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An integrated residual solver was developed in the Julia v1.6 programming language, implementing fixed and flexible mesh schemes for the solution of constrained DAEs. Dynamic variables were parameterised by Lagrange polynomials in the barycentric form {{cite:f688a29a5f6b3c240cef67e65875d056dbc0f41f}}. These were discretised across {{formula:a76508b5-fab7-4f06-8b87-439041936160}} time intervals, as illustrated in Figure REF . Residuals were integrated with Gauss-Legendre quadrature of a sufficiently high order. Derivatives were evaluated using forward and reverse automatic differentiation. The least squares method described in Section REF was applied using Ipopt {{cite:d1d133bdbd1a3102a92007d9b1f879774fe5d46c}} as the NLP solver (relative convergence tolerance set to {{formula:3f97aeab-9e65-4d59-a02f-d82231b3a2d5}} ). All tests were performed on an Intel® Core™ i7-1065G7 at 1.3 GHz with 16 GB of RAM.
| r | 560735bdeb9b189b48eec058d14ee8dc |
In certain cases this back reaction leads to a complete breakdown of the classical approximation.
The concept was originally introduced within the framework of the black hole {{formula:da934664-5c4e-4ca1-931b-766fbb21f193}} -portrait {{cite:9faa73fa66d9786e58659f14f456f14e416c20c4}}, with the first explicit simulation
of a prototype model conducted in {{cite:ddd9f36f3c2bf529e53c8b45175f6a40690ac8e0}}, where the effect was referred to as quantum breaking.
| i | 0b14228be1b4da34470f805639c70ec4 |
We have compared statistics of the properties of the narrowband
whistler-mode waves observed in waveform capture data from Parker Solar Probe during the first four
encounters inside {{formula:e19bcbab-98c5-4e8e-b128-763bd1e68a00}} 0.3 AU, to properties observed in waveform capture data from
STEREO at 1 AU. At both radial distances, the waves are narrowband and large amplitude.
The association with heat flux and beta is generally consistent with the
whistler fan instability although there are intervals where the heat
flux is significantly lower than the instability limit. In both data sets the whistlers are observed only for beta >1, and the average temperature anisotropy was {{formula:66e74a50-66dd-48da-8fc8-bdad4001f1b3}} .9. The PSP electron
data show significant scattering at strahl energies, as documented in
detail by {{cite:22eac7d05d5bcd21726629291432b48427162215}}. This is consistent with a study of
electron heat flux {{cite:9cd3b489cda0495c6cd28552df3fb11be2ae2066}} for Encounters 1 through 5, which showed that the heat
flux and beta were constrained by the fan instability threshold,
providing evidence that these waves regulate the electron heat flux.
| d | a4990d489c1aa9306b8b9c8c25c3c18d |
The encouraging results of this paper lead naturally to many new questions and further studies. The computed examples presented here were limited to double integrators, implying that {{formula:70bdfc27-654b-4034-8ad4-db84567ed309}} is a constant rectangle for all {{formula:6f43ce22-797b-4666-ad31-2da7a2ecf7dd}} . We are currently adapting the steering methods for acceleration bounds that vary with state, allowing for more general, fully actuated systems of the form {{formula:05d03fdc-c7d5-4713-83d6-b1c9beee23ed}} . Another important direction is to develop bang-bang boosted versions of asymptotically optimal planners, such as RRT* {{cite:fb32b58835a9e5e711979f886968df3d674f3216}} and SST* {{cite:a603b7afa0beb4d98c5c93ce5ba3645e7d0b37ce}}; this would enable stronger comparisons to the plan-and-optimize approach, both in computation time and solution quality. Also, improvements can be made to the iterative bang-bang optimization through strategic interval selection. Finally, efficient nearest-neighbor algorithms should be developed for the bang-bang metric over a tree of parabolic arcs (analogous to {{cite:9664882fba23a4441743accae761dbcf936fee2b}}, {{cite:40fdc3b56698bd3a8e3fe30fa6796f59d4fd656c}}).
| d | fd44ae6c6d794f533f2cbdab369d0fed |
This is one of the rare theoretical works that discusses pruning of FCNs and CNNs. We not only cover model pruning of general FCNs, but also establish the results regarding pruning CNNs. The results can be applied to a variety of other network structures given the fact that almost all networks can be represented by a stack of fully-connected layers.
Our theorems can provide precious insights to the iterative magnitude-based pruning as suggested by {{cite:cc69f90333f86a7e6f25ccd8197ec26dad78f0e0}}. For example, our results are able to determine how many weights we can prune in each iteration and the corresponding probability that the gap between the pruned and target networks is smaller than a given error.
| d | e742819e2b173111013963da8e4dc410 |
Image quality and View consistency.
We visually compare the quality and view consistency of our results with images generated by OASIS {{cite:524ba44eb9e1bab1ca9dac5377208471fc0b6520}}.
OASIS produces a geometrically invalid output, especially in the scene with complex geometry, which is difficult to infer from semantic maps as shown by the last two columns of Figure REF (a) and (b). Moreover, the content is not view-consistent.
In contrast, our method produces geometrically valid and view consistent as shown by Figure REF (c).
| r | f72bdae7dfc27de029233ee34f091628 |
The diversity of dust particles in an astrophysical context implies a richness of models that we
need to build in order to calculate realistic optical forces for space tweezers applications. Here,
we consider several models of extraterrestrial dusts with shape and composition inspired by
interstellar particles, DUSTER samples {{cite:423315a3d8d7998d2bffd8c397ab9037514fc544}}, {{cite:395638e9a1bca0633beba6667591ca72c67aff40}}, and Moon
or Mars dust analogs. We show these models in Fig. REF . On the top row, the homogeneous
and stratified single/aggregated spheres emulate hypothetical interstellar dust grains whose
constituents are olivine and aliphatic carbon {{cite:98ff8021ba410cfae0bdefa532594db228ed9407}}. The olivine refractive
index is provided by Draine & Li while the carbon one by Ashok et al.
{{cite:c42ee631ae0957641c1e4c02d05a477111b40073}}, {{cite:966c220da5f6cdef2572872ae90fcffcb92a91eb}}. In Figs. REF a and REF b, the
constituents refractive indexes are mixed in such a way as to treat the particle homogeneously with
a single effective refractive index according to the Bruggeman criterion
{{cite:9c419fb68c39e84f5aec31f84cd78a3a91a38aec}}. On the other hand, in Figs. REF c and REF d, an
olivine core is considered covered by a carbon layer {{cite:98ff8021ba410cfae0bdefa532594db228ed9407}}. The spheres
radius of Figs. REF a and REF c is {{formula:a1178d35-5471-4614-81a2-4af25f0d001f}} {{formula:fa982c7f-5390-45c9-97d2-fb542c8ad847}} m. On the other hand, the
clusters of Figs. REF b and REF d are composed by 9 spheres of different sizes
with the major semi-axis {{formula:231f93a4-1dd8-4ddb-8e98-2c16a12caf7a}} {{formula:894142d3-284a-44b5-b4bf-45ed004a3299}} m. In Fig. REF e, we present a model according to a
Field Emission Scanning Electron Microscope (FESEM) image of a silica particle clustering arranged
in quenched melt spheres, shown in Fig. REF f, and collected by DUSTER
{{cite:395638e9a1bca0633beba6667591ca72c67aff40}}. The refractive index is provided by Malitson
{{cite:bb4a0bb3d24f837d679d03ccf3435269857b795f}}. The model is composed by 4 spheres of different radius with the
major semi-axis {{formula:ac661d5b-8402-4a06-a6e0-5148d593f0f3}} {{formula:fe9aceb1-2a56-4ad9-8491-1992630f44ed}} m. Fig. REF g represents the model of condensed Ca[O]
nanograins that are accreted onto a larger melted aggregate of tiny carbonate grains, shown in the
FESEM image of Fig. REF h, and collected by DUSTER
{{cite:423315a3d8d7998d2bffd8c397ab9037514fc544}}, {{cite:395638e9a1bca0633beba6667591ca72c67aff40}}. The larger sphere is calcite and the other
spheres are CaO. The cluster model is composed by 30 spheres with the calcite refractive index
provided by Ghosh while the calcium oxide one is provided by Liu & Sieckmann
{{cite:3101fd845a3a6636b1aaa0c3e7ba25c03da2af95}}, {{cite:8a408ca67ee6aa40d371ed86a521d671690318c1}}. Moreover, its major semi-axis has {{formula:89ae622b-e08d-4f2a-8283-314874e73609}} {{formula:209b79e3-c85a-4592-aa6c-cc7ecfd6ec8a}} m. In
Fig. REF i, a spherical model ({{formula:6ade9530-5162-4255-a3ad-a4176b8018fc}} {{formula:79bc75de-1d37-4c2b-a1f1-178107e400f2}} m) of the particle Fe, Mg-rich TP2, collected
by DUSTER, is shown {{cite:858226e5744ca7f6de8d58a7b7fc59cea8d3df36}}. We consider an effective refractive index obtained
mixing iron (67 %) and magnesium (33 %), according to the Bruggeman criterion whose the two
refractive indexes are respectively provided by Johnson & Christy and Hagemann
{{cite:e9ce545caf4f42a29ff9d294d7f9056510e4caf5}}, {{cite:cd1ce330014c1e2b70c8d84d1ed7f2a185efba4f}}, {{cite:9c419fb68c39e84f5aec31f84cd78a3a91a38aec}}. In Fig. REF j, a
spherical model of Martian hematite ({{formula:df66a85d-6225-439a-a487-81724249aa69}} {{formula:b399b6bc-7fd6-4d9e-9e00-681e38bd76fe}} m) {{cite:b141d1a58ca07ddf78fad291f1870f301a2ebfd4}}. In
Fig. REF k, a spherical model of Lunar regolith ({{formula:c4e57f30-c5ba-414e-8a48-d25bd2fbda25}} {{formula:7be16f21-ba0c-4309-abbb-fa288222bd7a}} m) {{cite:bb0c3407e28240aea7c5ecdbf11b74d0da6eff04}}.
Fig. REF l shows the model of a microscale fassaite ellipsoidal, collected by DUSTER, and
shown in a FESEM image of Fig. REF m {{cite:395638e9a1bca0633beba6667591ca72c67aff40}}. We consider an
effective refractive index constructed mixing silica (65 %), and CaO (35 %) according to the
Bruggeman criterion {{cite:9c419fb68c39e84f5aec31f84cd78a3a91a38aec}}, the major semi-axis is 2 {{formula:6e46d7e0-8f2a-4b43-a2f4-2f9715503cec}} m. All non-spherical
models are oriented in such a way that their major axis is aligned with the incident light
propagation direction.
{{table:bfcedc82-b053-4574-b797-1c7594c18422}} | m | ff41b6ddf0442ade9c407438d3638921 |
In order to state a two dimensional variant of Weyl's equidistribution theorem which will be used to prove thm2, we shall need to introduce notations and definitions following {{cite:6b3a4a67b6b91b9e05d73e9d64ae8c3bad66dee4}}. Let {{formula:a2fe253a-054e-4a4b-a93c-031069e46343}} and {{formula:e76b199f-289b-4ff7-8bfc-faa3b02b7592}} be two vectors with real components. We say that {{formula:af5efbec-6e46-4d92-bbe3-3fac6ebbbd12}} if {{formula:94e9b741-9e52-4d18-8759-143eab729302}} for {{formula:aced0c07-8b24-4e39-bd73-8bfc30055fc8}} . The set of points {{formula:5274c8f8-f02c-4c68-999e-fa829fe12ae4}} such that {{formula:3032973e-a0cd-4ab8-9082-bd1111403055}} will be denoted by {{formula:beceb8e6-d321-4cea-a5ad-3ef721b79273}} . We denote by {{formula:cecc1846-95a2-44c5-960f-7b82716b5a75}} , the two dimensional unit cube where {{formula:8f876e25-f7cc-4ec8-8157-b3b8617e015b}} and {{formula:b1d8a601-af28-49ce-801d-a34aa0d58ab3}} . The integral part of {{formula:297bff1d-977c-4e9b-a91e-60a5d9b55143}} is {{formula:ad6dbefb-4a9f-4213-a5a9-3a132c8484b8}} and the fractional part of {{formula:b63455ce-4b4d-4707-aa0b-28b7e1622c0d}} is {{formula:831f97e8-d671-4a75-a9a3-aefe562274a8}} .
| r | aab61e2ab569fd1d1bead0feb7595a50 |
For the VoF method we note the following points: It is a sharp-interface
method, so it has {{formula:ab0d295e-aa07-42e6-a579-8e07fcc9cea1}} . The surface tension force for VoF is
{{formula:4c9ebe30-5170-416e-99ad-7546617e8300}} , where {{formula:7a37e34e-58a8-415c-b04e-2056933e887f}}
is the curvature, {{formula:e4dcb845-3f50-42ad-8c25-8101f18d56e6}} is the Dirac delta function on the interface, and
{{formula:c8e9c66d-2c71-48c8-be64-d5fedb562fd2}} is the normal to the interface. We use Basilisk {{cite:d396b6364e2a9b44336c332fc6c3c1382856aa2d}}, {{cite:9282d7e4691812d9d089ed861e0cc63180fb1286}}, an open-source solver for carrying out both 2D and 3D
axisymmetric VoF DNSs. Basilisk, which employs the Bell-Collela-Glaz advection
scheme {{cite:60bd6083d9a2a33cb1439a3257c528e1364b8f63}} and the implicit viscosity solver {{cite:d396b6364e2a9b44336c332fc6c3c1382856aa2d}}, {{cite:9282d7e4691812d9d089ed861e0cc63180fb1286}}, is parallelized over conventional CPUs {{cite:d396b6364e2a9b44336c332fc6c3c1382856aa2d}}, {{cite:9282d7e4691812d9d089ed861e0cc63180fb1286}}. The VoF solver does not invoke the Boussinesq approximation; and
it can handle large density and viscosity contrasts. The breakup of an
interface is sensitive to the resolution in the VoF, so we use an initial
configuration in which the antibubble is already punctured at the bottom; and
we then investigate its spatiotemporal evolution. This initial condition is
similar to that used in experiments and in Ref. {{cite:04605c29a2eeb247d6607232e45c201599390d5b}}. We
use the following boundary conditions in our VoF simulations: (a) In our 2D DNSs
we employ periodic boundary conditions in all directions; (b) in
the 3D axisymmetric case we use an axisymmetric boundary condition on the {{formula:53622a81-3e3b-4eb2-ae1d-9cf567f865d5}}
axis and the no-slip condition {{formula:3be9b603-afbb-4181-9bee-b3e943163631}} at other boundaries.
| m | f084945c785bc38db73782f240468a2f |
2. Use Pretrained features{{cite:51de6c92b7f287e792b21d626d010ccfb733c574}}, the embedding part of AR+ model is replaced by the features of pretrained ALBERT{{cite:a9c0d44feedb2ecd52ce1b044e75648e74b24127}} or ELECTRA{{cite:55dfabc4f7846bc33384c9da47144cff42451abd}}. The improvement of loss is very limited or even worse. We also test feature+embedding, feature replace encoder, features of different layers, combination of features of different layers, and pretrained models of different sizes, all the results are similar.
| m | 65115b8d552da68b472999f9cfd716c6 |
We should also pay attention to the following issues. Initially, for the structure of the system, this paper only studies the situation of a single island. The construction of multiple islands may produce additional entanglement entropy, but their contribution is high-order and can be ignored. They probably appear at Page time, thus alleviating the phase transition of entanglement entropy {{cite:6a9bf09c9af0d45831dd6552ac42c4ffd22d3394}}. Besides, we assume that the eternal black hole to be in thermal equilibrium with a heat bath in asymptotically flat spacetime. However, the island ruler was first obtained from the black hole in AdS spacetime coupled to a weak gravitational bath. Therefore, one should be careful to investigate in the asymptotically flat spacetime. At last, from the aspect of information, the Page curve is obtained by considering the construction of the island, but how the information trapped on the island is connected to the outside of the radiation, a innovative conjecture is {{formula:ef4b9678-8ef4-4e23-a682-28a272278ea9}} {{cite:bbf213b2b52d84d5b5c74e39416c45c150d5bcd5}}. However, it still lacks a strong proof mathematically. Maybe we still need a complete theory of quantum gravity to explain the microscopic mechanism of black holes, which will reveal the mystery of black hole information.
| d | 710bdd41144527920ca6b4ac8bce1c94 |
A thorough understanding of those datasets via graph analysis has resulted in insights behind them and facilitated the development of effective algorithms building on the insights.
