to the mass ranges
[{{formula:c53623f4-7cfb-457e-a8c5-37e71db840a0}} =5.27–17.8] and [{{formula:00e33521-e935-45ff-9141-49ce42eac882}} =1.58–5.34]. These values are broadly
consistent with the values (mostly {{formula:8e080585-b315-4d6f-a06c-a83bb2be57d8}} )
adopted in several works (e.g., Valtaoja et al. {{cite:2acdeaf4a21e37167b3149ab16f9eae910e64d08}}, Liu & Wu
{{cite:8670f54018e9bb7e1e9b6a10301a5074580bc3bc}}, Wang et al. {{cite:f35cd4974bf907441666571c03f20454307508d4}}, Gupta et al.
{{cite:0b5fba2aad3c0c7ca79e327439727237dbd3f25f}}, Katz {{cite:847ed94d5ed0101cff72d05d9dca9ff2b5bc0fbb}}). However, in the disk-impact scenario
proposed by Lehto & Valtonen ({{cite:b968cbc121d2ae82e8f6599823c6a8c90f5f8cd3}}; also Dey et al.
{{cite:b1e61aec26c818f20e279b0375ea67a83eeac45a}}, Valtonen et al. {{cite:9a1011a812098ade489f1948e45242c52dad3ce1}}), the masses of the binary holes
are modeled to be {{formula:07ff2c5c-5953-40d2-9fa7-26ac62b233a9}} and
{{formula:4d68b867-69dd-46a9-9b9c-a43a0d31edbc}} with a mass-ratio q{{formula:c6498591-5e72-4fe2-baee-caea90b83fde}} 0.008.
Obviously, the issue on the properties of the black hole binary in
OJ287 should be further investigated and clarified (Qian {{cite:394434f8662aab31fba421d0bdf3ba46a7888ff8}},
{{cite:ee2d78b469488cb64a2f3e69ada52e133d5e0e37}}, {{cite:61863121eb176350780536abb2d12d188092fb00}}, {{cite:7b382eee80103b57c79ab8dae88146641e9847c5}}, Britzen et al. {{cite:368147004ea7d770e735fa684f6f369a20e6544d}},
Villata et al. {{cite:0365c617382465b4de8dcbe20b40eac5b7739bab}}, Sillanpää et al. {{cite:7aa0adc89fc7cfbea88e9ea5b36b5911aa40c4a5}},
{{cite:a40710193ae2a3a832e370c86d4845ff7522a675}}).
In Table 5 are also given the ratios ({{formula:55ab5160-41c8-4710-a7ec-2e1e4b08a69c}} and {{formula:7d378bba-5e2f-493e-bfb1-e2c918b631a2}} )
between orbital separation and gravitational radius for the primary
and secondary holes. It can be seen that the reasonable ranges of
masses described above correspond to reasonable ranges of the ratios for
the primary and secondary holes: approximately a few hundreds to
a few thousands (for example, for 3C279 {{formula:48bfc303-37e9-44f4-abd1-3404c730115b}} =1280-721 and
{{formula:70b35d49-7b00-4b0c-8c54-d06767732838}} =2560-1450), indicating that the formation of accretion disks and jets
could proceed without destructive influences by the gravitational
interaction between the two holes. However, the formation of double-jet and
disks and their instabilities need to be investigated for understanding
the complex phenomena observed in blazars (including the VLBI-kinematics and
the multi-wavelength radiation and the connection between low-energy and
high-energy radiations). In binary black hole systems cavity accretion might
restrain the formation of large-scale accretion disks, but spin of the
holes might play more significant roles in formation of relativistic jets.
Perhaps the binary black holes in blazars might be rapidly rotating with spin
parameter j{{formula:33bcbc52-75da-4d49-966b-4dc243013da6}} 0.5 (j=J/{{formula:8b9958ca-9cd4-432f-adc1-e91991cb9b24}} , {{formula:53d98b01-106e-4948-a57d-7ad109935240}} =G{{formula:490fcad7-c0de-4c28-ae2f-2b9cfc67b493}} /c–maximum spin
angular momentum of a black hole). In addition, for the reasonable
ranges of the black hole
masses, the post-Newtonian parameter {{formula:f1cd3138-dcf2-4bac-84ce-e831fe5c5656}} given in Table 5 has its
values in the range of [1-4]{{formula:8d137767-5e20-4254-8e90-28859c81040a}} , implying that
the keplerian motion of the black hole binaries in the four blazars
is still non-relativistic. That is, the black hole binaries of the four
blazars have not been entering the stages of orbital evolution dominated by
the general relativity effects (Einstein {{cite:1267c2bffce1e1a191b06bc3636d6ee3837d7af2}}, {{cite:d8508e57d4dbd6c632f42b7575cf23d1ecff78ce}}). The
results listed in Table 5 for the physical parameters of the black hole
binaries could only describe the characteristic features of their initial
in-spiraling processes.
We would like to point out that our results derived for the putative
black hole binaries in the four blazars (3C279, 3C454.3, OJ287 ans 3C345)
were well consistent with the theoretical arguments about close binary
systems by Begelman et al. ({{cite:c6a55b5ca6191ad7caf67745bb821025b8b73e7e}}). This was unexpected and confirmed
posteriorly. They have shown that, when the orbital separation of binaries
approaches {{formula:1457ed60-735b-4748-92d8-11f19528b487}} at which gravitational radiation becomes to
dominant their orbital evolution, their keplerian motion will have an orbital
period of {{formula:17863368-ef76-4788-98d3-3eca6230efff}} =48.4 yr for a specific model (assuming
q=0.3, M={{formula:d1a69025-b354-40ba-a0a9-58b0cbd093bd}} and corresponding {{formula:ba61db0e-3879-4a44-86e2-ec4c39d35ca7}} =0.067 pc and
{{formula:b13a7e3f-8862-4a92-b560-62dc8c267b4e}} =1.8{{formula:db1f596e-551b-429a-8b4b-3b7185b04440}} yr; referring to Begelman et al.). If
the orbital separation {{formula:7d3ee8d2-c1ce-4dcd-8fdd-a7b486fa8ca7}} , for example, {{formula:ec816743-8c73-4d93-9bfe-9620ba68c3ea}} (0.021 pc)
and {{formula:61d2fefe-290f-4e6e-b98e-ed87511341e3}} (0.012 pc), corresponding
[{{formula:b293e235-a4a1-4816-9282-1efb6159b664}} yr, {{formula:b0390d5b-2300-4dd9-b1a6-486e23635c77}} =8.6 yr]
and [{{formula:668f9ee6-e1dd-487c-99b1-5f6a1ea0fea2}} yr, {{formula:ca3956fc-32f5-4f80-99cb-d3c1f94a6b32}} =3.7 yr], respectively. These
values are closely similar to
the gravitational radiation lifetimes and orbital
periods derived by our works for the four blazars (especially for 3C279;
Tables 3–5). The double jet-nozzle precession we tentatively found through
analysis of the VLBI-kinematics of the four blazars could be the direct
consequences of their orbital motion. Therefore both theoretical
investigations and VLBI-observations seem consistently to approach the same
conclusion: our investigations and analyzes of the VLBI-kinematics of
superluminal components in the four blazars (3C345, 3C454.3, 3C279 and OJ287)
might have revealed the keplerian motion of the black hole binaries
putatively suggested to be existing in their nucleus.Double-jet
structure in blazar OJ287 has tentatively been suggested by Qian {{cite:394434f8662aab31fba421d0bdf3ba46a7888ff8}}
through model-simulation of its superlunimal components in terms of our
precessing nozzle scenario. The secondary jet ejected by its secondary
black hole could be observed in near future (Dey et al. {{cite:3b5c90c67232ef81137629b5c6e468822cccf585}})
In fact, only in blazars one could possibly discern (or detect) the
precession of double jets caused by the keplerian motion through analyzing
their VLBI-kinematic behaviors, since blazars are observed at very small
viewing angles ({{formula:29596778-d193-4eef-a044-d981c784cb22}} for the four blazars discussed here),
which assure the precession cones of the double jets projected in the plane
of the sky being sufficiently wide and separated to be resolved by
VLBI-observations, and the superluminal components can radiate strongly to be
measured on VLBI-scales due to relativistic beaming effects. Search for
evidence of possible keplerian orbital motion of black hole binaries in
blazars may be a severe challenge for future VLBI-observations.
Relativistic jets in blazars (and generally in AGNs) are believed
to be formed through MHD processes in the magnetosphere of
black-hole/accretion disk systems in the nuclei of host galaxies (e.g.,
Blandford & Payne ({{cite:8b2d733da9d258f77ffe7424c1d20a37ed887bdf}}), Blandford & Znajek ({{cite:4ef290cc006750415303316bb7bedd6c4e550073}}),
Camenzind ({{cite:ee3725d9a2c634b694ec2c4072ecad05199d9d83}}, {{cite:b7c949da177dcda4a7a97356f990779f38194e90}},{{cite:2bc096739f8990ee927623d2c34dfb3752611bb4}}),
Lovelace et al. ({{cite:df9da77538cc2f72d497942fe72eab2fd2a665c7}}), Li et al. ({{cite:0fa139dabe9e68ccb1dfcb898d9b9751e82955fe}}),
Vlahakis & Königl ({{cite:2ec7f7f7c473a4382bfd37af1fc6e7847d565a69}}, {{cite:c871bac22977fd41ce98b63e4bb3bd00d87ff2ac}}). In these scenarios
magnetic fields dominate the processes: magnetic pressure gradient
accelerate the jets and magnetic pinch effects of the toroidal fields
collimate the plasma flows. MHD theoretical scenarios
can also explain the extended (parsec-scale) acceleration observed in
blazars. It is shown by Blandford& Znajek ({{cite:4ef290cc006750415303316bb7bedd6c4e550073}}), Li et al.
({{cite:0fa139dabe9e68ccb1dfcb898d9b9751e82955fe}}) and Vlahakis & Königl ({{cite:c871bac22977fd41ce98b63e4bb3bd00d87ff2ac}}) that there are
radially self-similar solutions for stationary axisymmetric MHD
flows in the magnetosphere of black-hole/accretion-disk systems which
allow extended acceleration after the flow passes the classical
fast-magnetosonic point approaching the modified fast-magnetosonic point
through "magnetic nozzle mechanism". Vlahakis & Königl (2004)
nicely explained the
accelerating component C7 in blazar 3C345 (observed by Unwin et al.
{{cite:9d901a46d1be4eec3181e6965469403a9194f35b}}) in terms of their radially self-similar MHD solution
for a proton-electron jet. The acceleration zone {{formula:b131317d-ccc6-4433-958d-59ee2dc5f414}} (30-300 pc)
and the range of bulk Lorentz factor ({{formula:e8586f13-659a-4a53-af54-482393ea60ff}} 4–20) derived in
our model fittings can be understood within the Vlahakis-Königl's
radially self-similar MHD model. Thus available
MHD jet-formation theories are already effective to explain
the extended acceleration observed in blazars.
We would like
to point out that the cavity-accretion models
may be very helpful to understand the accretion process, jet-formation
and ejection of superluminal components and alternative
quasi-periodic activity in blazars with double-jets, hosting binary
black holes (e.g., Shi et al. {{cite:13adacc74bdfe453d4037c5ff24f1bf102b18a6f}}, Shi & Krolik {{cite:4f6475f26af39d0738fdbc1f1dd39255badd8751}};
Artymovicz & Lubow {{cite:8a9c9227ef674798a7a4ced36a40d7751f7611ca}}, Artymovicz {{cite:5b778e6b136e031e2bb1b97568fd2911595f5b25}}). Specifically,
Shi & Krolik ({{cite:4f6475f26af39d0738fdbc1f1dd39255badd8751}}) argued that in MHD scenarios cavity-accretion
rates can be raised to the level that both black holes can produce a jet,
forming a double jet system.
One distinct feature of our results is the precession of a common
trajectory pattern around the jet axis to produce the observed inner
trajectories of the knots and the 7.30 yr precession period for 3C345.
It is worth emphasizing that for jet-A its nozzle-precession has been
observed over about four precession periods ({{formula:9fad8a24-7173-47cf-818a-29149c08d04b}} 1979–2009) and for
jet-B over about two precession periods ({{formula:ab9e8076-f5ab-4ca9-997f-e914f42042e8}} 2002–2016),
implying that jet-A and jet-B have been active during respective periods
with respective levels of activityThus it seems uncertain whether
the cores of jet-A and jet-B could be concurrently observed..
Precessing nozzles could possibly exist in the putative binary black hole
system in 3C345, which needs to be tested by more observations.
Based on the assumptions about the possible existence of a precessing
jet-nozzle and precessing common trajectory in 3C345, we have analyzed the
kinematic behavior of 27 superluminal components
in terms of the precessing nozzle scenario and model-fitted their
trajectory {{formula:82fb5ec2-b20d-4ac4-ba72-a5e24ca81a78}} , core separation {{formula:28bb5641-3143-4e36-b7b4-1bff631ad0f7}} (t), coordinates
{{formula:b03ad140-e78e-4ea2-bc27-2802a34b2ab0}} (t) and {{formula:093c853a-524d-4202-9f4d-ca14b7dc893a}} (t) and apparent velocity {{formula:568986f3-0e9f-4fcf-9d84-1b8470752fda}} (t) versus time during
a time-interval of {{formula:9d9c050b-9cb3-4074-a72f-afd66a7fb1d5}} 38 years (1979–2016). The double jet structure
was disentangled and their precession periods (7.30 yr) were derived.
The derived bulk Lorentz factor {{formula:df8c84e3-07b7-4495-9ba2-10f19043c60b}} , Doppler factor {{formula:297e9f22-3703-4d5d-b032-c4a9c767dff2}} and
viewing angle {{formula:8a528699-5556-474c-bd1a-b34c5505b01c}} as functions of time may be very useful for
studying the intrinsic emission and physical properties of these knots,
and the connection between the radio, optical and {{formula:db02714d-171a-4f39-86a4-65383b05531f}} -ray emitting
regions. The double-jet structure and their precession might be useful
for investigating the putative binary black hole system, providing some
constraints on its physical properties.
We have used a new method, which is different from the ordinary methods
for analyzing the observational data obtained on VLBI-scales.
The assumptions we suggested should be tested by future observations of
the kinematics for superluminal components
within core separations {{formula:ead749bd-af56-4c57-b824-d6696f922b4a}} 0.05–0.1 mas, where the superluminal
knots might follow helical trajectories with large pitch angles (or strong
toroidal field-lines; referring to Qian ({{cite:61863121eb176350780536abb2d12d188092fb00}})) and
might be more difficult to determine their
precessing behaviorsAt large core-separations helical
magnetic fields may have much smaller pitch angles and thus the motion
of superluminal knots becomes to be approximately ballistic..
The assumption of precessing common trajectory
would be confronted with future VLBI-observations with higher-resolutions
in order of {{formula:d9dd2f10-15de-4d64-9e1f-37cd60e0348f}} 10{{formula:e2cac55e-87ca-4316-a261-1a5ff86610a6}} as.
In fact, there have been different results by analyzing the kinematic
behaviors of superluminal components for 3C345 and quite a lot of
different suggestions were proposed in literature. For example,
Klare ({{cite:ff5dd54b47ea09e48f88b59cacdeec981543d6af}}) claimed the presence of jet precession of
{{formula:bdb29b7f-0e17-4240-8c07-d36bda086178}} 8-10 yr, but Schinzel ({{cite:a0ed0cea478280751f8c0a5649564b234399f9e1}}) claimed no clear evidence for
periodic trends in the kinematic behavior of superluminal components;
Lobanov & Zensus ({{cite:4f6b2035aa1b45f8c44d2cd02785ed9485e52a46}}) suggested a {{formula:288486a0-e3f1-49a3-b5e2-9987e98cd967}} 8-10 yr period;
Lobanov & Roland ({{cite:0a665a3eec9e58f3f28b6d3d93e2b9a8785d8ea9}}) suggested a binary hole scenario and
9.5 yr precession period, and Qian et al. ({{cite:58c0de2900c1bc1ee4970fea5102354e93c52a8c}}) suggested
a 7.36 yr precession period, etc.In fact, all
these determinations of precession period were derived by using the
observational data on the knots of jet-A only. One could not find any
precession by using observational data on the knots of both jet-A
and jet-B.
Our results in this paper may be regarded as one of the
alternative explanations. Using our new methods for analyzing the
VLBI-kinematics in 3C345 much more information on its kinematic properties
and physical implications could be obtained.
