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The main priority for developing further quantum PINN is to address their current low accuracy results. In all our tests, in practice, reducing the error below a certain value or increasing the convergence in a finite number of iterations has been challenging. This is likely related to the barren plateau problem {{cite:293cd01fa609eb688553b25de830e1b5c6aed44d}}, affecting all the hybrid quantum-classical algorithms involving an optimization step: the classical optimizer is stuck on a barren plateau of the training landscape with an exponentially small probability of exiting it. The barren plateau problem is fundamentally due to the geometry of parametrized quantum circuits (our quantum surrogate neural network) and training landscapes related to hybrid classical-quantum algorithms {{cite:293cd01fa609eb688553b25de830e1b5c6aed44d}}, {{cite:139834e5069c3bc43f6eeea7fe031679ccd175fa}}. When comparing quantum to classical PINN in our implementation, we found that the optimizer exploration of the training landscape in the case of quantum PINN is not as effective as in classical PINNs, and adaptive and high-order optimizers are less performant than basic SGD optimizers. Potential classical strategies to mitigate this problem are the usage of a quantum ResNet or convolutional surrogate quantum networks {{cite:c7d51616f484b19952eab6550d740061f529ddba}}, {{cite:293cd01fa609eb688553b25de830e1b5c6aed44d}}, skip connections {{cite:d4ad20584f06313ac9a8ab72c8cf91ad644b6b3f}}, dropout techniques (in multi-qumodes neural networks) {{cite:3a9b70970a7b002f1946ddb54af8a4dd52374893}}, a structured initial guess, as used in quantum simulations, and pre-training segment by segment {{cite:38b62942d95af082dc1a3329b7c0a09e7b2ca619}}.
| d | ea6915cdf1b990ea9a3bceccd0fc49a2 |
There also exists an intent in the opposite way, especially after the work of Aharanov and Bohm {{cite:540fd4b71ca77c843fd4beacc605f15e47771f2d}}, to think of {{formula:b3f0bfa6-f62f-4744-aed9-e6656d145401}} as physical reality. Another support for this idea is that the Coulomb field always accompanies a charge, and can never be stripped away. We do not claim either that our findings add to that intent. In fact, we must be clear-minded that our starting point, namely the semi-classical Hamiltonian (REF ) or (REF ) under the external-field approximation, is known to be unsafe if the external source is relativistic {{cite:4feee2e71b5bbfd5a74bedfefec8b16833f8dd65}}, while a safe and fully quantum-field method is still lacking. In such a circumstance, the gauge-dependence we just found is not a disaster, but an advantage: Since the Hamiltonian (REF ) or (REF ) is not justified anyway, there is no sense in sticking to the actual {{formula:651a7404-838a-45c2-8304-09eb4ff4d49f}} generated by the external source. Instead, one may always try to define an effective external field which, when plugged into the Hamiltonian (REF ) or (REF ), may fit well the experimental data. This is indeed quite probable, as we saw that by just tuning the gauge, we may fit the peak frequency of the radiation spectrum; and another overall factor may be multiplied to fit the radiation intensity. Namely, the effective external field may likely be parameterized with the gauge potential in a particular gauge. This gauge is not necessarily among the most common ones, and might possibly be individualized condition for the field of each charge, instead of the usual conditions for the overall field.
| d | 8bbb261f41239686ee758ab976c8223e |
Our proof of concept aims at replacing the calculation of the probability of interaction via Compton scattering. This probability is a function of the weights of the macro-particles, their momentum and a normalization factor. We formulate this task as a regression problem {{cite:bcf6c49875c925db54faf551dfe689b0b16e71c4}}. We use a NN to predict a value between 0 and 1, corresponding to the probability of interaction. The NN takes as input the momenta of the macro-photons and macro-leptons in the simulation frame in units of {{formula:02791c20-75f0-4deb-899d-a4a5418efee1}} ({{formula:dcee8ab2-60ba-40bd-b329-92d7a364c993}} and {{formula:2ea83a8f-93b7-4d30-b180-681261ef921c}} , respectively) and the maximum probability of interaction in each PIC cell {{formula:eaeb97f8-2e62-4f60-a9a3-451ba337a579}} , where {{formula:fd344607-8ae7-4789-adc4-4942b4d4ed9b}} is the Thompson cross-section, {{formula:c7edd3bc-d121-4321-85d5-ec938c29b428}} is the time-step and {{formula:c9b0f493-b2d1-414e-822e-7ae05ac26e1a}} is the maximum macro-particle weight within the cell {{cite:ae56091c149f174e32cf63bb7ec4bd355cd62a2c}}. During the training process, the analytical probability of interaction {{formula:c7763a86-bfbd-4246-9381-a3003e347e07}} is used to compute a loss function and to update the NN via back-propagation.
| m | b10415a1cf9cf55f7d6aae42168f191a |
In order to investigate the variability time scales of optical continuum light curves, we use standard methods like Lomb-Scargle {{cite:7526acc854dc85001a22774cfd9177cfad475108}}, {{cite:fd8b390d9801ea84dd1e030cffe8549d106ee841}}, and sine function fitting, that we use here to determine variability time scales. Here we assume that the variability time scales corresponds to the orbital time scales within the region of AD where the optical light could be originating from , .
Ripples in the broad emission line profiles could be produced by the effects of the same phenomena that drives the variability {{cite:d4fd9f4d226089d18e643ca8e770a9b7235d5e8e}}, {{cite:1b79fc89f0ab823e37ede1ae1de608d4848597e5}}. If we detect them, we would then be able to determine some dynamical properties , . In case we could identify more then one variability time scale period in the light curves that could be linked to the radius of an emitting ring in the broad emission line profile, then for each ring-radius pair we should expect to obtain the same mass (or at least very close value) of the central SMBH using Kepler's laws.
| m | f6f2cff75ba074273f1d484740db4a5c |
The optimization program in Eq. (REF ) includes data-{{formula:d3a6fa75-5bbf-49a5-802c-8283d0bf10f3}} norm and DTVs. It would be interesting to investigate additional designs of optimization programs and their associated algorithms for potentially further lowering the minimal-angular ranges obtained with the optimization program in Eq. (REF ) and its DTV algorithm. We are currently investigating to replace data-{{formula:0c763eba-fc7a-43d5-9405-cdda72f86b4f}} norm with data terms of different forms, including data-KL divergence and data-{{formula:f9cb8194-b79f-4fee-bf0e-f6714fc256ed}} norm. As long as these new optimization programs remain convex, they can be solved accurately by use of the general PD algorithm. One may subsequently seek to derive and solve the proximal mappings corresponding to the optimization programs, thus obtaining instances of the general PD algorithm for solving the optimization programs. The work focuses on reporting 2D-image reconstruction from limited-angular-range data. However, it can readily be extended to 3D-image reconstruction from data collected over limited-angular ranges. The ITV algorithm has been shown {{cite:7beeb9ac29f97f6b45437e63480b38af98b1ea6a}} to reduce the cone-beam artifacts observed in image reconstruction with analytic algorithms from circular cone-beam data. As the DTV algorithm is demonstrated in the work to be more effective than the ITV algorithm in accurate image reconstruction from limited-angular-range data, it would be interesting to investigate if the DTV algorithm is more effective than the ITV algorithm in minimizing cone-beam artifacts in image reconstruction from circular cone-beam data collected especially over limited angular ranges. We are pursuing the extension and will be reporting the results in the near future.
| d | e66c99ae622cb36b7035c30c75c5bddc |
table:fid shows comparisons of all the considered models using the FID score {{cite:116d99c6ea12033cb1553d3b3547ba7f5ab3a60a}} for the MNIST {{cite:ca4aa3067c0c95005006c2d0fb600a0d0a1715b3}}, FMNIST {{cite:d75ba693d55b46b1cc7b3544159da7b34c84b97d}}, SVHN {{cite:f70e1eb956842365871b8f36c3b11c5e727bb4b0}}, and CIFAR-10 {{cite:11052f73ae979a5d338a6f1a7941ee2b8d1bb540}} datasets. We opted to use FID scores as a measure of how well the models recover {{formula:061341a9-0768-40e8-8698-44feb0f57cfe}} instead of test log-likelihoods since the latter are, by definition, unable to detect manifold overfitting. We highlight that we tuned {{formula:98e41201-4573-4113-b01a-71e084a9869a}} for the Tweedie denoising models, as well as {{formula:1c28bc1f-147d-450c-9d56-65d554904f3e}} for the conditional denoising models. We can see that, surprisingly, the TD-VAE (TD-NF) and CD-VAE (CD-NF) models do not consistently outperform their VAE (NF) and ND-VAE (ND-NF) baselines: the only instances of denoising models obtaining a non-marginal improvement over their baselines are the CD-VAE on SVHN and the CD-NF on MNIST. We also tried annealing {{formula:10d6d41f-34e3-459a-b39e-5df235a58eec}} (for Tweedie denoising models) and {{formula:e2637698-020e-40dd-9624-217ddf8f2839}} (for conditional denoising models), but found results did not significantly change. Not only do our denoising models not outperform simply adding Gaussian noise, but in some cases denoising can even hamper performance: for example CD-VAEs on FMNIST and TD-NFs on MNIST both significantly – albeit marginally – underperform their non-denoised alternatives.
| r | 26f1136c5c346a79414fcfadc2aeda49 |
We extend conventional factor analysis{{cite:7e4d2c7798be1771df99f8d85c8a344927fbe9af}}, {{cite:388cbecf1270359145e2acd1225a2af1e1163908}} by introducing a global-local shrinkage prior{{cite:41648a6615b006244854521d9115bac76435c5da}} on the scales of each weight {{formula:e3587eed-9821-4c43-9971-6d376a16842b}} .
{{formula:b4fd3a9c-57e8-4a8d-b2e2-04c3f02a2e85}}
| m | 02acee50ef4b8eb50aa55de9d8795642 |
As the jet velocity is typically close to the escape velocity, {{formula:f56f81bd-d071-4311-991a-953780a5dde1}} (where {{formula:754263b3-67e6-4691-8221-4c3d0bef6e89}} and {{formula:44ac43c7-44d5-4c95-a18c-35c51e110824}} are the mass and radius of the object which is launching the jet), then equation REF leads to {{formula:03fc306e-a3be-493c-9867-6849514a6808}} . Since for MS stars, {{formula:94b54a20-0965-40ef-89fa-da475eb9097e}} {{cite:9d0e57f71b17587e891b0f3896f67158e1ef80c0}}, then {{formula:e1092057-b928-4be4-b172-82b7a7a5d138}} depends weakly on the mass of the main sequence star ({{formula:06ef130b-ee32-4946-937f-77fbfaa64e75}} ). Thus, the results obtained in this paper, in particular where the jet is successful or chocked, can be generalized to low mass stars ({{formula:dc614f05-4c9c-466f-8f95-089a0a0390ee}} {{formula:6a4ff0d7-76de-4e62-a161-c8eb3402f86d}} ). A very different outcome is expected in the case of compact objects in which the radius is several orders of magnitude smaller than that for MS stars, thus, {{formula:1c567070-5f02-4ba7-be24-89b1927cd91d}} is much smaller and jets are energetic enough to propagate successfully at any orbital separation {{cite:1efa7b37648f0235ef5cd4b9e1d93e4cd32e7ada}}.
| d | 98ac91612bacaf6f26b506179defb5e4 |
The double Wick rotated geometry may have problems with causality in the Lorentzian frame. We make use of a Killing vector to analyze the causal structure of the background. A Killing vector {{formula:09b76a41-5047-4985-9edd-971ec5c21b1e}} has the norm {{formula:e7af453a-7348-4122-b1f3-2e7e482d6911}} , which is spacelike for {{formula:e08fce76-ad07-4a8a-904b-ad06cc7ea99b}} . However, it becomes timelike for {{formula:9dd4e75b-f09b-403c-aabe-2cbf235e502a}} . In addition, {{formula:99a8ac09-afa2-4fe9-8309-64e054213423}} const and {{formula:581d1b3b-6a5d-4639-8729-d21c208a55ff}} surfaces become timelike {{formula:a12e3838-630c-473f-a2c9-9e98a6455ca5}} . It shows that the double Wick rotated geometry has a closed time-like curve {{cite:df1d37f5e56f0a40c0e6f7a7fbe6bac15f74a2e1}}. It will be possible to explore how the law of physics allows a closed time-like curve {{cite:a3b58007f90eda837de6869a54768ccc7aa0ce62}}. Second, the background is not a black hole in the Lorentzian signature because it does not have Hawking temperature, which vanishes after the analytic continuation {{formula:ab941ab1-73cb-486e-aedf-45cb16f8efe2}} (see (REF )). It also has negative energy, unlike thermal field theory. This negative energy will correspond to Casimir energy in the CFT side {{cite:7b5c23caaac4cbb92843cce94085a0c2fb76aae2}}.