Some of the well-known static properties are a small-world phenomenon, also known as six degrees of separation {{cite:d3abd71268de1cb3d756c9b02cf31c31c71377ba}}, and power law distributions of spectra {{cite:311a1d998275003e7f74508aad5c8174a9e9168f}} and degrees {{cite:29e29dc78400be7c2382186dd32d3bf7b34e5136}} of graphs in various domains.
Temporal properties prevalent in real graphs include triadic closure {{cite:2bf20c394d141d00fe271308132f49de346608b3}}, temporal locality {{cite:70dbfd23943b25e8c16483c9890c22484807285c}}, densification, and shrinking diameter over time {{cite:60a75b93937ec9eee1c4faf42cbbcc2be263a498}}.
These informative properties actually serve as useful tools for designing and analyzing graph algorithms {{cite:572e4be28c2b2583005693e2ab9b70661a5f0a74}}, {{cite:803bd38fe12b8424cd1b92c086a0faf000bdd67d}}, {{cite:df8412ad616934bf3d71a6601b6468635175b0a8}}, {{cite:53cc8b56a257b17744536e852ff884f8396b1984}}.
| i | fe3fbe79fe863033ce8ed6a72d7a82d2 |
When {{formula:4ee742e5-e0e7-4327-9a95-96b9f2a56e34}} is bounded measurable and {{formula:e10876a7-068e-490e-8f18-0202dab393d8}} satisfies the ellipticity condition (REF ),
it is well known that there is at least one weak solution to the above SDE (see {{cite:ebb47fde67954a291d5e70b014787933f8a2b34b}} or {{cite:409bfee99e4bc49c44e903bb378b0cf81a5be65f}}). Moreover, for {{formula:236fafb8-ca4c-4f22-8953-ab862ecba67f}} , the weak uniqueness also holds (see {{cite:409bfee99e4bc49c44e903bb378b0cf81a5be65f}}).
However, for {{formula:ff4824e8-463e-4f00-aaea-31f764107654}} , to get the weak uniqueness, one usually needs to assume {{formula:41cc6959-f0c7-4038-9891-3da98b5c7fa2}} being continuous (see {{cite:409bfee99e4bc49c44e903bb378b0cf81a5be65f}}). For the strong uniqueness, the well-known best condition for {{formula:e1cba846-bcf3-4560-8668-443ebe854ebe}} seems to be {{formula:c1fac456-1bd0-4ba5-b715-5b6174335b11}} , the second order Sobolev space, where {{formula:b078e94d-e23e-4921-93f3-c0b012cac92c}} (see {{cite:6486d07a10b2e4010c7b5b89dace535c5395c872}}).
It is interesting that for second order SDEs with discontinuous diffusion coefficients, we have the well-posedness of generalized martingale problems.
| r | 544a043210e73890648c1a9ccc619b47 |
Note that this relation requires {{formula:b4bdc3b0-ebf0-4814-8a44-ff9cb0597937}} .
From the work {{cite:4a31a9e42aeb59304fbce84f70eb25191d98e481}}, it is known
that under these conditions,
the maximum of {{formula:68c84cdf-7da6-4550-9825-e725bd69fbd7}} in (REF ) can be obtained as
{{formula:0208df90-5bce-4668-8f26-57b413d256f6}}
| r | 2d84cc0c68e2320bd9432bcbc1e1b4cb |
In the simulation process of this paper, we assume that the probability of all node to node propagation, that is, the probability of interaction on 1-simplex {{formula:5bc73880-0a07-442f-84b9-199e613234ec}} , is {{formula:f65a4c10-3a7c-4d50-bcdc-ebe9887acf49}} . Similarly, the probability of interaction on 2-simplex {{formula:dd516edd-ab9d-4500-bd8d-33345458d684}} is {{formula:b479fc95-fe9c-4669-b141-5032c2815759}} . Normally, we specify {{formula:a8e17bd4-7c2c-4ee3-88a0-d8c70efe7c08}} to express that the probability of three-body propagation is higher than that of two-body propagation. For convenience, we can associate them with the simple complex's two-body two-body and three-body average degrees {{formula:056b7910-6b5c-4620-8a45-a733bfa1e841}} and {{formula:68ff2e25-474c-4dc3-bc75-b2a9e94d8520}} . We specify that {{formula:9ca59722-f14e-4027-aa36-5ae55a45932f}} . At the same time {{formula:6014776e-e266-4aee-9234-13a4f4c383bd}} , where {{formula:b67d7d3c-f5e0-406b-b36a-b1f0741cbbc0}} and {{formula:d3b911ad-c3f7-479c-b743-bd96a55deff0}} are two pre-defined parameters, {{formula:421ff242-14e1-4d6a-8ec3-9aacd8e8c9be}} . The detailed definition of simplex and the dynamic propagation mechanism on it {{cite:3a92305df77273ff918b947ed4a79c673056bba5}}, {{cite:eae36eb0713ac1b6ada721a2e74bc1e2d1ddadfc}} can be viewed in the literature on propagation dynamics.
| m | f0cb30e75a811438d6a9a9cc244684d6 |
In the case of an even signed cycle, using Theorem REF , it is compatible only when it is balanced. Hence to check its metric dimension is 1, in view of Corollary REF , it is first of all necessary that there must exist a vertex of net degree 0 and thereafter the remaining assumptions in the theorem.
Now we deal with the metric dimension of signed stars. In the case of all-positive and all-negative signed stars, the dimension, with the help of the established result {{cite:c8ed60098b1843922093ab3413263a7973d520cb}} and Theorem REF , is {{formula:9b3fa34d-6a11-449d-8094-03da8e3363f7}} .
| r | 74baf24e0ba177dbb2bd8fd51fee63a3 |
To render the pixel color for a camera ray, we first find the ray's point of intersection with the SDF
by starting from the ray's intersection with the object bounding box and marching along the ray via sphere tracing as in {{cite:536750b7f5ffcd7f08dae3b59bcd8d3922815761}}, where the size of each step is the signed distance at the current location. The intersection point's location {{formula:a490f12c-02ec-4811-8208-4736dcf4a357}} and surface normal
{{formula:38e9b8ad-f4fb-4d36-a5cc-e0a9365ba6b8}}
are then used by our appearance component to render the pixel's color. Hence, to optimize the geometry, gradients must
back-propagate through both {{formula:38af084c-30cd-48d2-917c-4501b377a785}} and {{formula:76690c38-3ba1-438e-823a-0041833f843a}} to the SDF parameters {{formula:27a7b85e-103e-4bad-a49a-514557f13aa3}} .
Back-propagating through the surface normal {{formula:7889ae12-0aa4-4b73-bbc5-edd2f6c7d1cc}} is straightforward
via auto-differentiation {{cite:ad227369fc1806d7200e24507a2b2700dc9a1361}}. To back-propagate through the surface location {{formula:0f58f93b-27df-4445-8a97-238f9eb35425}} , we use the implicit differentiation method presented in {{cite:f1c0eef6ce2a8a965519117a35e981be0f79212b}}, {{cite:536750b7f5ffcd7f08dae3b59bcd8d3922815761}}.
Note however that the sphere tracing algorithm itself need not be differentiable, hence it is very memory-efficient.
| m | c5c6c745513739997ed7fd1824ac504d |
Near-field intensity patterns and Husimi functions -
The remarkable changes of the far-field intensity patterns as {{formula:0463beb6-6b9a-4161-9bbf-496a1aac7590}} increases are caused by the modification of the outer layer boundary, not by the significant changes of the near-field intensity patterns around the perimeter of the inner layer. Figure REF (c) and (d) show Husimi functions at the inner and the outer layer boundary, respectively, of cWGMs forming along the inner layer boundary. The Husimi function is a phase space representation of intracavity wave intensity and is defined at the dielectric interfaces by the overlap of the boundary wave function of a resonant mode with a Gaussian wave packet on the cavity boundary in a phase space {{cite:5193a8b164cf48ab911eca2c74f9429144b685d4}}, {{cite:4bc21ea5509558b41a9ea0b0e904b7b11ada567a}}, {{cite:4f39b698ab4e834fc4904d5d83e1ef511b9d76af}}.
In a conventional single TC, the cWGM has varying tunneling emission according to cavity boundary position since the ratio of the refractive indices at the dielectric interfaces of the cavity boundaries is given as a function of boundary position. Tunneling emission mainly occurs at the position where the ratio is minimum, and light is emitted along the tangent direction at this position. In the DLTC, however, the cWGM exhibits a nearly isotropic tunneling emission at the inner layer boundary since the ratio of the refractive indices at the dielectric interface between the inner and outer layers is constant, {{formula:5b513707-eccd-4f91-8335-f625b4c90a58}} , independent of boundary position as shown in Fig. REF (c). In Fig. REF (a), the modes are better confined in the left part of the outer layer because of the large contrast between the refractive indices of the outer layer and air. A localized high intensity of the Husimi function of the resonant mode above the critical line for total internal reflection around {{formula:d87f92fd-cf70-45b3-a93a-da15bc8bdb3f}} of Fig. REF (d) confirms well-confined light. In contrast, the modes are emitted through the right part of the outer layer boundary because the ratio of the refractive index between the outer layer and air at that region is small. The second highest intensity of the Husimi function around {{formula:8bbfb418-6a83-4a5f-9276-3ed743aee272}} mainly locates below the critical line for total internal reflection, and this produces the refractive emission in the right part of the outer layer boundary shown in the inset of Fig. REF (d). This mechanism achieves unidirectional emission in the DLTC.
{{figure:53034700-ee4b-471f-9f72-7208f88df36c}} | r | a4caebd1c8129c04570803e8e0ad7100 |
Data Description. In our experiments, we use four undirected real-world networks to evaluate the effectiveness of redefined centrality measures using hypergraph Laplacians (see Table REF for the networks' statistics). (1) Enron: each vertex represents the email address of a staff member at Enron. A simplex or hyperedge represents all the recipients, including the sender, of an email sent between the Enron staff. (2) High school: this dataset is made from a network of high school students in Marseilles, France. A vertex is a student, and a simplex is a set of students in close contact with each other. (3) Primary school: this dataset is made from a network of primary school students and teachers. A vertex is a student or a teacher, and a simplex is a set of students and/or teachers in close contact with each other. (4) NDC-classes: a vertex is a pharmaceutical class label used to classify a certain property of a drug. The network of drugs is taken from the National Drug Code Directory. A simplex is a set of several or many class labels assigned to a drug. These datasets can be found in {{cite:299bb0abc05416c07d0ace38a0f52aec9c764da4}}.
{{table:dcaff687-c181-421b-91a9-c8ac2ab9b8e6}} | r | 751e7d54a72b436739550cb6e20d197a |
adaptive thresholding (Otsu's method {{cite:542cd67e032538b39a89be7f0d6325cb482adfcc}}), after the GTV segmentation;
seeded region growing {{cite:5a609a553a9d2efdce121d01140f9ed07420ec96}}, after interactive seed-point selection;
interactive LSFs {{cite:4e909235a8179050af4c59a5857a524bddfee892}}, after seed-point selection for defining the initial region to segment;
Tumor-Cut based on a CA model {{cite:746059855214448820e93cef1e303528ec338691}}, after background and foreground seed initialization using Otsu's method {{cite:542cd67e032538b39a89be7f0d6325cb482adfcc}} according to the previous GTV segmentation.
| r | 019537cdb93d603c5fc0be58eefddfa0 |
Our approach is centered around the self-attention agent proposed by
{{cite:6a0285b4e0a8a02839263521d23c7d419b037444}}, described in more detail in this section. Their work,
in a similar fashion to {{cite:2a26b602e8af1ebef7eb2951fbe3c915390a20c4}}, is limited to 2D simulation
environments. To obtain results that are relevant to our use case of
real world navigation, we adapted the method for 3D navigation, trained
and tested the agent in a 3D environment, and subsequently evaluated its
performance on real-world images.
| m | bdcdc14eae86fc8bc0665779d685509e |
The bottom of Table REF shows methods with unsupervised photometric loss.
Results of purely unsupervised methods (without using depth consistency loss) are calculated by aligning the scale of the predicted depth map to the scale of ground truth.
First, for methods without leveraging depth consistency, such as SS-S2D (d) {{cite:ed1f1ef42abed1083ca652637eb2d1a0ad6e3ec1}} and ScaffFusion-U {{cite:308aa91c5c30824c362fb83f79188d65be8ccede}}, we can see that purely unsupervised methods demonstrate unsatisfactory performance. Second, we also observe that their performances are still inferior to supervised methods even leveraging both depth consistency loss and additional photometric loss. As also discussed in Sec. REF , this is because these methods {{cite:308aa91c5c30824c362fb83f79188d65be8ccede}}, {{cite:19e2e74238e2dcf0353a2bcd16c4b447b2e76571}}, {{cite:fb30994a4dc44109badbf38758ce34a61c0e0ceb}}, {{cite:a8fdb79da0880d2c4a9dd646dfc3f44d64486142}}, {{cite:0c6db8703e35f12ccf544c094af04881d3ad43c1}} use sparser depth maps as ground truths with a density of {{formula:6e9cde42-f19e-4cc9-b2b3-8f7035175784}} than supervised methods with a density of {{formula:5bc3a9e7-a313-434a-92cf-483d7a788ade}} .
| r | 41a0d4adf601e643b3813429a97a5b37 |
We record the best results reported in their works in which each sample has complete hierarchical multi-granularity labels.
In tab:fgvc, Chang {{cite:e3ce7de8f305855ea709ccd75ef0e6aa2677691e}} achieve state-of-the-art performances in the traditional single-label FGVC problem. Our approach reaches comparable results by simply replacing ResNet-50 with ResNeXt101-32{{formula:571fd9ae-a9cc-4b7f-8c4f-7a19830e96d7}} 4d {{cite:56077b18d46c1c27ce9562efc70a62072b6c10d1}}. Other techniques that enrich the feature representation in the context of FGVC can be applied to boost the performance, which is beyond our scope.
{{table:a6724a19-1650-402c-ba3d-038ecf306b4d}} | m | 7c8d60cdbc9df3b7ecb3752f85a8da79 |
To quantitatively evaluate the performance of our proposed approach, we conducted several experiments and performed the ablation study to analyse the contribution of each of the data augmentation strategies and the number of corresponding augmented data samples.
The network implementation and training in our experiments was done using Keras.
The hyperparameters we used in the experiments were adopted from LeNet implementation for image classification {{cite:ef38d1a0a51f674eada5996fcc7870d39d75f51c}}.
| r | ef7c514f437ab6794582ea386f6f74b8 |
Low-light image enhancement algorithms can be generally divided into two categories. The first type like {{cite:5586daba1401dcc4e9a6614282e65240871a8f7e}}, {{cite:c4af23a1170e30fa27dc3ebb610aed721621a937}}, aims to offline train a deep neural network with numerous pairs of data. The calculation of such methods is too huge to be integrated into UAV real-time trackers. The other is based on retinex theory {{cite:f69c639626155bba67354b01c23cf7aa1c509ba5}}, without deploying large-scale offline training, {{cite:84d02e0feec9423ed010d1326894210eaa709827}}, {{cite:618a2247cd380114e59eee8c3256966b52eaea95}}, which explores illumination and reflectance separated from the whole image to operate them adaptively. In particular, the proposed global adaptation output in {{cite:618a2247cd380114e59eee8c3256966b52eaea95}} is proved to be efficient and effective in low-light enhancement by experiments, which is suitable for integration into UAV tracking algorithm. In addition, the global adaptation output can be further deployed to generate a target-aware mask in this work to elevate robustness.