However, this work was established on the assumption that jets in blazars
should precess with certain regular periods. At present it still
remains unsettled as a question: whether blazar
3C345 has a single-jet structure or double-jet structure with or without
jet-nozzle precession. More observations and investigations are needed
to solve this issue.
Similar issues are present for other blazars, for example, for blazar
3C279. Recently, performing VLBI-observations at
mm-wavelengths by using Event-Horizon-Telescope, Kim et al. ({{cite:66a5addda572c7d40a3bebd670ccad67c7706c8b}})
found similar position angles in 2011 and 2017, suggesting a
precession period of {{formula:c2ff3733-4964-4978-94bc-119510f21bcb}} 6 yr and claiming to exclude the 25 yr
precession period which was derived through analyzing the kinematic
behavior of {{formula:0b39699e-9eee-4b5f-8ef2-d333590a46ff}} 30 superluminal knots observed during {{formula:6a14e178-48b7-4381-bbaf-146baf4e2566}} 30
years (Qian et al. {{cite:707e39dd1fbc78e3b760b02c6c31a7a7b219fa33}}).
Similar position angles observed
at two different epochs is inadequate to determine the precession
period, because it still needs to confirm that the two
epochs correspond to a difference in precession phase of 2{{formula:8e25f3b2-f707-4bec-868c-ad90c16ff880}} . In our
precessing jet-nozzle scenarios suggested for the blazars (3C345, OJ287,
3C345 and 3C454.3) recurrences of the curved trajectories observed at
different epochs corresponding to differences in precession phases
of {{formula:36330cf5-0ccb-4f21-a25d-d284d83cd7f8}} 2{{formula:fe671ecf-bfa7-4b62-b40e-408e3bde09bf}} and the distribution of the modeled precessing common
trajectory were very helpful for determining their precession
periods..
Here we would like to propose an alternative interpretation:
Kim's finding might not necessarily be contradictory to the 25 yr
period. It could possibly be compatible with the
precession period of {{formula:17b5598a-2b0e-4b69-929a-54e452a303e6}} 25 yr derived in Qian et al.({{cite:707e39dd1fbc78e3b760b02c6c31a7a7b219fa33}})
because the 25 yr precession period permits similar position angles
appearing at two epochs different within {{formula:54abd730-f307-4594-ae1e-f173a833bf80}} 12.5 yr (a half of
the precession period of 25 yr). Such kind of similar position angles
at two times could be observed at the either side of the projected
jet boundaries (or the "jet edges"). An
appropriate example may be: through model-fitting of the
VLBI-kinematics for OJ287 (Qian {{cite:394434f8662aab31fba421d0bdf3ba46a7888ff8}}), it was found that its
knots C11 and C12 were observed at similar position angles
with a difference in their ejection times of {{formula:c5002a90-6efa-4393-945e-472a1721f687}} 3.8 yr. The two knots
were ejected at the either side of the southern edge of its southern jet
with a difference in their precession phases of {{formula:25ab35f4-c155-4ce4-be8a-72ed283c7778}} 2.0 rad,
corresponding to a time-interval smaller than {{formula:fc93ab54-319f-4642-9f1f-f8a5f31b2ff9}} 6 yr
(half of the precession period 12 yr).
The presence of double-jet structure, jet-nozzle precession and periodicity
in ejection of superluminal components in 3C345 and other blazars are still
issues in debate and need to be further investigated. Recently,
Event-Horizon-Telescope (EHT) Collaboration has begun monitoring
observations for a few blazars at 230 GHz with resolutions of
{{formula:39603dd9-2d9c-4a60-aa63-5dd2b81dd172}} 20{{formula:e974693a-4dcb-461e-be31-fcfaa0235b23}} as (EHT-Collaboration et al. {{cite:117176780fba83df0e3917e7c3fb47102ea898f6}}). As suggested by
Qian ({{cite:394434f8662aab31fba421d0bdf3ba46a7888ff8}}, {{cite:7b382eee80103b57c79ab8dae88146641e9847c5}}) that the non-thermal radiation
emitted by blazar OJ287 might originate from its double jets with
precessing jet-nozzles. EHT-monitoring observations in the near future
would be helpful to reveal its double jet structure, searching
for the second jet ejected from the secondary black hole in OJ287
(Qian {{cite:394434f8662aab31fba421d0bdf3ba46a7888ff8}}, Villata et al. {{cite:0365c617382465b4de8dcbe20b40eac5b7739bab}}, Dey et al.
{{cite:3b5c90c67232ef81137629b5c6e468822cccf585}}, {{cite:b1e61aec26c818f20e279b0375ea67a83eeac45a}}). Similar search for double-jet structure
in blazars 3C279, 3C454.3 and 3C345 should be tried, and
EHT-monitoring observations will be very helpful. All kinds of
scenarios proposed to interpret the kinematic phenomena in blazars
would experience severe tests.
| d | b61e4c2bec0dd2f939cae332fa35587c |
It is also worth mentioning the flow of the ambient fluid, which we have so far ignored for this study.
In particular, wherever there are sharp changes in the interface shape, this may be associated with non-negligible displacement of the local ambient fluid, such that the dynamic boundary condition (REF ) cannot be applied. Likewise, in the case where there is a viscosity contrast between the released and ambient fluids (e.g. CO{{formula:abd970a6-c664-4c4f-94f8-54835357b0be}} is typically 30 times more viscous than brine), this can modify the shape of the current {{cite:2866d1e0820f29f899e78e748e735fd8f3687c6d}} and cause fingering instabilities {{cite:c619201e47ea0e0b24ee955247a7b24a7da2f2c4}}. In both of these cases a full numerical model would be necessary to resolve such flow details.
| d | 0eeb9f518e324b8b804fe3fcb0ef4553 |
Following the standard evaluation metrics on QUBIQ, we averaged 7 predictions as the confidence map and compared them with the average of seven manual labels with the continuous Dice similarity score. We note that the averaged value of each pixel is in {{formula:ef531bfb-eb0e-49a1-a38b-b87f575d493f}} . The confidence map can be regarded as the reciprocal of the aleatoric uncertainty. Fig. REF depicts representative outputs of a validation sample and the averaged inter-observer variability results. The numerical results are shown in Table REF . Our framework outperformed the independent training methods {{cite:34256ae8b783731b6818c5e56f3db146bb145fde}}, {{cite:20d3dcd6c4d3fdd61be927ab413c71597871583d}} and the Bayes dropout used in {{cite:3aa34dd33a3361663b48804b017e5bbb376117c4}} for the aleatoric uncertainty quantification.
| r | cb524b2a724af21492f2c78fd1ea32c4 |
To conclude, we advocate directly maximizing the average reward in RL.
It is the root for approaching Blackwell optimality through Veinott criteria.
It also eliminates any complication due to artificial discounting.
Future works include investigating to what extent exploration strategies
for discounted rewards applies to RL aiming at Veinott criteria.
APPENDIX
Experimental setups: environments and learning methods
GridNav-{{formula:ceb2701f-db85-442a-9aa4-588c187461f1}} (episodic) refers to an {{formula:d58018b0-ed2c-492c-944a-8d296e45370c}} -by-{{formula:f556a06a-a179-41fe-b8cd-e01a9370b919}} grid world with no obstacle.
An agent has to navigate from an initial to the goal (terminal) states.
Every state has four available actions, i.e. major compass directions.
The state-transition stochasticity is governed by action-slip parameters.
If an action brings the agent beyond the grid world, then the agent stays at the current grid.
There is {{formula:aa9f18b6-da4b-46f8-8ab7-1652caa35454}} reward for transitioning to the goal; any other movement costs {{formula:ac2d48d3-91ed-4c90-826d-ecbc98e79adb}} .
Taxi-{{formula:a32d7124-6bef-4c0f-93de-4279a12a38da}} (episodic) refers to the {{formula:fac7ea4d-88e0-48c6-b217-c5ae89d389be}} -by-{{formula:35818ecc-c785-48e1-aced-f97370e31834}} grid Taxi environment
{{cite:6059690747b7643ac51ee991ba78ff376e5f7a5d}}.
With respect to the original,
the number of obstacles are increased accordingly with {{formula:c8a4b309-a7a4-4af4-8eb9-7b2e5c474acf}} ,
whereas the number of passengers and pickup/drop-off locations are kept the same.
The environment families 1, 2, and 3 are adopted from
the access-control queuing task {{cite:364141f4289f34b3ad2f1685414d1f1f7974a26b}},
the Chain problem {{cite:a28088d8c579b61dd0cd309aa6000988e1e0605c}}, and
the torus MDP {{cite:697f3624b4b6d4e8f2ecd300d4d7df32aa58b2c9}},
respectively.
The learning method used for Figs REF and REF
is Q-learning that relies on the Bellman optimality equation to produce iterates of
optimal action value approximation.
That is,
{{formula:df384471-2808-41c7-a0e4-1dfdf0b36983}}
with a positive learning rate {{formula:2399333e-db00-4a22-88ae-702422736a80}} (here, we used a fine-tuned constant {{formula:2fc7562b-fb0b-479d-a225-19c447a7c306}} ).
This is for {{formula:53859004-78cd-4285-9d59-68676ccd7316}} -learning for discounted reward criterion.
Its average reward counterpart, called {{formula:cfbede28-132b-4f9b-934e-c03b8814a16d}} -learning, has a similar update but
with the omission of {{formula:6d6d4252-0175-4c42-99b3-b3d73d93f4cd}} and the subtraction of an estimate of
the optimal gain {{formula:18b7120b-1883-4ab0-899e-bf94b23d0637}} from {{formula:b2391feb-e911-4589-ab05-6d2a14f6812d}} .
Following the relative value iteration (RVI) technique
{{cite:57d9b61e43feb4d007dcd7648eeb26dcd1bf1758}},
{{formula:84982d35-6cf1-4b00-9220-5c767a533a48}}
with a prescribed reference state {{formula:3595cf5e-dba6-40ba-9e30-c4ec99837824}} .
For total reward criterion, {{formula:4153b94a-51c1-4c10-a9ce-9948e785c0fe}} is updated with {{formula:b6cd5979-7a45-468e-9425-576f78a4e840}} set to 1,
which converges as long as the total reward is finite {{cite:a25297372c3fb6abaf7abe68a449c42d8b116997}}.
The estimate {{formula:92c6a465-786b-48e1-80cd-a67dc6861860}} is initialized optimistically to large values
to encourage exploration.
0.135
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{{figure:abb40222-08d1-4950-a02d-895254368c77}}
Optimization landscapes as a function of two real policy parameters
{{formula:8521523f-99d0-4098-9abc-4f6bf34c650d}} (i.e. horizontal and vertical axes in each subplot)
on three environments (from top to bottom rows: Chain, Taxicab, and Torus).
All but the rightmost (i.e. the gain {{formula:167a0797-6325-4c98-bce2-776ba704c278}} ) columns correspond to the scaled discounted reward
{{formula:2e44e258-996e-41cc-9fc4-fc6b195d5a01}} using the indicated discount factor {{formula:9eabfc94-6924-49ce-8776-2ed74e71fcf9}} of
randomized policies {{formula:f729f125-f78d-4efa-bd1d-2554b5dd183e}} .
The color maps the lowest value to dark-blue, and the highest value to yellow,
where such lowest and highest values are of the “worst” and
the optimal deterministic policies with respect to the corresponding criterion
(note that different subplots have different lowest and highest values).
As anticipated, the discounted-reward landscape becomes more and more similar to
its average-reward counterpart as {{formula:7be59e42-0940-410c-9f85-c47de74a925c}} approaches 1.
Particularly, {{formula:f74761bd-b9d5-468a-bc74-a3dbec314694}} induces a landscape, whose
global maximum coordinate coincides with that of the gain.
Note that the gain landspace in the bottom row does not have yellow color because
there is a significant difference between
the gain {{formula:5424041d-e6b3-46e0-9162-256a78ef1dea}} of the optimal deterministic policy
and the maximum gain {{formula:4414062d-2e62-442c-9de7-dcf50d8bf13c}} across the shown landscape
(which is only a portion of the policy parameter real space).
Their absolute difference, i.e. {{formula:c37af921-3d9f-4384-8909-6dc2ddc5ea98}} , is of {{formula:b54281c8-93c0-4659-9840-2bf8610992dd}} ,
where {{formula:46a20047-5a8d-47ad-a9a4-73db65a4550a}} , and {{formula:cd4d5642-d4cf-48b7-bc4e-5b685857506f}}
(values are correct up to 3 decimal places).
For experimental setup, see Appendix .
| d | ca246e5497b0e8f04eaf2907b1c224f8 |
In an accretion disc around black hole, rotating
flow experiences centrifugal repulsion against gravity that effectively
constructs a virtual barrier in the vicinity of the black holes. Depending
on the flow variables, eventually, such a virtual barrier triggers discontinuous
transition of the flow variables in the form of shock waves.
Indeed, {{cite:02cd0a40c862db5a14e4e4dde351a06a6d52aea5}} argued that according to the second law of
thermodynamics, shock induced global accretion solutions are thermodynamically
preferred as they possess high entropy content.
Meanwhile, several attempts were made in order to examine the existence of shock
waves in the accretion flows around black holes both in theoretical as well as
numerical fronts {{cite:14fb14e1865c563ef72e49513625d229ff9e0538}}, {{cite:21b848454defefbefc83fbdf848be19ea0189e30}}, {{cite:124fa1527b43e7be550d2f0e8c152a94df7c385b}}, {{cite:3cf47f5eec15c9cb4ce36bb35c1bb8b482b88bf2}}, {{cite:6de3979383eb895db8105d2e84fa9fabc5fc4849}}, {{cite:b5cd4f1649bad36887a105c0feaabb7edab8862d}}, {{cite:02cd0a40c862db5a14e4e4dde351a06a6d52aea5}}, {{cite:edc37b5b7eb710d66791ffbfcc65f5d8c4526cfb}}, {{cite:8f0afa4145f75ec6a8fc6af7de2d17606976a937}}, {{cite:caab1be42fb2ac512d05c3dd65702afc34b2a634}}, {{cite:48f49026f1a60f45475e8a6f4839c3427ba3ac1d}}, {{cite:80c21c11d93a3743f2d84a143cc8525f15438f3e}}, {{cite:a2c0686d5bcc2e2924896341fa2e40644077d780}}, {{cite:482a617423680e039761d25fc4c91565e59c8825}}, {{cite:3c5db92db2bd1bcd495732102f448bde1f7132ef}}, {{cite:93611258ac0a28fed57e0700244ffb42d1ee7835}}, {{cite:ccb5f4bdfc8253e48859ceaa92b70fb293faec67}}. Due to shock compression, since the post-shock flow
becomes hot and dense, all the relevant thermodynamic and radiative
processes are very much active in this region that eventually reprocessed the
synchrotron and bremsstrahlung photons in the post-shock region
into hard radiations via inverse
Comptonization mechanism {{cite:133f81fecebfa65cba6b5d8126ab06d9a7b148ad}}, {{cite:640ebe81895ef9d29c34edd8e063b322e2035114}}. Apparently,
the presence of shock waves in the accretion solutions leads to the
formation of post-shock corona (PSC) around the black holes
and therefore, PSC
seems to regulate the spectral features of the black hole sources. Moreover,
due to presence of excess thermal gradient across the shock front, a part
of the accreting matter is deflected at PSC and eventually diverted in the
vertical direction to produce bipolar jets and outflows {{cite:c06421bde63bccf3918adb78b280b1496493681b}}, {{cite:147be13db6025d12dcaa010ab39463916b90510f}}, {{cite:6e5e05ec29c99237ce2411eb82ea35a83da6c9c5}}, {{cite:482a617423680e039761d25fc4c91565e59c8825}}. Interestingly, when PSC undulates, the
emergent hard radiations exhibit quasi-periodic oscillation (QPO) which is
observed in spectral states of many black hole sources
{{cite:a5782b387a9695491221ecc423dbd10d91ad12cd}}, {{cite:3a7d59aa5ca0fd7d741c2ac74710dc4a01b66cb1}}, {{cite:88bfde653a1ed36b57b8e492641aad87e1657773}}, {{cite:e7ba00c131a691c8f8bfa85979b2d70cb31f1357}}.
Meanwhile, with an extensive numerical study, {{cite:80c21c11d93a3743f2d84a143cc8525f15438f3e}} showed that
the oscillation of PSC displays QPO features along with the variable mass
outflows originated from the inner part of the disc.
| i | 831d1e51359174b8ea6b435ae44a0f97 |
In this study, we used a publicly available labelled DR fundus image dataset from the Asia Pacific Tele-Ophthalmology Society (APTOS)https://asiateleophth.org/ to train, validate and test the model. The dataset has 3662 DR fundus images categorised into a five-class scale of increasing severity, namely normal, mild, moderate, severe and proliferative {{cite:8c08a646c018c5605b8e1fae5da5931cd5c51a17}}, {{cite:52c2314c313a948dbaee98ff7ac49507ea289ad1}}. Figure REF shows the distribution of classes in the dataset.