| d | 4d6de560fd53d226e0c12bdd994bbe67 |
Given these similarities in results, even our very simple model may be able to lend insight into potential ways to deal with spread of conspiracy beliefs – though we in no way mean for these to be taken as policy recommendations. Our analysis revealed that the three most important factors in swaying any agent's belief were (1) whether or not an agent is exposed to a message, (2) number of exposures, and (3) the difference between prior agent beliefs and those expressed in the message. Even if (1) and (2) are met, as in some attempts to debunk misinformation {{cite:cf467d13ed751961471483c0c9e94f90272eb6cb}}, (3) would prevent staunch conspiracy believers from changing beliefs if exposed to a contradictory message. Some analyses attempt to focus on the network structure {{cite:2ea92632e95be9cf3588491a1233495cefd8707c}}, {{cite:3bd113826a4303bb142d365b19e9d363abd3469e}}, {{cite:e1ae243f407bff521256a54c17d22bc6a64ea6e7}} – i.e. (1) and (2) – without acknowledging that individual psychology is just as important – as in (3). Our model, which captures both network effects and individual effects, therefore gives novel insights into a more holistic intervention. Our analysis of results showed that for a highly homophilic network (a trait present in real social networks), certain messages have a slim chance of reaching those with certain beliefs. Any intervention would need to take this into account, and imagine what types of messages would be most likely to reach certain populations.
| d | 7d1eb7b75202cf7c0b9e0fda26a0e228 |
Our experiments also highlight the well-known challenge of graph learning in heterophilous scenarios. This is currently an active area of research {{cite:1d85d2f2435e607827256a37fe1ee743d54a0213}} and existing work is less established. We hope our proposed edgewise metrics can help the related research, and in general bolster the development and evaluation of new approaches for uncertainty-aware learning on graphs.
| d | ee79f487e9b8b737b1398579b7ee6b92 |
Based on the assumption that the process leading to the ubiquitous emission of X-rays – the Comptonization of seed photons
produced by the accretion disk – is the same in all BH systems regardless of their mass, this method can in principle be extended to any BH including the supermassive BHs at the cores of AGN. In the latter case, since the detection of QPOs is extremely rare but the distance is generally well constrained by redshift or Cepheid measurements, only the {{formula:af37d1e9-7f88-4e7c-ad6c-0d292dfb0b53}} –{{formula:6931b5ee-5dbb-446e-8351-1d6f11fd3a3c}} diagram is used to determine the {{formula:6d3cf9c9-ee31-44ac-a3a9-d0df8642e3d7}} . Indeed, over the years, this method has been successfully applied to stellar mass BHs (e.g., {{cite:6ffd611cedfd6ff8324bb63f846b42decf5c0e2f}}, {{cite:677435eebc1587f486b89579e095675941c0b4df}}) and to
ultraluminous X-ray sources (e.g., {{cite:579f091f2f03de27754f9d97de31b263387dff46}}, {{cite:418350bbcb8a00d7e8cb7c8ccb34ab7b505567d8}}), as well as to a handful of AGN that showed high spectral and temporal variability during deep X-ray exposures (e.g., {{cite:f3f61dcded87e51d113ec30b46531afdc87ef97d}}, {{cite:16beec91aaceca0cdd72c564fe110689dfc07c29}}, {{cite:c9a494e83e53cd5a1560324e85c0b62e8674decd}}.)
| m | 95ef71003c677ebdfd12460e13ab9e3d |
To investigate the effectiveness of HVT, we
compare our method with DeiT {{cite:11be2a1cceff55b98797a485e380eecb6a6deb08}} and a BERT-based pruning method PoWER-BERT {{cite:e0ccfdfb4cb2f09ba7db33636c08526a449c116e}}. DeiT is a representative Vision Transformer and PoWER progressively prunes unimportant tokens in pretrained BERT models for inference acceleration. Moreover, we
consider two architectures in DeiT for comparisons: HVT-Ti: HVT with the tiny setting. HVT-S: HVT with the small setting. For convenience, we use “Architecture-{{formula:76f9b1fb-53df-4510-9923-bcae316a477b}} ” to represent our model with {{formula:46d7e884-8d26-4c8a-adf0-3d3656ea489a}} pooling stages, , HVT-S-1.
| m | 08942b07f2208c246ec5cc1b379961ed |
The linear TECs of the considered phases of ZnF{{formula:0a5f3e2b-ddc0-40fd-921f-55917ebabbb2}} and BeF{{formula:096d0b75-d4f3-4430-bed5-b61ada79f00f}} are calculated within the Grüneisen formalism following the procedure described
in Refs. [Gruneisen26v10,Barron80v29,Schelling03v68,Ding15v5,Gan15v92,Liu17v121,Liu18v154].
To compute the mode Grüneisen parameters we considered two types of symmetry-preserving deformations obtained by changing the in-plane ({{formula:57fe0341-3af4-41d0-b6a7-c61d8452ca8c}} )
or out-of-plane ({{formula:a4bb9f6c-3366-4b6a-9784-e4ad7ce0c856}} ) lattice parameters by {{formula:07f6d019-d357-4455-8863-f17054adee09}} . These deformations allow for the full utilization of the tetragonal or trigonal point-group
symmetry{{cite:d1d2ba55c1d7233e6bcf32291336d9072e36a1b5}} of the considered systems, which minimizes the required number of independent atomic displacements (i.e., number
of supercells) to calculate the phonon frequencies within the direct method{{cite:d91ac1a134fb801ad768a9f9801acb852fbd302f}}, {{cite:ee5431461f381946da8cb3b71f3d795139b51a35}}, {{cite:660b2070af82724a393fd46524108f185be9c022}}, {{cite:860abeb05e0a9f4ad9765f397350fb6cfe75e595}}, {{cite:d57db00c8bcc9f2e79ca4288c4c20686754cc953}}. The
amplitude of atomic displacements, from the corresponding equilibrium positions, is {{formula:221352a3-0f32-4a41-aa99-0237efa254b0}} Å. The supercell sizes are of
{{formula:3fb95503-0e06-4201-9ff1-0e4e6cf18fdb}} for ZnF{{formula:82446805-6499-49d9-a68e-f71f971b7b97}} , and {{formula:599bb3a5-a68a-4f4b-82db-feb07a3065de}} for the {{formula:e0b2d17b-679c-4427-8d6f-9ba4c1d2f0f5}} -quartz, {{formula:58fc859c-f46d-41db-accf-c73d8cd03a59}} -cristobalite, and {{formula:540fa9d6-ac83-406d-8b8c-93741bd265da}} -cristobalite phases of BeF{{formula:f2f8ebcf-6cf1-43e2-a00f-41370436fdc0}} . The adequacy of these
supercells have been checked by considering larger ones for each of these systems, and we found that such
actions do not alter appreciably our main results and conclusions. The determination of the linear TECs also requires the
elastic constants that may be obtained through fittings of energy versus strain curves{{cite:319fc32d352f4bacd4f1cab606a147dcc45947f9}}, {{cite:a77f5aa8ad38c997a378410197b8b11453f6015a}}. Specifically, these TECs at temperature {{formula:ada1077e-675a-446c-83ee-6367313001c7}} in the {{formula:a1bc0df1-3ef6-40ae-b853-66e68eba385f}} ({{formula:bcc7cc77-6779-4998-bdcf-8856103be517}} ) and {{formula:7810d31e-6ecf-4861-a63d-9646369c0c74}} ({{formula:85a57220-424c-4a2e-a826-01656c39fc58}} ) directions of the above systems are given by
{{formula:3fc9f07c-e602-4424-9b7d-f6d5840fd8c3}}
| m | d800e28c49859b08cca0be25228ac196 |
Via numerical simulations, we investigate the scaling and robustness
properties of our strategy for 1D lattice models. As a benchmark goal,
we aim to variationally prepare the ground state, {{formula:da325a7c-d419-4b51-9437-9ac9201b0ddf}} ,
of the Su-Schrieffer-Heeger (SSH) Hamiltonian {{cite:af374cd68570701e149011a7f913279e7b27a1a0}}, {{cite:a37ab84410d1b3b1f16268cfcda7e5b3aa9150de}}, {{cite:4b050e65b1069eb90c4ac015c563d57958ad522f}}
on ion qubits in a linear trap. Using only blue-detuned sideband optical
pulses {{cite:11a39de1ab99923d61bf14975e94c999603919e1}} as resource operations, we design
the variational circuit ansatz shown in Fig. REF , which
can efficiently realize Matrix Product States (MPS),
a class of tailored variational wavefunctions capable of accurately capturing
the equilibrium physics of many-body quantum systems in 1D {{cite:0d6deba79ec27ad8a2e43421a005596702a7e473}}, {{cite:9e131c3a5598753fb1d0fe79535760563cfee1e6}}.
This `QDB-MPS circuit' can incorporate various symmetries of the target
model for enhanced performance, including approximate translational
invariance in the bulk.
In this paper, we will show that our approach is scalable, as we can
approximate 1D ground states at saturating precision in the system
size {{formula:bad23383-bbca-4c74-8438-916a554a2b9a}} , without increasing the number of variational
parameters {{formula:9519e743-9cdc-4ee0-a208-9f3155654a78}} [see Fig. REF (a)].
Additionally, we compare the results from the QDB-MPS circuit with
other VQE strategies, still designed for trapped ion hardware, but using different sets of (coherent) entangling resources:
(i) site-filtered Mølmer-Sørensen gates
(ii) an analog quantum simulator of a long-range XXZ model {{cite:c7b090528543d1bd9c947b6fe7a6519b9d1bfaf2}}.
We evaluate the respective accuracies in terms of various figures of merit, including excitation energy, fidelity,
and two-point correlations.
We demonstrate that
our strategy can realize highly-accurate ground states even for QDB
initialized at finite temperatures. Finally, we show that the QDB-MPS
circuit can be up-scaled beyond the single-trap limit by being implemented
in modular ion traps {{cite:e3770374dd88f49c033824db61c65cba5802dab6}}, {{cite:e7b8bcb6e534f95ad80e074a1cdb870b3071af83}}. Overall, we
consider our strategy a viable, efficient route towards quantum state
preparation in ion traps as well as in other quantum platforms that
rely on QDBs, such as atom qubits coupled via photons in waveguides {{cite:762050503335ab007316188a8b6ad593185b3b13}}, {{cite:5f6d96c1b58f4790eb46afbaec7567b8099d3ad9}}
or cavities {{cite:a9f1872a0d2d0ebd3e1922b197dc58090c9d3a4e}}, {{cite:ba4787a3b25e5866136fa09a84a4da2f21fce99c}}, {{cite:98c720ec720780b42471b7d409147b5ccdfbee2f}}, {{cite:a0938542511344ffda0b87bc57a05a8c76d30c37}},
or superconducting qubits coupled by microwave resonators {{cite:f070ea44d1037b5feb81927d24ab2f9b34571c5f}}, {{cite:d46f53fa80767f3003243db4c84df0c729a59c38}}, {{cite:6fdff78642b8e91b1e6619dfbd198e20bbe85a1c}}, {{cite:80a42d54833ab59db32ccac8f355b3c06d43a556}}.
| i | 9be5133c3489a84f264fe8e09f4fecdd |
Deep neural networks achieve state-of-the-art performance in many tasks, , image classification, object detection, and instance segmentation, but they are vulnerable to adversarial attacks. A small perturbation that is imperceptible to humans can mislead a neural network's prediction {{cite:a943c97c01e0f4e82aa78d573f6a8c4a23d229fb}}, {{cite:0161159f6dfe2abf4eab9979e2d3313b8e2ebb80}}, {{cite:cf9754fbd1b72295afadcc20ffa8f9eeef85873e}}, {{cite:5a3347619331c535e3dc43019bb2e323eccfb973}}, {{cite:f07eac252923115a7c401ca72d09d4b87f46b3f4}}.
To mitigate this problem, Madry {{cite:1d1110e697e35e3a15b391764f5244bc26827852}} develop an effective framework to train robust neural networks. They formulate adversarial training as a robust optimization problem.
Specifically, they use projected gradient descent (PGD) to find the worst-case adversarial example near the original image and then minimize the loss at this point during training.
Networks trained under this framework achieve state-of-the-art robustness under many attacks {{cite:20336dcdc2dc6ff1c66865f2600a220000425491}}, {{cite:0773e179c4798644ed2081e19a3d84792507342d}}, {{cite:33445825b6f240f9725838fda13febe2a0eee3ee}}.
However, these networks are only emperically robust, but not verifiably robust. They become vulnerable when stronger attacks are presented {{cite:256b32c40c621b4bc03d71c93606200c9c00daf5}}, {{cite:73ed01deaa07288330900887942d15b6ab73339c}}, {{cite:6f532c4243ab69bb3393c4db876a50c1448087ce}}.
{{figure:f8351124-81c0-4a11-b323-4c75e47d177e}} | i | dcb230c3c34cb916e45b0e456e533280 |
Assumption is standard in the analysis of SGD-based methods and has been used in many relevant works {{cite:e8b058ec9aac0263f04fd25ffdc57df7f1100953}}, {{cite:ff3634bb2a8c11c49946ff35c4ec303a6c8f8d06}}, {{cite:946b24c7ef364393797133fa0f8081bc495afeb2}}, {{cite:f8fffec6f84c616db32c156fa853d4faf9289940}}, {{cite:d158708fe0656cb69947b5fe17f2678d9e2ffd29}}, {{cite:e1ceea13998e2f9edd7ad9615c9b8808bcd89b65}}, {{cite:9ad7e7e877ea03968c556b56da4476df4bc006de}}.