| m | 39daa727e57d2daefc897fd87344c86c |
The randomized Kaczmard method{{cite:c8c2c63a5e02cc87cb2e4a7595c3eeae31cbec77}}, {{cite:18d48c32f7e4e293750cf1614024cf97e47cd950}} can be described as
{{formula:403eccfe-ba67-4b33-a729-16463ad2ce57}}
| m | f3edacadbef504b15f6f8d94bcf705c3 |
Following {{cite:8b0ede97a6f478340c9b914dfb21ca746aa24154}}, asymptotic estimates for {{formula:10c7667c-d7f6-458f-8c73-e6ca25e36963}} were obtained for various sets {{formula:5f847aa6-dcc3-4191-9e6e-7b2127d112a4}} . For example, already Hardy and Ramanujan {{cite:1ba07da5c1845871b6b92c543773aca7570bb581}} obtained bounds analogous to (REF ) when {{formula:b8a6eea3-4fbe-4d19-81ed-6d0bc8c754e7}} is the set of primes, when {{formula:e166aa5a-90a6-4053-a7a1-3298f62a5f96}} is the set of odd integers, and when {{formula:412cd37b-e951-45b6-8963-82e50f0124ea}} is the set of {{formula:defd1d9b-a254-4133-ac73-c2e1667189cf}} powers of positive integers. Szekeres {{cite:ae8a5a09e55daaca2cba700fc661615bcf018d28}}, {{cite:3f724f8cfd33ce27182ab5a4c692b6a2b6f172b0}} obtained tight asymptotic bounds for partitions
avoiding large numbers, that is, whenWe use {{formula:c2783109-e9c1-4117-b368-c9133b872731}} to denote the integers {{formula:23c36694-b67e-46f6-8a33-4cb6d70d1de4}} . We also use {{formula:322ca1cb-e1f7-42d0-aff2-60b5a5276370}} to denote the integers {{formula:1cbc6946-fd73-434d-91ec-44220d5384c0}} . {{formula:99c5ba4b-c090-463f-a9d6-d56fe1c172f0}} for various functions {{formula:f33a108b-c0ce-4905-9c27-b925588a3d8d}} , see also {{cite:2e5d4507040d4aa98eb1b9798d08fcbd16d13b1e}}, {{cite:11c2fc875d3ea963b9322421a36039e756a43bc2}}. In the other direction,
Diximier and Nicolas {{cite:c350d3f2e4b21ff43f14714d65ebd34346fbc3c4}} studied partitions avoiding small integers, namely, when {{formula:dbad4fab-8865-44f7-8a9e-631857a22d81}} for various functions {{formula:fa06e013-fa2f-4e88-990d-43c22af1b503}} , see also {{cite:a4db4536c551e3aa852dcd584acfa8ba7060d7f5}}, {{cite:aff23871e169571272044b748abce1ac7fb94f9d}}. Finally, Nathanson {{cite:2d32afdbb0dd05032bb859a346a906a6bd08d9dd}} and Erdős and Lehner {{cite:a45e888214afb77fcd27dd41bf7547751ac453c2}} studied the case of {{formula:61f84941-4cea-4084-bd72-402d1979c179}} of fixed size.
| i | dcc20985c2a0a6297369000bfe49d134 |
We perform direct numerical simulations of the three-dimensional, incompressible Navier-Stokes equations, either with a single phase (the turbulence precursor simulation) or with two-phases (air bubble and turbulent water) with surface tension, using the free software Basilisk http://basilisk.fr/ {{cite:8b7db596267ba6344d229812fdf37b2bd6e55ab8}}, {{cite:0d3810771a3703c49cd9a1871d51a8175762bf91}}. We use a spatial adaptive octree grid allowing to save computational time while resolving the different length scales of the problem and a momentum conserving scheme and the interface is reconstructed by a sharp geometric Volume of Fluid (VOF) method {{cite:8b7db596267ba6344d229812fdf37b2bd6e55ab8}}, {{cite:0d3810771a3703c49cd9a1871d51a8175762bf91}}. The solver has been extensively described in recent publications {{cite:548ad893cc468f56a5656a8aea5c081be046c55e}}, {{cite:0d3810771a3703c49cd9a1871d51a8175762bf91}}, {{cite:5a73238346c8daa1073809dc4757532b0f5baf6e}}, {{cite:33bccd95013063bf0becb6a8c71793ce613851ae}}, {{cite:17086f70df9ff7da1a7f2953f0cfb707f7a3c0c1}}, and its accuracy has been largely validated on complex multiphase flow, including bubble dynamics {{cite:70652dba8fe3fb28c9c2bd3790fa4f2bde93bceb}}, bubble bursting {{cite:417360141446d9c4b7aa9e688acf0421e4d544c6}}, {{cite:322224b461fa68337309eb2e4cf0f1629074303d}}, {{cite:da8c901912b52a669e14700dc62a52ff7955be11}}, and wave breaking {{cite:7598128d54786d5e2bff508f35f8d1ac745f0934}}, {{cite:17086f70df9ff7da1a7f2953f0cfb707f7a3c0c1}}, {{cite:5fb3849c54834d03827aa1be2dc24d9a12aa90d0}}. We do not consider the effect of gravity in this work. The turbulent two-phase simulations of bubble deformation in turbulence is presented below.
| m | 713b70e92e5ffdc3414dcae3d143ed2b |
GDN/iGDN vs Conv. To evaluate the visual quality of the analysis and synthesis blocks. We integrate them into our network. In this model, both blocks are removed from George's {{cite:992c81906ebc094e75db68579c101d5961817600}} architecture. We followed a straightforward propagation in the network. As shown in Fig REF . the only Conv layer does not perform well. Then, we added a convolution and GDN layer in all forward propagation operations. As presented in Fig REF , the architecture with analysis and synthesis block contains significantly better than George's {{cite:992c81906ebc094e75db68579c101d5961817600}} in terms of visual similarity and rate-distortion.
| d | 7e9479cc77541ad866705816aae982b2 |
In “double backbone” setting, our proposed STRAD excels the state-of-the-art methods by 5.1% on Sketchy, 3.3% on TU-Berlin, and 2.8% on QuickDraw in terms of P@200. In “single backbone” setting, we find that the “Simple SB” outperforms most methods in “double backbone” setting, which reveals that it might be the best solution for SBIR task to use a single model to pull close the image and sketch space. Starting from “Simple SB”, the performance gain of our STRAD is smaller than that in “double backbone” setting, because a single backbone has already filtered out most differences between features of images and sketches. However, there still remains extra appearance information in image features, so our STRAD also outperforms SAKE {{cite:3039d3965bbcbe19711fdf724ae2fd4678cb93cc}} and achieves the best results on all datasets.
| m | 4f157dc0ebefcec34936fe0a31e0cb74 |
ImageNet pretrained versus from scratch. Recently, it has been shown that ImageNet pretraining does not improve accuracy on the COCO dataset, and even better accuracies can be obtained with training from scratch at the expense of longer training iterations {{cite:137cfce1c00fb6fd3eee2667756099b9de9c0be4}}.
Another interesting question is if ImageNet pretraining improves the robustness across different image corruptions. During pretraining, the networks learn from an additional million of images, which hypothetically can improve the robustness of learned features. Results of this comparison are shown in Table REF .
Surprisingly, the models trained from scratch achieve higher accuracy on clean data and show significantly better robustness across different image corruptions except for JPEG corruption.
ImageNet pretrained models achieve significantly higher accuracies than their trained from scratch counterparts in JPEG corruption (22.65 vs. 19.89 for group normalization and 19.33 vs. 14.83 for synchronized batch normalization models).
On the other hand, among all other corruption types, models trained from scratch achieve higher robustness.
The same also holds on the Cityscapes evaluation, where we observe that models trained from scratch achieve higher accuracy results as given in Table REF both on validation and training images.
| r | eeb639ad1d29a0b228b7bfc66364a5e9 |
Existing theoretical analysis of the uncertainty focused on the calibration performance and tried to clarify when a model over- and underestimates the uncertainty {{cite:28ad643c5966a5d2fd6517b706c658bcc656f253}}, {{cite:88486117cd9db7797bce858b944d86c2a94bb649}}, {{cite:5e149d7c2b42315c674686577d5589aa783d62fd}}, {{cite:7e40fd23b59cfc2816f099dc614cf63b0ad72408}}. Other than calibration, the analysis of the Gaussian processes has been gaining attention since its posterior predictive distribution can be expressed analytically {{cite:730ce693818c6b0b3fa84eb6a32eba44ab10c83e}}, {{cite:a7863c61d59439f1b3146fffe770bd1a0bfc193b}}. Some research focused on the distance or geometry between test and training data points to derive the EU {{cite:3477cc04816c55f5c9b30cc62748afe09967df15}}, {{cite:c9711405fd57a0f66acd25e538e964ecb597ac00}}. Other approaches connect the randomness of the posterior distribution to the prediction by the delta method {{cite:132717bf9b5cbf0f3d087159566feaeef682ad8b}}.
Differently, the information-theoretic approach in {{cite:5a6c380dcbb121cb866f901dd0c2f9919d16964d}} focused on the loss function of the problem and defined the excess risk as the EU. The loss function-based analysis has been proposed in the deterministic learning algorithm {{cite:3d6b1e38f9de9722783c851da4e1516d89f1a785}}.
Thus, our theories can be regarded as extension of the information-theoretic approach in {{cite:5a6c380dcbb121cb866f901dd0c2f9919d16964d}} to the frequentist settings and derived the convergence properties of the variance and entropy of the posterior predictive distributions for the first time.
| d | 23e4e794d5c3c2541984eadd61e5afa6 |
In Fig. REF , we plot the average per user SINR at the CPU as a function of the time index for different UE velocities with {{formula:daa6dd9f-663f-446f-850c-f5a7e99d63a5}} , i.e., the channel ages at the same rate at all APs. We see that the theoretical and simulated curves match perfectly for CF-mMIMO. In the figure, theoretical and simulated curves are represented by the lines (no markers) and the markers (no lines), respectively. Also, we also compare the relative effects of channel aging on CF-mMIMO against those on cellular mMIMO and small cells. In the case of cellular mMIMO, we consider a single BS at the cell center equipped with {{formula:cf6358d2-c3ab-46f3-9645-3cf940de3da6}} antennas. For the case of small cells, we consider {{formula:1f2d490c-48a0-4552-9326-1036d9111436}} single-antenna APs deployed over the area of interest (the same as in the CF case), with each UE associated with its nearest AP, under the transmit power assumptions considered in {{cite:0fc5a281c6a926fae12954b6a91556df8687f89d}}. The theoretical expressions for the SINR achieved in these two systems can be derived in a similar manner as the expressions presented in this paper. We omit the details due to lack of space. CF-mMIMO achieves much higher SINR than both cellular mMIMO and small cells. Moreover, we observe that the impact of higher mobility on CF is more severe than that on cellular mMIMO or small cells.
{{figure:f706c36e-e669-40f0-bd2f-b167eb20feaa}} | r | 6a039b086bf6eb72394c5c7658dc51f7 |
In this case, each component {{formula:9e93fa98-7242-490f-a4b9-15a4c32d7412}} implicitly includes information about the dependency mapping. The copula model uses this representation to isolate the dependency structure of {{formula:3043f69a-9c9c-42ef-a180-2a6e0ebb6edb}} trough a function of marginal distributions {{cite:b3965efab574ba2928b515f35be722524642ca1b}}. According to the {{cite:3c1493cf8b7e7343f602d02c1b56e13fc5b6f435}} theorem, a multivariate distribution {{formula:1f1e3c57-7913-4a2a-9377-65df7d1a0e9e}} depends on the marginals {{formula:46cdbb73-f49b-468b-ad19-f09a09e3466f}} based on the copula function {{formula:72fea6af-ae10-48f2-9954-6964e21cb9a8}} given by:
{{formula:1243d1e6-d94b-4a67-807a-be607fb525d2}}
| m | 695a621f6585ddd52dcd580faa519bfe |
There are many treatments in the literature, and the idea goes back to Lagrange, and possibly to J. H. Lambert although his claim rests on his story that Acta Helvetica lost part of his manuscript; a beautiful algebraic exposition can be found in {{cite:e0fcfec36432d3c0904f42b9fe65693330a0ece1}} , although Henrici there calls it the Lagrange-Bürman formula, whilst most authors just call it the Lagrange Inversion Formula.
| m | 616cbda0991346bd793f785052bba185 |
Further relaxation is much slower. During the next 40 min the resistances of both structures relax by a small value ({{formula:1af3a7ae-d467-41b5-8a0c-78e643a6cf0a}} 20{{formula:72589dbd-521b-4d1c-8c9c-57cd4c31c141}} ). Moreover the most notable changes are occurred by sudden jumps simultaneously in both remote structures (see the inset of Fig. REF (b)). Taking into account that the structures are separated by macroscopic 2DEG reservoir of the length of 250 {{formula:2b857d24-5ed9-4d3d-9434-38e552d02f07}} m and the width of 50 {{formula:5b1cb061-c383-4c0b-82da-bf1eecd33e4a}} m it can be concluded that these jumps are caused by relaxation process in the macroscopic 2DEG reservoir. This observation once again confirms the conclusion that the narrow conductive channel is a tool for the study of the non-equilibrium phenomena taking place in a macroscopic 2DEG.{{cite:e09e95d4b3658adfef8d1ad125d6649d935b27f7}} The observed stepwise relaxation is phenologically similar to Barkhausen jumps observed in the ferromagnetic materials and originating from spin domain structure transformations.{{cite:8d2823889c7573e57dc47ec9fa8d2c0ab5ba035d}}
| r | 13ea49c7c31630d512250dd211f52f0d |
2020 {{cite:a9b705aca02a607e022180f840778318047a3020}} YOLOv4 [c] Improving precision and
| m | 8d517d6a46ad7d3f4b84454fbedb0797 |
Note Added: While finishing our main computations, the work of Roberts and Stanford {{cite:029102a38f8034034b90fc140478d4bcdbdcbd89}} appeared. The latter has a detailed account of two point functions in the presence of localised excitations over thermal states and briefly mentions the behaviour of the mutual information in the same set-up. Thus, it has some overlap with our results.
In our paper, we literally evaluate the mutual information between the thermofield double in both 2d large {{formula:f939ad5e-647b-44cf-afbf-d0b14fcc141e}} CFTs and their gravity duals independently and show their results perfectly agree. Our gravity solutions explicitly have the regularization parameter {{formula:7318dbea-1a44-4566-b43e-4112bf0a4e17}} and our matching between gravity and CFT results holds while keeping this parameter small but non-zero. We would also like to mention that in the interesting recent paper {{cite:7f6bedf95b48cc4cb329fecafade3c164c5c82c1}} by Maldacena, Shenker and Stanford, the fast scrambling behavior of the correlations functions has been interpreted in terms of chaos.
| r | 42f8d0b63555ea863151693a614dee67 |
This manuscript showed numerically that the k-space pseudo-spectral method proposed in {{cite:ed8a30c8b146e14296b3386ebf8d8d38271e8735}}, {{cite:db1fcd2dd6cddf9b5e89431939114fc09f172c76}} for solving the three-coupled first order wave equations is almost exact for homogeneous media. A Matlab toolbox for a numerical implementation of this approach is available and was used in this study {{cite:0f3e9d7b9fbaef5a9799db8e3941d2c459b911f6}}, {{cite:94e056b7c6a923e3201697857523751cf6ce2947}}, {{cite:e8af43bf302519277d3d5e305554da8a29f28166}}, but the approach taken for including source in the system of differential equations was revisited and modified. For measuring accuracy of this wave solver, an analytic solution to the second-order wave equation using the Green's function was used as the benchmark. After applying the corrections discussed in section REF for including the source in the equation of continuity (conservation of mass) in the system of three-coupled linearised wave equations, a good match between the wave solver and analytic solution to the wave equation was obtained.
| d | 1ea525d6a71af7f520eb37daf2b62844 |
Another striking consequence can be formulated in connection to the famous theorem of Brooks {{cite:1b1e6cdf9e5c5e30ab7ae78f8a640c30e5380540}} which asserts that every connected graph {{formula:ed949b8b-15cb-4ba6-b0f6-83dbbccef305}} of maximum degree {{formula:f1b68131-aaff-4fdb-87eb-fbcbd93fe176}} is {{formula:03229c09-9cc9-4884-9223-096308554261}} -colorable, except for the two cases, when {{formula:892e56e0-3ab4-4d51-bc30-078b39be4bc3}} is a clique or an odd cycle (see {{cite:d252051f80f1f969d217ca64489d0e3e62af3890}} for a short proof of some more general versions). By Theorem REF we get that the number of colorings in this case is at least
{{formula:4b7f3ff7-5c91-496d-bb60-9895c1cce9bb}}
| d | 4d5c349d269b75f58a0e9d112f1443bb |
0pt
Implementation details
{{table:576c1ebb-20d0-4e65-8eee-b42275cb4744}}Our framework's network architecture follows the baseline CycleGAN {{cite:a43331b77b265e919b1b2ca257fa77f8ffa44ce8}} with some differences in the generator to support self supervision.
We use “ResnetBlock” to denote residual blocks {{cite:a3408fff4adb5ba494768333d899aa257e9a3410}}.
“C{{formula:82e6169c-f09a-4c90-b7f6-0f5e5372ac06}} H{{formula:97f6bafd-82c4-406f-87d1-efb057eefdc5}} W-S-P Conv” represents a convolutional layer with C channels having kernel size H{{formula:c7c872c6-4878-4842-b951-6f81c3a39df9}} W with padding P and stride S.
“NConv” denotes a convolutional layer followed by an instance norm.
“TConv” denotes transpose convolution layer proposed by {{cite:717f2539b7d27465eccd07d20fc2d8504f6a1cb5}} followed by instance norm.
Discriminator Network Architecture.