{{figure:c56c338a-d09c-4765-ab66-f6f2a8b7dd22}} | m | 24fc2e9ae280b72ddc901ab4f26914c3 |
However, in general the three point function for different interactions and in different models does not necessarily lead to {{formula:fd24199e-5ee6-4aa2-8aaa-8d2a31b57e67}} -dependence presented in (REF ) and it can have crests and troughs at different locations. Therefore, over the years there have been different templates developed to best extract possible non-gaussianities in dataReaders are referred to {{cite:c521a7c82f7a5e3a0386ce7e7731140fe8e8bed2}} for details on different templates fitting for different models. in order to test different types of models. The next famous example are non-canonical single scalar field inflationary models {{cite:3d0d13ab2315332a8d9ac926c839eea4153b9142}}, {{cite:4f7ebbcb408060eb68247495f6b0e5ca9e73c24b}} that usually peak at the limits of equilateral shape triangles {{cite:63f6e1252c656e11fea2a657cf028203fa877fef}} and can be approximated by
{{formula:e95625ea-b782-4e13-a956-c9eab280f5b0}}
| r | 8d4cc67232f14d3ce1991c430235ec67 |
The choice of baseline and path function. Although Sundararajan {{cite:ed60065849343d5740ac6de072afd60e9c3acab8}} suggest to use black image as baseline and linear interpolation as the path function, Sturmfels {{cite:6a2e330f08e194ad77cc0d2db18b1495fd40abd2}} argue that it may not be the best choice.
We experimentally show its disadvantages in REF .
As can be seen, the linear interpolated images of black baseline image does not present the “absence” of important features, although the feature detection output of the baseline image is reduced.
It reduces {{formula:4f924ce4-5f30-436e-bf82-abe4b10f2dcf}} by reducing the intensity of all the pixels, resulting in saturation for the gradients of all these interpolations.
On the other hand, {{formula:ff44e379-11fe-4c27-97b7-6e6fe4d4d6cd}} is equal to {{formula:1c953a5c-c5b4-49dc-adc0-52e3d882af94}} for all {{formula:cc4ea907-ea00-4cf7-90c6-a99e46bf0245}} in linear path function, which provides all gradients the same weights.
For these reasons, the black baseline image and linear path function are not suitable for interpreting the SR networks.
Alternative choices are proposed in this work for SR networks.
We use a blurred image as baseline to represent the missing high-frequency components.
The the progressively blurring function is presented as a natural choice of path function.
With the mathematical characteristics of path integral gradients, the proposed method can provide reasonable attribution results for SR networks.
{{figure:19a654e7-b2a3-42c7-83ea-25bfe95c3e01}}{{figure:428ac152-5eb4-4c99-88ff-b3a104e629c8}} | d | ec0bb189367cb680409b46eb54eaf0b1 |
Figure REF shows the overall performance of the tested algorithms in different scenarios. The results include the median performance and {{formula:793ebf7a-3d5f-4c99-8337-ff5e45ce3ed6}} percentiles are shaded to avoid the effect of any outliers as recommended in {{cite:9347b0755b96844a800f646ddd4fb43bcd56510f}}. For the sake of demonstration, here we select the best plug-in method, referred to as S2RL in the following, to compare with other baseline algorithms.
First of all, we can see that S2RL performs best on up to all six tasks, which means our proposed method can efficiently enhance the performance of agents in different scenarios. In the easy map, some algorithms have achieved good performance, and our S2RL is not significantly ahead. In contrast, our S2RL significantly improves the learning efficiency and final performance compared to the baselines in some hard and super-hard scenarios.
Specifically, in 6h_vs_8z and 3s5z_vs_3s6z, our S2RL consistently outperforms baselines by a large margin during training.
This is because the number of entities in easy maps is small, all entities are critical, and the selection gain brought by the sparse attention mechanism is not apparent. However, when the situation becomes more complex, and the agent needs to consider which entities are more critical to the decision, the benefits of the sparse attention mechanism are more pronounced.
| r | 3edfaed563c62d54b3d211fd1717ab1e |
Given a simple graph {{formula:76a938d4-8b88-4cd7-b6ef-8549b3e3bedd}} , a set of vertices {{formula:b326bbf8-81ab-46da-9589-0ed306325f6b}} is an independent set if the vertices of this set are all pairwise non-adjacent. Finding an independent set with maximum cardinality is a fundamental problem in algorithmic graph theory, and is known as the MIS problem (MIS, for short) {{cite:c7c7ec1a8c392e38887cf92cd0da2511669a24fd}}. In general graphs, it is not only {{formula:f3aa76bb-9ae3-45ee-962b-1b1762cbc799}} -hard, but also not approximable within {{formula:f42a3520-de87-41ad-804b-03d2ce4e350b}} for any {{formula:b32e6620-a04e-4ae7-8bfb-fafe20bdf5f9}} unless {{formula:1c9d2147-7cd7-48ba-9c04-1f109ccc0db2}} {{cite:8c47c35c1ced80107e4cdaddceb4141a568ee395}}, and {{formula:215e824c-17bf-4dc8-805e-c7b4c91f86fa}} -hard {{cite:8a38afcf73fba3e2253343a68658cffa0e6f5503}} (unless otherwise stated, {{formula:f0cb2cee-bcea-489c-9793-48d97fb84a4c}} always denotes the number of vertices of the input graph).
Thus, it seems natural to study the complexity of MIS in restricted graph classes. One natural way to obtain such a restricted graph class is to forbid some given pattern to appear in the input. For a fixed graph {{formula:74e675e1-b2f6-4961-a2cb-a06e3c5113c2}} , we say that a graph is {{formula:b7d8480b-711a-45fe-9211-df4e0da8d63b}} -free if it does not contain {{formula:cd187106-1476-4db7-a6fb-a322030f1ef3}} as an induced subgraph.
Unfortunately, it turns out that for most graphs {{formula:299206fa-d844-43b7-8fd9-f8b0e2eb49d5}} , MIS in {{formula:411cabce-0767-4dbf-8557-c7f19f2bd1c6}} -free graphs remains {{formula:fc3668df-f408-4b0a-9052-e6c983686034}} -hard, as shown by a very simple reduction first observed by Alekseev:
| i | 20a46e525793c4a942ab123184545c5c |
Recently, the {{formula:af4be171-9042-497b-80c9-af6133e4b637}} norm was successfully used in low-rank representation {{cite:13f5fb2ff6724ace9d202ee55c62a14374fd4143}} to optimize the noise data matrix {{formula:9da07252-5178-48a4-910a-7b24069bd563}} . The optimal {{formula:2e3400ac-8396-407d-9383-a08563a4a080}} can be updated by solving the minimization problem as follows:
{{formula:cb5ef9bf-bf2b-4e5c-b6f5-09e7bf2342fa}}
| m | 78305ce85cd35181e590ffa457de9cf5 |
Following the work {{cite:b30e4a805cb3fa4fbcdd1a03d1c03aedccf5b42c}} of Agler and Young, this domain has remained a field of extensive research in operator theory and complex geometry constituting examples and counter-examples to celebrated problems in these areas such as the rational dilation problem {{cite:4f1b136a39e922b6e9beba353876e35efb6f9f32}}, {{cite:f10c4bc42e8f89736c5679cecfc9daf7f5f3b566}} and the Lempert Theorem {{cite:641c0118d4116f9ad77a531c44ca43f5570b503b}}. In quest of understanding the determining sets we shall actually consider the following more general situation.
| r | 8681deb99ff337627e06a0943e1afad2 |
The length of path between two vertices {{formula:6a2ac94f-67cf-46a7-a672-e079d63370ae}} in a connected graph is the shortest distance {{formula:55a2c16a-9dfd-48b5-95a8-6bdee195fb43}} between them. Let {{formula:ffecb4d1-eb3f-4b75-a87e-59f81f5472e4}} be a vertex of {{formula:489980e7-34fe-486b-b517-0c806e550dba}} and {{formula:b3f21252-e836-44a8-92c3-617963193ad2}} be an ordered set of vertices of {{formula:7d3c6fa1-c672-4727-93d1-1d961fa187aa}} . The representation {{formula:a5e5bb24-5b00-4a9e-b88e-53d135d42bc2}} of {{formula:e9f9926b-1a3a-4fe6-8ec0-c03578e8997e}} with respect to {{formula:98ad0d65-0dc0-4947-8779-114d5fbb6523}} is the {{formula:21ce5eca-0867-40e9-85bc-d358c70ea547}} -tuple {{formula:1135f216-f1fc-403a-9f25-2e7c3c121e7a}} . If distinct vertices of {{formula:43a0218e-731c-4ddd-bf0b-dec86eb719f5}} have distinct representations with respect to {{formula:4522e4cb-db32-4fdf-9812-abbc6d4516ac}} , then {{formula:46ab966d-43bb-4bdf-b936-16d77a71588c}} is called a resolving set. If the resolving set has minimum number of elements then the set is called a basis for {{formula:c918d97b-4bc2-4296-b3c0-b10d26a6d00d}} and the cardinality of {{formula:5233d174-72b1-4210-9840-60e87c0c3205}} is called the metric dimension of {{formula:ea8cf8ae-b266-4308-9568-a3fabe148a00}} and is denoted by {{formula:a38e3484-05c4-4ff2-9368-81bb8bae2499}} . For further study about basis and metric dimension see {{cite:aff820c17699c48cec0ebbbf02ee320f289e3c13}}, {{cite:8516b707263342be5b5f1a87dec6d80bdbbc330e}}, {{cite:ed7c77f64cae900088cba5889241b66e355b5622}}, {{cite:71b8b030c422d4daf7d24f2819662cc279882ce3}}, {{cite:65d4160499768c225d8db5adce7cbb75bd332148}}, {{cite:dab957c7f1ae5f0484202161598e7ed5d07d62e1}}, {{cite:777016c6c6e6208a1ce90aef82c9de8efb1a47df}}, {{cite:7e36f05078c8c5f11c75f3b2a9778218b860d1db}}.
| r | c48cb4e5cea5bca88ac0fc53562f4b40 |
Since when {{formula:4ed61a43-b0c9-469d-8f5b-5a45df0017d3}}
and {{formula:53e6a6ca-5fc2-4b59-8997-d2f93cdff6b7}} , the mountain pass value for problem (REF ) is not a critical value of the corresponding functional,
all the arguments based on the concentration compactness arguments {{cite:003fae9e432df33a1af0f1072522f90d6b503029}}, {{cite:70cc827b47dc8422ecfd4c3da36c79e967630a5e}} can not be used to obtain an existence result of solutions for
(REF ). So far, there are very few existence results of solutions for problem (REF ).
To our best knowledge, the first existence result for problem (REF ) is from
{{cite:e5148eed4a9e98157da896a9c1f92db415b3de9c}} where Benci and Cerami proved that if {{formula:b3b15b59-3382-4065-951c-b96cc94320c9}} is suitably small,
problem (REF )
has a solution whose energy is in the interval {{formula:b8cf7995-691c-408b-a831-602a74c3a7f0}} , where {{formula:79fc104f-4649-4f1e-b0f1-1bf362147f09}} is the best Sobolev
constant in the embedding {{formula:c1f5de27-824a-4af7-850c-06453dea5d30}} .
Note that the assumption {{formula:df661a8d-620b-424a-966b-18922b0c60f5}}
excludes the case {{formula:1625e828-663c-4506-99c1-cd358199f19d}} .
Later, in order to cancel this restriction,
in {{cite:3b7e0800febb112a2db6d63d929b759f1ea6f065}}
Chen, Wei and Yan has proved problem (REF ) has infinitely many non-radial solutions where {{formula:0c4327e0-949b-4abf-b887-685d59bb7dc6}} is a radial bounded positive function, and {{formula:ef52f5fa-ebae-4774-bb59-48077e197fd7}} has a local maximum point or a local minimum point {{formula:8d5c4d2c-68aa-45e9-949a-e29489c6a535}} with {{formula:f7b2b930-061b-4b4d-9d2c-50d97c7dfeff}} .
Assuming that {{formula:8e8864e9-fa31-4a07-821e-0bc67b60eb31}} satisfies a weaker symmetric condition, Peng, Wang and Yan
in {{cite:4a923d523668e2c27f37673d5e82a59d6f6b5cc3}} has shown that
problem (REF ) has infinitely many solutions by combining the finite dimensional reduction argument and local Pohozaev identities,
where the concentrated points of the bubble solutions include a saddle point of a function involving the potential function {{formula:74c870a4-a959-46cc-b1e8-2bb0acc72470}}
Very recently, He, Wang and Wang in {{cite:a28a98f5b138f56369945b9279b73f55a3837546}}
have proved the non-degeneracy of the bubble solutions constructed in {{cite:4a923d523668e2c27f37673d5e82a59d6f6b5cc3}} by some local Pohozaev identities
and also construct a new type of bubble solutions for problem (REF ).
| i | dbc5afe18ca9daa59816f0370d92a0fd |
An ultimate signature of the dynamical topological phase transition is illustrated in ssh:fig:2 b), which shows the band gap structure of the evolving soliton lattice. We see that for {{formula:6c697322-f284-444c-aabe-75d348936443}} values up to the first topological phase transition point at {{formula:1611584f-c203-40b4-80f7-6e963bbe54d4}} , there are two bands without any states in the gap. At the transition point, the gap closes and
immediately reopens, while two eigenvalues are pulled from the bands to stay within the gap. These isolated eigenvalues correspond to the topologically nontrivial edge states of the SSH soliton lattice, with characteristic phase and amplitude structure, illustrated in ssh:fig:3 d) {{cite:bf83aa3e0dd684585b2b3df6e9dffe675c056bec}}, {{cite:e24272b875415de4c7d00dc23819a221c6e4e1e1}}, {{cite:c2ce415b19f33adaba397191de42d0ad410b5895}}. They dynamically emerge at the transition point. Gap closing is an inevitable and necessary ingredient of the topological phase transition that is clearly illustrated in ssh:fig:2 b).
| r | 40efeb417d93481d1c56b5a28cee3bf2 |
The results in Fig.REF clearly show that when no TPE contributions are considered, the extracted {{formula:060d9897-52bc-40b8-8a7a-86e058c566ab}} {{cite:d91532db75fe8d41405a5bcbcfc4bbb9038938a9}} are totally inconsistent with that by the PT method {{formula:78dc84cc-710f-48e5-927f-9f3670b90ff3}} {{cite:e429aa5b9865ade65e0480018ad0e78e95974306}}.
After considering the usual TPE contributions from Figs. REF (a,b), the extracted {{formula:b9d6c0e0-7368-4cc4-a1b2-7c1bc69382f3}}
are much closer to {{formula:a87c2e2b-1e23-4a3e-912a-105e2d3b6427}} , while an obvious discrepancy still exists for {{formula:e40c1fe6-7a9d-43e2-ad42-70a1dc7496f1}} GeV{{formula:52d90b5c-cd7e-4718-9f27-dc989a6ddbe7}} cases.