Since we perform updates using data batches, we also need to show the stochastic variance for the sampled batches. Recall that for simplicity; we assumed that all batch sizes are larger than {{formula:bec65066-2198-4f6e-9ced-d242249141e6}} , thus, we have:
{{formula:f40a76d8-7105-48d0-80a5-ca0223ed5744}}
| r | edc7ca0b53542ac62a02ae2f4d794153 |
Among the existing data structures for static all-pairs approximate shortest
paths, the approximate distance oracle of Thorup and Zwick {{cite:5c00d77d629fe94d5bd949182abecddcc0b10c88}}
stands out due to its amazing features.
Thorup and Zwick {{cite:5c00d77d629fe94d5bd949182abecddcc0b10c88}} showed that an
undirected graph can be preprocessed in sub-cubic time to build a data
structure of size {{formula:553622c6-6869-4437-a4b6-49c85324a12e}} for any {{formula:274cc1aa-f4a9-4deb-b92d-38d67c803e59}} . This data structure, despite
of its sub-quadratic size, is capable of reporting {{formula:5adfe138-ecf0-4fed-b834-fe1e74acc0f0}} -approximate
distance between any two vertices in {{formula:b6c88059-fa16-4676-844a-24bfa974b43c}} time
(and the corresponding approximate shortest path in optimal time), and hence
the name oracle. Moreover, the size-stretch trade off achieved by this
data structure is essentially optimal.
It is a very natural question to explore whether it is possible to design
all-pairs approximate distance oracle which may handle single vertex failure.
We show that it is indeed possible for unweighted graphs. For this purpose, we
suitably modify the approximate distance oracle of Thorup and Zwick
{{cite:5c00d77d629fe94d5bd949182abecddcc0b10c88}} using some new insights and our single source
data structure mentioned above. These modifications
make the approximate shortest-paths oracle of Thorup and Zwick handle vertex
failure easily, and (surprisingly) still preserving the old (optimal)
trade-off between the space and the stretch. For precise details, see
Theorem REF .
| r | 0b0a9c88e84ad8c30b120551440c3c42 |
[rgb]0,0,0Although VAD has been researched for years,
developing a model to detect anomalies in videos remains challenging, as it requires the model to understand the inherent differences between normal and abnormal events, especially anomalous events that are rare and vary substantially.
Previous works treat VAD as an unsupervised learning task {{cite:8856ad98eb15179baa5a459b14910a1dbabdb6e9}}, {{cite:ca37a17a8aa7ad029b532f81e85eed6b8b4402f6}}, {{cite:999070176f4a351a652929194eff225b22a16cee}}, {{cite:f6e0c7ede1ddf9e301a5f920ae90cedf4b7a09a9}}, {{cite:230f814922d1128709a34a3ba60fa0bb2979f413}}, {{cite:05c5a9fdb33f005e76a66bdc1945be781efa9b0c}}, {{cite:d7f5a63719ffb6a904ac5f57421a264a449c3063}} [rgb]0,0,0, which
[rgb]0.,0.,0 encodes the usual pattern with only normal training samples, and then detects the distinctive encoded patterns as anomalies.
Here, we aim to address the weakly supervised video anomaly detection (WS-VAD) problem {{cite:a5e347b737e293caa8967e2a557af75b243017d8}}, {{cite:69c061757987f83c92d87626c446cad9b268c708}}, {{cite:81a20768173a8046739090638661510f0132c860}}, {{cite:f0759694e27221678c525954a371474ba74c87ed}}, {{cite:f664080c61a78803bc078d1a280aaaa43263dba7}} [rgb]0,0, 0because obtaining video-level labels is more realistic and can produce more reliable results than unsupervised methods.
More specifically, existing methods in WS-VAD can be categorized into two classes,
encoder-agnostic and encoder-based methods.
| i | 954cbadfdc473e64494c9cea24ccb54b |
With this lemma in hand, we now prove the theorem.
Let {{formula:884360ff-7d3b-4ba7-a116-ef0c74ff9960}} be a structure that is preserved by
{{formula:53db10b5-0eee-4bcf-8644-4da60f9ccb38}} or by {{formula:6557790d-15e5-4ad1-8213-9fdce2141a78}} .
We now present an algorithm for {{formula:f671c44c-5ec5-4cba-a9a0-55c022a0fd45}} .
For the sake of notation, we assume that the input instance is of the
form
{{formula:349ab3a5-5e75-4aa4-88bd-39776b98b15b}} ,
that is, it exhibits a strict alternation between the two quantifier
types. The result for the general case can be obtained, for example,
by considering an algorithm that inserts dummy variables/quantifiers into an
arbitrary instance of {{formula:40ec2a3b-88fc-4de3-87b6-ab06c59a3abb}} to massage it into the described
form, and then passes to the algorithm that we describe.
We make use of the fact
that CSP{{formula:32c132cb-0d83-4ff5-b77d-c9faad2045cb}} can be decided by the algorithms given in {{cite:36757ecbf607738f9da4635be2c0f792afe57be8}};
indeed, those algorithms describe how to compute satisfying
assignments in the event that they exist.
{{figure:a50e28ec-aea6-47c5-8f43-875c0586fa14}} | r | b5032c46e85a8eec4d1fa68e62edb1f5 |
The values of {{formula:32e029f1-c019-41b1-972d-85d41d22edd7}} are given by {{cite:e86a1e15635751f62034f303fe5edd68ff9ece2c}}
{{formula:b6e43157-3270-4423-afd0-c2ec919bac9b}}
| r | 7413ee6e584e12f7746ef93ea58a0916 |
The simulations in our scenario analyses show behaviour comparable to Cambodia with parameters consistent with literature and expert elicitation. Many of the model parameters are location-specific such as the bite rate, relative infectiousness of asymptomatic carriers, probability of death from radical cure and the initial model state. In the future, we aim to provide a statistical framework for fitting this model, so that it may be applied in contexts where parameters may differ. The complexity of the multi-species model poses a challenge to jointly fitting all model parameters because of the high dimension of the parameter space and the run time, which was on the scale of minutes. Optimised approximate Bayesian inference methods such as Bayesian Optimization for Likelihood-Free Inference (BOFLI) and Likelihood-Free Inference by Ratio Estimation (LFIRE) may provide solutions to both of these challenges {{cite:4eea9f3f0cd62e17ab709d28fb157b05ab7767f4}}, {{cite:5535fed2ae9bcaa633f46114939cd50ef5fc858c}}. If the run time of the stochastic model becomes prohibitive for inference, as may be the case when applied to larger populations with high prevalence (where capturing small fluctuations in low numbers is less important), a deterministic or hybrid model equivalent could be applied instead.
| d | 1501dd33cae1c6fa7e19ca982c1dc19e |
For the first-principles study of NbAs slabs, we construct films of (001) orientation to allow direct comparison of our computed Fermi surfaces with the available ARPES results, which have been experimentally measured for the cleaved (001) surfaces {{cite:5c88802344db6db32a54c7db1f0c84c4b1d720a3}}, {{cite:6c7e26ebb3eda6313ac741d732f2cefe7fdaa29c}}.
These slabs have tetragonal unit cells, and are constructed with a vacuum spacing of {{formula:7753d356-5b91-4d70-a748-c2865d6aa815}} thickness along the {{formula:2ff9c006-22d4-4b96-b0c3-a4ef2f1fcf72}} direction, employing Coulomb truncation to eliminate long-range interactions between periodic images along this direction {{cite:8e9b7f981d84bee08df6dd83c79159d9bba72557}}, {{cite:c22d2c4608040003e59086759abe9792a77db127}}, {{cite:63310345c9880cab1398241aab468c51062a2aad}}.
Cleaving the surface along (001) direction leads to two asymmetric surfaces with Nb and As terminations respectively (Figure REF (a)), which produces an overall dipole moment in the unit cell.
Figure S2 shows that the Coulomb truncation scheme accounts for this dipole correctly and produces zero electric field in the vacuum region away from both surfaces.
| m | 66cd09fbe84488af5ca5cbaab8d8d03f |
The results of the six transfer tasks of the ImageCLEF-DA dataset are shown in Table REF . Although the number of images in each subdomain in the ImageCLEF-DA dataset is similar, it is still challenging for the transfer task because of the images from various scenarios. Compared to ResNet-50, which only utilizes source domain samples for fine-tuning, the above-mentioned domain adaptation method achieves significant effect. Compared with other methods, the method in this article has achieved significant improvement.
The CAT method also adopts the idea of semi-supervised learning, but it only adopts the Pi-model {{cite:afc3ea31e0dfc95277935252eb4351289327f441}} prediction ensembling method, and we utilize model ensembling, which is more effective. This also proves that the student-teacher model of REN can learn more transferable features.
{{table:80a8c22d-cfac-4438-ae00-b92ee99ea19a}}{{table:4711d761-8078-4e38-b607-0b89d63ec91b}} | r | c846b4c467fa801c26e5f30f71bd840e |
Fully supervised: train the deep learner only on the annotated data, as a fully supervised task.
Semi-supervised by transfer learning: create a representation of the data by training with a self-supervised task on the unlabeled data, then train a simple model on the ensuing representation in a supervised manner. This framework is intended to capture the basic benefits of semi-supervised learning, regardless of the added benefits provided by the sophistication of modern semi-supervised learning methods.
Fully semi-supervised: train a semi-supervised model on both the annotated and unlabeled data using FlexMatch {{cite:5b36d3050fa63c01929efc2123cadacee50b05ee}}.
| m | 1e5e25af8b0b510202f233c0e146e945 |
1. The one-dimensional GLL equation with pseudoscalar {{formula:1bdbf46d-2f3a-400a-bce9-97042d00fdbf}} -function potential is reduced to the Schrödinger
equation with an effective {{formula:d00c3a36-e83f-452e-a1ba-613ba1566b73}} -function potential the coupling constant of which depends on both the energy of the Fermi particle and its rest energy. The energy dependence of the effective potential appears here in the same way as in the case of the Dirac equation reduced to the Pauli-Schrödinger one {{cite:01ff35badf8c68f88da9260118b97ab1ce8ea899}},{{cite:6d0a783f64c5f448f8080e6dedaa1d4486805f97}}.
| d | 55af15153c9fbae4540c5e292b549168 |
where {{formula:a5267655-d964-4cdc-a927-d6663b675f6b}} .
Importantly, the advantage function {{formula:5202a4f0-104f-44aa-bf54-fabef484948f}} appearing in (REF ) is the average-reward advantage function, defined as the bias minus the action-bias, and not the discounted advantage function. The constraint set {{formula:157cee91-e5b3-4333-ba19-2520958ea1ea}} is called the trust region set. The problem (REF ) can be regarded as an average reward variant of the trust region problem from {{cite:1b2e5381ce77a558848bfbe6093668f9a59b6c4a}}. The step-size {{formula:26429071-6cf1-46b4-94c8-c62613a67489}} is treated as a hyperparamter in practice and should ideally be tuned for each specific task. However we note that in the average reward, the choice of step-size is related to the mixing time of the underlying Markov chain (since it is related to the multiplicative factor {{formula:2972e252-7785-4b47-9f02-a55573c0d8a7}} in Theorem REF ). When the mixing time is small, a larger step-size can be chosen and vice versa. While it is impractical to calculate the optimal step-size, in certain applications domain knowledge on the mixing time can be used to serve as a guide for tuning {{formula:7c135616-fa1e-42f3-8a37-c3780003bc2d}} .
| m | ffbd4d9feece651958bf2f224193de77 |
There are three different approaches described in {{cite:0bb0be00d94e56be64669f18b3f159bdc5897676}} to deal with the hierarchical classification problem:
| m | 315246935233f0ba84d1e5c6f12a3959 |
In {{cite:f44cc1fa0fd4071007ec65a19b67a23d0850732a}}, the authors present a new method, ESPIRiT, for sensitivity map estimation using the SVD of the calibration matrix. The approach is combined with regularized least-squares reconstruction ideas and is shown to offer similar performance to GRAPPA {{cite:b75072180d542cb4d80ab380052cc9fce86c80f4}} on in vivo (e.g., brain and knee) images. The proposed sensitivity map estimations are shown to be accurate up to absolute value for varying levels of measurement noise, but do not encode the phase sensitivities accurately (the phase is selected at random). Absolute phase estimation has more recently been addressed in {{cite:d472a60e2106c94cf8844bc96bdb3174c2748ea9}}, where the authors introduce a new post-processing step to explicitly calculate the coil sensitivities that include the absolute phase of the image.
| i | d24d311d3aaadfb0d7e31451fd00b29c |
Remark 1.5 The uniqueness of the discrete uniformization factor was proved by Thurston {{cite:316b4c29d051710434b214fb8afd86415ba72cef}} in terms of the rigidity of circle packing metrics with respect to the discrete curvature.