We use {{formula:10d8aa38-80df-479f-b29e-bf55df8f1a15}} PatchGANs {{cite:a289506cc8b347767a37dd36f044ddc6c530a222}}, {{cite:c858a8339316608b70eed81402080dd8d47dbf33}}, {{cite:11075cba3f63c9c3e77c353191d89aba66c214fb}} as the one used in the original CycleGAN {{cite:a43331b77b265e919b1b2ca257fa77f8ffa44ce8}} baseline model shown in Table REF . The discriminator's output is a real or fake label for overlapping {{formula:8a82e506-da64-4fb3-9583-60c2e977c683}} patches. The GAN loss function then compares the target's label real or fake to the average of patches predictions of the input image.
{{table:05d2572d-caa9-401f-a426-d45fe0a638d3}}
Encoder Network Architecture.
The encoder network's architecture is inspired from {{cite:0299a3dcc3f88ab973a470399e11cbbcd8fd35ef}}, as shown in Table REF . The network starts with a reflection padding of size 3 and zero padded 7x7 convolutions to avoid severe artifacts around the borders of the generated images, followed by 3x3 convolutional blocks with padding 1 and stride 2 to downsample the input image and finally by 3 Residual Blocks.
{{table:c2088f2e-00ae-4235-aebe-97e2a4f1add8}}
Translation and Colorization Head Architectures
The translation head's network's architecture follows the standard CycleGAN generator {{cite:a43331b77b265e919b1b2ca257fa77f8ffa44ce8}} as shown in Table REF .
It consists of 3 residual blocks followed by upsampling convolutions. For colorization to share the encoder with other tasks, we repeat gray scale images along the channel dimension.
{{table:0a48ea9d-5109-4570-9871-db89f4f42178}}
Rotation Network Architecture.
The rotation head's architecture is inspired from {{cite:2606438b9c6a20c4a81c896bcd892aa301c518f7}} and shown in Table REF .
The network performs a simple classification task out of 4 possible rotations ({{formula:e5fed014-8bc1-4454-b638-a0b061d301ba}} , {{formula:3dc0d4c4-1042-47f7-aa85-180aed4a3a73}} , {{formula:9e6ddacc-36d4-44b2-bd23-f21d05b8d7c8}} and {{formula:0c865e51-ea7a-4b7f-8c53-be67ca833f1e}} ).
{{table:2e608a47-f010-4b81-94f1-946412fa0737}}
Jigsaw Network Architecture.
Jigsaw's network predicts the correct indices order of shuffled patches of an input image.
The network consists of a set of convolutions extracting useful features from input image and then a fully connected layer to map it to the possible permutations.
The model's architecture shown in Table REF performs a classification task over 64 possible permutations of shuffled images order.
{{table:8d52294a-a46f-470a-ac84-36c8678ff8ac}}
Depth Prediction Network Architecture.
Depth network architecture is inspired from {{cite:e85c3c1475a11ba76fb4c2d465fb7984c9163dea}} and shown in Table REF .
The network is trained on labels predicted using a pre-trained MegaDepth Model {{cite:94b93d2950a2f50831b0517a62a5c617cef361d5}}.
{{table:3dc8fcf9-0670-4848-bb05-762af62544a7}} | d | 9b5a76f9965705fd11b0e90ffb63b160 |
For the unseen, in-the-wild datasets, the performance of LEGAN is mostly superior to the other models, as shown in Tables REF and REF respectively. Due to the non-uniform nature of the data, especially the facial pose, most of the metrics deteriorate from Table REF . However, the boost in quality score overall suggests the high quality images from AFLW {{cite:b1da28e0da346852df597124e4f0b2fbdbc17795}} and especially CelebA {{cite:81f48675fc978ee9c54c4c48936e69b589aa4e14}} to be visually more appealing than images from MultiPIE {{cite:c39ecaf96c119499d7f2a8cc20074f14e5874395}}. Some sample results have been shared in Figure REF .
| r | 17244850db9f990bf50ed543699dbb5d |
Developments in the field of deep learning have led to a reexamination of the problem of jet tagging, as new architectures have emerged which can operate on constituent-level data.
Alternative proposals include casting the particle data into a 2D pixel image in order to apply to a CNNs{{cite:a73397e14319d10f1f9586344feccaa25346ba5f}}, {{cite:e4b0d8f7119a678f293a87404cd0a7a5ccd44e15}}, passing the particle's features one at a time as a sequence into an RNN{{cite:49faa10f273382b6c7137cdb0343a7580fbd80fb}}, {{cite:865ae74147eee1fecc6e8fdb260b8daad9328f4e}}, {{cite:1c38ca964a46dca0d6e8dd95cf9102e35e18883e}}, or embedding groups of nearby constituents into a graph for use in a Graph Neural Networks{{cite:edefece421fa1bcf44f6176e0a85655db409642f}}.
While RNNs in particular have seen successful application in experiments, more recently the field has been moving to permutation-invariant set based networks{{cite:1f8ca2ed350c2d17b59b589884bbbb6841007d28}}, {{cite:d9dc5a7997f163968adec811ee5a33516494498f}} which are easier to train and achieve comparable performance.
| i | 574d7af0d30039a7e5cddfa686d5c0c6 |
for sufficiently small {{formula:2519bfed-fb97-4028-8780-54349fd339c6}} . Then each alternating update is itself split into two updates and solved using an ADMM algorithm {{cite:933bda06be97b69b447af9eed8bf4ec1c1ee635a}} as described in further detail in {{cite:f2c5990b7f2a422249660b32dc66e90b17e20756}}. Note that we also use an Iterative Shrinkage Thresholding Algorithm (ISTA) in the ADMM algorithm when we update {{formula:e2ee083b-b254-4dc8-b8eb-c40d61ff035f}} . We also use the same adaptive scheme for {{formula:b12ca655-6ba7-4962-ab7f-b3eeddbd6e55}} given in {{cite:f2c5990b7f2a422249660b32dc66e90b17e20756}}.
| m | de8affb96cac364639a04a022136a221 |
One point of active debate has been the role that quantum mechanics plays in coherent Ising machines and in D-Wave's quantum annealers. In the context of coherent Ising machines, there exist models of their operation that treat CIMs quantum mechanically{{cite:46a69c0f33b5d59c271f42c8440647dd273f2940}}, {{cite:38157cf08445a373fa22a3c073badf9572730789}}, including, for example, a description of the initial state as being in a coherent superposition of all logical states{{cite:38157cf08445a373fa22a3c073badf9572730789}}. However, experimental realizations of CIMs thus far{{cite:095df0a4ac8dc776190757cb050ecce1a6cd0d92}}, {{cite:ac4af59f65d08d5c35b46c1e884ff76925a9305f}}, {{cite:222cb70553652990729c5a27416cab2d122f0643}}, {{cite:3cd407dab851b119cb9af4ad8e5c683c332f7c9e}}, {{cite:a257e7b0ed3a87b2b0a53192885c9c9a912942f6}} have been in regimes of high photon loss, where purely classical models can accurately describe the pertinent dynamics of the systems. The clearest indication of this is that similar performance to demonstrated coherent Ising machines may be achieved by simulating the mean-field dynamics {{cite:0119ac4a01ee88fb5ebde6dc0892bc35e88879f5}}, {{cite:f59e9b435008400cf4ccd94bb2c1ddb537b7dab3}}, {{cite:d1ab3f54dcc28ff0ff40aba42ecb154291fff99a}}, {{cite:22cb575a115b07c88da1715ba727e0ff53c247b5}}. With sufficiently high nonlinearity to loss in their constituent OPOs, CIMs can be firmly in the quantum regime{{cite:b40982bb83a811a157ed7ed38a159ed4a0657e20}} and have a strong connection with quantum annealers{{cite:f543ecd85bdaabe156936437cbe6ed01629bf692}}. Exploring how to construct experimental CIMs where quantum effects play a crucial role, and designing them so that quantum effects improve the performance of the machine, are two topics of active investigation {{cite:c4b88c5393e5d30fd97c9843d523fa508d57e8b6}}.
| d | d0f7655c6ae21676be7e398850bfa69f |
Given a planar phylogenetic network on {{formula:e88ec940-8d80-45cd-9ebd-49e049dee589}} ,
let {{formula:2bb27a23-5441-49c3-84e6-065aa0c6da73}} be the digraph obtained from {{formula:f55f5989-fc4a-4945-b1b8-3e88e14264f1}} by adding
an additional arc {{formula:46d0bbbe-3086-48dc-9ba7-91663d4c12f6}} for each element {{formula:7a984ccb-0f3d-46bb-a9e9-d63cf04e6859}} in {{formula:b6909f0e-9329-43c4-b5ae-d265c9ba4297}} if {{formula:c02d05b8-fea1-446b-a0cf-4f0d0e6ef035}} is not already an arc in {{formula:85e4526c-dcb0-44fe-a5c1-b18a6f3e18e2}} .
If {{formula:dce12951-7d81-4d31-861d-a7b67ec5ef9d}} is tip planar, then it is straight-forward to see that
{{formula:d4643ae7-841a-4e0b-9065-63031adedd3e}} is planar, but does the converse hold?
Given a normal network {{formula:e5a350af-cbf9-4306-9956-5a034d19c4a9}} , we define {{formula:f989b2fc-f1f9-4083-9a62-0a806d6afbea}}
to be the network which is obtained from {{formula:8d44b1e5-ed2a-44dc-9b4f-fb936a67563e}} by collapsing
any arc {{formula:3731e437-c64f-458c-b39a-b4411c19cc45}} in {{formula:72e20ae9-02c9-4cb0-bf79-dc6e1ecdf0e8}} , where {{formula:13eb15f0-55fd-465b-82d4-cd394dc8d3d3}} has outdegree 1 and {{formula:b5c05778-cc2a-4bcf-b08f-f36e7a9c9550}} has indegree 1.
Note that that {{formula:11b09980-c53c-4456-99c2-3c90e322474f}} must be regular (see e.g. {{cite:62613848eb39938118ff60031a76bec6bce633e5}}).
Is {{formula:be32adc8-3d9a-470e-9f5c-15eb047eda48}} is tip planar if and only {{formula:947c8112-0259-41c3-90ba-d516f0ca7c4e}} is tip planar?
Is there a prepyramid cluster system {{formula:f509bfb3-963c-4f1e-8796-773aa4834fe9}} such
that {{formula:60ff857f-b991-4d12-9f63-b2a3c93eaee0}} is not upward planar?
Although there are some general algorithms for drawing
planar, upper planar, tip planar and outer planar networks (Theorem REF ), are there more
specific algorithms for drawing special types of planar phylogenetic networks
such as tree-child networks?
| d | 94d3ee23686c8c4f6c71e922b36776a4 |
The topics gained popularity recently by using neural networks to learn depth information from pictorial cues. Eigen et.al was the first to use multi-scale neural network to achieve coarse-to-fine prediction {{cite:91150e37f6eeee713f08c2d13adf1991c8e1836d}}. Since then, various learning-based approaches were developed based on monocular color images {{cite:2768aeb65d61f1f97a68a71444f5125e574a0c14}}, {{cite:660f205f6643f38e4ed78c6f9cded112412dfda4}}, {{cite:3aa51b639b95e1c51b9b1019b821737cab501346}}. Yang et al. {{cite:75b5f1abd9332c508f11180ee507627f95167d29}} introduced surface normal representation for geometric constrain. Built upon this, they then further introduced edge consistency in parallel with surface normal consistency for fine detailed structures recovery {{cite:fb179da5908f1a3a8fca62e7af29b0d576af1892}}. Recent work in this field focus on improving the prediction accuracy and reducing pixel relative error through various methods, such as depth discretization (DORN) {{cite:ec73fc9b19bc69dbc3b1934b1bb7b299573f2567}}, 3D geometric constraints (VNL) {{cite:b2cf89d4a5818687a7c2fe31819c92ab2be187d7}}, and local planar guidance (BTS) {{cite:2aa1cdfcab31e6297dc0265b59902a0a249dbdc7}}. These methods share some ideas with our work. However, the motivation of these works is usually to compensate the constraints on camera size, cost and image quality. And therefore, they are not suitable for predicting accurate pixel level values on semi-dense depth measurement, specifically on the pixels that are missing from raw depth measurement.
| m | 71d10415481ad68c787a699f9deb1bab |
Finally, we point out that a number of recent studies have proposed improving out-of-distribution generalization via incorporating physics constraints into NNs {{cite:2361c1546f43bbc06df8aadcb066e2122a38f4b0}}, {{cite:8ca5286df6c3011a9ae1c5e635b074ebf78b605a}}. While promising for specific applications, such an approach requires the existence of a physical constraint that is universal (e.g., a scaling law), otherwise, it would deteriorate the performance of the NN. However, the availability of such constraints are very limited. In contrast, TL provides a flexible framework that beyond improving out-of-distribution generalization, is also broadly useful to blend disparate datasets for training, an important application on its own.
| d | a3688f8e416e4059e9555024f19a33e7 |
At first, we report the application of the Zernike fitting on cluster {{formula:b77ba243-154c-4b7e-a557-6e6bd2ab0f36}} -maps. We summarize the results in {{cite:3a1cc2a4ea6b195b44b1fb8aa80189f74d6c3fa1}} for mock {{formula:1a2e55dc-0e45-4772-83cb-960733c8c64f}} -maps and then the preliminary analysis on real maps for clusters in the PSZ2 catalogue. At last, we briefly discuss the ongoing analysis on X-ray maps.
| r | d113bf48ac8895498550d62b4b9d7584 |
Numerical results on rates and direct {{formula:07e41986-adfa-4d3d-b32a-07fa51cf8370}} asymmetries will be presented in this section.
In our numerical study, masses of mesons and baryons are taken from {{cite:43029a6f36030d022ae602a11f1abf80690c810b}}.
In addition, quark masses and decay constants are also taken from {{cite:43029a6f36030d022ae602a11f1abf80690c810b}}, namely, we use
{{formula:8d68608d-da0e-4529-a4fb-001defb5ad5b}} MeV, {{formula:7d7f014b-e360-433e-943e-ca24e2828693}} MeV and {{formula:78291d5c-f755-4e7e-b10d-257a6298762a}} MeV.
For the {{formula:64aa6192-fb5d-4b02-adba-1134d81fcc39}} decay constant, we follow {{cite:25b1adc88864b503e07e0778273de5bbba4543f1}} and use {{formula:04fbb590-7816-43ef-929d-710b94e6d032}} MeV.
Cabibbo–Kobayashi–Maskawa (CKM) matrix elements are from the latest fit in {{cite:87af093da65d588cce7fc26fcf49080a1c70587e}}.
| r | 70756c352bee11c8f57ccad69b8b1def |
In a final remark let us add that
the main starting-point technicality of the GSP approach, viz. the
choice of the positive-definite
solution {{formula:8692f7c2-a5d9-427e-93c4-3bd7653f15e5}}
of the constraint (REF )
is, in general,
ambiguous {{cite:ed13b6250cca1ef3bfa909e73859fd9164f8ed03}}.
In this sense,
any choice can be considered and used
as a starting point of the GSP-based metric-multiplication
strategy as summarized in Table REF .
Naturally, every such an initial selection of the
physics-determining
operator {{formula:bee67176-e958-424b-85fb-1e2460a007ac}}
must
satisfy all of the obligatory mathematical properties
as listed
and discussed, say, in review {{cite:043d328e9bcb32ea0933f1c5594739b3875c22c9}}.
In {{cite:9f2e9142fbc2026c875c4dba990efc1a7454aa9c}}, {{cite:b89cf74fbb4db17ae9e834097bf37032ea50984b}} we emphasized that
among them a key role is played by the mathematical requirements
imposed upon the separate factors {{formula:112bee0d-0c9c-4656-8f9e-668b15136bad}} of the metric.