When the meson-exchange contribution is also considered, the extracted {{formula:44331f5d-81e2-474d-93f2-069c134c416e}} are naturally close to {{formula:cf0344b3-08fd-4504-a0a3-71e4e1552ea6}} .
| r | 6d3d5750ed9a630b6346c715fac162cc |
For a fair comparison, we also competed with the state of the art methods that differ in terms of losses and feature extraction modules: GMN-PL{{cite:69412c17e426d29d7af12296c489e79659eb8ed8}} using permutation loss, PCA-GM{{cite:8b56dc8c5c3be842d34bfc34e866d4c0c02dd2e5}}, GLMNet{{cite:d04ee4b9c0b53978c320fa4149eb62d9cfe219d8}}, {{formula:fcc18a42-bb3c-47e1-b0fc-6e68f0ecde95}} -H{{cite:0cf10d75292aae942de12f617d2698db35dfa722}}, DGMC*{{cite:4e162947235c35ccda2f0702bcc4c97346f5d3a8}}. Among them, DGMC{{cite:4e162947235c35ccda2f0702bcc4c97346f5d3a8}} uses the keypoint intersection sampling strategy and renamed it as DGMC{{formula:d6a1617f-64ec-456f-88c2-b425dc90422a}} .
| m | bf4825392bc0e5e927263ba9f9a3b3d5 |
where we take {{formula:531cd288-88f0-42b7-bf7c-6e46ad19798e}} and {{formula:dbcb703b-8eb6-4526-9633-166a84b33a30}} with {{formula:539c4b87-8b1e-4326-bd66-6264b40d1ba0}} and {{formula:200d18d4-23f7-41cf-88cb-4e1b4e174731}} the conformal time when gravitational waves are generated from the thermal plasma. Note that {{formula:9cdbe12a-6c52-42c1-bbf2-83381ab7d071}} is not suppressed by {{formula:e7bdb427-b722-4a66-ba60-b6bddecf092e}} and depends on three parameters, {{formula:95af2ec8-1480-43ad-be55-931e3c152364}} , {{formula:c43614fe-0cac-4c76-baf1-6df635e79a4c}} and {{formula:7238e096-6597-4e96-9dd3-4b5b38ce5160}} ;
the parameter {{formula:b33828f6-ede6-4f06-b500-2b3ff3cc3cd8}} can be related to the momentum (wavenumber) of gravitational waves measured at present time via {{formula:b76b12a9-44ec-48e8-aebc-59f8a6de00e8}} , where {{formula:cfd4b993-69b4-4502-ae40-c985e991c0bf}} denotes the present conformal time and {{formula:bfd40fba-b930-4819-a721-b5f7999cefc9}} corresponds to the measured momentum of gravitational waves; {{formula:dfa607f6-ec6c-4d05-887c-80d76c135755}} may be chosen as {{formula:5a28cfc8-8125-4317-bc1b-5306836a2005}} when neutrinos are still in equilibrium in a primordial plasma during the radiation dominant era; {{formula:5983c315-2651-4dc6-bc79-603b885e1138}} is not well constrained, but at least for electron neutrinos known to be small, the recent ref. {{cite:c95950b6762095709005a00a5954721776f3f828}} for instance obtaining a value of {{formula:2828d71a-6afe-461b-b8b6-7125d7d9592c}} (see also the recent ref. {{cite:61519fbf9dab3e8ce0e2dbc438f747271a1c49f6}}, which reports a similar result and refs. {{cite:e3626bda49be9397b0516e62b5481761a44b6e28}}, {{cite:f6d56efc08385a1e8294ac859d23bcd7b2389525}}, {{cite:737f6a34dfab317b4985451e5a32a78f34c8d6f1}}, {{cite:f445975b429c75b258c708f0f899c763942df5be}} for earlier estimates). In ref. {{cite:ab171df83587580936db9b246ec39033035a797d}}, a possible theoretical model that could generate a sufficiently large lepton asymmetry consistent with the estimate in ref. {{cite:c95950b6762095709005a00a5954721776f3f828}} is also proposed. Yet the exact value of {{formula:4a174d76-aa6c-486a-80d3-4f583616d893}} is still not fully determined from present observations for all neutrino types. In this work, we assume that the chemical potentials of all neutrino flavors are equilibrated and hence {{formula:18d4e243-6cb5-4b96-bb47-ce5d2691abf3}} {{cite:f445975b429c75b258c708f0f899c763942df5be}} and employ the numerical
value of ref. {{cite:c95950b6762095709005a00a5954721776f3f828}} quoted above.
| d | 3f2b9306f2528d70c4a6f1c5786119de |
As we see, its decay width is very small and its decay to {{formula:53c191de-37b6-4a7a-bb51-79075a119bc9}} occur very slowly and with delay. Because of that this particle is the longest living exotic state discovered till now. The discovery of the first doubly charmed tetraquark state will, undoubtedly, usher in a new era in the study of hadron spectroscopy and improve our understanding of the non-perturbative nature of the strong interaction. After the experimental discovery, some spectroscopic properties and decay channels of the {{formula:bb4781e2-c82d-4eaf-aeff-5ef3435525b5}} state have been investigated within different theoretical models {{cite:a64e53b73f7872c75cd32109baa22fcdfe2f554f}}, {{cite:6656a9ca7c1a77f5c81f347a0c13ce69dfa02e32}}, {{cite:4e6ed384cd9f00e80ca424ae7fac7bc665456e00}}, {{cite:75f745c800178e1b937d91a3fde37691e5780526}}, {{cite:9e75efe100ff863a9d401c9a19d0c0a3970b7b53}}, {{cite:46ed60e924c000a99edb0355833e4cf58b745249}}. Note that the spectroscopic parameters and different decay modes of the scalar and pseudoscalar {{formula:4e11841b-7bda-4c20-aac7-7d122dc8ece8}} states as well as the {{formula:ab1b2d7a-ce29-4513-9ed1-5fd291bc9816}} and {{formula:66e262e8-fcc8-4e2a-99fc-4ab9e24a408b}} states of different quantum numbers were already investigated in Refs. {{cite:fe197cf5c8a695f5e7b015fbdec2c2bae2497d20}}, {{cite:3dfda10764060a7bc85141edc08629d2389aeb9b}}, {{cite:cb8cdecc82af3f0ddf631f2d51d7e00b15c76264}}, {{cite:6120d08f68ff4371efcdacbc454a71ecf5dd96b2}}, {{cite:84ac9437560165637bda95f31056a9c6e7d723b1}}, {{cite:14f7a132c1105b2f31e960d8da2d58772b6f5df8}}, {{cite:19903bbf720ad0a1277278e58846ec0a3a883dcf}}, which may be in agenda of future experiments.
Another important subclass of doubly charmed tetraquarks includes particles that bear two units of electric charge. Spectroscopic parameters and decay widths of such exotic states with {{formula:dcdf7e4c-92f8-48cd-9a91-4ac39ff241bd}} and {{formula:6196d678-8106-4cb8-ab60-fe9c984ba5cf}} quark contents were investigated in Ref. {{cite:9566d90ae7de0ed05e055f770a6c2d9c0e01ee69}}. These particles have not been observed experimentally yet, but their existence is important for understanding the nature of exotic states. We calculate the magnetic dipole moment of {{formula:6f386b22-fb0d-49f0-9c4f-920f94c279fb}} state newly detected by LHCb collaboration {{cite:bd9c108755f990ee0f138bb908ff1aed538f7879}}, {{cite:418b87cff4a1c69f5d74ec69d1925e4d4b5f6f37}} in order to shed light on its nature and physical properties.
| i | eb5cebc2404092ff91609e5e6f501c00 |
With the unprecedented growth of mobile data traffic stemming from a growing use of data-hungry applications, next-generation wireless networks need to adopt a paradigm shift in the way the resources are managed. Millimeter Wave (mmWave) technology is promising large and underutilized spectrum between 30 and 300 GHz, which addresses the well-known spectrum scarcity problem of the sub-6 GHz band {{cite:e6309961d92ca753b3fb60c61c7b729a76398a7b}}. However, mmWave suffers from high propagation losses that hinder its coverage range. One approach to combat such losses is to use directional communication where beamforming is used to reshape the pattern of propagation in the direction of the user.
| i | 78be878a73b853ea41ce6995a3724f00 |
The kinematics of the gas in the M1931 BCG point out to such a scenario. According to {{cite:69c6f11246358b820232ff2c852263b0638d316f}} and to our observations, the molecular gas in the {{formula:bc1e6ff6-822e-4897-a853-8cb5e68b1164}} tail is probably falling inward at {{formula:63dbb0b3-4d01-43dd-a3db-db23f0f11d01}} , with the ionised gas component closely following these motions, as can be seen from the left-hand panel of Fig. REF . The redshifted stream of gas we observe would, thus, relate to the material that is radially in-falling towards the centre of the system. These infalling clouds can provide a substantial component of the mass flux toward the SMBH accretion reservoir, while the physical conditions of the gas within these clouds could satisfy the criteria for the ignition of star formation.
| d | 3531794409e136f42eae0c60cc90e921 |
For the two–dimensional Dirac operator {{formula:b15cbe42-6995-4d63-9fe7-fe36effb2fc3}} , the most general boundary conditions have been studied by three of us in collaboration with Søren Fournais in {{cite:7f4ccc3aa643d49937abba3468721069e7c50767}}, {{cite:9fa5d9d0e958bb50a758f9e3582e85763f7ef459}}. It turns out that there is a one-parameter family of boundary conditions (equation (REF ) below) interpolating between the zigzag and infinite mass cases. We refer to {{cite:7e46b3c62dce132b1d16853310e8a9eea7150c24}}, {{cite:70c9d74fe0857cc2dd9cfc5a463389ca552b071a}}, {{cite:e30e41dd2217007f8bb33aebe40a9f4e69de526d}}, {{cite:6fb0193363054bf3564b1884891b0321f8a0c737}}, {{cite:33a88a387bca7c604e173d77adbbcf2c627cfe0b}} for the definition and results on the infinite mass operator and {{cite:1f91dc40c96916f859e9f3cf32c9f26dd09239c8}} for early results on the zigzag boundary condition. Further papers on the mathematics of boundary conditions generalize two-dimensional domains with corners {{cite:95f2438d0f098d6937db48f8c46a6773f1dd3e7c}}, {{cite:ec1efcc2d7b33e50392aa3b13a99867b0f28a580}}, {{cite:c042e3a7887f705eb7b0012d7f14ea23337a75d2}}.
For a discussion of the physical meaning and realization of boundary conditions, we refer to {{cite:94743453453f920566edf3af22d9cec0cd63f789}}, {{cite:f0ddd16e0748d090db2f5fb0e74c3aa82b6b91ed}}, {{cite:c4c9e6518798640183d8a6c5f2a3443077ac41bc}}, {{cite:7cf713b5bb9c3d2cea4b05383b7ad5c3850f7282}}, the review {{cite:7b78b4f61823109854ae6246ddd2dd13722bdcac}} and references therein.
| i | 0952555e2523cc347fdaba5e6ae00499 |
For reference, the band gaps and lattice parameters of different boron nitride polytypes are listed in Table 1.
While all the experimental band gaps are from the literature, the theoretical values are obtained for the respective unit cells.
Here, one can note the wide spread in the measured band gaps for h-BN, between 3.6 - 7.1 eV. There are several reasons for this, related both to the specific methodology and quality of different h-BN samples {{cite:ee66341b63190b3367bb37931f6c1c7d6d7df78a}}, {{cite:42add089f1058768ae9d45d9f078b622fe97cc62}}, {{cite:43da3477103803efe37520173dd1e3a65d45c0bd}}. This includes the possibility of different stacking between the layers, see for instance ref {{cite:2b11dff1fde7c1040f1bc48a692779d32e65f945}} and references within.
A recent measurement by Yamada et al. gives 5.97 eV for the band gap in h-BN, while they find a smaller value, 5.82 eV, for t-BN {{cite:0f9db5bb25196157e7850c5cd354ac6b9b2c099c}}.
In case of t-BN, c is shown for the model structures including 7 planes. The theoretical t-BN band gap varies between 3.76 - 3.96 eV, with the shown value taken as the average over the 10 t-BN models, which happens to coincide with t6-BN.
For the 1 ML BN system, the smaller and larger experimental values refer to the optical, respectively the electronic, band gap {{cite:aea0f9cdbb68c92e2dbca09e42eba372721e99bb}}.
The different 2D layered BN polytypes are compared to the cubic (zincblende) phase, c-BN.
It is well known that using the PBE GGA exchange-correlation function {{cite:eac74d608b1bd67cce2768ac2a9fedc16fe6bd80}} typically underestimates the size of the band gaps in comparison with measurement.
The calculated band gaps of h-, r- and c-BN agree well with previous ones computed within the same methodology {{cite:12ad4650d4f7bb3847cac8d31b620d6a2ce9e28f}}.
{{figure:2be55236-5559-4323-aa36-2f0536ae41cb}} | r | 62e84e8520b300bba9dec2c3ebc2b38a |
Lemma 3.9 (Theorem 4.3 of {{cite:d0063e9675000b6a365264eda3c26f145e31dc20}})
Let {{formula:49c4c6b5-e030-4f57-81fd-eda7f8c8dc11}} and {{formula:5c4ace3a-ad74-4ed2-9b58-ae4f3ef688dd}} be given. Then, we have
{{formula:8ffbf65d-2d96-469e-9604-ae15d9419e4f}}
| m | f0ef33c69119d66a90c953a5a43bd14a |
where {{formula:9db0c090-27be-41fa-bb42-f348a72272be}} is the temperature coefficient introduced in {{cite:2469f981b25719fc153822f0ac3cb692b5b689cf}} to make the softmax prediction sharp. Vanilla MSP {{cite:9296de25fb3277affd4cfc751e11a40ea3b891df}} did not include temperature scaling, which was proposed in ODIN {{cite:2469f981b25719fc153822f0ac3cb692b5b689cf}}. For the ease of our overall formulation we add it here.
| m | ec68314f6d6f2960ff5e9d9c3f3515af |
Notice that transmission probability of Eq. (REF ) is different from that reported in Ref. {{cite:003c248e3fb34d0703ffe68315011d444b62b2fc}},
which depends upon the imaginary part of the susceptibility instead on the full susceptibility function. As we will illustrate
in Sec. , this difference leads to notable differences in the numerical results.
| m | 8e5f38f6e3af32f9922771d44b46a778 |
Inverse propensity weighting (IPW) is the first unbiased learning to rank algorithm proposed under the propensity-based framework {{cite:fcfc5992e1490a8d388286f35c89b2ba92bf1e1d}}, {{cite:b40e7b43ffa93a5d0857edfa45dcae919cb30a34}}. Let {{formula:0de0ab9f-d166-4292-a314-b054241c2572}} be the binary variables that represent whether document {{formula:c3ee593d-087e-4ed1-8beb-ce6f52ebc586}} is examined and clicked by a user, based on the Examination Hypothesis {{cite:f5b474fcdeea73c0a18cde017e91d6307c3cb763}} that a user would only click a document when it is observed by the user and considered relevant to the user’s need, we have
{{formula:21d79ad1-2185-499f-bb92-94276d91bc4c}}
| m | 54f99528d1c902936eb3b7717ce0dacd |
Quantitative Results:
We first show quantitative results on the two settings, GTA5{{formula:10c88a2e-767f-4c21-a3c7-8df809e93cab}}Cityscapes and Synthia{{formula:dcac8e6d-082c-476e-a41d-40699df6cc1a}}Cityscapes, in Tables REF and REF respectively. We compare our results with existing UDA {{cite:f964332e944c1afe25df317e90c0565ed0feeb63}}, {{cite:af5259acb3c297223f6384f557c3469f2f1251cd}}, {{cite:a5396c38295a2db7340cd45203800b3badc25be8}}, {{cite:003caa539f33b67d0b973525e862432805c8b83a}}, {{cite:e087125c5f9ca64dab5fb8c7b58a8998413ea2ee}}, semi-supervised {{cite:cd3933f8ae6aa55b646286b0f9ced30f71797f44}}, weakly supervised {{cite:dfa78101423c77b18baee652858c546acffecd0d}} and frame based ADA {{cite:c9c551ed6570dd256193cbbeed635f7944a775eb}}, {{cite:28cf88fb766e6f522a235fd50959d1a75911548d}} techniques. We observe that both of our proposed approaches, aug-based and anchor-based, surpass the SOTA techniques, reducing the error margin from {{formula:e68fabc9-eca6-4b65-bbb2-935bc3086c48}} to 3 in GTA5{{formula:285b8f47-fe4e-44ca-9945-b01fb33bbf26}}Cityscapes and from {{formula:1372e4d4-4612-4f0e-bd90-78b7339a2ef2}} to {{formula:98e6c290-e68d-445c-87c1-68ff0ffd2a97}} in Synthia{{formula:d4564d15-4d45-424e-bdd5-1c34f534479b}}Cityscapes using merely {{formula:77bffcb2-5d0d-4116-b9a9-af8afef79430}} of the annotated data when compared to a fully supervised model.