The existence of arbitrarily dense, {{formula:eaad225a-ca99-476b-862f-e1751afab02b}} -regular, and uniform geodesic triangulations on any {{formula:56c8dcdc-9872-4329-b892-bca9ad36a890}} can be deduced from the work by Colin de Verdiere {{cite:485e10091ef14432f0ef80b734b91c5e51d6fe42}}. It provides a family of geodesic triangulations on any Riemannian torus whose angles of triangles are arbitrarily closed to {{formula:22175d75-129b-4552-a092-a44fce4c8b0c}} and sizes tend to zero.
| r | 86255520965fad10d23825e9f57f789a |
In Kalman's celebrated paper with Bucy, it is shown that the problem
of minimum variance estimation is dual to a deterministic optimal
control problem {{cite:d684ad28078f0be3315db6bf05dbb07e24adb7d3}}. Duality offers a constructive proof technique to
derive the Kalman filter equation from the optimal control solution {{cite:25f8a784da196be3e8debd91d52c6a1793921d08}}. Apart from the formulation's aesthetic appeal to
control theorists and aficionados of variational techniques, the proof
helps explain why, with the time arrow reversed, the covariance
update equation of the Kalman filter is the same as the dynamic Riccati
equation (DRE) of optimal control. Given this, two natural
questions are: (i) What is the dual optimal control problem for the
nonlinear filter? and (ii) Can the equation of the nonlinear filter
be derived from the solution of an optimal control problem? These
questions are answered in this paper.
| i | 8763df14bc88bd163b35f4f87bd682fb |
One promising testing ground are Weyl- or Dirac-semimetals {{cite:155f5c2f6dbf7ef8ab2a6bfe7816a3c5ecd9151d}}, {{cite:ca4ebca1888bce282602d1237142929a6175adc3}}, {{cite:a8a05a63564dabeb9a62f39a43c65a96bb1b29b4}}, {{cite:45130bf0375aaaf78f06df6d1488208e9af265e1}}, {{cite:c68bcf42b1618c8f3ed77646a841c61f3d0a34b1}}, {{cite:6813b200b2f80ef0312945d037b8b41aeb68bd51}}, {{cite:6d3fc347fb640cb94934b264f69920107d118d01}}.
A quantum Hall effective action for the anisotropic Dirac semimetal is discussed in {{cite:adab37a51751066824e5a1c815103772014d8c6d}}.
Experiments with Weyl semimetals report the observation of chiral transport effects in presence of magnetic fields {{cite:b68fa95518dfc5921a9da3a5284421de5d19c151}}, {{cite:57306b33ea350c544ea366dd6eeafcf6c5bcc634}}, {{cite:82182dcfc4f411ae904c99ca3dd954d889735914}}, {{cite:a4218e1c2dcb4638370eb83b8c681473a3d9e424}}, {{cite:592ad935e8c92fcb94db4428bb953e355f433e9c}}.
In these experiments, the relevant observable is the negative magnetoresistance.
However, note that negative magnetoresistance cannot unambigously be related to the presence of a chiral anomaly (see e.g. the holographic computations in {{cite:269051f6de241e1e44281fc49d1f09097b9bdf1f}}, {{cite:d3540b2c5966ac6d8b30c44dfd098d0e7d4a0623}}).It is not yet clear if Weyl- or Dirac-semimetals are governed by strong correlations. Thus an exploration from the strongly-interacting perspective is rather interesting.
The interplay between external magnetic fields and a chiral anomaly within holographic models of Weyl-semimetals is discussed in {{cite:c81f3871567df0b152d036648c5cd26120b6cf12}}, {{cite:0bc5405a92a6de26df82bd305ebdedfbec2ec3b7}}, {{cite:addc16d848a3827b5ea92c693baddf0f7aaa908e}}, {{cite:00fc791564daf4fc68dc9046c4c59b58eff5c480}}, {{cite:9fdfca4505ba440ea8701ec23c3406f9325d237e}}, {{cite:be30a05b92323ab50e8e79a1c287db0ed8a6a84d}}.
Hydrodynamic behavior has been measured most reliably or has been theoretically argued for in (2+1)-dimensional materials {{cite:1943b10362912feb1b06cf135876d6885d5f159e}}, {{cite:b9f3e1dda5cd4cc30d4ba6252504e0cb4bbcf624}}, {{cite:f3d4eba6526feaee2f368664f56eecc84172ac2c}} where the parity anomaly leads to anomalous transport effects {{cite:8a88942aba06dfa1627be2e84313012f633a3e75}}, {{cite:e8f6ac747090512aa5a19e53fd41fe2a752f529e}}, {{cite:f2db579b57c640ad4949dba844175159be8cc487}}, {{cite:b06f89b40b11df437d12f8f268b0e335201f7a5b}}, {{cite:4e74bf6a09173ec386f9d6a8b53d2038b3b16ef2}}.
Our discussion of (2+1)-dimensional hydrodynamics in section REF will help relating our (3+1)-dimensional hydrodynamic transport effects to these lower dimensional experiments and theoretical descriptions.
| d | 9ba453e71c605a407b8c42ff5de72fe4 |
Our MAE pre-training, using only IN1K, can generalize better: the gain over training from scratch is bigger for higher-capacity models. It follows a trend similar to the JFT-300M supervised pre-training in {{cite:aa9a21fdd6868296cede97d8e26669e20b47502b}}. This comparison shows that our MAE can help scale up model sizes.
{{figure:038f13c1-f029-488b-9fc9-dc78e35ada1f}} | r | 954d1dc3b980ea1ef3d9d89e37de2292 |
In Fig. REF and Fig. REF , qualitative results of ReSTR on the Gref dataset are presented.
Pixel-level predictions and the results post-processed with DenseCRF {{cite:1ddb314b4d2a8030cbf95a4202738a4861e86597}} are provided together.
The results show that ReSTR successfully segments masks of the target entities described in various language expressions.
For example, ReSTR predicts accurate masks for language expressions about non-human objects (Fig. REF ), partially appeared objects (rows 1-3 in Fig. REF ), and occluded objects (rows 5-7 in Fig. REF ).
Moreover, the qualitative results of the pixel-level prediction show that the segmentation decoder of ReSTR produces the fine-grained prediction as well as removes false positives in the patch-level prediction.
As shown in Fig. REF , we also present more qualitative results of ReSTR according to varying language expressions for each image.
The results show that ReSTR can comprehend various types of objects (rows 1-2 in Fig. REF ), a sense of locality (rows 3-4 in Fig. REF ), and fine-grained details (row 5 in Fig. REF ).
| r | be75d7a1cbcb36c152fe79a201f985db |
Within the DEM formalism, there are various kinds of contact laws to determine the contact force {{formula:74663b6a-e45a-44e9-ad9e-35eee80d5dde}} . One of the most widely used models is the linear spring dashpot model introduced by Cundall and Strack {{cite:ab5f0f1e2f378e0647a800a51af65ecccc39716a}}. The normal component of {{formula:3ceada3a-a6e6-40d0-a96a-fd2585124252}} between particle {{formula:f40edec5-4a07-447a-80ba-fefa779de12f}} and {{formula:1d4365d6-6f0f-42af-b474-ee099f6c69c3}} is given by:
{{formula:634fd30a-5500-41ec-816c-3a3719e4bf60}}
| m | 9e8f4d7cc90afce6b7262449cb5add3e |
Self-supervised methods have emerged as a promising approach to achieving appealing results in various applications without requiring labeled examples. This is typically done via pretext tasks closely related to the downstream tasks of interest and typically differs from domain to domain. For example, in the image domain colorization {{cite:ff049a6ca1832689a6f5e6c92c6441c54a76fcd3}}, jigsaw puzzle{{cite:f9ff4410599951bda8f6d698654e4f91db5a3af2}}, rotation prediction {{cite:d746990d7e21a8e0a2b53bb23a5b922607ab89e8}} have been previously presented as pretext tasks useful for learning such representations. Similarly, in the text domain, commonly used pretext tasks, such as predicting masked words and context words, have been widely used {{cite:c855a84b1947eb27170d7cc6a83a5eb57ec76c0d}}, {{cite:c188e5f9e3163890251bfa44ed93d27d7b4801d7}}. More recently, contrastive learning methods introduced leverage domain specific transformations to create multiple semantically similar examples such as random cropping or flipping for images that preserve the semantic meaning and encourage the network to be invariant to such transformations achieving great success. Such pretext tasks and transformations cannot be readily applied that do not have the same structural information, as an example tabular dataTabular data contains a set of rows (examples) and columns (features) that may be permutation invariant..
| i | 9dff56ba4cefb30374b84fa83ee3a5e2 |
Another important question is how to calculate {{formula:739feb08-f89b-4fd2-83ce-fc421aa30e79}} for general assemblages: a big result here would be to classify for which assemblages the steering weight gives the optimal value, since this is easily calculable. This question is a direct analogy to asking when the “fully entangled fraction" {{cite:0610800fb5a419f41c1df11aee40ee823b82d29b}} of a state equals its entanglement of formation.
| d | b75607ceea2f00094bc5a911fc2fddac |
Much of the current interest in Majorana particles is focused towards quasiparticle excitations in condensed matter physics (e.g. {{cite:694363cf62290352d6b612128f295541ad1917f0}}, {{cite:e60c10f0a674ee48399f3f7a25007d328ad42f4d}}, {{cite:1e23364867e838bdd9382b08744747de3d5cdf8d}}, {{cite:4c54a3dbd8fb145796c814a6bfb24cd3931daee1}}, {{cite:17d9ed5dbd60764e2e08e621cfc2f810d4265b45}}, especially associated with topologically protected edge state modes.
Photonic analogues of various of these have been proposed (e.g. {{cite:04e587c910d35b87072bcaf0c8b7634415dfa5d2}}, {{cite:474c2615b24c552aec7aab9b21bf7cce17c09330}}, {{cite:a61f866cfccc1b710b96aae716b35f2866b6d6c3}}, {{cite:a77a506565026b5bbb48aae3df22ef5d0cf48299}}).
It would potentially be interesting to take the case of the optical Majorana equation into materials and interfaces, especially as the natural {{formula:3fa9e4f0-2df7-4077-91db-e9e7956b3314}} and {{formula:223a1480-30dd-47e3-96ef-7ba4698b0098}} polarisations associated with reflection and refraction at the edges of dielectric materials are linear polarisations, i.e. Majorana-like states.
The true exotic nature of Majorana particles—their Majorana mass—may yet arise in an interpretation of the behavior of light in a suitable medium.
| d | 13931722084984aaaeef0ffbe140bacb |
All experiments were carried out using the Python programming language with standard Python libraries Pytorch {{cite:a44ace4973b41afa5b6ebad3f100b368e7d5bd22}} and scikit-learn. Before describing the experiments in detail, we first describe the evaluation measures and comparative approaches used.
| r | 0a6ac045d23285a4282274d85b80d1ec |
Given the recent discussion in the field about label quality in datasets {{cite:6ab303cc2c824d5248b1d123dace4b688ca13ea2}} and the "success" that crowd-based re-annotation had for the FER+ dataset, here we presented results of re-annotation experiments on the popular AffectNet dataset.
| d | 9f7a6387462cbdaff1d6f2e28ad5612e |
{{cite:96d8838b6e4a3de91756c1fc5d0c7cd2fc20224c}} and {{cite:704e63742fddf1c01e6d9160181df95087b1f395}}
challenged the usefulness of statistical confounder selection (without
structural knowledge) and suggested that other modern techniques such
as regularization and model averaging are more suitable than variable
selection. The same philosophy underlies influence-function-based
causal effect estimators such as the targeted maximum likelihood
estimation {{cite:8010a7e859965edd269ca05b49a60994fb71c01d}} and double machine learning
{{cite:aff42a64bca45e728b5da7d662cb433c4ca52328}}. In view
of the secondary objectives in sec:object-conf-select, this
criticism is reasonable if we assume the full set {{formula:4ce15701-0e94-4f62-b745-c97c1bea1270}} already controls
for confounding, because statistical confounder selection simplifies the
final estimator (especially if one uses matching-based methods) at the cost of
sacrificing robustness or stability. That being said, statistical variable
selection could still be useful in other scenarios by complementing partial structural knowledge.
| d | be2508e2b2ae39045ae33af145240218 |
Distance Metric We consider three distance metrics for the nearest-neighbor matching is Sec. REF , which are cosine distance {{cite:ba746deef6fcc0a3dd0995616c994ea589af3d5d}}, Euclidean distance {{cite:1f8a630f273b158d3da2da0d072a5f8b0996ba8d}}, and earth mover's distance {{cite:24358def0d322cec6c5173bb333738edfb775b7d}} (computed with Sinkhorn-Knopp algorithm {{cite:319ead0e379d36d797b7f3f495b438b6041c2d87}}). We choose the cosine distance based on its empirical robustness. It achieves an average F-1 score over the UCs of 0.67, while the Euclidean distance obtains 0.6 and the earth mover's distance obtains 0.43.