In the present paper the emphasis has been shifted to the
physical aspects of these factors. We revealed that
the phenomenological
information carried by these factors
is given by Theorem REF ,
i.e., by their re-interpretation as factors in the
candidates for observables
{{formula:bef04bb9-2516-46f5-aa2e-c69120305d58}}
| d | 1e5fb2775e14172a1f46107a7552653a |
For simplicity, we will assume a flavour-invariant quark condensate. The model is insensitive to the scale dependence of this quantity, and we will choose {{formula:61cef49c-7d05-4f13-8fa5-538c927e5293}} , which is consistent with the phenomenological determinations at 1 GeV. The size of the fifth dimension can be shown to be inversely proportional to the vector meson mass scale as {{cite:fb86a82ed29295a2ee9a8b37d231105cf587adf3}}
z0=0,1m ,
where {{formula:d80ec73f-c347-4762-930f-a9f79a6b4772}} is the first root of the Bessel function {{formula:090ef600-130f-4f39-8331-b8df7f7387c6}} . We will fix {{formula:cfd9bfa1-576b-43c6-8706-88b54c6aa288}} MeV{{formula:7633e259-3eb2-46d2-a4a5-f76af1ba0a6c}} , which guarantees that the first vector multiplet lies at {{formula:fcd61342-7e26-48ab-8a4e-cd80b8097fbe}} MeV.
| d | cb71a7c04f9df5a2dff5d88284daf333 |
With the values for {{formula:de52e7e4-2391-4058-80b9-48dd59d22142}} obtained in this analysis, an interesting feature can be similarly tested as observed for the proton results {{formula:c9ef71ad-3276-4dc2-9bf2-24c96192e2b2}} by the BaBar experiment. {{formula:a072ba81-072b-41e1-a559-08c847bed080}} shows an oscillating behavior around {{formula:877d3064-efa6-463a-8052-375816e96174}} {{cite:59cff66ac277b0193dfab99c64eec9b4f60726fb}}, {{cite:42fdc660d9496c06badcda88a43f022b05e62787}},
{{formula:630fcba9-b8f0-4bd8-b202-b195f798bd64}}
| r | 96138364fe50d4e459df7e5d054ef5e8 |
We propose to utilize multi-task learning by incorporating mathematical equations through a new loss function embedded as a neural network for better representation while learning.
We train a convolutional neural network to predict the extrinsic and intrinsic camera parameters. To achieve this, we use dependent regressors that share a common network architecture as the feature extractor. We use a Inception-v3 {{cite:a1545fa43833d753b813d7a404f97da948315c96}} pretrained on ImageNet {{cite:6d8f8ad2d529251885e8fa60308f280787e97711}}
as a feature extractor followed by the Lambda layers for loss computation with 13 regressors, 10 of which correspond to the camera parameters while 3 correspond to the 3D point cloud. Instead of training these regressors to predict the focal length, principal point, baseline, pitch, and translation, we use proxy variables that are not visible in the image and are dependent on each other. This allows us to directly relate our method with the mathematical foundations of multi-view geometry {{cite:119ac211c3eda4527a49c5d36de9a6af0aa6e2fa}} resulting in better performance.
| m | 5ab8f777191941dfe38a223f84df78ad |
Most previous CSST approaches require a reference utterance conveying the desired speaking style to obtained style descriptors, either in utterance level {{cite:ebd6c771b3bbbe578cc52feacf9008278e9c40ff}}, {{cite:d5600465f056737572be171e80f8c6553afe73d5}}, {{cite:f607046e72609550eb74a67c0277a3ae1e98c3f8}} or in more fine-grained levels {{cite:1eee48a93b0ad5732ed43efdebe8fcba781314bb}}, {{cite:f823daf32ca09898f5b10b279b6a8447513e01e5}}, {{cite:4e8b21aff534d9534244accb9b3929ad2e56995e}}, during the run-time inference phase. This hinders their practical use since a reference utterance is not universally applicable for different textual input and should be carefully selected for the desired speaking style.
Hence, reference-free CSST approach for expressive TTS is more applicable in real-world scenarios.
| i | 3bf341c85893ebfc214c5bd0ab63d4b4 |
The 144 MHz radio morphology of NGC 5322 appears that of the classical FR I type (see {{cite:82000764d519ac38fbb401113b2ee984d521bc68}}) as the jets are edge-darkened. The 1.4 GHz radio luminosity using the NVSS flux is estimated as {{formula:601b2e73-3eff-4c69-ae88-f6c43bba1392}} W Hz{{formula:60aa8d2e-d37a-436a-abf0-9b162756107a}} that makes NGC 5322 as a low luminosity radio galaxy. The radio luminosity of the large-scale faint radio jets outside the optical extent, detected only at 144 MHz, is estimated to be {{formula:b78656d7-5594-42fb-8823-c3aeb3ea6b3f}} W Hz{{formula:5c978cda-e100-4a51-9e91-812982ecaef2}} , and that of all radio emission at 144 MHz, associated with NGC 5322 is estimated to be {{formula:328e9b36-71ee-4384-97c6-d26385312b60}} W Hz{{formula:43561ba9-bf4d-424c-8a82-5b91b192e7d3}} . The projected end-to-end extent of the radio jets is {{formula:a92690c1-79c3-42f2-89fb-8b97daf7f751}} kpc. For its radio luminosity, this source size is exceptionally large as can be seen from Fig. REF , where luminosities and sizes are plotted for FR I and FR II galaxies up to {{formula:05246b04-3149-47fa-a87c-e9dd913b70bd}} , detected in LoTSS DR1, using data provided in {{cite:a2dc57ab60a2d7f316f65acff6099c731143f8ed}} and {{cite:f08807cd4ed6166f3ced21038449300592b0b9fc}}. It can be seen from Fig. REF that for sources with their sizes similar to that of NGC 5322, typical radio luminosity of galaxies is more than one order of magnitude higher than that of NGC 5322. Same inference could also be drawn from an earlier luminosity-size plot made by {{cite:c8335ee9d687d19528d7244e45f165bff51c47da}} at 1.4 GHz. Therefore, NGC 5322 is a rare radio galaxy, detected for the first time to the best of our knowledge having oversized radio jets with at least one order of magnitude lower radio luminosity than the normal. The 100-kpc scale radio jets in NGC 5322 are detected for the first time, thanks to the unprecedented sensitivity of the LoTSS survey at low radio frequencies where jets become bright.
{{figure:30056e21-bf95-451d-bdfd-9958d358b405}} | d | 009babb477a4234c40aa7c92a21a4bbf |
The classical stochastic control theory appears with the birth of stochastic analysis and developed rapidly in recent decades due to its wide range of applications (see Yong–Zhou {{cite:859b14b3457c89a7cd9f18f3aefa2b331c828150}}), and one of its important applications is the optimal consumption-investment problem under stochastic differential utility (SDU, for short), which was put forward by Duffie–Epstein {{cite:0638607e01ac056a8c311d23b5a3e966c7ec8862}} in a conditional expectation form. Actually, the SDU is equivalent to the nonlinear backward stochastic differential equations (BSDEs, for short) and its control problem is the stochastic recursive control problem introduced firstly by Peng {{cite:0144fec9cfc42c2707b680275e3b785a538c52b2}} and developed by Buckdahn–Li {{cite:36a7e0b6cd0a9b55ba043705440a8587f88e8b80}}, Wu–Yu {{cite:9ad0297f36d8cb837147841ea1050dfea2b8f606}}, Li–Peng {{cite:000fa3d9f22018ce59b8031f9d98b4c7ceb73c73}}, Pu–Zhang {{cite:aedbea6deba8d6fae1ff518ef1b4887496422b03}}, Zhou–Dong–Pu {{cite:66e38c27e58f13493749de4394e5fb88610dbdb3}}, to name but a few.
Thanks to the importance of BSDEs in modern mathematical finance (see El Karoui–Peng–Quenez {{cite:a551262f85816f0832213889fc759d2d008a434a}}), both stochastic recursive control theory and the optimal consumption-investment problem of stochastic differential utilities achieved great progresses in the past few decades.
| i | f60c12ee96aa5d529e856d6487f1fedd |
Following {{cite:20098a35741b5297c30446c3e4c0f837b7b388f3}} we remark that at MHV, the sigma model correlator gives the theory whose Feynman tree-diagrams give precisely the tree formulae of {{cite:a5deb6dfed525bd36e9f4847fa6f1812da8eabe2}}, {{cite:814e2cb656377e8fa277d2d72095abf4aab812f3}}. Furthermore, in that paper, it was shown that the formula at MHV yields the Einstein-Hilbert action of a space-time generated by {{formula:48bef180-8bab-4132-bb2e-78703a2248cb}} perturbations at {{formula:2d825f06-d157-408e-a1f2-350b434130c8}} . We expect a similar proof to be valid here too.
| d | 7d7262680137cd887abffc4308e48494 |
However, for Experiment 2 with highly skewed gender distribution of a 5:1 male to female ratio and a subset size of 544, the accuracy rates are much lower than those of Experiment 1 where the subset size is 166 with equal gender distribution. It is also noticed that the run times increase dramatically from our experiments in Experiment 2, comparing to Experiment 1 {{cite:9db8cb0bc08552297f00104c9f39e9f0fd9e0f44}}.For 5 to 5 training to testing ratio, the combination of PCA and SVM achieves 68.82%, while LDA and Cosine Distance lead to an accuracy of 71.47%. However, further studies are needed to investigate whether the changes in accuracy rates and run time are due to the unequal gender distribution, the increased subset size, or both.
{{table:c0a183f1-aaef-4953-8c81-c5718c39ef06}}{{table:7e6b7097-9c2f-4e79-9f0a-c8d04bf508b2}} | r | cb4aa42eda413bfcaca20d9b13cdb53e |
{{cite:0cd2546b18de3059420299c7e32661a14152d29d}} 2017
{{table:2b1ec132-35f2-4fe5-834c-485b7a5ea29e}} | m | 292ffc0a77b09182b94cf5819069d8e3 |
In this section,
we demonstrate the efficacy of using low rank approximation in the simulation of
four quantum algorithms: QFT, phase estimation, Grover's algorithm and quantum walks.
We implemented our algorithms on top of an open-source Python library, “Koala" {{cite:a7c6e68e692e11a99143b14d406213d3b764e083}}, which is a quantum circuit/state simulator and provides interface to several numerical libraries, including NumPy {{cite:3420379a88ba8be6c9323dc59ba98e6085d7fd02}} for CPU executions and CuPy {{cite:f9ec9f427acf42b6d691f98fe376e1bd7af79b49}} for GPU executions. All of our code is available at https://github.com/LinjianMa/koala. Most of our experiments were carried out on an Intel Core i7 2.9 GHz Quad-Core machine using NumPy routines. For some QFT simulation experiments with large number of qubits and large CP rank limits, the experiments were carried out on an NVIDIA Titan X GPU using CuPy routines to accelerate the execution.
| r | 31396ab9b4850aac0291c83929973d95 |
where the deviation from the SM prediction is {{formula:ca8ddc13-c921-4587-b893-2125a38e5bfa}} level with
a positive value; recent theoretical analysis further indicates 3.7{{formula:f66cb7ae-ab5b-4af4-9836-74e12c953590}} deviation {{cite:0c13bfd577bc04ebe76e6220cbfa0ba919ba211a}} and other analysis is also found in refs. {{cite:4240409c46bb0ec5b3b38385cdec005795b3bfa1}}, {{cite:74ada0167d5ea5bb9f28736fdb6ccf1935e0c14d}}, {{cite:d18357aa2e579fdb64cce04d498614caf7479ec6}}, {{cite:c331d716179c60cdf2fd677e3c44e9c532138da8}}.
Moreover, several upcoming experiments such as Fermilab E989 {{cite:2f8ebdab90b0cb868f01218f5dbfcbc513642651}} and J-PARC E34 {{cite:a7947b988efff9c4a536bc5252f6fc36bcd76f41}}
will give the results with more precision.
Although the recent result on the hadron vacuum polarization (HVP), calculated by Budapest-
Marseille-Wuppertal (BMW) collaboration {{cite:4d811e3540b20b7ad987c7be14fd4c7d663aa300}}, weakens the necessity of a new physics effect, it is shown in refs. {{cite:89397ae91b1ab0365c0e9c9465f25f3388f39362}}, {{cite:6c4524c9d8a8ae9cf240444d1a5342ce9e552284}} The effect in modifying HVP for muon {{formula:0c93ba52-6605-4b4e-bd09-234e6766315d}} and electroweak precision test is previously discussed in ref. {{cite:c6412ff3a41865d7c18f4877acfa0e062e5d2609}}. that the BMW result indicates new tensions with the HVP extracted from {{formula:4ed397a3-f595-41f4-a21c-9129acccbf90}} data and the global fits to the electroweak precision observables.
If the anomaly is confirmed, the muon {{formula:bcf67484-a257-43e5-b712-da4a783d84c3}} is a clear signal of a new physics effects; various solutions have been proposed to explain the anomaly such as scenarios shown in refs. {{cite:327036667c04937faabe78cecb3e104ac3be1376}}, {{cite:0927368c05c7388939fed408c7109dde263afba5}}, {{cite:ea528f9bc4089af1bfc3e42cb076cd0e75ee1c11}}, {{cite:160dc3e5bbf3c83ba5be3985e4acf175dd336268}}, {{cite:8d255f9e3c74f9e11bfb6aaa018d92a0e3f5e0b2}}, {{cite:d1c805cd744e7cd9f1e1c4cb6c8d9061ddcf7908}}, {{cite:016c49b970e44237213532feb29538b509e17fcf}}, {{cite:1c97ca25469ef3224a059556c1c9eb8edb7a1690}}, {{cite:40ccad02af92ef61713b49edb76615a1775e1d51}}, {{cite:a57d2d0096c46ded9e226526ee55b945d4488ddd}}, {{cite:ab9c056dc883d688951853e51c05bbf32c843ed5}}, {{cite:6327dda7bafcddb19bcb2247ad10ff185df592bd}}, {{cite:b9537a72c79abd5ee8da7b8801bfc168a67e506f}}, {{cite:81296d7913975b6d7a38aeedccd86d99141d3745}}, {{cite:4ed623244380ebd50be85416e82149c7271dae81}}, {{cite:c2e6782e7eb10280c10beea80267947b811c9a1f}}, {{cite:cdc5dba7308c7b9898a937a0b77809794176f25d}}, {{cite:06136cae56de00ba3e18c595d9af66e19c44217d}}, {{cite:98c632d85201a533e974edaa45972120e50b2fad}}, {{cite:eb6b19437acf0e223a2494cd28f693d31ce19c4a}}, {{cite:b1d51e07cc3a7317efa73a6730492e4bced6580c}}, {{cite:16c1d7df6350a25af4e7d8f52560146f93920f10}}, {{cite:8c3a13844f5aa872ae9d231d55540d38c0bde430}}, {{cite:461411b6c12329c882259f57c6ca3ab5059b69dd}}, {{cite:ae61ec54e9c1c66866fcd113ae1d6ee4ee42588f}}, {{cite:59aef0faeab961cb1c7e8ec8c1a9a0a471f91d6f}}.
One of the attractive solution is given in general THDM where lepton flavour violating interactions provide sizable contribution.
| i | ee09ca4ec4ef47f164c3e24b7ba47164 |
The Newton equivalence principle states that gravitational and inertial mass of a body are
equal in the non-relativistic and weak-gravity limit {{cite:d603967067cae6c7f34532de4c426ac0039c98eb}}. This principle is a result of
numerous empirical tests and appears to be entirely accidental from a theoretical standpoint. Still, any
experiment has a limited degree of accuracy. Furthermore, quantum field theory and
general relativity are the most fundamental theories utilised nowadays
for the description of matter and gravitation. Quantum theory of both matter and gravity
should be capable of addressing the question how underlying the Newtonian principle actually
is. Even though we have found {{formula:7b3d65a2-6ef8-41c3-a03b-39223a161742}} , the definition of {{formula:5d253379-50a3-4c96-b631-2e7791eb6f79}} does not follow from
the computation of Newton's gravitation potential sourced by the quantum particle. This
computation requires to go beyond the test-
particle approximation. In this sense, our model is incomplete, because the quantum-particle state
{{formula:68faf2ee-543e-4763-bf9a-7117509845c2}} is oblivious to gravity-field
operators, e.g. {{formula:f81d119b-4da0-460c-99cb-caafc0bd72c1}} , where
{{formula:33772375-3194-476d-b58c-934c97accc3d}} is the graviton-field operator defined in the framework of
the effective field theory of quantum gravity {{cite:f880ce1e85752e6a1db36a6f20ae7c2564f58c5f}}. Appropriately dressing
{{formula:8080c534-fe1d-499e-a46e-c9d1eab17f01}} by an operator depending on {{formula:224f03bd-4561-4507-a2ff-77bf36c8c92c}} in the sense
of {{cite:0ab4e8836ccc32c375f89050d3733c9d96b57b7b}} should give a way to determine active gravitational mass of a quantum particle. There
is a priori no guarantee that it matches passive gravitational mass, {{formula:e87fc5e4-3841-4d82-84b5-01b02fcaaa74}} .
| d | 014d976413b070157dd47da040292d47 |
To validate the IBD method, a prototype of a chromatin-like polymer chain with artificially set interaction strengths ({{formula:243bb82c-2fac-404c-8f11-1fe553430e3b}} ) was constructed. The data from this simulated chain was used to test the IBD algorithm, as described below. The IBD algorithm was validated for chains of length 10, 25 and 45 beads. Here we discuss the 45 bead chain case as a prototype.