{{table:d2fc61df-2d62-4c25-aff1-956a162497e0}} | r | e402a84819dc6453ecf61f4f909cc21b |
The spectral method {{cite:8a91421495d19ae8eed6c943eeab256783574182}} is applied to validate Theorem . Let {{formula:05cbf47f-273a-451b-8fa5-f7bb01d0b497}} then the full set of eigenfunctions given by (REF ) can be written as {{formula:2f667e3d-c9df-4e89-9507-2ae08f64eccf}} . For the numerical simulation a polar mesh is generated through a combination of non-uniform chebyshev discritisation {{cite:8a91421495d19ae8eed6c943eeab256783574182}}, {{cite:3dd7c032a698b40d8bfd9c7e83863db736926549}} in the direction of radial variable {{formula:1022ddc0-b0f6-496f-aad4-5a21ad1e0ba8}} and uniform Fourier discretisation on the periodic variable {{formula:c48e4e5e-94fb-4bef-ade2-fbf81e5438f7}} . The domain is considered annular region centered at {{formula:dcf74197-c73f-49f3-8e64-c841380a4dac}} with parameters {{formula:d77bbc18-c57e-4b4d-95f3-cf7f28fc2f2a}} and {{formula:6f3b3f69-b7a6-456e-8e62-3f3c9338dd7e}} . A spectral mesh in polar coordinates is constructed on the region {{formula:f97654ea-1a11-4dce-be63-4be73a4a6f84}} , where a periodic Fourier grid is used to obtain a uniform angular mesh of step size {{formula:c6b77816-e7e9-4e60-bbba-7ac36c5b18ca}} , where {{formula:89c8c4e2-3cb0-4a84-9c48-48c42d893abe}} is an even positive integer of the form {{formula:3923194c-c2c6-4cd3-9ff1-c4f2138b60e5}} . The {{formula:c023afe3-5450-4f3d-866c-623a1d684e6f}} mesh point on the angular axis is obtained through {{formula:52067279-e094-4d91-a611-16fcbe3bd6cd}} for every index {{formula:c17ae76a-e26f-4992-bb5d-3245be3ec61a}} . The non-uniform mesh on the radial variable {{formula:913fe2a8-c89b-4a5e-ad60-6e5fbc6e0693}} is obtained by using the chebyshev discretisation formula {{formula:604b9e5c-c6de-45cf-b6c2-f556921022aa}} on the interval {{formula:56c78832-c2e0-434f-a0fc-fff3e76c4a5f}} , where {{formula:9d1cdd89-bca7-4c63-a35a-90ab301effa3}} a positive integer and {{formula:382071f6-65e6-49e0-ab35-514e27d69bbf}} .
Figure REF (a) shows a coarse structure of a combination of a uniform Fourier grid applied to the angular variable {{formula:e424dcd2-792f-48ac-8e0c-c786cb727ce4}} with {{formula:285ef5e0-6ce3-4c06-96ad-10dd3fc498b9}} , which makes the angular step-size of {{formula:b31abb33-b46a-4a4e-98cd-da5b93e3d9d3}} and a non-uniform chebyshev grid applied to {{formula:ff4a7874-3366-4636-877b-e19c43405b22}} with {{formula:30955479-5b5e-41f4-bd1b-1ef7a3f6a3f7}} .
Figure REF (b) is constructed in similar way with {{formula:1f755bdd-016a-4831-9514-a8b899d5b2d5}} resulting in angular step-size {{formula:7a31a37d-e35e-413f-b93a-113fe4d8d83d}} and {{formula:f1b2764f-20d8-4dc4-a2e1-da4129cf53fd}} , which is used to depict few of the eigenmodes proposed by Theorem with their respective approximation of the eigenvalues {{formula:69d25e04-bbc6-4713-8613-21288afac5c4}} proposed by formula (REF ).
The eigenmodes {{formula:e34f5893-9371-4db4-afed-f40c7c46ce51}} given by (REF ) corresponding to {{formula:48cfa2b6-c3fb-4515-bea3-c8e5d416e58e}} are visualised using HSV (Hue, Saturation Value) colour encoded scheme, which is a method presented in {{cite:02c1e94af5484b32a55086db1fd7449f72f97d19}}, {{cite:6d2e36652424779dc7d98f533ef5ffdf9d37bb2a}}, {{cite:37a138da0f89fa49d9bf099ce8f2383e74408fa2}} specifically for depicting functions of complex output. Direct methods of plotting functions of two variables do not provide a meaningful representation of the formula (REF ).
It can be noted that only the angular part in the formula (REF ), namely {{formula:c2358702-97f9-44f1-974a-c4cedb9218e7}} contains imaginary parts, therefore, the variable {{formula:839073c5-8c34-4c82-a6e7-6b45bc2960aa}} is colour encoded through the application of HSV scheme and the resulting output is depicted directly on {{formula:ee0de129-5874-4ea7-b494-c19cde3f30ec}} . For full details on depicting complex valued functions, the interested reader is referred to {{cite:02c1e94af5484b32a55086db1fd7449f72f97d19}}, {{cite:6d2e36652424779dc7d98f533ef5ffdf9d37bb2a}}. The eigenvalues corresponding to each index {{formula:92ecc1d6-6ef9-4772-b881-cd9b6c9fd9b5}} for a fixed value of {{formula:8fa4096c-d1f8-415f-9fa5-f570937e911a}} are computed and presented in the respective captions in Figure REF . The values of {{formula:17f08d66-7c98-471f-ada5-b9ba48042899}} are also computed for combinations of positive integer {{formula:027eedeb-a62a-4cb4-b331-27d6de54a072}} with a variety of values for the associated order of Bessel's equation {{formula:3dd2a430-0b68-442f-8d0a-b4b07e3c8724}} . Table REF shows the computed values of {{formula:56bf56c3-1d71-46c2-a727-2d55a10b9632}} for different combinations of {{formula:1b34bfa9-578f-4aa0-9954-bd9590be9ba2}} and {{formula:7959c908-c314-46f3-951c-b90a447a837e}} , which offers an insight into the variations of the semi-discrete spectrum of the diffusion operator {{formula:b6597cb2-7b5d-40c6-b87f-2566811e4a53}} , with respect to {{formula:8c436733-aa0c-43e4-9b32-ef732eeacea2}} for a fixed choice of {{formula:a8ca9fab-242c-4fd7-b726-7c2fd1f5e1e1}} and how {{formula:8923f614-6745-4161-9c95-93ebe399b585}} varies with respect to {{formula:fe094ee8-c07c-4741-b663-3b511047f49d}} for a fixed choice of {{formula:9f23353e-8337-4354-a537-5163cdbf20ab}} . In order to obtain a pictorial representation of the variation of {{formula:1963575a-ea9f-4a8b-b48b-6cc3a8ffbe95}} with respect to both {{formula:988ac32e-48cc-4867-bbd9-5ebc7ba08828}} and {{formula:68d46e25-ed57-491a-bbfb-82d1c0a2c06b}} to observe how this variation is influenced by the thickness {{formula:fee806ba-8cc9-4e70-991d-3a25290a7d1b}} of the domain size {{formula:93a5362d-37ff-4911-bdd1-8e1214803f58}} , a finitely truncated spectral matrix that corresponds to negative and positive values of {{formula:0e2c1bdf-0bb0-4e25-afe5-ddb8bed876d5}} is simulated and presented in Figure REF .
Figure REF (c) in particular is simulated for the choice of {{formula:57ac2753-48be-4238-82ca-9e2629047be3}} with {{formula:59926740-484f-4de7-82d5-cd3676190c2e}} and {{formula:10a0cb69-f26e-44be-8f53-d6f76956a738}} to encapsulate the eigenvalues that are associated to eigenmodes shown in Figure REF . In particular, since the value of {{formula:d56fd68a-654c-4430-8210-e58515f8641c}} in Figure REF is kept fixed at {{formula:a3e80fb2-8ae5-4233-8570-4479e6c49c3f}} , therefore, the corresponding eigenvalues can be captured from the intersection of a vertical line at {{formula:26ececec-b002-434f-ae85-9ed5bb8b6107}} and the spectral lines for {{formula:48ffdb04-634b-4770-b1f9-5074011a319a}} in Figure REF (c). The intersection points extract the eigenvalues given on the first column of those given in Table REF , which are precisely the values presented in each of the sub-captions in Figure REF .
{{figure:3ab7edef-2f80-4449-ad2b-7199ad2434c5}}{{figure:f3f95a22-20ef-4180-9fca-6bde8bc95e66}}{{table:114f9311-1b95-4a2d-b89c-8623edb2d65e}}{{figure:050187b0-4860-42fe-9dbc-a9c6f1124508}} | m | 87cc96e4a6efde0dc90535299692c0d0 |
In addition, the paper {{cite:c01240470ef35ae2d48c8da364966fabbee447f3}} relies on the approach of {{cite:e7eb4c045d0d5fdbd58b5b1994c4510163ed15cb}} by using commutator estimates to prove conservation of energy. We rely on the approach of {{cite:629935c2cafbf48ae1503baa1737497691bdea29}} by using an equation of energy balance and analysing the defect term. One advantage of the approach of using defect terms is that it is more straightforward to analyse them. In Remark REF we will consider what happens to the Onsager exponent if the Helmholtz regularisation in equation (REF ) for the inviscid Leray-{{formula:dce71c1d-68c9-4795-a266-7ef3fb82f77f}} model is replaced by {{formula:dbfe1c7d-8cb8-4f7e-8781-4b8172196da9}} . This leads to a linear relationship between the Onsager exponent and {{formula:33d4c5f5-b9c9-4ab7-915b-36e9ee9a322c}} . Deriving such a relation by using commutator estimates is possible, but would be more tedious.
| r | b7cb76c62224f539bcbe4c8595efd22a |
The NLL BFKL computed in {{cite:79369c32b1c87c591b796314f28963c53e17284e}}, {{cite:5e630765168f4e381fb45ebeef2ef0929b7d3196}} and in {{cite:4e02cd6ad02edd50aa552e3f21c3d21d4ac90045}}, {{cite:e2efb968bde79e1063ba4995364fc78fb3cad4f6}}, {{cite:4eba6ff94ca7cbaabbe6efb2a922df8b21b21954}} (in the context of high energy processes with saturation) turned out to be very large and negative. The result even leads to a instability, like negative cross section, and thus hinted at the neccessity of the calculation of yet higher orders or a resummation. The main part of the NLL corrections stem from the running of the coupling, non-singluar terms of the DGLAP splitting function and kinematical constraint. It can be shown that these contributions exhaust most of the NLL correction {{cite:46f2e448abeee21c5bf8ff7ee42b21a4d8247ac7}}, {{cite:782c32f691a3b3ff7404aceae0ad553229008173}}.
| i | 77ffed57392b6bec054c3f9dc576faa9 |
We first implemented LTH-based pruning on single-modal systems described in {{cite:1f2e787474f6a1b72e2647fbbc5c50a2b047c319}} with the results shown in Table REF . When LTH-based pruning in {{cite:1f2e787474f6a1b72e2647fbbc5c50a2b047c319}} is firstly applied to the single-modal models, the performance degrades rapidly in both audio and video modalities.
Compared to original unpruned model, using LTH with iterative fine-tuning (LTH-IF) achieves better performance especially in the audio modality even though over 80% model parameters are pruned, which demonstrates the effectiveness of the iterative fine-tuning strategy.
{{figure:0d0ef03a-3ed4-4273-bfb2-694a52f567d1}} | r | 836365da974ace67c7e9239e9346ac3e |
Label Tree
Label tree methods usually assume that labels are organized in a tree structure.
In label trees, each node consists of a set of labels which are then distributed to the child nodes. The tree structure is determined by recursively clustering labels until terminal conditions are reached. Specifically, the aim of label clustering is to split {{formula:90f3a89c-d5f8-4115-8fc6-9f8f18b7c78e}} into disjoint subsets by taking label similarity into account. This is achieved by {{formula:ed79bd8e-e542-4d54-95c6-559b230e6f7d}} -means algorithm {{cite:ed56e70b8dd5fa908e254c3779447c29e3519177}}. Let {{formula:b999578e-a08c-4403-8022-49a2965e2656}} denotes the set of labels of the {{formula:e21e6b66-45a5-4e11-81e2-ecbf12bb7f8c}} -th cluster, the objective function of label clustering can be formulated as
{{formula:838b7b69-0bf1-4aa5-a107-82a9cda8e910}}
| m | ae043b4ba0a1be0e78de3d627e7f7ec9 |
In this subsection, we present a state-of-the-art method for comparison. To the best of our knowledge, XGNN {{cite:cfbf84746ab986cac4ad56fec46abb34cb6aa96e}} is the sole model-level explanation method for GNNs, which trains a graph generator that generates a subgraph pattern (i.e., a prototype graph) via reinforcement learning in the sense of maximizing a certain prediction of the underlying GNN model.
| m | 289464b961b23e7a672c79997db09251 |
Ilyas et al. {{cite:8f21863e530beebe732a366d12517f82ee36b181}} showed that deep networks richly represent so-called “non-robust” features, but that adversarial training can be used to avoid extracting non-robust features at a modest cost to downstream performance. Although in-distribution performance is harmed, Ilyas et al. argue that the reduction in use of non-robust features – which are highly likely to be statistical coincidences due to the high dimensionality of input data in computer vision – may be desirable from the point of view of trustworthiness of a model under input distribution shifts. In this section we consider similar questions on the effect implicit feature modification on learning of robust vs. non-robust features during self-supervised pre-training.
| d | f8f8395f65f6d438b790b57c3d3d70c4 |
Figure REF (right) points to an interesting observation. Depending on the region where the training is performed, the carbon emissions can vary drastically. This is due to the regional carbon intensity as shown in Figure REF which reflects the extent of clean and coal-powered energy in specific geographic locations. In the past couple of years major datacenters are offering options to select datacenter locations for computations. Whenever users are able to control this, the preferred choice should be to use infrastructure that uses cleaner energy. Further, even within a given geographic location the carbon intensity can vary depending on the time of the day{{cite:f9d3e2559d6a82aec2741e396276f2c5373cec7f}}, {{cite:cd4941565dfe59237d43b3eb00f5b607001590e8}}. Using carbon tracking tools can provide insight into choosing the optimal times to schedule jobs in order to reduce the carbon emissions. Job schedulers like slurm can use this information to minimize the energy consumption.
| d | e7d13c7d89f06c665375ad27d6a505fe |
Data processing was performed with the Python programming language. All statistical tests (except the power analysis) were conducted using the SciPy library {{cite:75300b19cfe571a6e27054b593320596a262b83c}} while data visualisation plots were generated using the Matplotlib library {{cite:fdf550e85159a0c92988279d3379fc8bc6a5d2b5}}. The power analysis was conducted in Microsoft Excel, using the Mann-Whitney power function {{formula:441ec014-0e9e-4568-9424-9feb8e714154}} from the Real Statistics library {{cite:6f46056d68bc456a434927c36e410d92c7ae57ce}}.
| m | 0a7ffd5734cbfef632df0000c0160232 |
Figure 6(a) shows the extracted {{formula:208396a5-7c0f-4c7e-afb4-84d5e2f5ae2f}} (T), with values indicating remarkably metallic behavior.
As the temperature is reduced from 300 K to approximately 200 K, each {{formula:1936a6c3-e74a-4b9f-b67a-f70a442d3435}} characteristic displays a positive slope, which also suggests a metallic state.
However, with further temperature reduction, all data show an increase in {{formula:77590dea-8ba8-4832-9436-f2802ad0b9e5}} according to the -lnT Kondo signature shape (see the solid lines in Fig. 6(a)).
At approximately 70 K, each {{formula:e72c5c6f-4f9d-42f2-bd64-e8c58e03fbf2}} characteristic shows a broad hump, which may be caused by a crystalline-electric-field effect or a photoinduced phase transition.
It was noted at this instance that the La-based counterpart also shows an anomaly at similar temperatures; this phenomenon is further explained below.
Some carrier-localization effects might potentially be attributable to the upturn of {{formula:d17c75d9-f904-477e-b5ab-1b5469cf7823}} below 200 K in CeZn{{formula:10845d35-e46c-4e65-aa81-9c8392b52667}} P{{formula:4c56c17d-83cb-4640-b559-1443dadda3e2}} , which is discussed in Appendix A.
Hall effect measurements indicated hole conduction in CeZn{{formula:3bdcfbad-afd6-45ee-bffa-54c66d673c5c}} P{{formula:2366f6d1-a1b3-4107-b88d-19ba619c5fb7}} .
The Kondo effect in Ce compounds is generally induced by Kondo interaction between 4{{formula:c5cfd500-cc16-4f2d-ace0-aa32a51f8545}} electrons and hole carriers{{cite:17d57586537901d572e03bfd6553d486582e52aa}}.
The study team therefore proposes that photo-illumination produces more hole carriers that interact with Ce 4{{formula:ea5cc8b0-8b73-4507-8446-15e8d9337925}} electrons, with separated electrons ultimately providing a negligible contribution to -lnT dependence.
It was determined that the -lnT dependence of the metallic state supported by a low {{formula:11c456a4-991f-488c-b925-f346aff6c44f}} -value demonstrates the occurrence of the photoinduced Kondo effect.
It should be remarked that the large photoconductivity is not intimate with the conventional theory, but the comment on this problem is given in Appendix B.