{{table:31bff193-85b4-40eb-89cf-d5969b28ca84}}{{table:1f59f55e-1d69-46af-9e1d-04582cc2d64b}} | r | 5c3598e966e492ef127a1be1225e35e7 |
The Alternating Direction Method of Multipliers (ADMM) algorithm {{cite:fa6286b0d5d2c62b2bd28d1a453ca84b87b00704}} is designed to solve problems of the form
{{formula:46a4bcd6-745e-408e-b338-d5e06346f337}}
| m | ef704e9e7ae5d4513afbef95687725cb |
In contrast, all the indices of the 3-fold state change continuously but largely in Fig.REF , where {{formula:34e0c838-1db5-4e39-b6b4-405ea96737d0}} decreases from 490 to 0 in segment B.
The index for the degree of nonaxisymmetry, {{formula:0898d925-63f6-4175-a9b1-314b4edc3580}} , monotonically increases after being annihilated around {{formula:3fd9fecb-d88e-4570-b077-53529e18a687}} with {{formula:da1a8f3a-45fb-451d-918e-ab8778ede313}} decreasing in segment B.
The transient decrease in {{formula:2ac5b5d6-5012-4d65-8d2e-b8789449d712}} at {{formula:738ac7ba-611b-4e39-87bc-aa1cbf7e344c}} suggests that segment B passes through the neutral curve, {{formula:dc323683-af0d-4a1e-a7f7-ae124c60cbdc}} .
Note that the denominator of {{formula:295a4539-ad7a-4d31-8acf-bc4a9c260fc2}} is proportional to the strength of the Stokes flow; that is, {{formula:aeaed662-3fea-41c2-81ae-39a148853edc}} .
Thus, the divergence of {{formula:c75f700b-6a8a-4a79-83e5-ce8b9239badf}} to infinity at {{formula:73a9b560-a381-498a-b081-1b5c4754dd98}} in segment B implies that the numerator of {{formula:12ada02b-1518-4605-b1ff-ce17d6809497}} converges to a nonzero value in the limit of {{formula:380319fe-aa73-4f34-82c1-3b7406deb815}} .
This is not surprising because a variety of non-axisymmetric equilibrium states {{cite:19cc79493ceb19661ff9addc29fc1c5db7b08d0b}}, {{cite:b40bf69f8aafe0b9d77c30ee1d881651c09802fe}}, {{cite:c040bfc51e1806afaf171ce337b41c09b6b252a4}} can be realized in the purely thermal convective state, {{formula:cdb96e26-3244-4a4f-a41d-0bb0c2cec15a}} .
| d | 313614e1e99c1728b2bae726a5745ee8 |
One of the ultimate goals of Video Question Answering (VideoQA) systems is to assist people in solving problems in everyday life {{cite:36dea1c47f516c72645abbf3516124abfabfc03e}}, {{cite:dc663357b9787043490cfc014cf086e36da10af2}}, {{cite:f123215a4b883f4f8b326a95082db86ded8548d9}}, e.g., helping users find something, reminding them what they did, and assisting them while accomplishing complex tasks, etc. To achieve such functions, the systems should be able to understand and seek the answer from long-form videos with diverse events about users' activities.
{{figure:47aca636-aa7a-489b-b011-317c2c3d9f25}} | i | a81c2b072cfff6169c2ad5f39bdc92b8 |
Unfortunately, to the best of our knowledge, there exists no holistic solution to reliably estimate the confidence score for the task of document information extraction. Current confidence score approaches are either generic methods verified only for simple image classification tasks {{cite:aad1b007dc5a7f2022ebfcb3c652bb2b9cde9088}} or applied only for part of the information extraction process {{cite:e88bfcb3d598ee44704dc623c0dc0b11393c1c74}}.
| i | 9a02b2ccf370b6bb220bf7faf53767c4 |
NĂśrlund's logarithmic means with respect to the trigonometric system was
studied by Tkebuchava {{cite:5121adabc4da655bdddd201a52f27d7d66e2dae7}}, {{cite:56d92ad0545d0b4ba8f206d64d365cf0ddee3771}}. The convergence
and divergence of this means with respect to the Walsh systems was discussed
in {{cite:3fbba0d92312fe89fe8e94631e5714a34468b9da}}, {{cite:13a80c48511e69510626f7b9586e338f73996317}}, {{cite:05e0c943b92245d37d1ab5e06529d97ce830194a}}, {{cite:f4f46b8cb03218350d9d58300471876fc13645d8}}. Since
{{formula:ec357bad-91bb-43e9-bfdf-35c52eb36398}}
| m | 2e176331a4439256a23b0cf422dac572 |
For comparison with other representation types and encoders, we use MeshCNN {{cite:1c06d411f5a793c2d065a28f901eaf1cf78367f1}} for meshes, and Pointnet++ {{cite:714ef83309ef50778717af0ae9a58354266e165a}} for point clouds. We use Pointnet++ over DGCNN {{cite:9a68b86795621a8280ca38374bb7210ebaaadcf7}} or Pointnet {{cite:43cb72f7e6f3872bcabfe1959ac91105300e2bb0}} since we are drawing upon 2D style literature. DGCNN aggregates intermediate layer activations according to locality in feature space rather than coordinate space, and Pointnet does not perform hierarchical pooling, thus Pointnet++ is a closer point cloud generalization of the 2D CNN approach used in {{cite:3d4bce519ab38a33145ff8cab967433ac4371457}}. In mesh and point cloud representations, there is no information regarding local grouping of samples, thus it is not possible to apply face-wise re-centering, so we use instance normalization for the extracted activations throughout.
| r | 6399c0e12c2d6eb4c9e91ae976b9e61a |
The offline coreset construction of {{cite:d1feb532c217d949d7c53d727c1dc39fb4745123}} has the following structure: first, a bicriterion approximation is computed. Second, points are sampled according a distribution that depends only on the distances between points of the input and their assigned bicriterion centers.
This suggests a two-pass streaming algorithm (which we later combine into a single pass): in the first pass, construct a bicriterion using an algorithm such as {{cite:000b8d06a017013aa77ad96e61f3c595b1f39655}}. In the second pass, sample according to the bicriterion found in the first pass.
This provides a two-pass algorithm for a coreset using {{formula:6f302ddd-51db-4d3a-9815-9bee7cb5be65}} -space. Our contribution is showing how these two passes can be combined into a single-pass. Using the algorithm of {{cite:000b8d06a017013aa77ad96e61f3c595b1f39655}} to output {{formula:194ba6c4-e74e-4421-9d17-20f17ae79d5e}} centers at any time, we show that this is sufficient to carry out the sampling (originally in the second pass) in parallel without re-reading the stream.
Our main lemma (Lemma REF ) shows that the bicriterion, rather than just providing “central” points to concentrate the sampling, actually can be thought of as a proof of the importance of points for the coreset (technically, a bound on the “sensitivity” that we define at the beginning of Section ). Moreover, the importance of points is non-increasing as the stream progresses, so we can maintain a sample in the streaming setting without using any additional space.
| r | 87388aac919a4efa7ef9a434dec84b3b |
In Table REF ,
we show the domain generalisation results on the three benchmark datasets.
The baselines are divided into two groups: non-causality-based methods
(from DeepAll {{cite:af238ec5fa9fc085c7f2e44685d073dc1e128e76}} to FACT {{cite:9e346b2bf4aa54db150ce83cb3b204e8b5acaf94}}),
and causality-based methods (from MatchDG {{cite:26b1ca793136c8d2914bb293dce34a02d87de0fa}}
to CIRL {{cite:431f24a26ea8ac2f8ad60920bbff628fbbd6e1f2}}).
{{figure:e12d2835-13fa-4f8e-bce7-cab9643d1005}} | r | 68b48e1e8af471e301654a23cc34bcf2 |
Robustness to input corruptions. In this experiment, we investigate the robustness of DDPM-based representations. First, we learn pixel classifiers on the clean images using the DDPM and SwAV representations on the Bedroom-28 and Horse-21 datasets. Then, 18 diverse corruption types, adopted from {{cite:b66b9a65f37f7f215f3261ce6c601218b2672f37}}, are applied to test images. Each corruption has five levels of severity. In Figure REF , we provide mean IoUs computed over all corruption types for 1, 3, 5 levels of severity, denoted as “weak”, “medium” and “strong”, respectively.
| d | 8b5a8155afe4fb7af06e607adf40d7b6 |
Latent structure. We also envision extending the sing algorithm to learn the
structure of graphical models with latent variables and partial observations. For Gaussian
distributions, {{cite:e31db3355c5a5b5e0438fd775e5bbadcf1aed744}} proposes a penalized maximum likelihood approach to
identify a precision matrix with sparse and low-rank structure. A similar approach may explore other
properties of the conditional independence score matrix {{formula:5d322781-663a-4b96-9dbf-0ac33d712624}} , besides sparsity, to reveal hidden variables and multiscale structure in the target density.
| d | 2b7d2cb21319e3fd1ccf592544a7a795 |
We have chosen three data sets. The first is a small molecular water system in the liquid state {{cite:731461a8b7df6a039204bd84c2bcecb24b14e169}} containing 32 H{{formula:24d73319-6500-464e-bf53-fdcb654b410e}} O
and a single Hydronium ion. The system is a single time frame of a CPMD {{cite:2d14d955f8b271b7e55a755ba44dd77fd519c73c}} water
simulationhttp://www.theochem.ruhr-uni-bochum.de/ legacy.akohlmey/files/32spce-h3op-1ns.xyz. The second set contain microarray
transcript readings of adipocytes with accession information: GSE2508,
that employed the {{formula:5d675a4a-4788-49e3-98ae-125173787f59}} platform, describing 20 obese and lean men and women {{cite:62d62895f79b78735f7c1891e7fbddfe843c5e3f}}. The third data is the first
35000 MNIST digit images {{cite:6c3ff24bfe1303c33d0effc0deffe0af4ed2ce47}}http://yann.lecun.com/exdb/mnist/.
| m | 59468ecd5fc18ee31abac1fb3339bacb |
be the affine space whose coordinates are indexed by rays in {{formula:eeca5d7c-553d-4c94-8e9c-1331fd51781b}} . In {{cite:9535e92bc2dc796124b7436eb98dcbcfa7d4ce15}} and {{cite:badcd2d85f5612cf597b0355d112f1ba48178df6}}, Cox showed that every projective toric variety {{formula:828ab198-d6ac-4347-82a2-5cdce14de0f4}} is a GIT quotient of {{formula:71808d84-e052-4601-8677-51efbc9c3213}} by the diagonalizable group
{{formula:0a25daf9-7eea-458e-9d69-55942072cac2}}
| i | 81bfb0be2ea941b5a1c765ecb1d7a11a |
In this paper, we showed that an EF1+fPO allocation can be computed in pseudo-polynomial time, thus improving upon the result of Barman et al. {{cite:537939dc5f8f39d2fa03c27b7e8254522e093854}}. Our work also implies polynomial time algorithms for two special cases: (i) computing EF1+fPO allocation for {{formula:40837cb0-c2ab-48ce-9728-ca46a3c6f0c7}} -ary instances where {{formula:1d0c5dae-462b-454c-be6d-f2a2f792cd78}} is a constant, (ii) computing EF1+PO allocation when {{formula:1fd3041b-f7d4-45cb-82cb-46533f361d97}} (number of agents) is constant. Settling the complexity of the problem for general {{formula:4f58699d-55e2-4d38-b3ba-406b5231f685}} and {{formula:e4516251-be38-4bb5-84c6-d68eb6386648}} remains a challenging open problem. Our results extend to the fairness notions of EQ1 and weighted-EF1 as well. We showed that computing an EF1+PO allocation reduces to a problem in the complexity class PLS. Showing the membership of the problem of computing an EF1+fPO allocation in PLS is another open question. Finally, showing the existence of EF1+PO allocations for general additive instances of chores is another interesting research direction.
| d | ec7896208d5ecf0c75f16a22ea77004c |
Pre-trained language models are few-shot learners, i.e., GPT-3 {{cite:fd576c51b2137c774448cb84e739c56182777cb0}} that surprisingly perform generation tasks from a few examples without any further gradient updates. Although it lacks a rigorously theoretical proof, prompt learning inherits the few-shot
property {{cite:d2d87d5863e9b6be55011afe98c45df4f0387cb1}}, {{cite:05abbd12783ad7b93419d597c93940534776e300}}, {{cite:6d80153b71bd773028c709976f51d04a1f5dc6e7}}, {{cite:f36ce557caa75c4ebf78c9b68d4b93fcb7f51f0a}}. Commonly, this type of learning is considered to retrieve relevant knowledge from frozen language models, only tuning continuous prompts to quickly adapt to new tasks with very few examples.
| i | 1c7dbe236c4b836445927d4a1e81c4f9 |
By other hand, black holes are probably one of the most suitable objects in nature to test – at least theoretically – some features of quantum gravity. For example, logarithmic corrections to the area-entropy law seems to be a common characteristic shared by different proposals of quantum gravity {{cite:da4229ea9806116f8563b72e30857de8b8f85fe3}}, {{cite:5701c8d9cc4536badf82a34274fd641443fa02a6}}, {{cite:dc26e90e05e70f6c3fbca7c2f770af0dcf710c67}}.
| i | 36bf27d4dcbb6158ee6f5be8fd310d61 |
A key component of multi-object tracking techniques involves constructing newborn object tracks (i.e., track initialization).