A few bead-pairs {{formula:a6033c35-c8ef-4e62-98e4-a7138728f219}} were connected arbitrarily with a prescribed value of the well-depth {{formula:10118e11-a89d-4770-9ec8-699c894ecf7e}} of the SDK potential. The non-zero reference interaction strengths for the connected bead-pairs {{formula:5b0c0530-7728-46b7-ba36-6a563fb0aaf4}} are shown in Table REF ; the remaining pairs were considered to have no attractive interaction ({{formula:e20fd90b-81d0-46a2-a583-0445c8cf5b99}} ).
The beads-spring chain was simulated until it reached equilibrium, which was quantified by computing {{formula:85858341-c9c4-4faa-9751-4e96c556c882}} as a function of time. A stationary state was observed to be reached after eight Rouse relaxation times {{cite:6ecf61a370b7745fd5e4257d6b7c5227307435a1}}. However, equilibration was continued for a further fifteen Rouse relaxation times. After equilibration, an ensemble of {{formula:82216cb4-9c11-4cbc-844b-24bb8455a070}} polymer configurations was collected from 100 independent trajectories, from each of which {{formula:7393860c-c63d-4ba3-ae27-626e0804b24a}} samples were taken at intervals of {{formula:7903c2eb-2348-4197-9fad-01b6683c264b}} dimensionless time steps, which correspond to roughly 2 to 3 Rouse relaxation times. From this ensemble, the contact probability {{formula:26d94e65-7d3e-4d27-93ab-215e000cc8e1}} for each bead pair in the chain was computed. Here {{formula:29ebcb95-6e7d-4ab8-bdd1-5549749696f8}} is an indicator function which is equal to 1 or 0 depending upon whether the {{formula:32b2da50-8e1f-47bd-96b5-f9a8812fb910}} and {{formula:6b353805-3da5-4916-a6d0-8d8984b51603}} beads are within the cut-off distance of SDK potential ({{formula:d8ac35d3-1028-49d9-8dea-a724c18d4008}} ) or not ({{formula:2472bb0f-ec4f-474c-98f5-fe414df64e4a}} ). The reference contact probabilities {{formula:7618f814-22de-4002-8841-c271e4929834}} , determined in this manner, are shown in Fig. REF (b). In the present instance while {{formula:da662125-79a9-4c12-bb67-2186f8bcb1d9}} has been constructed by simulating the bead-spring chain for the given values of {{formula:53dcfa05-87e2-4cc9-bcdd-3fc536f44cba}} , in general it refers to the experimental contact probabilities.
{{figure:720bc3a7-cae9-42d1-baab-bec623a47e56}}{{table:6a32c31d-26b2-40b3-ab39-9751596fe85b}} | m | 8329f3ce19ffdac3266d529471baa220 |
Efficient exploration strategies in reinforcement learning have been well investigated on many models from tabular models {{cite:85278b59e3dd012482fdc87a90723e7ddd18bd54}}, {{cite:97c233b668a8df5ad389f88954fe175b4758a297}} to models that enable us to use general function approximation {{cite:8a33d2b81e16750bb85097a880b0c97b6f3bf03b}}, {{cite:a48856bf7dc899474085ec99246c3a49a6010d5e}}, {{cite:29c175a06f586302083c7bf9ba0b39823cccabdf}}, {{cite:333f60f750b6f86f784a249b8ba8d887f5472cfa}}, {{cite:8c09825509f1b0dcd46584111969ffcf524db572}}. These works have focused on fully observable Markov decision processes (MDPs); however, their algorithms do not result in statistically efficient algorithms in partially observable Markov decision processes (POMDPs). Since the markovian properties of dynamics are often questionable in practice, POMDPs are known to be useful models that capture environments in real life. While strategic exploration in POMDPs was less investigated due to its difficulty, it has been actively studied in recent few years {{cite:76b34d6fa202c226baedd68a42c9b65501ce65bc}}, {{cite:d2ee388617ebbd954f0700089c95ef90882fdd3a}}, {{cite:8f1a7646865cd56488880b88bb9471bad0a27e98}}. In our work, beyond POMDPs, we consider Predictive state representation (PSR) {{cite:455975467ade496cdccde76a2937776b8c2b0e27}}, {{cite:7c5050f3ce95193014b4be5ffaf11c2ef0bbc12b}}, {{cite:daec021e2088f06accdb2ce62986746d71faa156}} that is a more general model of controlled dynamical systems than POMDPs.
| i | d7c6968ee368c8ce3834b3a327b7534b |
This section evaluates the performance of the proposed CGGD-MLDR beamformer and compares it with the MPDR beamformer and the newly developed MLDR beamformer. The performance of the oracle minimum variance distortionless response (MVDR) beamformer is also presented to show the theoretical limit, where the interference-plus-noise PSD matrix is assumed to be known exactly. Ten 20s speech signals are taken from TIMIT corpus {{cite:5b647face1022da8301e9ea6c3e51f56a28077ea}} and the babble noise is chosen form NOISEX-92 database {{cite:6e3b679e2a22656feb0dd443d09fb8a9dc74d87d}} and is split into multiple segments as interferences. The room impulse response is generated by using the image method {{cite:42bd9430d7af86757a2f8356f0f4ba754479d852}}, with a room of size {{formula:b78ca57d-185e-4214-bf98-eb6d88781594}} . The reverberation time ranges from 0 to 640{{formula:690f91ee-8829-4836-9339-7581a6aa5931}} with the interval 160{{formula:f033286b-8ec4-483c-96e4-7b6afe33708d}} . We consider a uniform linear array with 6 microphones and {{formula:bec2df58-6e90-4e0f-bf4d-cdacfc44d026}} inter-sensor distance which is placed at the center of the room. The desired speech is {{formula:1d1a691d-d7c7-4607-a624-32b20e6408a3}} away from the array center propagating from {{formula:d9a50d74-2670-4962-82e4-1fba4984ce33}} , and two interferences propagate from {{formula:5e5c5149-65a0-4b1a-be16-285d924a6bba}} and {{formula:49ba8295-9610-4075-a2b6-a07904cb784f}} , respectively. In this evaluation, the PESQ improvement {{cite:b5fc5d1456c2d9b437781f9a45272bba832eb511}} is chosen as an objective measurement.
| r | 44161ed679dad96a7419ee978ef55317 |
A final limitation of this analysis concerns the rarity of the outcome: only 3% of subjects tested positive for HCV. Whilst the rarity of the outcome supports our view that inclusion bias is likely to be small, it does raise issues around the stability of classical estimation algorithms. Logistic regression for rare events may require the use of penalised likelihood instead of maximum likelihood {{cite:00fb3f7ad951491f409440a82d12322dcc4eabc6}}.
| d | 8f9f08f5d80c1166dbccaf7fccf4c1f4 |
We consider Markov Decision Processes (MDPs) which are defined as the tuple ({{formula:b8fdb62d-d0a2-4566-990a-dcfc232ddc08}} where {{formula:4e8b5a1d-cb9f-4821-b1cc-65390bfd00fa}} is the state space, {{formula:4584a49e-4474-4bbf-8546-d1e280a2a7a8}} is the action space and {{formula:1315cf0a-4bd2-461c-bc2f-7cef6a58e20b}} the discount factor. The transition function {{formula:e5626263-9395-4a70-b0d5-b12f1955e11e}} and reward function {{formula:c5cfe316-7875-43d8-865a-8ed3334cb2b0}} depend on the latent parameters {{formula:129c6ef8-1f99-49ec-b0cb-876dd55039d4}} that completely specify the task. The agent's policy depends on the current state {{formula:f9ba4353-2f2d-4623-bc13-e0d843538f39}} and a history variable {{formula:2f8e2be1-2d3b-4828-ba04-6409766d07a3}} of state-action-reward time-step data. Our memory-based architectures summarize history via {{formula:b109a300-d3de-48f0-887f-b1200d0d78ef}} , i.e. a memory variable {{formula:60ad71f4-1884-475d-877f-ae99a5e60676}} and the action-rewards from the previous time-step {{formula:1014dddb-28d2-4065-ae9d-5e0d66722505}} {{cite:509e3f46b20cb062f64688fbe6ebae439b7b06f4}}. In our case, the memory space {{formula:ce18deea-a6ae-4663-a842-b5279bc26b29}} is {{formula:cb4bd55b-896a-4a30-af50-3645cc024853}} , and corresponds to the memory of an LSTM trained using Backpropagation Through Time. Our policies are of the form {{formula:ff87e5c7-bef4-4496-8583-72918c21280a}} . Trajectories {{formula:868e8ea4-f459-4ded-89ee-363117a2d4fd}} are distributed according to
{{formula:187406de-f587-48cd-8adf-18d981e70929}}
| m | ae4ba37aa1ed4893f58f459bb09fc62b |
On the other hand, we have identified an opposite tendency in the development of JITAIs in mHealth applications. Here, the majority of the surveys refer to real-world applications, generally targeting a specific problem area such as promoting physical activity {{cite:7e156f9e9db9ac4745f71019dc475a851de16bd7}}, rather than a methodological review, which currently does not exist. In this case, we recognize that the application area, mostly related to behavioral aspects rather than clinical, might have fewer concerns in terms of treatment costs, risks, and ethics, and the general aim is more focused on optimizing a proximal (behavioral) outcome, rather than allowing for generalizable conclusions. As mentioned above, inferential aspects of existing RL-based methodologies in this field are still poorly addressed, even though recent studies have demonstrated that data adaptively collected through RL and MABs may have a remarkable negative impact on inference {{cite:096c9a2106f69a8c571cf6e635c2b0409f5feb03}}, {{cite:63fe529d58a21a381a87921f1c9eae0a9333d317}}, {{cite:75f82165791a5292925d29f74fcf64e4458255c7}}. Thus, despite the growing popularity of JITAIs, owing to several existing challenges (extensively discussed in Section REF ) and a lack of guidance on constructing high-quality evidence-based JITAIs which may allow reliable comparisons across different interventions, the field is still insufficiently mature.
| d | dfc4f12707d10bcf1e24a2b379651657 |
Proof of Theorem REF.
The high level road map of the proof is a standard one just as shown in Candès et al. {{cite:6febc79316a9e9e61a192e701abfe30e3e7a4a36}}: by convex analysis, to show {{formula:5a7e29c9-f7ec-4fb8-8d73-fa5dd2860045}} is the unique optimal solution to the problem {{formula:35b06be0-0e1a-4472-b1a2-376ceead3f8b}} , it is sufficient to find a dual certificate {{formula:36c4c9a4-699a-4871-831a-b30a6002b63d}} satisfying several subgradient type conditions. In our case, we need to find a tensor {{formula:b364e1da-9901-4460-95b4-dd019dc78eed}}
such that
{{formula:2a3cf4be-4789-4bd1-bbcb-c49510338401}}
| r | d9e5d0ae6d99630f2867da48ed6bcb89 |
() = -1 * [
k(, ) - *()(+ )-1 *() ],
where {{formula:f76cc5dd-a878-41c9-b008-fd4fd58e432f}} , {{formula:ddbfb535-44db-478a-9146-81ca0cc8658b}} and {{formula:8538b058-7f7b-49b2-847a-483f5e1a633c}} are kernel matrices approximating those under the RBF kernel {{formula:33ddb28e-51e1-4658-b805-0075f73f60ff}} . Consequently, under a distance-preserving mapping {{formula:978d58d1-d5a4-4de9-84c1-c43c293e0b16}} , for a test example {{formula:0b5a199a-53f7-47f2-93d6-f3aa0e831885}} that is moving away from the training-data manifold, its predictive kernel matrix {{formula:c0318a19-b644-4de6-ae6b-ef957604219b}} systematically approaches 0, while the testing-data kernel {{formula:6e4db2eb-2cc5-4cbe-beab-3bc6c8d58a01}} and the training-data kernel {{formula:0b2cf9cc-622c-4e5e-83a7-eef7f18fc7c9}} remain in a constant range. This causes the predictive mean {{formula:bd324207-5557-4117-997c-d84ec5d89c64}} to approach zero, and the predictive variance {{formula:8272bb02-e809-4667-972b-da94d12e688a}} to approach its maximum
This conclusion also holds for non-Gaussian outcome. Where the predictive mean and variance can be expressed as {{formula:79ed8ff6-e416-4fe9-8c0e-5108b2e49941}} and {{formula:f012c645-74b1-4b8c-9a19-c6d5328d1ebc}} , where {{formula:49316b70-ee93-42a9-a812-4cec41411ddb}} is the model prediction on the training data, and {{formula:282138fb-24fa-494e-bb1b-209749c8c27e}} is the inverse covariance matrix calculated using the Laplace method (i.e., via Equation (REF )). ({{cite:5fd55bbeae69c783c8a8fd207e9601e49ebf8566}}, Chapter 3.6). As a result, the SNGP model achieves the behavior as motivated in (REF ), i.e., generating a maximum-entropy predictive distribution for OOD inputs that are far outside the training domain.
| m | 9e4ca265fc9d920df8da30b20277392b |
start from an intuitive assumption that the change of outputs could reflect the importance of certain elements when they are removed or preserved only in the input. However, in order to find the optimal results, theoretically it is necessary to traverse the elements and their possible combinations in the input and observe their impact on the output. Due to the high time cost of this traversal process, how to obtain an approximate optimal solution faster is the research focus of this problem. Occlusion {{cite:bb28c9911045b0e5269d0b69a8ccc6bce063e332}} and RISE {{cite:89de4b3fb4ff4f5dd85ae111b8338478b5f680ed}} perturb an image by sliding a grey patch or randomly combining occlusion patches, respectively, and then use changes in the output as weights to sum different patch patterns. LIME {{cite:e3fb49d102cc1a42b9a49123fea3f68bf3b06fdc}} approximates networks into linear models and uses a super-pixel based occlusion strategy. Meaningful perturbation {{cite:a94aedfb562b06e95fb6cc608df902205c6c9c36}} converts the problem to an optimization task of finding a preservation mask that can maximize the output probability under the constraints of area ratio and smoothness. Real-time saliency {{cite:1373a328ec83d588e6ce8e36ea10491bfac37011}} learns to predict a perturbation mask with a second neural network. Qi {{cite:6ce0917be77f0d684883daadde7c3f8ea5bfa62a}} improved the optimization process by introducing integrated gradients and Wagner {{cite:d4243cc8bd01630014351f3f89344e76776e1cae}} introduced certain restrictions in the optimization process to avoid adversarial results. Fong {{cite:a2ae2a98a0714b0a5f522290e5691282770701b2}} introduced the extremal perturbation scheme and a special smooth mask to solve the problem of imbalance between several constraining terms.
| m | 573d9be6f4cb37bac48234f82ad32ea3 |
To compare the persistence of PerDoor against other traditional backdoor injection techniques, we follow the methodology discussed in {{cite:93cb7bbb7eda869712cd56d969abbd39186a07de}}. We consider a pre-defined set of backdoor images with
{{figure:1ae4a680-94e0-43ce-a11f-1df008aa8adc}} | r | e86462d459d4008135f27f4ef7c68c04 |
where {{formula:34488913-a78a-4864-b878-fd70f6c80f0f}} and {{formula:49747703-349e-4721-b660-1261c6132fa5}} are the central density and isothermal sound speed of the atmosphere; {{formula:c2ea3c58-89d3-4cb5-b53e-d001a94983f1}} , and {{formula:6b602e81-ac9d-46e5-a053-8ee44f034d9a}} are the initial gas temperature, Boltzmann constant, mean
molecular weight per ion, and proton mass, respectively. The gas temperature {{formula:59a44953-0382-4c0e-96c7-dfddf38c7430}} is fixed at {{formula:39ad18f7-13cd-457d-bc15-6142f24444af}} in our simulations. Note that we do not consider gas self-gravity in our model. The parameters used in Equations (REF ) and (REF ) are selected so that our density profile is similar to that of the Perseus cluster within {{formula:1deb9d35-f70e-4cbe-b348-1f9e4f532b1a}} . Fig. REF shows the initial radial profiles of the gas density, enclosed gas mass {{formula:630c9d2f-6622-4fda-a8f0-d057f62ffe0e}} , pressure scale height {{formula:f32573e5-b605-49fe-9b18-076c525b6292}} , and Brunt–Väisälä frequency {{formula:1ec1db4c-705b-4392-a617-7e31fc312682}} of the atmosphere. For comparison, an analytical approximation for Perseus's gas density profile is shown as the dotted red line in Fig. REF . We assume {{formula:ef85f3d0-015b-45dd-84b0-47ab58dfc426}} , where {{formula:f6df6171-34d0-42b1-ab72-c658a9b96a02}} is the best-fit electron number density profile given in {{cite:f081440c22131372f48654f2ee157df23e9efb4f}}.