Moreover, in the case of polycrystalline samples, the photoconductivity due to grain boundary effects is important, and is discussed in detail in Appendix C.
| r | d4ff68095b7562de79d91f2732b271cf |
In the literature, many techniques for secure consensus or synchronization within a network are available. Most of them rely on the concept of resilience, ensuring robustness to attacks or faulty behaviors. In {{cite:a6a21f98d81e53e7319fe43b602728dd611329f5}}, classic tools from system theory are applied on networks modeled as discrete-time MASs in order to design observers and algebraic tests with the target to identify the presence of misbehaving agents. These identification-based techniques require a deep understanding of the processes to be controlled and thus their design is quite complex. Also, to the best of our knowledge, continuous-time MASs have not been studied by means of those tools yet. In {{cite:4ddf1a4a9c051a8ccf2c8f54876b3118a06d36ee}}, {{cite:7f174ae7bda0ace9c15568191a54fab83eac445a}} part of the information being exchanged by the neighbors to a certain agent is chosen and then fully neglected via thresholding mechanisms. These selections are executed according to a given order that imposes some priority on the information itself to achieve attack mitigation. Such an approach can however lead to strong biases, since it is possible that the designated order is not adequate. Moreover, global information on the network topology is required in the design leading to a centralized implementation (see also {{cite:edf772cdbe62846d212c9555d0b90c8d1c964ee7}}). In {{cite:5375cf79c1f17ecfe6e798b1392ff9028ed0e996}}, robust synchronization is attained through protocols based on regulators that make use of a state observer. These methods require the computation of maximal real symmetric solutions of certain algebraic Riccati equations, also involving weighting factors that depend on the spectral properties of the network graph. There have been additional works focusing on resillient architectures for microgrids {{cite:c85ff9bbb5128ee7391dcf9887f9bceaa612af1c}}, and multi-agent systems under denial-of-service attacks {{cite:bd251e6e6dec39d41f6b76b29e42c8a13833607d}}, {{cite:b94b90a08e2ca17f3197cb3fff08bb0f3841ad32}}.
| i | 8587de960b27a7754ef386b3e006aac0 |
As it is well known, in a rather good approximation, the nucleus can be considered as a system of {{formula:9c03fe5a-6437-4925-b068-16f880a2fb60}} protons and {{formula:4a3e34e2-e40b-4a43-99ab-61ed864a760a}} neutrons
moving independently inside the nuclear volume and attracted by the nuclear center through
a central strong nuclear force. This central attraction is well described by a mean field which, in our case, is assumed to be
a Woods-Saxon potential with a Coulomb correction and a spin-orbit parts {{cite:87e0a119e86677db5c673aff0c62ebb57fcf5da7}}.
For the latter potential we tested two different parametrizations: i) that of Bohr and Motelson {{cite:36962ef7e7e532bcdf5e56151de87226e96626b9}},
and ii) that of the IOWA group {{cite:0e2f2c9b6af8801bfb21b3ee6e7433bf1ed856b1}} and found that both give rather similar results. For the purposes of the present work, however, we adopted the more realistic IOWA parametrization {{cite:0e2f2c9b6af8801bfb21b3ee6e7433bf1ed856b1}}.
| m | b801886e2b6b7a5a5dc097323e5ddf16 |
Lung cancer has the highest incidence and mortality rates worldwide {{cite:e893a5441023874e413467bd2553943c2ac256a1}}. Early diagnosis and treatment of pulmonary nodules can increase the survival rate of patients. Computed tomography (CT) has been widely used and proved effective for detecting pulmonary nodules. However, manually identifying nodules in CT scans is often time-consuming and tedious, because a radiologist needs to read the CT scans slice by slice, and a chest CT may contain over 200 slices. Accurate and precise nodule segmentation can provide more in-depth assessment of the shape, size and change rate of the nodule. When nodule is identified, a follow up scan in 3 - 12 months is usually required to assess its growth rate {{cite:650d3fd93fbf308b25e45be2e8c94954fb6fbe6d}}. The growth of the lung tumor may be an indicator for malignancy, and an accurate nodule segmentation can be used for measuring the growth rate of the nodule.
| i | 3d2b8b605743ff8bbc1ce8b1c481ebe0 |
formal models implementing alternative mechanisms for generating synthetic TTIs to be compared against the empirical ones.
The underlying idea is that some models reproduce relevant structural features of the empirical TTI with higher accuracy than others. In other words, they provide a higher quality explanation of the empirical evidence and, therefore, we assume them to be more likely to resemble the actual mechanisms of regional organization {{cite:c519efa6cab64ac73a4516f476a4f2454c773c6d}}.
We adopted network science as a natural framework to address the interplay between connectivity and functionality of TTIs. Indeed, network science provides us both with tools to identify and measure structural characteristics of empirical TTIs and with a conceptual framework for formal model building {{cite:ec5a9b11eb4c118a15ade5cb4ba5dab4d0964957}}, {{cite:5a0c035e29b5b54ea476e98cc80120a78215706e}}, {{cite:bee8b2afbe8266fdcc2145c78dfd8eb22b3d4838}}.
The task of translating road maps into networks is not straightforward and can be performed in many alternative, not equivalent ways. Since we were studying inter-settlement interactions, we needed our nodes to represent the human communities connected through the regional TTI. Then, as the simplest possible option, we established a bidirectional link between any two sites that were directly connected by a terrestrial route, with no other settlement in between. To include the geographical factor in a simple way, we represented sites as geo-localized nodes and assigned weights to the links according to the geodesic distance between the nodes they connected.
We designed a minimalist set up in which each node, at each step, expressed a preference concerning the new link to be established, according to a variably well informed assessment of costs and benefits. Then they could either compete against each other or reach an agreement about which connection was going to be built next.
It is worth stressing that our goal was not to understand why in a certain region there were more or less settlements, or more or less roads. On the contrary, we were addressing the question of why and how the settlements that existed in the region built those roads instead of others. Consequently, the models took the set of settlements with their corresponding geographic locations and the amount of available resources – here quantified as the total link length {{formula:834eb2f3-2ce8-41d1-8a04-3f9da63d97a2}} – as inputs, not as parameters to be fitted.
The process ended when the total length of the connections added was equal to the total link length of the corresponding empirical network. Consequently, any synthetic graph generated by a network model replicated the following characteristics of the corresponding empirical network:
[label=(0)]
| m | 9755c814c37612bd40591c1a2da74e84 |
Understanding quantum phase transitions (QPTs) lies at the heart of quantum many-body physics {{cite:dcebcac140155e2fbbca44eaedf5e010df23f1f0}}. Traditionally, QPTs are dealt with the Landau-Ginzburg theory, which is built upon the notions of symmetry breaking, order parameter, and correlation length {{cite:dcebcac140155e2fbbca44eaedf5e010df23f1f0}}. Despite enormous success in relatively simple systems, the theory fails to capture QPTs exhibited in some complex systems. This can be either due to
the difficulty of identifying proper order parameters for
systems whose symmetry breaking patterns are unknown or because of the very absence of local order parameters, e.g., for QPTs involving topological order {{cite:797eddf8f8646a26c547d9942a7de25a11c90036}}, {{cite:13edfdf5fe5f1f265507b9be4bef7ccf919bb996}}, {{cite:f9d2e3c3bb445aa3e2b1795eab3a1b0273313a0c}}. Currently, alternative approaches to characterizations of QPTs are under continuous development.
| i | f17ae4fad4802df50ca4d32db762f083 |
In the string theory literature on the intermediate matrix model, the 't Hooft limit has been considered, where one takes {{formula:ce6fa054-f42d-472e-8f73-d038651c33ee}} and simultaneously {{formula:d742aa63-7b74-4c71-b13e-1016ce496ade}} such that the `t Hooft parameter {{formula:c44770ef-3c86-44ee-a419-63968970c1ac}} remains finite. This idea goes back to pioneering work by `t Hooft in the context of {{formula:78be41bc-3e6f-42cb-a3bd-046ebe1d9d7d}} gauge theories at lagre {{formula:010095bb-2924-4681-801d-c2c289d193cd}} . In the type {{formula:76fc9b5c-c86d-4c03-9f96-77be9d64f18c}} topological open string theory on {{formula:23cb9c3c-be2d-44d2-aa28-0f12ff7c4040}} described by the intermediat matrix model, certain large {{formula:8c9bc5d8-0461-47fc-aa56-f7c3e0511237}} dualities appear. In particular, it has been argued that the topological {{formula:d603b640-bf92-4ef4-b2a0-a0a99f3288f3}} -type open string theory on {{formula:ba99efb3-720f-4080-baf4-65e8467b3e1f}} undergoes a conifold transition to a closed type {{formula:8b9daa1a-ab63-4d31-97c2-d2c629639bf3}} topological string theory on the resolved conifold {{cite:92ec5262919b0f8878b36523ef183028a90aeead}}. The magnitude of the {{formula:028ad20d-9b9c-4e71-9330-a44d3f8c8d4c}} -field on the {{formula:b4d7822e-e8ef-41b8-965c-9e2e88623733}} blowup of the conifold is given by {{formula:82bb3790-1d36-4a06-b2e7-67af6bac592a}} , the `t Hooft parameter. The mirror dual of the conifold geometry can be seen to arise from the resolvent of the matrix model in the large {{formula:4457256b-7685-4dba-b0aa-c97f85baa7b1}} limit {{cite:e66316d4fb79f29a3e3e25db7f8eae811b624d90}} {{cite:dabde6ac1f3b31760bb7cdc125e5cbb512117a53}}, see also {{cite:ce6953edea87f21874f0cc9356cb4463532d6faa}} {{cite:feaf28cd099e509498ab9d6f6a1b1ba931f41cbb}}. These dualities and related results have important applications in enumerative geometry and intersection theory.
| i | a27084c4277f69e5714b084abaff482b |
The first DL based JSCC architecture proposed by {{cite:b8f83df083fa8d8aea5161fd0bec438137005ba2}} consists of convolutional modules for image source. Each module consists of a convolution layer followed by a parametric ReLU (PReLU) every layer except the last one or a sigmoid activation function in the last layer. It has led to comparable performance to the standard SSCC scheme (JPEG/JPEG2000 + LDPC). {{cite:cf3328abb00c6aa86ba6835d0f3adafb3eaf3098}} further improved the performance by introducing the generalized divisive normalization (GDN) as a normalization method and widening the channel of the convolution layer for each module. To prove the efficiency of our proposed ADJSCC scheme, we adopt the state-of-the-art DL based JSCC architecture used in {{cite:cf3328abb00c6aa86ba6835d0f3adafb3eaf3098}} as the basic DL based JSCC (BDJSCC) architecture as shown in Fig. REF . The layers of the BDJSCC Encoder except the normalization layer, the reshape layer and the power normalization layer are divided into five modules. Each of the first four modules consists of a convolution layer, a GDN layer {{cite:cab476e125821d8224196cf93da210ad8e4e50ef}} and a PReLU layer {{cite:9c94d118dfa9728d66b8abb6e426a9208bcec02e}}. The fifth module only consists of a convolution layer and a GDN layer. Similarly, the layers of the BDJSCC Decoder except for the normalization layer and the reshape layer are also divided into five modules. The first four modules have the same construction consisting of a transposed convolution layer, a GDN layer and a PReLU layer. The only difference between the last module and the first four modules is that the sigmoid layer replaces the PReLU layer. The notation {{formula:4d12eacc-350c-476c-b17c-efaa39bdc915}} in a convolution/transpose convolution layer denotes that it has {{formula:a930aae6-bc8d-4868-ae41-fd7357aabb2a}} filters with size {{formula:860484c7-0de1-45ef-ab21-e2b479b13c13}} and stride down/up {{formula:e3ec212d-03c2-4ed3-8252-aa691cf4e8ae}} .
| r | f4a181596e15223a2d09fa2b0bd93ad3 |
In 1939, Fierz and Pauli introduced the first massive spin-2 field theory. They presented the unique Lorentz-invariant linear theory without ghosts in a flat spacetime {{cite:a03b2ec18af77bb61d912eb9307edfdc24c42182}}.
But, there was a discontinuity (van Dam-Veltman-Zakharov i.e., vDVZ discontinuity) which the theory does not reduce to general relativity in the limit of {{formula:6b41b0ea-3a7e-4957-b81d-6b8e5f1fbe90}} {{cite:c6f78a5121abf6addb6b755c60a3359c8532a2b0}}, {{cite:2897dcb8b35f6a937a9c4ac30617141ea52aa5bd}}.
While Vainshtein solved this problem by considering the nonlinear Fierz-Pauli action instead of linear {{cite:41b2d2d5c8f1650dfb63bf6c87714369460df41a}}, Boulware and Daser claimed that the nonlinear Fierz-Pauli action has a ghost which is called the Boulware-Daser ghost {{cite:d77682147c1b0c939c36cc0d8fb85f82c897735f}}.
Also, Arkani-Hamed et al. and Creminelli et al. confirmed this issue which the
nonlinear massive gravity is an unstable theory {{cite:c3b855acace71d562d59ffda11da1bdbc69f0320}}, {{cite:61f381dd94e58470b8fa15d718b57ad1fe95bed2}}.
However, de Rham, Gabadadze, and Tolley (dRGT) demonstrated the fully nonlinear
massive gravity without the Boulware-Deser ghost in 2010 {{cite:73237b6d2e57d315a355db8d99c0de79321a7aca}}, {{cite:26415a55e5d615707901411ad708e1caa86b8155}}.
They constructed a theory with nonlinear interactions which can show the massive spin-2 field in a flat spacetime.
| i | 3336e96132f5db090a2924cf7152f757 |
In the regression setting, asymptotic analysis requires studying small ball probabilities (SBPs). Very little is known for Fréchet and Hausdorff distances in that respect. Such analyses are therefore promising, yet technically challenging prospects for future research. In a more general framework, one might be interested in deriving functional SBPs based on corresponding results for the underlying (pseudo)metric {{formula:c265551b-498b-4e71-939e-5253537328be}} . For existing results on SBPs in FDA or the setting of Gaussian processes, see {{cite:068e472d80904235940d75d37a86d0cb030f521e}}, {{cite:123973de1670d299dc40934b58bff214545e029f}} and {{cite:21a8f1b1891afbfd102ba51f32aba5e0d8fa77f7}}.
| d | 8c4f3f02f9fa087c6d7717921ca6ed9c |
The proposed architecture was evaluated on the MICCAI STACOM 2017 ACDC dataset in a stratified five-fold cross validation. Figure REF shows segmentation results and the ground truth masks for both 2D and 3D cases. Table REF summarizes the comparison results, which show that our proposed model significantly improved the segmentation performance against several state-of-the-art multi-class segmentation techniques {{cite:ceb06f26f141ed54abea49db4885bc8f09e64c07}} in terms of Dice metrics, Hausdorff distance, and clinical parameters. Our proposed L-CO-Net architecture achieved Dice score (Hausdorff distance) of {{formula:e6a7d62a-b454-495d-8da6-6c8a25316f1f}} and {{formula:3b36b8d9-9944-4384-af30-7a3bc888b073}} for the LV blood-pool, {{formula:643fd2d2-b14d-456e-9329-f278cea54de7}} and {{formula:2b09cfcc-545d-46aa-9330-604722775158}} for the LV-Myocardium and {{formula:99247a89-8356-43d9-b007-67eb560fa721}} and {{formula:5080ee6a-4b30-4023-baaf-4d3ce0dfda94}} for the RV blood-pool in end-diastole and end-systole, respectively.
| r | b3924c8aa38382dc2d174b84f619f27a |
We analyze in this paper the long-time asymptotics of various geometric flows,
in particular the stability of self-similar solutions.
From the point of view of calculus of variations, many geometric flows can be
seen as the negative gradient flows of some geometric functionals with respect
to certain underlying metric. Heuristically, the gradient descent nature of
the flows evolves general initial data toward a critical point of
the corresponding functional.
These evolutions are often modeled by nonlinear parabolic partial differential
equations. The long time asymptotics of the solution is one of the key
questions to be investigated.
For instance, in the celebrated work {{cite:33de4a07919b036c53fb42e6283d8f1cb22e77a5}} of Leon Simon, the asymptotics of a large class of such geometric evolution equations are studied by
infinite dimensional version of the Łojasiewicz inequalities combined with the Liapunov–Schmidt reduction.