In GNN, MHT and JPDA techniques, newborn objects are constructed directly from unassociated measurements using application specific procedures {{cite:e783f9da1d099c1b79bbaa72f0a1e22a2677414f}}, {{cite:2a6abacaa385212404c9a829b3c635cf3cfaf0d2}}.
In contrast, RFS trackers leverage concepts from FISST {{cite:4910f1d6047af4e85c21d436cabfb82bc0a5ec05}}, {{cite:f6e6cddd6e1a7ddb29e67ee73c0df3d4da2b2224}} to create multi-object prior distributions representing newborn objects.
For the PHD {{cite:2afbaeb54ddfb4bb79485837c7e9542a18d2c300}}, CPHD {{cite:8b23bd6d6dfcc491272c91aec5922cb22b912134}} and PMBM {{cite:53080744dc4a4201e8b7b50a9ebbeccded9b3ece}} filters, the multi-object prior is a Poisson RFS describing the average number of newborn objects and their joint spatial distribution.
For the LMB {{cite:6d7a241309b9ba4f1ad9f848493e9f01a901ab3d}}, {{cite:dfa336a2ff923c56215a3cd599345c88d5a2c14f}} and GLMB {{cite:268763d8d4eae538ed3c74fd2ef43f388a2a1727}}, {{cite:736c059ae63afdb1abb98beb4cb5ebea63c9a53b}}, {{cite:ef24ff31e0e5f9f7f0203ec074db5011c3b03a81}} filters, the multi-object prior is a LMB RFS representing tuples of birth probabilities and spatial distributions for each newborn object.
In a static birth strategy, the multi-object prior is fixed for the duration of a filter's runtime and encodes known prior information.
Static birth strategies are typically used when objects enter the surveillance volume in known predictable locations (e.g., air traffic control {{cite:717e1ced05056626f8d12c6afcb8cf4aa13dc409}}).
However, they do not include methods for re-acquiring dropped tracks.
In a measurement adaptive birth strategy, the multi-object prior is determined from measurements each time the filtering recursion is called.
This approach is effective in many applications since minimal prior information is known about where and how objects can appear in the surveillance volume.
Care must be taken when designing these strategies to ensure that tracker performance is maintained without adversely affecting computational complexity.
| i | c38bf9f0ed3e64af8fad6698f60ae4e9 |
Atrous/dilated convolutions {{cite:abd7c28ec60bf728672b3187d0315f413be405a8}} have successfully demonstrated capturing the spatial and contextual information, and simultaneously also reducing the computational complexity of deep CNNs with wider receptive fields. The popularity of atrous convolutions has led to its adoption in various efficient/mobile existing architectures like atrous spatial pyramid pooling, efficient spatial pyramid, etc. In our approach we utilize the benefits of using atrous convolutions too, but instead of applying aggressive parallel dilated convolution which might cause a loss in spatial information or aggressive series of dilated convolution, we propose a method which combines a parallel and series combination of atrous convolutional layers in network in network blocks.
| i | 21b68cd076b1d6f8ed7b4620dc9ccf04 |
To set our approach into broader perspective, we also shortly discuss limits with moving objects, like satellite-{{cite:27f90c5619402654a6da5ee1e0fd8457e0647147}}, {{cite:f17fe7ccb96d094143440ce40d76d4818cdc8457}} or emerging drone-based {{cite:2f6c997db7460d0c1841d9a1c3348838ea476018}}, {{cite:5e3d05a757c2b12a7d0e3c0a49ed433a241aa8af}} quantum communication. Satellites introduce an effective clock skew, due to the Doppler effect caused by varying distance to the observer. At the smallest distance is the clock skew zero and may increase to a maximum of 20 {{formula:6098206a-65fc-402d-bd4c-55108594920d}} s/s over a time scale of 6 min for low earth orbit satellites{{cite:71b10e76fa2449bc62e651b6d1fd6bda4176d44f}}. Whereas the maximum clock skew is comparable to our crystal oscillators, the clock acceleration {{formula:d57cc441-e152-4230-b42d-e775feb5826d}} is orders of magnitude bigger and amounts to approximately 55 ns/s{{formula:83f3b5d8-3b0c-48eb-981e-413c7f2b07fe}} . Thus, it is desirable to reduce the feedback and acquisition time to 100 ms or smaller that could result in clock drift jitters of 265 ps. However, with only a few correlation events per second{{cite:27f90c5619402654a6da5ee1e0fd8457e0647147}}, {{cite:db771f945bccc2e05cf61f775c8b628e1fd7e941}} available, it is impossible to choose acquisition times {{formula:20da8fe7-454d-46ca-b2d1-8700ac0caae9}} second. Ignoring noise, the absolute minimum would be to find at least a two correlation events. In conclusion, it is hardly feasible to correct for clock drifts without knowledge of the satellite's orbit. Drones move much slower than satellites and may be suited for synchronization – at least classically{{cite:7a0ed692215afdc3b150e7b65d4ac1017d1aae37}}. The speed is up to 30 m/s, introducing clock skews of up to 100 ns/s, being much smaller than the clock skew of our crystal oscillators. The main concern is acceleration of the drone, reaching up to 7 g (gravitational constant) and translating to 228 ns/s{{formula:eabc6309-94ff-4567-83fc-8818abf53787}} clock drift. Sufficient kcps coincidence rates{{cite:2f6c997db7460d0c1841d9a1c3348838ea476018}}, in contrast to satellite links, give opportunity to select short feedback cycles for compensation of high drifts during drone acceleration. With small feedback loops and enough signal, correlated photons open doors for live remote detection of velocity and acceleration of moving objects.
| d | 897d30d574af71ca3ba1b8223e174835 |
To address the CDFSC problem, numerous Domain Adaptation (DA) methods {{cite:cc82205a084e5b33292844499360804dc61b2240}}, {{cite:7c5e4d508b603ca9bfff302e45a37815c53b6afb}}, {{cite:e5d357b4384e77dabda54c0b60013253ab5b307a}} aiming at minimizing the impact of domain shift between the source and target domains are certainly helpful. blackRecently, many Multisource Domain Adaptation (MDA) methods have achieved great success by leveraging knowledge learned from multiple fully labeled source domains {{cite:6cfe2e852b7fc4a6a108b77382e039fb69365b1f}}. Inspired by blackthese contributions, black {{cite:c9787542bfde1d022e312383b05807faef596b8d}} proposed a multidomain benchmark for FSC. And {{cite:d3cd40b0143b190c9aa005e8caeefc1ef471e818}}, {{cite:88b48cbb9e6a8f664218d311e6e6c2b6d4fa0e25}} further propose the methods base on this benchmark. However, on the one hand, {{cite:c9787542bfde1d022e312383b05807faef596b8d}} is limited to natural images and art images, implying that methods designed in this benchmark {{cite:d3cd40b0143b190c9aa005e8caeefc1ef471e818}}, {{cite:88b48cbb9e6a8f664218d311e6e6c2b6d4fa0e25}} may not perform well when applies to other domains with types of satellite images, medical images, and so forth. On the other hand, in many realistic applications, obtaining lots of annotations even in the source domains can be costly. Therefore, rather than using multiple fully labeled source domains, this paper intend to explore a more generalized scenario where only one single source domain is fully labeled while the rest source domains remain fully unlabeled.
| i | d41664ac0df85607d75bb11867a1da2f |
Vertical shift in KIITI (Fig REF ) has high ID {{formula:aa8b9b20-4876-44a8-b1b8-ab63e28bf27a}} 187 whereas the normal data has ID {{formula:87273370-722b-48d3-b37e-5cf92f0854d5}} 84 at pool1 layer. It may be because of irrelevant features like filling of resized image with interpolation that attribute to increase in ID {{cite:18c30ec1d65eeeb1262ef812d9c39e91bc6a9791}} and due to original image size of KITTI being around 1200 x 350. When image is shifted vertically and empty pixels are filled by interpolation, the added pixels are irrelevant features to the network. Comparing with COCO and VOC (Fig REF & REF ) large difference between vertical shift and normal data is absent. Therefore, claim of increased ID can be confirmed due to aspect ratio 3:1 of KITTI images because in case of COCO and VOC the aspect ratio is close to 1:1. If the increase in shift was only due to filling of shifted image, it would be also present in horizontally shifted images. But the absence of increased ID in initial pooling layers for horizontal shift supports our claim.
| r | 4a1472e44d8180599846b4f8ed434986 |
For the sake of simplicity, in Eq. (REF ) and hereafter, we fix the lattice spacing {{formula:6ceea550-ed21-4816-a729-41f0b62caa95}} and the time step {{formula:13689bb3-225e-4e12-863f-c184cd1a52eb}} to one. The left-hand side of Eq. (REF ) rules the streaming of {{formula:3dacfc59-b3ba-4a14-afb2-c63b60277065}} on the lattice, while the right-hand side represents the collision term. This operator models the relaxation of {{formula:f838f684-a0d6-4e24-b60e-8bb96a0ce598}} towards the discretized local Maxwellian distribution {{formula:79f62a47-54a1-4ca7-933a-1a787d5cbcec}} with a relaxation time scale {{formula:a8f6a782-3e35-4701-b4f8-77a163feb615}} . The explicit shape of {{formula:193f47ab-3e8a-4ab9-8f52-1a64b9788fd9}} is given by {{cite:adbdffd4d89f024c4e22f603b6084d281f493b74}} (repeated indeces are summed up)
{{formula:3da00646-12dc-4ad8-8a13-c27803e4e28d}}
| m | 253fb9e5a72ec282f64f3c2d5cb80cc7 |
Here I will follow other studies (e.g., {{cite:720e5d303c16cf4e6be7bda05e19ff166d876f69}}, {{cite:0f1e7e6fb0c28862b9adfb7606096a9c99a068d7}}) that explore the relation between the direction of the jets' axis, i.e., the axis along the two opposite jets, and the kick velocity direction. These studies assume that two late opposite jets shaped some CCSN remnants (CCSNRs) that possess axisymmetrical morphologies, and take the jets' axis to be the line connecting the two opposite ears in some CCSNRs or the axis along the faint elongated inner part of the SNR. As well, I will follow {{cite:a16211b7e1436b1ff2b4f5b362a37fb19d76d98a}} and {{cite:749718be36c5dcdb4c300dc333ccc957598e4534}} in considering post-explosion accretion of mass with large amount of angular momentum onto the newly born NS. However, instead of considering the final spin of the NS as a result of this post-explosion accretion, I consider the role of this accretion in determining the power and direction of the final jet-launching episode.
| i | 616bb3143e38caf8021baf8d2e8a7288 |
We have proposed an extractor-paraphraser framework, which is inspired from the extractor-abstractor (EXT-ABS) framework introduced by {{cite:2343f909ace1effe15c4aae657e257645e2458cd}}. The summarization function {{formula:a60c5904-82d4-4fe6-8276-fc5bfa74ed3a}} is approximated as the composition, {{formula:e77c48e4-230c-4152-8186-d4936b88bc70}} , where the functions {{formula:c645a8ce-e4ce-4f01-bf70-b1223bee8a21}} and {{formula:3c6f018d-26e1-4c7f-a2d2-29b506801a24}} are modeled as the extractor and the paraphraser components of the model, respectively. Given an input document {{formula:3e4c4b24-2ef5-4f16-929d-1ac7bfc0e66b}} , the extractor {{formula:c870ed29-c1d6-4fd5-bbcb-bae2c1989665}} extracts relevant sentences, acting as the primary noise filter. These extracted set of sentences are fed to the paraphraser {{formula:778c0453-2cc3-4c5d-9528-483de0790852}} , which accumulates the information into a concise gist of the extracted sentences, simulating the natural language generation module in the proposed system (Fig. REF ).
The paraphraser in our system is capable of summarizing multiple extracted sentences to generate one sentence, in contrast with its predecessor `abstractor' from EXT-ABS model {{cite:2343f909ace1effe15c4aae657e257645e2458cd}} which rephrases one extracted sentence at a time. The proposed framework consists of an `n-to-one paraphraser', that compiles {{formula:e9604065-da57-4d81-8531-5a1d2f7b8c8b}} sentences into one sentence, generating a richer summary. Formally, given a document {{formula:e3c1ebcc-887f-4c3c-8109-94c0a7a09514}} , the extractor is defined as:
{{formula:d5cbf5ff-42d3-40ee-b4d5-330d6d76e667}}
| m | cc4d5e518936a0ac16d3e30917ab7891 |
A CNN with 16 layers was designed and trained to analyse the algorithm accordingly {{cite:b0d7196d1375138d9916b105c7ee02daecad9c5e}}. The network consisted of residual connections after every 4th block and used batch normalization to improve the understanding of the data. The network was deep enough to understand intricate details of data presented to it and was large enough to pair up with the deeper models such as inception and squeezenet. This custom designed neural network is referred to as "custom model" on the context here after.
| r | a7e2474c4c300c807df7d9a1f7e990dd |
Currently the neuromorphic hardware community grows fast and it is probably only a matter of time until new or updated hardware systems will emerge.