{{figure:d4daf74a-66fa-4baf-a646-cd81df270206}} | m | 37249f72b6abf6ff44b1abcb0bf6e0fa |
Otsu's method {{cite:b2a9093e9ed4963f0e56b4327b510a8754794704}} is a widely-used approach for image thresholding by grouping all the image pixels into two classes in a way that maximizes the between-class variance. In this work, we transplant Otsu's method to the thresholding of the residual errors in our framework, in order to accomplish automatic thresholding regardless of the statistic distribution.
| m | 6b2f8a3c8f07a616986d032368756c02 |
The task term scales with all quantities of interest as expected. First, it is {{formula:f6a2552c-dbf0-4359-8770-7298c5ebee37}} , where {{formula:2eb13244-c7d8-4a43-9001-ef394e4ff478}} is the number of task parameters and {{formula:82b87a27-ea43-40f8-9373-ba21564387b2}} is the probability that the bound fails. This dependence is standard in linear bandit analyses with an infinite number of contexts {{cite:6b2cb836af73eedd54a447a90fbe87f24d8b14d4}}, {{cite:0448b668de3d84b3f5bdcd8a083d03d2cb83efae}}, {{cite:037774e94ebfd551d5ac4acefc3ae966f3fa8c1f}}. Second, the task term decreases with the number of observations {{formula:76832ba9-a8b0-46c7-8c54-6c91a966ab81}} at the rate of {{formula:3f7fec7e-ac55-4bfe-a4eb-ab1f5149d439}} . Since {{formula:a683b523-b93f-466b-9c38-41e827fc6343}} can be viewed as the minimum number of prior pseudo-observations in any direction in {{formula:1e33c693-9c7d-447d-98c3-f75684b016bb}} , the task term decreases with a more informative prior. Finally, the task term decreases when the observation noise {{formula:8a9d990e-c5a4-48b2-a4d9-06528fb63583}} decreases, and the similarity of the logging and optimal policies {{formula:67cd42e8-4c3e-41c3-9997-40f1572ae7d1}} increases (ass:multi-task precision lower bound).
| d | d5da48bf551cc567cc9c4eafe9ffd4a1 |
Sequential {{formula:67caa614-c852-494b-a736-81205881e867}} decays also provide an independent measurement of the {{formula:186bf981-7484-44d5-bd30-0699a1458e2f}} decay parameters {{formula:82109d36-4d3d-4d68-a9b6-8cc19c54439a}} and {{formula:f29cb1ae-6916-4c3d-9b48-3ee5b8d8b86e}} . Being the lightest baryon with strangeness, many other baryons ({{formula:9ffee08f-76cc-4ed6-9e68-bb6315c8253a}} , {{formula:d2f6aa9c-b50b-40c3-a9db-2b33033afb6f}} , {{formula:75be1864-51d2-4953-81f1-f25a646c38ee}} , {{formula:b4b9a062-c85e-4e48-b4f4-d29b8bfdf73f}} , {{formula:9fce9682-6f86-42c8-a24f-77c1f77eedfa}} etc.) decay with an appreciable fraction into final states containing {{formula:85b134ee-f66d-4d85-95e8-9b28211b5402}} . The measurements of spin observables {{cite:fbd51f35651b163bcf5a9a7b6a8e2339c7ff64cc}}, {{cite:e83e32bc64807c19d1d6b6a18cb94d33383bb7d3}}, {{cite:5d729a5dfdd454a6b695063cd8000ea43d1f17b7}} and decay parameters of heavier baryons {{cite:cc38d9a989615fe1bed4c28853b6aafe6e00138a}}, {{cite:522f7c6d498b75994e97ab40b8e3bd60e62aff12}} therefore implicitly depend on {{formula:c2b8980a-6685-46c2-8d83-f9eb18995ded}} . Furthermore, since decaying {{formula:e532310f-a6f2-4738-a490-fefca8e273fb}} and {{formula:06664160-87cb-4895-b423-460d48964f2a}} beams are used for producing polarised proton and antiproton beams {{cite:4fccec711041f517b065f1ff0b3abff731c52a23}}, all physics from such experiments rely on a correct determination of {{formula:0da129cd-3daa-4cc4-953c-0b60f8623e2d}} . The value of {{formula:40cb2022-fe4e-438a-89d5-78f607084162}} measured in this analysis is in excellent agreement with that obtained from the {{formula:b4057f13-ac88-4d54-b936-2d4fead8e18d}} analysis of BESIII {{cite:fd77107725a769cdd1d9f31330c44debd2debea5}}, while it disagrees with the result from the re-analysis of CLAS data {{cite:2eed0a8dc0e2633de0401585d48aabc69faa4b8f}}. The precision of our measurement is similar to that of the {{formula:c82cc7ed-c5ba-4247-91c3-e2451686f3aa}} study {{cite:fd77107725a769cdd1d9f31330c44debd2debea5}}, despite being based on a six times smaller data sample. The larger sensitivity is primarily explained by the fact that {{formula:68243410-b801-4dd0-b9a2-b18ee5732e08}} in Eq. REF appears in a product with the polarisation, which is much larger in the case of {{formula:d3b78a36-989d-438b-a35a-f93750e6f134}} baryons from {{formula:2ac2b642-a960-4d32-a5a7-b50da310b77d}} decays compared to those directly produced in {{formula:276ddae6-546c-43c0-b564-c0ecb474beb6}} .
Furthermore, the multi-step process enhances the angular correlations between the baryons and antibaryons to such an extent that {{formula:a1837744-5228-4d7e-81eb-4f2863d28f56}} and {{formula:b09a5949-4453-41f6-8abb-2113c73aa596}} can be measured with the same precision even if the {{formula:b1a6ebcc-5252-4705-bd07-187e89b009ec}} pair is produced unpolarised {{cite:5a692dd806e0d3f4ade0dcf55553693f527edcf7}}.
| r | 8c6546dfad9e416d5b9e6d3eda312649 |
The goodness of the resonance energy locations and the associated particle decay widths obtained from the R-matrix fitting have been tested through the reproduction of the elastic angular distributions from Ref. {{cite:1ec2416a0f9214918049d6f0e96ff0e9e722f3ec}}, shown in Fig.REF . Quite good overall description of the angular distribution data is observed except a tendency of shift in the positions of the minima towards the higher angles as the energy decreases.
{{figure:8c2c20f1-093e-4282-b169-055543670a87}} | r | 2cfaa7b9f55dbf665cdacee1bd5ed60b |
EditSQL {{cite:37f4b8c6e47d63e5bbc4c8b69c7e9d3d03dc02cb}} is the previous state-of-the-art model on SParC and CoSQL datasets and it focuses on taking advantages of previous utterance texts and previously predicted query to predict the query for current turn. Table REF shows the user inputs, ground truth queries and predicted queries of EditSQL for an interaction. In the second turn, EditSQL views “Kacey" as the name of a dog owner. However, since the context of the interaction is about dogs, “Kacey" should be the name of a dog. This example shows that a model using only historical information of user inputs may fail to keep context consistency and maintain thematic relations.
| i | e38796965e99629b2c5e33a66b67de13 |
There are a number of future directions to be explored. Perhaps the most immediate task would be to incorporate the coupling to gravitons by modifying the integrand. In flat space, the CHY formulae provide a powerful tool for analysing soft {{cite:7f4e26c074f6a0c3153b7a71bbddf0bea468bbdf}}, {{cite:c1897e74409c2992ee5cf59f673422cf896c4b1a}} and collinear limits {{cite:20a28668586c622c12c7207b38aec403a72d07e0}} and their relation to asymptotic symmetries {{cite:a07044bf8136546638f6f0f1c8cd3052d2da280a}}. It would therefore be interesting to use the results presented here and possible higher-spin generalisations to explore similar limits of cosmological correlators. Another natural direction would to extend our construction to loop-level by including additional punctures with possibly deformed scattering equations, similar to the flat space constructions in {{cite:c7cd84aa40a5f331a1fdc1cb038b69ceaf695287}}, {{cite:fe1643f69441f5b37ed135e7d68a33c73122e5bc}}, {{cite:f3d36cc8ecb0aeba67911f508ccd704be22ae2b2}}. This should provide a complimentary approach to the unitarity methods recently introduced in {{cite:53f9779430757cab307ee5bbb990158ec4b7ee8d}}, {{cite:bcc5e9a48e569e38de0f6d2cee50625fdbb1b248}}.
| d | 12f558610e74339c7a251561e1ce61f3 |
The SHiP experiment is
designed to both search for decay signatures of models with HS particles, such as
heavy neutral leptons (HNL) {{cite:3010760eae7015eb24e848e7b02adaa4852a313c}}, dark photons (DP) {{cite:6b14e269ef92040603a3b984d0ed3235a9c7a88e}}, dark
scalars (DS), etc, by full reconstruction and particle
identification of Standard Model (SM) final states, and to search for LDM scattering signatures by the direct detection of
recoil of atomic electrons (or nuclei) in a high-density medium {{cite:f386c0a1f7ffd5dd18afced776e1f022a47454a7}}.
The experiment is also optimised
to make measurements on tau neutrinos and on neutrino-induced charm production by all three species of neutrinos.
| i | e86399b83cc2d70201ed87bf6be8e121 |
We consider only GWs originating from sound shock waves generated by the bubble's violent expansion in the early Universe. In Fig. REF
we show two pictures of the early universe. In the left panel the singlet has no VEV at zero temperature and no SPOPT occurs, as is the case for the SM. In the right panel we show a universe
where the singlet has a VEV at zero temperature and a SFOPT may occur giving rise to GWs.
The impact of the SM parameters in the GWs was done by first fixing the SM particle masses at their central values according to the PDG {{cite:f417edfa9fa490928d5f81267bd39cc942fc2eb4}} followed
by looking for points within the reach of the LISA experiment. For each point found we then varied within {{formula:58797b29-086d-4e23-ac46-cfa2d33d6f91}} and one at a time each of the fermion masses, from the electron
to the top quark, the {{formula:df6a32ca-7b08-40dc-b3be-64fd2eba35dd}} and {{formula:136acc07-4d28-4190-870e-9394ed279219}} bosons' masses and the Higgs mass. We concluded that the only SM parameters with a meaningful impact on the
GW peak amplitude and frequency were the top quark mass and even more so the Higgs boson mass.
In Fig. REF we show four points within LISA's reach for the scenario with a non-zero VEV, identified by a red circle. In the left column we present the variation of the
peak amplitude with the Higgs mass in the interval from 124.96 GeV to 125.24 GeV ({{formula:418cf78f-7f24-4f76-9595-a0a6b45aac14}} uncertainty), while keeping the remaining
parameters of the SM and the ones from the dark sector constant. The maximum variation found for the peak amplitude was 250 % for the Higgs mass. For the top quark
mass a maximal variation of 50 % was obtained for {{formula:b6079029-75fc-4741-9199-f062e042d635}} varied between 172.46 GeV and 173.06 GeV.
| r | 227682f20dcf24e7e754181b74e90dcf |
Two heads are better than one. Instead of using a single model, leveraging an ensemble of multiple models is a simple yet effective strategy that can usually boost the accuracy {{cite:136a056f9a6b4193d2534e70c06c7d341b4716e4}}.
Ensemble techniques have empowered various classification {{cite:6e18bd186968e01edd4772920926fd4faa56e97b}} and regression {{cite:d5ec1cefdc6d0932494b8ca2a4ae39fb55d3ea32}} tasks.
However, different from traditional shallow and small ensemble models such as boosting {{cite:8677e42a820583f89c9c11fdbe15cb64dddbadb5}} and random forest {{cite:0cb30ce57833bc5cb999dfb6f5b29cb5866cf581}}, it is difficult to use ensembles of big models (e.g., BERT {{cite:f908e89ad4c5edc7d95c00572955f9aa17d1690c}}) for inference in low-latency systems due to the huge computational cost {{cite:fbf4632fbc6b7c75de6771327c12298aefcf5a21}}.
| i | f58cba1cfd4fcae391e89afc77039bd5 |
On the other hand, as for the non-integrable equation, up to now there is no systematic construction on the RW solution for the non-integrable model with MI under the non-vanishing background except for the non-integrable defocusing NLS equation with time-dependent potential possessing the RW solution {{cite:3b58111984c9ae5fa2c67f39e47bb99ca5f840b1}}. The existence or non-existence of RWs on the non-integrable systems with MI is still a puzzle up to now {{cite:f9f165a5a6a56f91b367708820bea76fc8629d7d}} which is similar as the existence or nonexistence of two-soliton solution in the non-integrable KdV equation {{cite:398fcdd2888a492a8b2e4e201330fe7dbde2c06b}}, {{cite:5bad0c6d22ce44626f70a6d812253f0d5fcac208}}. It is widely believed that the mechanism of RWs is MI. The RWs were grown in the background of MI. Thus the orbital stability theory will not adapt for the studies of RWs {{cite:7c4aa0bd0d74803f3d0bd7ce45497d0a735e0973}}. Thus how to develop a theory to study the stabilities of RWs is also open for us. All in all, further studies on the RWs will not only impulse the development of integrable systems but also bring the new topic to the theoretical analysis and numerical studies of non-integrable dispersive equations in the fields of applied mathematics and mathematical physics.
| d | 76ccd71da83b2448ed41659d0c37bcc5 |
Viewed as a geometric distribution problem with a probability {{formula:db63667f-5b36-49a6-aefd-bdec5bdd3c9b}} of discovering a UU, we expect to need 1/{{formula:f74f5033-6033-4e05-8ae1-6ef5fad8eed5}} queried points like point {{formula:2b6e3399-77df-4377-ad9d-36c66e8e7f19}} before discovering the first UU {{cite:d51fae446b6c3efdbe63b2f8d3f0c26f8bde35eb}}. For heuristic insight into the reward behavior construction, if we assume that {{formula:5c187e1f-8ec3-4f11-8dc1-2398d6a3b53a}} , then our reward is a log-scaled count of the number of randomly selected points we would expect to query in order to find the UUs in our query set. We use the log scaling to avoid over-incentivizing the search for incredibly rare UUs, as we know there is a limited budget for oracle queries. The optimization step will provide the highest expected rewards for selecting the most overconfident points relative to the updated probability estimates, that is to say when {{formula:e0ca77d9-d96a-4335-827c-5a0dbd31bd28}} . Note that unlike the UU definition, this construction does not require the arbitrary definition of a confidence threshold, {{formula:c9629940-6cec-42a1-b5ea-d26032f4b279}} , beyond which we search for misclassifications. The reward component of the facility locations utility encourages the search procedure to select points where the model is most overconfident. We define overconfidence as the difference between the confidence values given by the classifier and the actual rates of correct classification.
| m | 0335b213e09bb0f4df5a53b66ba0d7d8 |
While we applied curiosity search to a canonical but in silico model of a complex system, our algorithm can instead directly interface with a physical system by taking control of experimental knobs. This direction will allow for discovering functional behaviors that exploit unmodeled or unexpected effects in experimental systems such as non-linearities{{cite:9b69c38a366dbe34f0681720bd08735086934b09}} or feedbacks. Much like reservoir computing{{cite:1fa49edcafc99916f61976f4c98110163c8cc111}} or model-free control{{cite:1f13df5ba39b32d9979650d632dbe3234e84068a}}, our work here gives a systematic way of revealing behaviors that exploit complex unmodellable effects, rather than discovering them through serendipity. However, questions of time and resource cost of experimental iterations and the effectiveness of our method with only partial observations remain to be explored.
| d | 6c4d2228e8b95c79dac3c0c48be09513 |
Through the study of the average occupation we will identify a specific multi-species interacting particle system (see again Theorem REF ) for which
the closure of correlation functions
is accompanied by the existence of a
dual process. This then leads to the proof
of the hydrodynamic limit with the standard
correlation functions method {{cite:d612ecb24657fa84dca2364d00a653998006a253}}.
In other words, for this specific model the linear reaction-diffusion structure is obtained not only at the
level of the average densities, but also for the
empirical mass distribution of each species.
To our knowledge, this is the first multi-species interacting particle system
with reaction and diffusion for which
one can prove the existence of a dual process
(see {{cite:d612ecb24657fa84dca2364d00a653998006a253}} for a perturbative treatment
of reaction-diffusion in the presence of duality
for the diffusive dynamics).
| r | e97b5fe34be9ae62bd50c035ba13bac6 |
Fig. REF displays a few such examples for TSR{{formula:5e1bd368-bcc1-4981-8aac-d1523c2c3599}} 8.
We compared our results (both visually and numerically) to the leading methods in the field (DAIN {{cite:c9da2b3455fc1fdba5ae211348a2c050eadc8150}}, NVIDIA SloMo {{cite:f9b23311574ff9c4d1eecbcdbc5b767cfafa9159}}, Flawless{{cite:a0add2b33233826be74e44b3e2cd6c66c991f412}}). As can be seen, complex dynamic scenes pose a challenge to all methods. Moreover, the rotating fan/wheel, which induce severe motion blur and severe motion aliasing, cannot be resolved by any of these methods. Not only are the recovered frames extremely distorted and blurry (as seen in Fig. REF ), they all recover a false direction of motion (counter-clockwise rotation), and with a wrong rotation speed.