It is also worth pointing out that in {{cite:fca0e40a11635b599c6b3ef6be93e9894d102a4f}} Eells and Sampson
used the long-time limit of heat flows to construct harmonic mappings between Riemannian manifolds under certain curvature assumptions.
| i | 8c32b48677b2515c6a7cb3bb1c6679a6 |
Note that, as we are imposing a homogeneous Dirichlet boundary condition, we do not need to rely on the very technical construction of a recovery sequence presented in {{cite:35c7a08a705fe1b7e0c738242ebb967caa6d6cea}} as we can simply perform a cut-off procedure as in {{cite:178a92df66b074d73b040fede0265008080d938f}}.
The idea in {{cite:178a92df66b074d73b040fede0265008080d938f}} is to approximate any finite perimeter set by truncated sets that are compactly contained within {{formula:8c5ad2c7-2c43-4aa9-ba3e-792c8ddbad2e}} . For these truncated sets, we then perform a diffuse interface approximation in the spirit of {{cite:3a43c32a027f248cca5b0dd5d0beefedc796076b}}, {{cite:c2f15bc41888cef370e5dbf538f505289fb61193}}.
Using this approach, the need of the additional boundary integral in the limit cost functional can be clearly seen:
In the course of this approximation, the boundaries of the truncated sets are getting closer and closer to the boundary of {{formula:4b609206-bf23-4dc6-a753-065c1a44e00b}} . Therefore, the whole boundary of the limit set has to be perceived by the limit energy. For more details, we refer to the proof of Theorem REF given in Section .
| r | 5fa65d65ce35e79a11b010620a6f0c75 |
Finally, the differences between the magnetic and density structure of the simulated and real solar corona, and hence the limitations of the model used for our analysis need to be addressed. The forward modelled EUV emission from the simulated corona is comparatively more diffuse and lacks a lot of fine-scale structure seen in real coronal observations, especially fine-scale coronal strands revealed by observations from the second Hi-C flight {{cite:d6416e96031b0a8315d1b16a326b439175ba8f37}}, which are not resolved in SDO/AIA observations. The simulated corona also suffers from a lack of coronal loops understood in the traditional sense as distinct structures denser than the surroundings with distinct boundaries. As the simulation does not include any flux emergence, the coronal loops in the simulation do not correspond to overdense flux tubes lifted into the corona from the lower solar atmosphere but are instead filled with evaporated plasma due to impulsive heating events. Due to enhanced heating regions having an irregular shape {{cite:8e517002ef00e03e308b4c9223118682c2b6e3b6}} the structures filled with evaporated plasma have greater spatial extent and lack well-defined boundaries. Simulation resolution might also be a limiting factor, eventhough the characteristic transverse scales seen in time-distance plots are well above the horizontal grid size of 48 km. Distinct oscillating strands are however still observable in Fig. REF . Furthermore, recent numerical studies of evolution of initially homogeneous coronal loops as a response to transverse motions suggest that our highly idealised picture of coronal loops as monolithic plasma cylinders is not very realistic in the first place {{cite:8a65cd93d73aca45e069e5c2e431801dc3f792b4}}, {{cite:208e4ffc9a57b2900bf97bfaacb88573aaa20d62}}, {{cite:6a43f026f1ef958eb52cf644e7d4980186740b4b}}.
| d | 5ec7d37883dcc531193a18eb66058939 |
Then, for {{formula:cacb5e4c-6577-466c-bd51-7b0544db02e3}} we get better accuracy since {{formula:4a86bbaa-f844-4319-9cf4-318158bea42a}} is
increased, whereas the opposite happens for {{formula:e4b26ea0-c84d-45bf-8b73-49f909575ffe}} . (iii) The
theory above refers to the estimation of {{formula:073924ec-62ca-4b7e-a0dd-420530b554f3}} from the
measurement of an observable {{formula:6d68b883-5b15-4411-856e-d362be96892c}} , but it applies also to POVM
measurements. Indeed a POVM can be extended to a projective POVM
through the Naimark dilation theorem {{cite:9b263ff5ecab67597021a54ad2d0972439c3ac37}} without changing
the measurement outcome statistics. One can then assign arbitrary
“eigenvalues” to each element of this POVM to obtain an observable
{{formula:676d8a4c-4043-4c5e-bccf-c511634a5e9b}} to which the above theory applies. (iv) As for entanglement-based
quantum metrology {{cite:f5e0aefb96185f4bbd1f0ead56deb0524aadb092}}, {{cite:809c8a5112bdc36b5d3e298ba9741dee757d80da}}, {{cite:ae3d3b2b964f8d898ef8a609bafba409eeef26ac}}, the presence
of noise complicates the situation enormously and will be analyzed
elsewhere.
| d | 951f8b47b2e8736b1e5eb66eb29c3dba |
we can minimize {{formula:0e730263-2f84-4c2a-b4d2-659cf13d80fb}} not only for {{formula:0ff900ed-965b-405c-9c9c-f79f52f62a17}} but for {{formula:e02b7e82-fabc-4453-b791-4a583bae7243}} .
The same arguments hold for the case of RQF.
Actually, we can efficiently compute the gradient of the cost with respect to {{formula:b7195266-6e60-4ded-9e22-be35ab436fea}} using the parameter-shift rule {{cite:9dcd3c0c591770240e51e8889573f294d3d22d2c}}, and therefore, we can update {{formula:3e364c60-8a92-4841-99e0-1904695c4bf2}} by the gradient descent.
Note that training the parameters {{formula:d94a8217-3661-4ef9-8cf2-897cc06aa961}} corresponds to learning the quantum kernel.
As noted in Section REF , QKM involving such kernel learning process corresponds to the data reuploading model.
Certainly, the optimization of {{formula:01987470-650d-4bc6-bf10-30ba93b2d2e2}} is a non-convex problem, and the difficulty of training QNNs may appear in this problem as well.
Nevertheless, in our view, the quantum kernel method may still work with even roughly chosen {{formula:225fb45c-f383-4c28-a5ca-293932ba4f5d}} , as such a difficult optimization problem needs not to be perfectly solved.
We will study the learning problem of the quantum kernel in a separate work.
| d | 10bda26144112aafe146e11c6b9abae1 |
The method SEPO, determining the orbit by using only one pulsar, has been proposed and demonstrated with POLAR {{cite:639029364edab1f0256950eba9bf4f0cd52b3e60}} and Insight-HXMT in this paper, respectively. As POLAR has an effective area of about 200 cm{{formula:12e08a15-ae6e-496f-bacb-7401713e0ca6}} and high background rates (about 4000 counts s{{formula:4b13a613-f5c6-47c6-a1af-c216bd9792e6}} ), the orbit was determined within 20 km (1 {{formula:f85340aa-5173-4b33-9238-bfbfd0f63376}} ) by monitoring the Crab pulsar for 1 month. However, it should be pointed out that the POLAR's response for photons varies with their incident angles, thus the obtained different profiles are mixed and become `broader', decreasing the navigation precision which is shown in appendix A. For Insight-HXMT, with the pointed observation mode, the response to the incident pulsar emission is almost the same. With the observations of the Crab pulsar for 5 days, the position is determined within 10 km. So it is feasible to use one detector for navigation by monitoring one pulsar for a long time, which would result in low request of mass, energy, and less spacecraft control. It is favorable for the navigation applications, particular for the deep space navigation during the cruise phase of flight.
| d | 9b4a7cb96cc4ae2ad3d6dec1685cdd9e |
Cluster algebras, introduced in {{cite:36160d78a27449e1121ea2dfe3bb06fcc29dc77d}}, are a class of commutative algebras which, rather than being
specified a priori, have distinguished sets of generators called clusters, which are produced recursively from an initial {{formula:eaef5582-63a4-4789-b357-c1f65fef4591}} -tuple
of generators {{formula:a90186d4-3827-4374-b02f-5bf0d778a48a}} by a process called mutation.
One of the basic features of cluster algebras is the Laurent
property: the {{formula:2817a993-96d3-4cde-9c54-96695d0bc5b8}} elements in each cluster are Laurent polynomials in the initial generators, with integer coefficients. In fact, Zelevinsky once gave the following informal definition {{cite:7322d5986d4d832219a69f49329621fd6ae83e9e}}: “A cluster algebra is a machine for generating
non-trivial Laurent polynomials.” More precisely, a coefficient-free cluster algebra
{{formula:5e8e3aa3-1082-47d0-a1ed-90ba93e20c48}} of rank {{formula:2772ec9e-2679-473a-b8e3-c7355d564e82}}
is generated by starting from a seed {{formula:b8f7b93f-f0a6-4276-99e8-626392a6e940}} consisting of an initial cluster {{formula:83d8d421-984e-4ba8-ad88-5e36fc83a922}} of {{formula:f78ed68f-4595-49bd-9777-b07434e9f33a}} variables and
a matrix {{formula:53aa3cd2-8f34-4f19-9a3c-59c023b49ecd}} that is skew-symmetrizable, in the sense that there exists a diagonal
matrix of positive integers {{formula:48fb6c4d-cc44-41b1-8ec4-df6258b8b8d6}} such that {{formula:751d627b-fbaf-416e-988f-b58e4e2bcf12}} is skew-symmetric.
Then for each integer
{{formula:e97cabe5-12a0-4d71-a3c0-3a93a60dabc4}} there is a mutation {{formula:62150a5c-297b-4ffd-9aae-81d3a3abde92}} , an involution which produces a new seed
{{formula:f2eb84ea-2ba8-4cfa-8f77-4a22c10e6b46}} , where {{formula:98c236f9-5259-4a61-a803-eb7717eadd8b}} with
{{formula:477fad30-71d3-4f72-9cee-28fa48dc776e}}
| i | 645259cda2c10c7f5e4bca876f24a6a3 |
We could also generalize our tree level higher spin correlator calculation to a wider class of theories. For instance, the ABJ quadrality of {{cite:010bd87a7ff4b9ed8f4bceb98aa57bca687e16d7}} considered not just the 3d {{formula:39b9a47d-0389-405b-b1fd-1abfcfdb5002}} {{formula:02c8bbe9-465f-4e2f-93ce-e5b7fc7ea302}} theory considered in this work, but the wider class of {{formula:aa27465d-ec45-4bec-bc65-579d45ed2843}} {{formula:daf661c0-0bf3-401d-9a72-dd950c534ff3}} ABJ theories, which also have approximately broken higher spin symmetry when {{formula:313e100c-723d-4a16-9f29-5c775f2d7dc0}} are large and {{formula:a750ec87-db80-4a74-a9fb-1b8b6147209e}} are finite (similarly for {{formula:028b76b9-0aac-4bd5-a871-8df0fef7a164}} ), and so are conjecturally related to {{formula:0a2ca6dd-cba8-4ee9-a1a7-a0cf46c28b68}} higher spin gravity on {{formula:447b53f8-df1c-4091-9e4d-8a61082d138f}} . From the string theory perspective, these theories are obtained by orientifolding the brane construction of the {{formula:d0d6bc4f-19d0-4b79-bf68-a84b589a6632}} theory, so that the {{formula:027e7184-0edb-4612-897d-fbf89f25f9cd}} theories are dual to type IIA string theory on {{formula:014856c9-720b-4b0f-8bcf-2265b324a839}} . In the string or M-theory limit, orientifolding changes the single trace spectrum, such that certain tree level correlators vanish, and the 1-loop corrections are suitably modified {{cite:2c4d275e67e6214d148be27271333d4bdbd9ed46}}. In the higher spin limit, however, the orientifold does not affect the single trace spectrum aside from reducing the supersymmetry when {{formula:7499bc46-2f5f-4289-be36-50e4a841b218}} from {{formula:9edaa44e-501f-4a5e-af0f-af43be276c14}} to {{formula:f1c0665c-d7b1-46da-946e-6b5402679be9}} , so we expect that the general structure of the {{formula:13bd94b0-4ae6-4022-b244-13b0db58ac90}} tree level correlator should be very similar to our {{formula:71f920bd-73a4-4834-a116-d8508cbd1e07}} result. The precise dependence on {{formula:730bedad-6bba-4bdb-ad26-bebf172cea5e}} could still be different, as that depends on the Lagrangian of the specific theory, as well as the the specific form of the {{formula:9b4060e1-ef86-4e42-bd74-091c93060f56}} version of the {{formula:0ed87d2c-1cf3-4f78-9e5b-084a9bf8cb11}} integrated constraints discussed in this work. It is possible one might also need to consider integrated constraints involving the squashed sphere, which can also be computed using supersymmetric localization as in {{cite:4ca698f8b6f04ebed75233d8512926ab1add7ccd}}, {{cite:4a064abbe0c6e22c4469307f464f40f3f4627ccc}}, {{cite:1d8e8c8ce37544b2b3e597a58664e3d0aaff4859}}, {{cite:61d12fc780e0221efff61f7205ac4e1dd583f55c}}.
| d | 3fecc9f9c8c667a29219d88afaf4664a |
Origin of the seed photons for the IC scattering in blazars is an open issue, which include the synchrotron photons {{cite:7b360a20c011e05408321cef0ff9c5af90697a7e}}, {{cite:a95d7d0bc22814f7216d6e05510de890082cc720}} and/or external photons (EC process), where the external photons possibly originate from accretion disk {{cite:ebac124252289152b12b0fcb06ca5f62a10c1ad5}}, broad line region {{cite:ae70413a5c4ab00c7138a39bb5ec53a95ba9a9a6}}, {{cite:e6026dbf2c3828427337a074b2d8315bef759030}}, and/or molecular torus
{{cite:6cb253783e78b0b4e83a393e94d627c86191b862}}, {{cite:b781ce68c02b4889323b83fe7ca473e05f01cf33}}, {{cite:b2189a21485c50e1be01107b4072bdd6234e5256}}. Normally, the SEDs of HSP blazars (e.g., BL Lacs) seem to be consistent with the pure SSC models {{cite:5414796ff1d10b1f9295ba4ad41089b0526114c5}}, {{cite:4e7e6cf7fc5fc40ca44586e35b706efb14438781}}, while the LSP blazars often require an EC component to explain their {{formula:3e90a9af-f9c5-46d6-9fe9-3e25ae9ff2a9}} -ray spectra {{cite:1e1efcc88a09b507cb6937b646e2c65224e1b757}}, {{cite:801f455e2282e3d458079974c0e35b35ea40a0c9}}, {{cite:ee158849d42a9e35a9e8955d95e9910a961a26a1}}, {{cite:fbf265e8cf2317ac66229d41c9a91bcc166379c2}}. No EC process in BL Lacs may be caused by the disappearance of the
BLR {{cite:79a8e32063fed5cdc51fe7364312babda0dc1fb0}}, {{cite:1afda84e2e736826804483377b8b44ee143e2a9f}}, {{cite:f93030fcd27732d6f39d8d6e3c93c66289de398d}}, {{cite:c152adaada1219b5e030684bdb34b2dfcd8d6c8e}}, {{cite:5249ea7bf43ad67e0a70593b5c7d0b4b18b4c7fb}} and/or torus{{cite:6ea092dc119d24590663d1e8fc9fa11b24badfee}}, {{cite:4d36decd40efce6a567dd9d5af51b389401172af}} in the low-power sources. Identifying the origin of external seed photons in FSRQs is also a diagnostic for the location of the {{formula:53f84ce1-d560-45d9-86af-771c5468a9ed}} -ray emitting region {{cite:36afd785e031da049cba44ebbd1ce69c8cce952c}}. For example, the external seed photons will dominantly originate from the cold disk if
the {{formula:cb2e21e5-6ba6-439a-9dc1-7ee28b0ad6fa}} -ray emitting region is less than several hundreds Schwarzschild radius ({{formula:b1ef14c3-e003-41d6-a041-42f30ef3237a}} ) from the central black hole (BH), while the soft photons will mainly come from the BLR if the {{formula:c5cf284e-42aa-41fe-9505-af3612ee64f4}} -ray emitting region is larger than several hundreds {{formula:01a60b24-baaa-4dcd-8d44-18c04bc2e132}} and less than several thousands {{formula:b5d3795b-2807-4e2f-9148-6237e307141a}} . If the {{formula:6e263171-cbd7-43d8-9acd-1d0cfcfb37fc}} -ray emitting region stay
outside the BLR and less than {{formula:15759c31-8dbb-424a-a644-f10b08c81482}} , the most abundant seed photons are IR photons coming from the molecular torus. The cosmic background photons may be important if the gamma-ray emitting region is much larger than {{formula:fba63ca7-c043-4304-bd24-af8912909705}} {{cite:42bfedb2f6f371d1307f2c663d3312808d3a9eef}}.