The field of applications is very broad for such hardware, including the estimation of linear models, like LASSO {{cite:44580d8bf1c099aecd462574517964868dcdd9c5}}, {{cite:e1ee7603c79bdd2bf0c27d88d474d27a86c1fe51}}, non-parametric classification with k-nearest neighbor {{cite:4cb02f3cd02f49c482b858cc4e77befd04e3d205}}, deep spiking neural network {{cite:e78627f98607fdd498001038d317e4f63078e4c4}} or reservoir networks {{cite:4f9389a69c9fbc6041cf7116a12cf004d336becd}}.
High-level libraries and frameworks are needed to cover these different specialized application areas.
While for deep spiking neural networks the SNN Toolbox {{cite:dcaf2f3d3837e2c7ad9f5f3e8653e0072abe85cd}}, {{cite:36aeaca514210a6832e0d4b1529498317e574a7f}} is available for ANN to SNN conversions (also for Loihi) or SLAYER is available for training SNNs via backpropagation, reservoir network frameworks are still rare for neuromorphic computing.
{{figure:8b7f9fa0-9fb4-4e36-a380-e63933f69826}} | d | ee4ef482a8dac2079e814ba1e0d8587c |
Section describes the Moffatt and Kimura (MK) model. This is followed by Sec. where the Hamiltonian structure of the MK model is given, which is essential for our analysis. Here we discover two constants of motion for the MK model. One invariant serves as the Hamiltonian for its noncanonical Hamiltonian formulation (flow on a Poisson manifold; see {{cite:07fa5fe05329c9916157e1b3991f6b18812905c6}}), while the other turns out to be a Casimir invariant. The Hamiltonian formulation allows us, in Sec. , to obtain geometrical intuition about the solution space by examining the intersection of the level sets of the two invariants, akin to the visualization afforded by the constancy of the energy and angular momentum magnitude for the Euler equations that describe the free rigid body.
Also in this section we show how to reduce the MK system to quadrature and obtain for special initial conditions explicit solutions that have exact Leray scaling, which is representative of the finite-time singularity. Conditions for singularity within the range of applicability of the derivation given in Refs. {{cite:6cf55e754f7cce67f3dc791bc16c979b927896ba}}, {{cite:1f467556ecf9732ea87ae403766d6b50f5c2a6a5}} are presented.
In Sec. we summarize our results and mention some future avenues. Appendices are provided that exhibit additional features of our results.
| i | 403fe427ccfd45d581254d6e3d6467e5 |
Our basic setup relies on Qgraf {{cite:6ac230308fa7faadb3c3b8fffb30b200294f909f}} and
Form {{cite:edeacebc140035805e33a9b9ae54454c709e7744}}, {{cite:ddbc12c90e58b797d28c16f63e0939a2bf338df8}}, {{cite:0d54a8747a591d482b8a8e2ad170dfd11903751b}},
employing the program Minos {{cite:96618c64e0c2b99cda2461497e34edccd27b2857}} as a diagram database
tool.
Many of the Form libraries we use have been employed in a
substantial number of earlier calculations, e.g., in
refs. {{cite:301f01ab0f23a6140f38befe7fef142062dcde95}}, {{cite:f726ba7381a889923c6babbb537690fbed5267dd}}, {{cite:74e8802852a623ceeffe7928e6cb888f24e2a073}}, {{cite:3213cb52edb5adfd0953f672ceccd2393df290af}}, {{cite:fcfe8561bad4d392ac4e6ea6a45dcad9d8fb2648}} and have been highly optimized for multi-loop perturbative
QCD calculations.
In a particular, as in refs. {{cite:74e8802852a623ceeffe7928e6cb888f24e2a073}}, {{cite:3213cb52edb5adfd0953f672ceccd2393df290af}}, the
database combines diagrams whose underlying graph topology is equivalent
and whose colour factors are the same. Such sets of diagrams lead to
faster evaluation times as they allow to realize algebraic cancellations
between the individual diagrams.
| m | 47cdeb205426653d613edf6c7caa0d7e |
Our results clearly show that the parametric statistical methods used for group fMRI analysis with the packages SPM, FSL and AFNI can produce FWE-corrected cluster p-values that are erroneous, being spuriously low and inflating statistical significance. This calls into question the validity of countless published fMRI studies based on parametric cluster-wise inference. It is important to stress that we have focused on inferences corrected for multiple comparisons in each group analysis, yet some 40% of a sample of 241 recent fMRI papers did not report correcting for multiple comparisons {{cite:3ec28795aceb67aa3f500f35daa8b717eb27fb9f}}, meaning that many group results in the fMRI literature suffer even worse false positive rates than found here {{cite:b942cdae272d1c5fc0eb25595011041a33eef9e7}}. A possible explanation for the lack of multiple comparison correction is that the correction methods are believed to be too conservative, resulting in familywise error rates far below the expected 5%. However, we have found that correction methods based on parametric assumptions can actually be very liberal for cluster-wise inference, yielding familywise error rates of up to 60%.
| d | 8ec39ca600a1d86124e062a4371ffa82 |
Generally, our main contributions are highlighted as follows: 1) We propose a weakly-supervised approach based on subset scanning over the activations of the inner layers of a pre-trained skin disease classifier to detect OOD samples across two use cases: detection of OOD samples from different collection protocol and those from unknown disease classes; 2)We propose perturb input images with ODIN{{formula:fe716794-d326-4fc6-a347-dd9a2139ed93}} noise, for improved OOD detection performance;3) We evaluate our methods against existing OOD detectors: Softmax Score {{cite:57fdd4200fe5789b74d42d7e531fddb94e603cab}} and ODIN {{cite:1137675615727e47ff17718bc18d9e4c9330e533}}; Furthermore, we evaluate the fairness of the proposed approach and existing methods in their detection performance across skin tones.
{{table:3c8c9e34-4b4c-43b1-a85b-24d0cce4f4e3}} | i | c64220d1cccabd9a3a4b86a045bf83bc |
Another potential issue with refs. {{cite:6c8b5360e7ce201795ddfeca1a5f0606690a3c21}}, {{cite:6fe0b53c0c3314e1e455a17e9a9ee4c0c34ea1fb}}
is that the C̆ech approach is not so widely used in contemporary
works on twistor approaches to field theory. Instead, it is more
common to use the language of differential forms, where the
ambiguities inherent in the Penrose transform can be characterised by
Dolbeault cohomology {{cite:bbbed11c22b0a0565f883ec108d694fc0c7194e9}}, {{cite:8fd63e62fc4371b0d034ba74be29a8ef8a6b5ce4}}. That
this is equivalent to the C̆ech approach follows from known
isomorphisms between C̆ech and Dolbeault cohomology groups. Thus,
if the double copy has a genuinely twistorial expression, then it must
be possible to describe it using the Dolbeault language. Preliminary
and very useful comments in this regard were made in
ref. {{cite:9bbd9f42b277a9e6094db7ce9eee8dce2f7c32d5}}, which presented a classical double copy
defined at asymptotic infinity in spacetime, and showed that it could
be used to constrain Dolbeault representatives in the twistor
formalism (see ref. {{cite:9204fcd645dc5cd523cf34781bc997a6bdff0d1e}} for earlier related work). Our aim
in this paper is to explore the relationship between the Dolbeault and
C̆ech approaches in more detail, and also to go beyond the purely
radiative spacetimes considered in ref. {{cite:9bbd9f42b277a9e6094db7ce9eee8dce2f7c32d5}}. We will
present two different incarnations of the Dolbeault double copy. The
first is ultimately a rewriting of the C̆ech approach, using a
known approach for turning representatives of C̆ech cohomology
groups into Dolbeault representatives. We will see that a product
structure in twistor space indeed emerges in the Dolbeault framework,
which is ultimately not surprising given that this is essentially
inherited from the C̆ech double copy. Furthermore, this first
technique for constructing a Dolbeault double copy will suffer from
the same inherent ambiguities as the C̆ech approach, namely that it
is not clear what the recipe is for picking out a special
representative of each cohomology class. Motivated by this puzzle, we
will then present a second Dolbeault double copy, which uses known
techniques for writing Dolbeault representatives associated with
spacetime fields in Euclidean signature. We will argue that the
spacetime double copy is again associated with a certain product of
functions in twistor space. In this case, however, special
representatives of each cohomology class are indeed picked out: they
are the harmonic representatives, which are uniquely defined for
each spacetime field. We hope that our results provide further
motivation for the use of twistor methods in understanding the
classical double copy. They may also prove useful in relating the
classical double copy with the original BCJ double copy for scattering
amplitudes, given that twistor methods have appeared naturally in the
study of latter (see
e.g. refs. {{cite:85cf163916fde0b718d4b8dbbe9698d3866f1fc4}}, {{cite:1880be45c8a1595736a961093d28b65398b95d81}}, {{cite:47b871e69b4d449443c22c01a975ee3c186081cd}}, {{cite:dba5a97526452780243115c9b95c4090d5d9794c}}, {{cite:3c9c1630e40f159d4c754673c435e1289dffa984}}).
| i | a577bba3ee3fcbe5aace9034102f24a6 |
No doubt to say, the effectiveness of such an edge/cloud collaborative architecture depends on the accuracy of the predictor that is responsible for differentiating `easy' and `difficult' inputs for the edge DNN model (see Fig. REF ). Mis-predicted `easy' inputs result in accuracy loss while mis-predicted `difficult' inputs cause unnecessary communication and computation cost.
Existing works typically rely on the “confidence" level of the model as the main indicator and design the predictor accordingly {{cite:7c2041b96fbdf023a0c92694381a587502c2a9db}}, {{cite:b50ab0d49330eff7f75075917bad3bca142c7fbf}}, {{cite:9188f5bbdf30dbe6312c55a2f2b7146e10d466b2}}, {{cite:114d0a1e29869eec7e6c83505cd68de1d66588af}}.
However, such kind of softmax probability-based confidence measurement has been shown to be inaccurate, as DNNs tend to produce overconfident incorrect predictions {{cite:b5244c39231380140e72d9bce3ee25aee87c64a2}}, {{cite:287cb2a80ebe78bc41ea0285366edde72d35f850}}, {{cite:9048f1f4b384124ca2d5adaeec602a6b974dbaf3}}.
{{figure:2f66e666-261d-465e-a448-f5f68d1da06e}} | i | 1638b12e638ba30ababa17074022fcca |
The raw event camera output is composed of a sequence of events, {{formula:fb7326ba-3455-4f83-96d0-57746eebd727}} , where {{formula:83eb0fad-b3dc-4524-99dd-fbcacc2b2c91}} indicates brightness change with polarity {{formula:fe19193d-40f2-4287-9728-b173dfd16b33}} at pixel location {{formula:7a43ca6a-7c05-4d6b-b073-f9fea11acad3}} at time {{formula:c24eebff-ba2e-4c6e-906e-32aebbf554ce}} .
While there are several approaches that asynchronously process events {{cite:29f9be1d25807a858012edb193ca8a7fd98817e2}}, {{cite:bb4bda918c8f1e46c31f683f0e02283541ac332f}}, {{cite:3f2406823463dc9e7fd5bdb7e01a1795e31e0f78}}, we retain our focus on more prevalent approaches that employ image-like event representations.
The classification algorithms {{cite:b8d867cf1ea16cd2459ebe1b1f0cd22a69ea85df}}, {{cite:f21a87077d9599488a64ba6aa7a51f3413519988}}, {{cite:fa81a0f42d6f709ec3d840744c72e4e52bb8cbfa}}, {{cite:b838fdcf7b8d5aee4c674ef949a5b39636c9248d}} are composed of a two-step procedure, where events are first aggregated to form an image-like representation, and further processed with conventional image classifier architectures {{cite:51a87e1f3f6fe1bf45b82f52e8bfdc449b443234}} to output class probabilities.
| m | 2fcb482db3825a01e4d4d122ba8f1bed |
To ensure that the robot tracks these commands, one possibility is to simultaneously train a low-level controller using RL that converts the high-level velocity and gait commands into joint torques. Such a scheme has two drawbacks: (i) sim-to-real transfer issues and (ii) large data requirement for training. Another possibility is to leverage an analytical model of the robot and solve for joint torques using trajectory optimization – a scheme commonly known as whole-body control (WBC) {{cite:70af80171394ac7ee1ce36c8c1199606581de1fc}}, {{cite:16dd84112ad7c44cb99b48cbe63e50121149647b}}, {{cite:57ef255a100036178297f82bf16f4c9999ce7b8d}}, {{cite:e1cf4afdf648650ec5dabd03a42679affd0f59e6}}.