The reader is urged to view the videos in our project website in order to see these strong aliasing effects.
Table REF provides quantitative comparisons of all methods on our dataset – compared using PSNR, structural similarity (SSIM), and a perceptual measure (LPIPS{{cite:d9dbd906fa66af5a98e066663367bd7916f95f49}}).
The full table of all 25 videos is found in the project website.
Since Flawless is restricted to {{formula:825c9072-5bad-4497-9a3e-467db8e4ad42}} 10 temporal expansion (as opposed to the {{formula:165d9d00-ca2c-4120-8f99-7e32794e679e}} 8 of all other methods), we ran it in a slightly different setting, so that their results could be compared to the same ground truth.
Although most closely related to our work, we could not compare to {{cite:83ea9d8bc6a415fc7d3ff72d68c34ded165da8e9}}, due to its outdated software. Moreover, our end-to-end method is currently adapted to TSRx8, whereas their few published results are TSRx2 and TSRx4, hence we could not visually compare to them either (our TSRx2 network can currently train only on small (coarse) spatial video scales, whereas {{cite:83ea9d8bc6a415fc7d3ff72d68c34ded165da8e9}} applies SRx2 to their fine spatial scale.
| r | b714bc8085cd809d2a8a7bdfd4ea7188 |
Now, we would like to numerically analyze the stability conditions of the DIAWs in the
presence of non-thermal electrons. The mass and charge state of
the plasma species, even their number density, are important factors in recognizing
the stability conditions of the DIAWs in DPM {{cite:168f6d23bd34c04236a8bd9bdfdaa7f94ce795ba}}, {{cite:2d90259f0d21d2e3ccf8f86c5931f5275071969b}}, {{cite:fc594abb342ca6a1067e0bedaae2859ad283346e}}, {{cite:3459e71ee968e2cea7e183ade1e975fc28688abd}}, {{cite:26e6a7a05e5015a9bc52fddb55eea175f4497c07}}, {{cite:b02b9f2ea095ac76faf4bc033a217ef6182de1c2}}.
The mass of the dust grains is comparable to the mass of the protons. In a general picture
of the DPM, dust grains are massive (million to billion times heavier than the
protons) and their sizes range from nanometres to millimetres. Dust grains may be
metallic, conducting, or made of ice particulates. The size and shape of dust grains
will be different, unless they are man-made. The dust grains are million to billion
times heavier than the protons, and typically, a dust grain acquires one
thousand to several hundred thousand elementary charges {{cite:168f6d23bd34c04236a8bd9bdfdaa7f94ce795ba}}, {{cite:2d90259f0d21d2e3ccf8f86c5931f5275071969b}}, {{cite:fc594abb342ca6a1067e0bedaae2859ad283346e}}, {{cite:3459e71ee968e2cea7e183ade1e975fc28688abd}}, {{cite:26e6a7a05e5015a9bc52fddb55eea175f4497c07}}, {{cite:b02b9f2ea095ac76faf4bc033a217ef6182de1c2}}.
| r | 1aae3de0e7e98bce29c0dacd50863339 |
where {{formula:49e327a7-58ff-44cd-a0a2-4d56c3c3db5f}} is the periodicity cell.
This is easily solved, for instance by a saddle-point algorithm {{cite:5a39d83204ef0b938215e47869b3f73e2567f86d}} which aims at finding a solution to:
{{formula:09e29c78-680a-4734-9eaa-356230ff7a38}}
| m | 9850a09c6dddd0fe7b912395cc36df8c |
The results of the proposed methods in this study have shown how episodic task formulation affects the performance of few-shot learning. This supports the emphasis given to meta-training distribution of episodes by different studies {{cite:f6b81759189624566d2632ca84b85ce38cec004c}}, {{cite:bfaf3a120e759560f2cfb9313607fff12a4efad4}}, {{cite:977548441c1e0751f1f63f3d4ae8c2a138490514}}, {{cite:c824854717f9405aaa7792c946724b4f36183a01}}, {{cite:ec884d169e6e4f6d3e7a41772b75b1fd9eef7e45}}. However, as attempted to explore in this study, the proportion and the pattern of formulating the tasks from character label, row label, and col label will remain an open area of research. This is particularly relevant during the training phase for few-shot learning since the test sets contain previously unseen classes with their own labels in the support set.
| r | eb867312a409a7e1aed2b6f9b626313b |
Equiangular lines have long been a subject of interest {{cite:57f70cb0c0c1450d5fea144088f8f4d6ae3bdf61}}, and since equiangular tight frames have minimal coherence, they are particularly useful in a number of applications. Recent work on ETFs was spurred by results inspired by communication theory {{cite:d90fa42576d2b6b4075fb12fd5d5cd0631233065}}, {{cite:ff9adcbb19bc9c46cecb304e9a6a830e75f30388}}, {{cite:75db52f14201eed4c818d7b2faac8b8bec845da5}} that show that the linear encoders provided by ETFs are optimally robust against channel erasures. In the real setting, the existence of an ETF of a given size is equivalent to the existence of a strongly regular graph with certain corresponding parameters {{cite:ff9adcbb19bc9c46cecb304e9a6a830e75f30388}}, {{cite:1fddd9c04fc26f7ca944f6d223ca5fb06963f668}}. Such graphs have a rich history and remain an active topic of research {{cite:496eadaa076774fa6e7d618a5e6560f274b596a1}}; the specific ETFs which arise from particular graphs are detailed in {{cite:0c7bd226d1de137f0a3859b765aaddc59e427315}}. Some of this theory generalizes to the complex-variable setting in the guise of complex Seidel matrices {{cite:b817763b4555ebe185a36e22cdafdc6f45b9cb00}}, {{cite:b10bff5e13d03ec071a0aef09baba8761b1f60d1}}, {{cite:257f41beca3646a15af85591aa3c393aa6c3951a}}. Many approaches to constructing ETFs have focused on the special case in which every entry of {{formula:304f8ef4-7af0-4df8-bfc8-a7f6c9bc08ca}} is a root of unity {{cite:7d3b760a97c784e63faae5821e02a4c7458e58f0}}, {{cite:3db0e6f00ff90376a97de614a069e22fa999a8af}}, {{cite:0938f9cce63f18bfd1666bac435d0e44ffc45908}}, {{cite:682c376887d2ded10c6ac867a45223af09c707a3}}, {{cite:c08ceaed0e4e1fce99ee94f178f20b8fa5822f9d}}. Other approaches are given in {{cite:957b00063d927784ea9c058d181b23f96583e554}}, {{cite:6612d6146a89acfb2f7407c2a910539a68ce52d0}}, {{cite:3eac3460e49c2c32260779a8ae12467fea6c3429}}. In the complex setting, much attention has focused on the maximal case of {{formula:1b3c7b66-72ec-4186-b0ac-f41d4d3fde01}} vectors in {{formula:a255d51b-168b-4f94-9b44-857345bd89ee}} {{cite:58d965aec7ef79a20099f19dc1c5fe288348d2c6}}, {{cite:02df09f3102e2215434680e3d60dc9554c08ffc5}}, {{cite:5cd87d9720261a302472fc8fa0c4243a76be68d5}}, {{cite:653ee0d4ead4f1bf6a8660d07c3789c340ea4fd0}}, {{cite:b2371731daa1c1ea6e03eaba9fecbd1faa6a680b}}.
| i | 62865527d3142a30edb1c4ad82904f95 |
Summary of the example:
To demonstrate its applicability, the mathematical framework was implemented in AUTO {{cite:28a20a6bfb16dd5410920aaa5a29120827bc3303}} and illustrated by the example of an ecosystem subject to a moving or shrinking habitat. As a result, we provided new insight into nonlinear dynamics of the moving habitat problem by performing:
| d | 1cd5881664aaee35fb21d88a86c3e4a5 |
I have performed molecular dynamic simulations of SPC/E water model using the GROMACS package {{cite:201139f3db75295ccb00124128e9b5e320ce4f28}}, {{cite:2dd25f688f729f5231c84014cfa9891092a5802e}}, simulating fourteen similar systems of 1185 molecules at 1 bar of pressure in a range of temperatures from 213 K to 360 K. I initialized the system at 360 K using an aleatory configuration of water molecules, assigning velocities to the molecules according to a Boltzmann's distribution at this temperature. For stabilization, I applied Berendsen's thermal and hydrostatic baths at the same temperature and 1 bar of pressure {{cite:6fde7762076d0392d08f901235151b108ca3b47d}}. Then, I ran an additional MD obtaining an isobaric-isothermal ensemble. I obtained the other systems in a similar procedure, but using as initial configuration that of the system of the preceding higher temperature and cooling it at the slow rate of 30 K ns{{formula:282b56c7-fc46-487e-b371-a85ed028ca6a}} {{cite:c100d047e2e255ac546fbc6870cd45230f7b8c3c}}. Stabilization and sampling periods for the systems at different temperatures are indicated in Table REF . Simulation and sampling time steps were 2 fs and 10 fs, respectively. The sampling time step was shorter than the typical time during which a hydrogen bond can be destroyed by libration movements.
{{table:fa566cff-96e1-43af-a2ab-8a3948b2c756}}{{figure:681ddbce-105a-43e5-9d68-a6cd239c1415}} | m | e24f98ba7c0242a8fcdf72c7e31ddd92 |
Our analysis here is based on the set of inclined air showers ({{formula:ad1f5be2-0c05-4f7e-b502-554eed9df352}} ) that are reconstructed both with the SD and with the FD between 1 January 2004 and 31 December 2017.
For each event we obtain independent measurements of the muon content (with the SD) and the calorimetric energy (with the FD).
To ensure the showers can be reconstructed with small uncertainties, we select only events with at least four triggered stations in the SD array and we further require that all the stations surrounding the impact point of the shower on the ground are operational at the time of the event.
Only events with good atmospheric conditions, (few clouds and a low aerosol content) are accepted in order to guarantee a good energy reconstruction with the FD. In addition it is required that the entire shower profile and in particular {{formula:e31aa9c6-b3e7-4510-8ca7-9409083d5f0b}} is within the field of view of our telescopes.
Since heavy primaries penetrate the atmosphere less than light ones, the acceptance with this selection would be mass dependent.
To avoid this bias we constrain the field of view to the region where all values of {{formula:07867ef6-2582-447a-be2b-6e913b30a147}} are accepted.
Further details are given in {{cite:9126a08040b6c98b0b5f8fdd9daf44892c3292aa}}, {{cite:79e4f7b6a8967f2d8f0d20da56847d3b21bdb694}}.
These selection criteria result in a total number of events of 786.
| m | 1ea9f63cbb2a20ac455c2557e99c5863 |
Recall that {{formula:f141633e-36e4-4592-9b1a-90185aa147ca}} is topologically graded with conditional expectation {{formula:dba8a96a-2c99-4e87-a8fb-453fda4efa04}} . Since {{formula:bb9149ef-7042-45f0-93d3-7e80717e0a21}} strongly reduces to an amenable group, then by Lemma REF , the gauge action {{formula:6331ac2e-d429-40ca-9eaf-ab049420bfc2}} is normal and thus the conditional expectation {{formula:db83a40d-0eb2-45ba-a86c-da8f119595d8}} is faithful. But by {{cite:f8d843e14c51201f8c2ea14e6c59ccf7aa829e1d}}, the kernel of the regular representation {{formula:6f859e8d-0f83-4c4b-98c8-40e5b53b8f32}} is given by
{{formula:9ca371e1-631e-42fc-8e97-7189d3733610}}
| r | 58041bfe5f996b207be9d04a52fb8674 |
Introducing correlation between graphs is a natural next step in modelling graphs, thereby acknowledging dependence also in this non-Euclidean setting. This clearly goes beyond the mean of a graph, a topic with significant interest {{cite:a56fa0235117d7995eab8a22b42d247f70a9b851}}.
Graphs can naturally also be dependent without being perfectly replicated. In graph theory the notion of graph limits were partially introduced to use tools from analysis in a combinatorics setting.
Our framework shows how simple `linear' operations may be interpreted in the space of graph limits.
Further, we note that marginally the edge variables in a single graph are correlated when one of the indices are fixed to be the same. Edges in exchangeable models, and scaled exchangeable arrays, can only exhibit positive correlation inside a single exchangeable graph {{cite:f25abf491c555f85235083e3dad832a7dadf1962}}. Once we move between two “layers” or graphs on the same nodes, negative correlation can be generated. One simple way of doing so would be to take {{formula:5a1ee530-6445-4dd9-a8b6-ada737b04d35}} and {{formula:ec9812c8-89ed-45d7-a4b5-a51c3a9fa5a2}} for some positive {{formula:ef6c3f29-dbf2-4eac-9856-01e1c0370c35}} and function {{formula:74539e66-acf4-48aa-9dea-e77e81d8ffbb}} , {{cite:44910db479e3b1058ac66165264da79269021c52}}.
Of course as the dimension of the Bernoulli vector increases data structures become more difficult to characterise {{cite:bdb4c8563b76d300642d89062c310a46a98412ab}}. Given this, for multiplex networks with more than two layers, one may proceed by applying the proposed framework to all possible pairs of network layers. Thus, reducing a {{formula:c4334a18-da64-4f91-9899-3a6b1df13380}} -dimensional model to {{formula:192918e9-d524-417b-a6d0-7a7fdf3c49ff}} two-dimensional models parameterized by edge coherence. Edge coherence between a pair of networks is a weighted graph itself. It summarizes their dependence structure and may be used for key applications such as detecting changes in second-order dependence structure across network layers observed over time or space.
| d | a038556afe7b09471c769f654497c28e |
Since the effect suggested here involves integrating out infrared degrees of freedom, there might be a parallel to non-perturbative renormalization group approaches, investigated elsewhere {{cite:981bec56bb985141e411b5a95a8011f31f8bbf68}} and motivated by the analogy between renormalization group scheme independence and general covariance {{cite:b7824e6c26671256a424edcbd85b007f1ef842be}}, {{cite:6d5aeb18dfb559682664d22029b639967e7eb270}}. In both cases, the approach does not rely on new physics, but rather on making sure the underlying theory's local physics is insensitive to unobserved infrared perturbations.
| d | 96215055a11ddac61f9eb3407629ad69 |
FD methods offer gauranteed accuracy and controllable convergence properties for the training of neural network surrogate models. These are critical features for solving real-world complex physical systems using neural networks.
NBM offers a straightforward path for applying mesh-based FD methods on unstructured random points. This is an important ability for augmenting observational data in the training pipelines.
The algorithm is highly parallelizable and is ideally suited for GPU-accelerated computing paradigm.
Multi-GPU parallel solution of PDE systems is reduced to the much simpler problem of data-parallel training using existing machine learning frameworks. Data parallelism involves distributing collocation points across multiple processors to compute gradient updates and then aggregating these locally computed updates {{cite:9bac65b325742d2e288b2abdac078b7dd5043a40}}.
| m | 7cfdc6b797126250eaeb0a6b40b4861e |
Video frame interpolation (VFI) aims to increase frame rates of videos by synthesizing intermediate frames in between the original ones {{cite:e41282a12f4b0b85576aaa9295682bca4ca45aeb}}, {{cite:f33ef1062da356c8a75e48bc9a39f5fab56d013e}}.
As a classic problem in video processing, VFI contributes to many practical applications, including slow-motion animation {{cite:6f63b833db4705f8c48892da2596a61e96fb5aab}}, video editing {{cite:bea3443fd8525383eda07b1731e5b69bfef53063}}, video compression {{cite:6676bfd608c8fb368138e06fa1262984a4953469}}, .
In recent years, a plethora of techniques for video frame interpolation have been proposed {{cite:9409de9ea51faa902d2f97b53254670f0eb48f8f}}, {{cite:8094fe5a61ab6cef24ee37b8f90c20cff86e19f8}}, {{cite:ab84202e64462d4af8eaabbf6095f6125dbaf43b}}, {{cite:6bec1bf73acbd5aa54d27cd8aeb2e8456eb1cb73}}, {{cite:72f5e60f45d80393010471d3fd7622ea92f942e5}}, {{cite:960ab3fb8b7659ace9fc4e9b2fb3e95824320444}}, {{cite:426e6843ab9af1800657ec4f1973f875b6f21157}}. However, frame interpolation remains an unsolved problem due to challenges like occlusions, large motion, and lighting changes.
{{figure:efa7d370-e73d-4ffb-a3f0-89076c97dbb4}} | i | bd1e3804bef96ac792557a9a7be3e880 |
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