| i | 1c2d3144ca261bf14d396d7ee725d998 |
For a few decades now the phenomenon of spin polarization of the {{formula:530fc35f-589a-40d6-aa22-745ec327e5f5}} hyperons produced in proton-proton and heavy-ion collisions has been an intriguing topic of both experimental and theoretical investigations {{cite:9f81f126a6af89b0be1e6e163c10321568753abc}}. For example, the longitudinal polarization of the {{formula:f502514f-b518-485f-af60-69842ec6d338}} hyperons was discussed in 1980s as a possible signal of the quark-gluon plasma formation {{cite:d50a365703ed4119ec70fd96ddb9f37de0df51f9}}. However, the first heavy-ion experiments that measured the {{formula:7239becb-bf7b-4427-ae46-4347e2969297}} spin polarization in Dubna {{cite:7db0ee9ef6e8ab40cb4d75dc4cfbdd1c6be3374b}} and at CERN {{cite:9253f13b96aee1914d2b04a80424534e2683d913}} reported negative results. More recently, several theoretical predictions of the global spin polarization signal in A+A collisions were given in Refs. {{cite:51549d9d58479ce356fb6308c8de2cceef9dc7be}}, {{cite:95c1f7e7ac47275982df25996264e93960d69a57}}, {{cite:c88b12d1118e3f439240c241f21da02b917fbfee}}. These works predicted a rather substantial experimental signal, of the order of 10%, and were not confirmed by the STAR data of 2007 {{cite:5180950f1705b144a13713d329f693bdaa9046ba}}. The idea of a non-vanishing global polarization reappeared in the context of statistical physics and equilibration of spin degrees of freedom {{cite:528114512f24caa0a2f5da5dcf1a72f59df07365}}, {{cite:982233c1ac6a43c11b26956aed4a5370e9349e09}}, {{cite:3c9d1b2f135c477109d4c0b80b5db9f64aea5285}}, {{cite:0bee963b26cd29614649b00b7af0aea0663e6a5b}}, {{cite:4e19456e5632f634dd81dcde18c4854b02a8a7eb}}. The much smaller predictions of this approach {{cite:6a5f78eb98b4287aaa14231b074d7727801c7ecc}}, {{cite:e268b50aab3c6a448bb20119be2bb40dbf995b60}}, {{cite:f636fd8103f7bf657628891460832a0392411c8a}}, {{cite:471404f87709771f9de9577e8e6c5fd82ef50d26}} have been eventually confirmed by STAR {{cite:e5745a6db34e6e3bd51bb7dcc7448e2d80be446c}}, {{cite:18da4f00d8ed3546f08a301caaf75710456e7d04}} and independently by ALICE {{cite:742e401f0a01f0c8f06509182463a758599a8207}}. This has triggered a vast theoretical interest that includes several highly debated topics: the importance of the spin-orbit coupling {{cite:5252e4e291e1c98010389666cdd3e240b0584365}}, {{cite:cfbf2d7a02531ae07940ba7c259e19b35dc380b2}}, global equilibrium with a rigid rotation {{cite:900a6857eee6048f2ef62b963683bc6f1abfb4a5}}, {{cite:7858873d138d2f0dddab8e801dadb593bc4ef5ef}}, {{cite:53d10a98a927ff513db9518e37b35b83056b9f63}}, {{cite:847d0c017efed8d41ef19dfc25bdfba6cd99bbca}}, hydrodynamic {{cite:33991cb087cb856b60c2653dd3b9873633cab38d}}, {{cite:8d998f4b9537bd2aca35859b5d8000f8f792c02a}}, {{cite:cf9ef3b6a470d38863ea09d35a75697c175d5bad}}, {{cite:c8c3e8fc8c4fbc7f7db46626e71bd789c3e498a1}}, {{cite:e51a34589551637edf232490f55aa754ad46f77c}} and kinetic {{cite:07074582ab5423a80cf7c74c17a8db019da37b1f}}, {{cite:6c4eae06b65d9c0cd5fe68d63ae231b120798e5f}}, {{cite:7cd768be966aa956a2db274a2775971e99b10084}}, {{cite:67c59866e52f4ccefca229071a990c30b4aee50c}}, {{cite:c83c85876d13acc55cc3122c0c2f619371b59e21}}, {{cite:52352a742ac482f580d496a590383c4c75f9c275}}, {{cite:f5388077b89237f1b048bf48ad5ae70c8fc14b15}}, {{cite:95ed43c010c93055ef36ada1ee6750c04451c6dc}}, {{cite:9b0a9d4187171bf273c10b1bd19fc56728e3e509}}, {{cite:b60fd6076d8318c816988628d5c90d3ef025693b}} models of spin dynamics, anomalous hydrodynamics {{cite:3e0a9a5efcb1dbe28fec0e695ed291e7745714af}}, {{cite:7e69211c1fbab077639661c012f5ec2e32936e5c}}, the Lagrangian formulation of hydrodynamics {{cite:f6a01faf59a69ce08a2f533da6f47ebf270ad14c}}, {{cite:7e111542c1e0af5cc1c52703a8b971c4ef72f1a6}}, and hydrodynamic treatment of the spin tensor using holographic techniques {{cite:2e85731c289d97d532a40c202b0b18930e859cb1}}. For recent reviews of the experimental and theoretical situation see, for example, Refs. {{cite:eb896b43221ecefa34105d36ec43faf9a881e156}}, {{cite:8d22615ee5f29fac3dc52fbba21920c9292a7f33}}, {{cite:6c0f8ded183a045eadffbdc462b69eda7cf5551c}}, {{cite:a6950493509447aa4055977888a6a7edca2c264c}}, {{cite:fc5e3ed2a9160e44f4b43b05bfd1f4adfbd414d9}}.
| i | 0bbf47ccadf5112b8491ffa05b27f5d1 |
The results in Figure REF are in agreement with the ones
in {{cite:6ff1ff2ad0a46112b78d119fa9e4b9d18b6e808d}}: F1-scores are not identical but close,
and trends are generally consistent. This general agreement between our results
and the ones in {{cite:6ff1ff2ad0a46112b78d119fa9e4b9d18b6e808d}} reinforces our confidence in our
results. The slight difference between our F1-score values might be
coming from variations in the way the F1-scores are computed. F1-score
is a harmonic mean between precision and recall; in case of multiclass
targets, it can be computed in different ways. For instance, metrics
can be calculated globally by counting total true positives, false
negatives and false positives, or they can be calculated within each
class. We calculated the F1-score globally, using the so-called “micro"
method in scikit-learn 0.20 {{cite:7db5e595b035ae9789081232b483b499e1ea23f2}}. The randomness
involved in sample selection for k-fold CV, as well as other
hyperparameters of the classifiers such as "classification criteria" and "max depth" for DT, might also explain
some of the observed variations. In the future, we recommend to share all the parameters of the classifiers, for instance by sharing the scripts used for training, to improve reproducibility.
| d | 656123379af6a33a35160816081f02f8 |
where
{{formula:543af8e5-3e38-40be-924d-bbc35eb9fb83}} is the dipole operator and
{{formula:ce0654af-7b3b-4077-9e88-72cf4b9ad109}} is the incoming-field operator.
Here,
{{formula:3041ffdb-f13a-4d6e-8a22-079434b09a5b}} ,
{{formula:cbd8087c-bcde-4454-90f2-55605a89ed1f}} , and
{{formula:7c4e4f14-5bf1-405c-84fb-46ff4c9c7922}} .
Definition (REF ) is very close to our classical notion of work {{cite:7da6a9a6eb984ab67ac12f2598eeaacb36099320}}, {{cite:96a8f06f90d73c32665581190b6247d5e0163050}} (to see that, one can think of an initial coherent, or semiclassical, incoming pulse {{formula:0df1d928-9ae5-498f-b86a-91ff89d31aac}} , fulfilling {{formula:b938a5ba-774a-44c9-8614-4eb68a61da45}} , as established by Glauber {{cite:09ae64bf134740aac9faeb548494d96baa359522}}).
In the rotating-wave approximation, and using the initial global state
{{formula:258cf6e0-5288-49e2-a148-d4eba526075f}} ,
we find that (see Methods)
{{formula:ffde1feb-ab87-4935-aa50-1cd5ebe6fd2c}}
| r | 3bd4da2752b53663198f0094c03694fe |
Representation embedding. The current method uses an online learning algorithm that updates its belief dynamically during the B&B as new data becomes available. This is a significant change compared to the standard supervised learning approach where the dataset is generated offline {{cite:7df82ae7fb58c3fd6de5806fe73713ff06fc4a4d}}, {{cite:7c05ebaeb972ddfe682abc604bb2128b6f87e325}}. In the online paradigm, the feature vector needs to be updated at every iteration. Let {{formula:d2fa46d4-9e9d-4b54-99dc-cf9cf877d213}} be the feature vector associated with variable {{formula:0d4b7ddb-70de-4f09-891b-e65d7264a44c}} in the MIP at iteration {{formula:f38d9575-0952-4964-9720-522016ee0b9b}} in the B&B. To avoid performance concerns, the complexity of the function that computes {{formula:8247e982-bf21-4f44-a8cb-9814f20c8f89}} given {{formula:c63d6ee8-33d4-40dd-8e47-e8a06a6264f3}} should be {{formula:4fa11bd8-0332-49e2-a607-c438298e15ab}} . For this reason, {{formula:2841bb10-b1d5-4e9d-9d44-29fb44a793f9}} is calculated using statistics that can be easily updated such as the mean, the variance and the extrema (min and max). These statistics are evaluated on the solutions collected during B&B up until the current iteration {{formula:e378856b-c914-434e-9c98-174f3b01de13}} : {{formula:313fcd07-b603-42a5-94d5-b8835e6d0b6c}} . Formally, the feature vector {{formula:1d009291-d016-4f90-8e3c-f9af0a957d55}} is calculated using the expression
{{formula:50091232-2597-48e9-a7f5-f32fdc1cac9f}}
| m | 77594bf3b76a35fb1c82591c5aa5bbf5 |
Classical black holes with absorbing boundary conditions
cannot support minimally coupled scalar field configurations
{{cite:e70c1c4fb3a0287510202f327161cab58cc1fb7e}}, {{cite:f051d6dccbf8d176c2d64b78129ace720682d9dd}}, {{cite:e603880a924f1eab8d1a0609a03f191014cb68cc}}, {{cite:7ab861becb348587cdeb673f91332902d9d0febd}}, {{cite:f9cc67bce4c6e444aed88ba779b9bf6f9a162bd0}}. Interestingly, this
remarkable property is also shared by compact reflecting stars
with repulsive (rather than absorbing) boundary conditions.
| d | 0df0839f368af83517433a6ff5d2d3e7 |
We first train the TCN-based baseline system and proposed Conformer-FFN and TCN-Conformer systems ({{formula:c3d5c72e-8c81-4f11-8f8c-3698d22aa0c1}} stacks) using only the 2-mix dataset. We then train all considered systems using all datasets (2-mix, 3-mix, noisy-mix) together. For both training conditions, we evaluate the performance for the 2-mix, 3-mix and noisy-mix test set individually. As performance measure, we use SI-SDR (dB) {{cite:978f4fcc6bba46bbf09763338cf6899cba018b6b}}, which is considered to be more robust than SDR {{cite:b531279bc1c7be8361c68f9c024fb9fc88bde301}} for single-channel speaker extraction.
| r | 6ecae65298a1cc9c4baced660b04fa33 |
The theory developed in this paper is presented under the strong assumption that the domain {{formula:40c12959-7ca2-4c01-8714-baeec48ac11f}} be bounded with a {{formula:17987116-1601-41b6-96a0-eff92c843195}} boundary.
The boundedness of the domain is only present to simplify the proofs while the constraint on the boundary is impossible to overcome for the
large values of {{formula:690a8077-99ed-46aa-be3d-e6c1dfcd1228}} , between 5 and 100 , which one typically encounters in the engineering problems underlying the {{formula:e285435d-bfdd-4a9d-bf98-9292de77ea7b}} -CurlCurl.
This strong assumption requires some explanation since it excludes the type of domain which one would typically encounter in finite element
discretizations. Going back to counter-examples of Dahlberg {{cite:e013412846f80939519e8965034a4c6624aa1e50}} and the work of Jerison and Kenig on the Poisson
problem {{cite:3b071aa667b690303c5a93c4258073106e21e41d}}, {{cite:da15eeb19ecc8b1528995ad059567f57c2f92665}}, it is known that singularities in the smoothness of the boundary impose restrictions on the existence theory in {{formula:75439e0c-1bfe-4f39-914c-98d08189110c}} spaces.
This work has very recently been extended to general mixed boundary conditions for elliptic boundary value problems
by Mitrea, ... where they show there exists
a neighborhood of {{formula:7aa9c482-815d-4d74-a17b-6f458bb445ef}} for the values {{formula:a16372b2-ed70-4851-930f-cecd2366de50}} , where {{formula:f54f2af1-553f-4644-b8de-d14002d23bfd}} the regularity being {{formula:0da033e7-d712-427b-91ee-20329d590d2f}} and {{formula:694beb12-597b-4bb5-b1ee-0bfe73e48c72}} the summability, for which the problem is
well-posed; see Section . Mention that Mitrea uses different techniques.
As such, the constraint imposed on the smoothness on the boundary is a fundamental obstacle which will require the engineering community to
improve their model for the resistivity. Interesting work in that direction is being done by .
| i | 73faf8c05c200868e5f40bcaec99af58 |
Many M31 GCs are resolved in HST observations. Some authors,
including {{cite:9d6ae251e93eaf6fb96f65eae00d32a4f8022206}}, {{cite:01a82d46727e215f2d8ee24f6ed6d51312f04f4e}}, {{cite:cf4e02674a515d8f4b52951e727d01591a32924d}},
{{cite:6686b26a0dfea210ec1deddc488d1dc22ac7a57e}}, {{cite:d19fed3f1987fbf851c7d20dad14c18894b185bd}}, {{cite:c979c1d87a6dea7d78f85bf248e4c2783ef79b2b}},
{{cite:e367a38064f534e9d0afe6a5e1547a79b290e4a7}}, and {{cite:1baa01ced78d2460995ac3bd5feac668c0a57fa3}}, used WFPC2 images to
construct CMDs for determination of the clusters' metallicities,
reddening values, and ages. However, these CMDs are usually not deep
enough to show conspicuous MSTOs and thus be useful for robust age
determinations. In fact, only {{cite:c979c1d87a6dea7d78f85bf248e4c2783ef79b2b}} and
{{cite:e367a38064f534e9d0afe6a5e1547a79b290e4a7}} managed to estimate the ages for four blue
massive, compact star clusters and 79 candidate young star clusters
by fitting isochrones to the stellar photometry.
| r | 7d196dcfac667bd1a406b8f88c3366c2 |
Local Approximate Gaussian Processes: {{cite:74a4d2152a36ccbf6390354ef37ffc6e1cd070f4}} proposed a sequential design scheme that dynamically defines the support of a Gaussian process predictor based on a local subset of the data. The local subset comprises of {{formula:6b307f7f-e7bd-4278-978c-e60f9bfb59c3}} data points and, consequently, local approximate GP reduces the time and space complexity of GPs regression to {{formula:874697e2-e428-46f0-a723-dc09b8ff5243}} and {{formula:0b4a9b16-026b-4664-8bea-de0787704eae}} respectively. Local approximate GPs can achieve a decent accuracy level in empirical experiments but theoretical properties of this algorithm are still unknown.
| m | c64d753a4392b6e94e0431ba5ada747c |
One popular version that attracted much attention in cosmology is the braneworld model with a single large extra dimension and with `induced gravity' on the brane {{cite:176fb2a921642c336bf40e1565611d1422c8ded1}}, {{cite:961b6d762af43b6b9bde64141d767cc413f728ad}}, {{cite:241f943c103a359bf587b99f0abe65e099f17009}}. Among other features, quite incidentally, it was discovered that the stable branch of solutions of this model describes effective dark energy with supernegative equation of state {{cite:b2cb85649d63c7d3c0be206be070a1fb987d69a0}}, {{cite:a3895ab5da75fb362b88bc4337d808a51f2177b5}}. Because of this phantom-like behaviour (hence the term `phantom brane' {{cite:9b5812b7382e3b2df56c1171af65aefbf5729e0f}}), one can also expect that cosmological tests of this model would yield higher values of {{formula:3fffc6e5-ecf9-4489-99f0-ddef0e5f85f2}} . This observation lies behind the idea of alleviating the {{formula:bc96a8b1-b6a2-4f41-858b-518d0a300cc6}} tension in cosmological scenarios based on this model.
Note that the braneworld cosmological model under discussion does not suffer from the usual instabilities associated with a phenomenological phantom field; it rather smoothly passes on to a De Sitter phase in the future without running into a `big-rip' singularity.
| d | 3a213ff08c12c07f34b53286215140db |
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