One issue, however, is that a typical WBC tracks the robot's center-of-mass (CoM) {{cite:70af80171394ac7ee1ce36c8c1199606581de1fc}}, {{cite:16dd84112ad7c44cb99b48cbe63e50121149647b}}, which is infeasible during the flight phase of agile motion due to under-actuation of the robot's body. To overcome this issue, we leverage a prior control scheme built on the intuition that changes in body velocity can be realized by modifying the forces applied by the robot's feet on the ground. This frees the controller from the requirement of faithfully tracking the CoM and instead tracks the contact timing and the ground forces applied by the feet. This approach, called whole-body impulse control (WBIC) {{cite:e1cf4afdf648650ec5dabd03a42679affd0f59e6}}, enables tracking of highly dynamic trajectories set by the high-level controller (see Section REF ). Our proposed method, Depth-based Impulse Control, integrates WBIC with a vision-aware neural network (Figure REF ).
| m | 306e51e040bc88fd16979dc829f93b57 |
The network embedding problem that we have addressed in this study is distinct from the more popular node embedding, which aims at mapping individual nodes into a low-dimensional space such that their pairwise similarity is preserved as much as possible. Examples of node embedding include DeepWalk {{cite:c3421ed127b80d8db70757a6e2004dcfc58224fe}}, node2vec {{cite:0648248ada57ff9a27c1ebb6a546d57ed8db3334}}, and LINE {{cite:815075bc5df69d1d9753dd27a1bd39fc73fed05b}}. Node embedding methods for temporal networks are also available {{cite:057d84f030f0e2b852f057e971b8ed8e88b4aa63}}, {{cite:1c23f64fc3ab2ce8a9599566bb4f7735e16efe9a}}, {{cite:7c587ad6a55b045f9e6d4f1bb60ceb58a2f7ca9b}}. See {{cite:7736068dec508e73ec6e4ef8245f2992dbf26de7}}, {{cite:d7a49cf2bb478b18786d10f44241a91179fad4c4}} for reviews of node embedding for static and temporal networks.
With node embedding for temporal networks, each node moves in the embedding space as the input network varies over time.
In contrast, we have proposed to embed the entire network structure at any given time into a single point in the embedding space. Thus, the sequence of networks observed over time generates a continuous-time trajectory lying in the embedding space.
Node embedding for temporal networks and the embedding of a temporal network into a trajectory in the embedding space have different goals. With the latter, we drastically coarse grain the original temporal network by representing the snapshot network at each time point, {{formula:4f0ea0a0-3b95-44b9-bd48-30b16862838e}} , by a single point in the embedding space.
In this manner, we are not focusing on the individual nodes and edges, or their relationships. Rather, we aim at capturing both structural and dynamical features of the evolving networks.
By construction, the distance between two points on the trajectory reflects how different the networks at two times are. This property is potentially useful for downstream tasks such as identifying macroscopic states and dynamics of the system state of temporal networks {{cite:c5e21d0842cf150c845d409452e3d488b4136813}}, {{cite:50cf19d19ae98f91e2fdca8810b228831c96c9ae}}, change-point analysis {{cite:f9bcd9c31d75f385ded50a5a534e3e28070eb034}}, {{cite:cfbef3d8b69a12c21dc03e47842b98051a5fa015}}, {{cite:ec873deb41640f95f020a3837f4dda5543ed7631}}, anomaly detection {{cite:3e367cc921fdb9bf4f7ebd7b123bd8165661fdc0}}, systematic identification of recurrence using recurrence quantification analysis {{cite:edae0d78689240932d2b5a4089487abadd1e1e7f}}, {{cite:50cf19d19ae98f91e2fdca8810b228831c96c9ae}}, and link prediction {{cite:057d84f030f0e2b852f057e971b8ed8e88b4aa63}}, {{cite:fda5c76e1e1c32d93d58e41d916fd706699c60ac}}.
| d | 9d1047dffaa52d3cc2aecd64040f7e56 |
It is worth mentioning that in {{cite:26f4460cfe2d63c6b078c5e05687e6af85fd9fb9}}, the authors have employed the PINNs framework to approximate the Euler equations that model high-speed aerodynamic flows; both the forward and inverse problems in one-dimensional and two-dimensional domains were studied carefully. Here we numerically study the compressible Euler system (REF ) by using our proposed approach.
| r | 2015e2e9ba1306fbfef1720cf51372e4 |
The main motivation for using data storage and computing at the edge stems from the desire to make high quality computing resources available closer to the users and to reduce the need for end devices to exchange private data with centralized servers . There is an ongoing trend to deploy machine learning (ML) algorithms at the edge enabling consumers and corporations to enjoy and explore new opportunities in different application domains, such as automotive, security, surveillance, and other smart city services like healthcare {{cite:ed415732a2e68d0532788b925e3e0b05f7ac6d92}}. This desire is particularly strong in the healthcare industry where the stakes are high and various stakeholders (including consumers, governments, and service providers) have stressed the need for foolproof safeguards for ensuring data security, user privacy, and ethical data use {{cite:dc2bfbe57ec2b3c967f70c4a3be6464aa978fdac}}. This motivates the use of edge computing in healthcare settings to meet the high expected standards for patient privacy and security as well as stringent requirements for quality of service (high reliability and low latency).
{{figure:5e08ffde-ec50-4386-b155-4be88cf69a03}} | i | f007db123a8bb2f1cccb58b3f6754070 |
All eight of the stars are relatively low mass, {{formula:b0a8d134-fded-4e03-bbc0-97e11f35b007}} , so
none could be a significant (relative to the initial mass of a
neutron star progenitor) mass gainer. They also all have
relatively low proper motions (see Fig. REF ), so none are candidates for
a disrupted, short period post-common envelope binary. If
the progenitor of PSR J1124{{formula:3086d220-fe1c-46e0-81e3-b4a0d3e69a67}} 5916 was a highly stripped
star, as argued by {{cite:83e51fd5512801a5b6090a180c53b2c28bd6a9c7}} and {{cite:df1bf0e28afb23ff0055f2c2c71d2f222628617e}},
it seems unlikely that it was stripped by binary interactions.
| d | 8cb91ef135a48090ba3dc15ae69f23d8 |
NH{{formula:a1e8064e-24d5-40d0-ae6d-649919901f28}} has been detected in disequilibrium in some cooler T dwarfs
{{cite:4cc0a30ab1c8b804397621ed7d966ddd09ebc70d}} and Y dwarfs {{cite:6e5d6e105d8ef0df920b5c15a1607b560768dc43}}.
Overall our coolest disequilibrium model at 500 K, for
{{formula:85a31586-0cf9-4ca4-bab0-fd7e626f9a22}} = 5.0 was depleted in NH{{formula:7cefa6c1-de1c-442f-af6e-6118262b0350}} (relative difference of
-50%) as expected. This was detectable in the major NH{{formula:76fc8053-b867-4386-ad6f-c4b6d8bbfaba}} feature around
10.5 {{formula:e5273c2a-3f5a-4bc9-ba22-8e6ba1c8ff8c}} m, which showed a lack of NH{{formula:1c86e005-fdaf-4c1e-bde8-e119f3583127}} in the quenched model atmosphere.
However, in the deeper pressures probed in the
1.0-1.3 {{formula:aec5250b-29f5-4000-be0f-9a0483233550}} m and 1.5-1.6 {{formula:7429ff0a-3ed8-4cc7-909a-dd548fd92177}} m windows, which include
NH{{formula:978c8dd6-94ce-43a1-9f41-20e267458397}} absorption windows, the cooling in the TP profile
of our atmosphere (at those pressures) resulted in an overabundance
of NH{{formula:a9c07824-deb7-4232-a8fb-841cdd9f9183}} which should be detectable for some atmospheres. We are
currently extending our grid
to cooler atmospheres (down to 200 K), in the realm of Y-dwarfs,
where {{cite:6e5d6e105d8ef0df920b5c15a1607b560768dc43}} reported a possible detection of NH{{formula:5c4229a8-5e53-4689-90e2-23563118b635}} in the atmosphere
of WISEP-J1738 (350 K - 400 K) in the 1.5-1.6 {{formula:88200bc6-abdb-42a1-8af2-8c47684bd5d7}} m window.
Fig. REF shows an example of how NH{{formula:09b9f21d-47d2-481b-890d-b79f9372a05f}} excess in
our cooler atmospheres changed the H-band in a comparable way to the
tentative detection on WISEP J1738+2732 by {{cite:6e5d6e105d8ef0df920b5c15a1607b560768dc43}}.
{{figure:8cdd526f-901f-4001-8ca1-b06f20d8e44f}} | d | ee0c35ca78ef1004b2445d3264df14ef |
(2) In the theory of general relativity, the Einstein's equations are assumptions {{cite:dc0685bc1e53f49c526e7fd942170f90a4594c42}}, {{cite:c03a041e73bf3ee325952cb5a79cc4bf79cca231}}, {{cite:3d33c1d4a93c2480767bc1ad25f3656fdb167c24}}. Although A. Einstein introduced his new concept of gravitational aether ({{cite:88d6daf3fbb89e2173efe1c71644fea9c0698139}}, p. 63-113), he did not derive his equations theoretically based on his new concept of the gravitational aether. In our theory, the generalized Einstein's equations (REF ) are derived by methods of special relativistic continuum mechanics based on some assumptions.
| d | ad5f5a9607b9a29447ac2a0b314095c4 |
Equal task split scenarios: Exemplar-free comparison.
In Table REF we compare our method with other exemplar-free approaches from the state-of-the-art on the equal task split scenario. We observe that our method outperforms PASS {{cite:3978eb1cc93fc30ff256f38b674e62ed77e25801}} (that uses self-supervision for guiding incremental learning) and SDC {{cite:624e44713893d3183965ab0264a967e139e281c8}}. The results show a significant drop SDC performance compared to the results in Table REF . This is because SDC is very sensitive to the size of the initial task since it requires a strong backbone. The original paper only includes results on larger first tasks. The good results of PASS show the strength of self-supervised representations which generalize well to new tasks. We think that this observation is complementary to our method and that they could also be combined in future work.
{{table:dc0b7f6a-f21c-4e66-a424-cb407e3c5721}} | r | dea70b136dcb1799ef96d219d3d44255 |
During the past 25 years, observations from IRAS, ISO,
and Spitzer have revealed substantial mid-infrared (mid-IR)
excesses associated with hundreds of normal main sequence stars
{{cite:cf43306a729232b383e7c9e12239cd3f9d45740f}}, {{cite:b79b5f21f14f75df28c22ae86e1d04c10cf91498}}, {{cite:7616a256c978424eae5a721ae7d84f39a1b29acd}}, {{cite:ec730dc89349d81494e3207e09e0c21833dd1c62}}, {{cite:dbf008377b567affa0c70fe45bee1ba91768a32b}}, {{cite:89cede9eecacb78d37fe78db71104c330a76cd5f}}.
Current samples include stars with spectral types A–M and ages
{{formula:dde1549a-db62-42fd-8a09-c9c56dc21172}} 5 Myr to {{formula:14283171-50e0-404d-9fac-95f25a2ce6d9}} 10 Gyr
{{cite:a7ab1fc600e8c982682ddcfae31274e730c78cf9}}, {{cite:87daa1dd87ac5ad6569201cc934747b38bf7c545}}, {{cite:7616a256c978424eae5a721ae7d84f39a1b29acd}}, {{cite:06b319a8251667a079b756b54b3a0187dc9c6602}}, {{cite:2525102115cb9dd43c3166d92e6bc0f1546c4f25}}, {{cite:a019f913be7084554f448629b81aac10c6a1e37c}}.
Although binary stars and single stars in dense clusters and in
the field are roughly equally likely to have IR excesses
{{cite:be90df349d7073c0fe1a35b13df86e711a90e00e}}, {{cite:2525102115cb9dd43c3166d92e6bc0f1546c4f25}}, {{cite:ec730dc89349d81494e3207e09e0c21833dd1c62}}, {{cite:f386261ca326c28d9edfdc53b6635363a1b69cd6}}, {{cite:4daced9e2431a75a6c0f3c70b4312ea64e4f85a7}}, {{cite:55289bde469aee30a3f039b81beeccf09e62aca3}}, {{cite:1262507c43052f98b618f7852922f316f9ab70c4}}, the frequency
of excess emission declines from {{formula:5856883e-a43d-484d-9a39-121fe3a19b6d}} 30%–40% for A-type stars
{{cite:2525102115cb9dd43c3166d92e6bc0f1546c4f25}} to {{formula:9db96e34-f65b-437b-a3ff-bfa5a78edeac}} 10%–20% for solar-type stars
{{cite:a205301a5c7c83383c1e6dc7ac1e4cd716dd2f75}}, {{cite:e51dbc9f2514de5ee5354ed875037c5d5ca135ba}}, {{cite:a0ee16eec770ec15449df7c87c3ed493097723e4}}. Thus, this phenomenon is common among
main sequence stars and may depend on stellar mass.
| i | b5b61a23b0b826a66b538c976e64894a |
With regards to the choice of ML model, we admit that there is no unique model that is capable of forecasting all types of data more accurately than other models under all conditions {{cite:b5ff6f389d7d4cd3bbed38000ba96b26cdd677d0}}. However, various empirical studies suggest some effective models for certain types of data {{cite:f0a708df8c2f9180013e7d6a283d1f389700eec7}}, {{cite:f7bce8ea8e179cb6c87822987ca60b8f60627076}}. Given that we have a sparse data comprising the parameters of the optimization model as input and the optimal values of decision variables as outputs, we use ML models with regularization. Note that the algorithm is flexible in terms of the method that can be employed for predicting the solutions. That is, users can choose their ML regression method of choice using this algorithm for predicting the decision variables of the optimization model. We implement three ML algorithms, including Ridge regression, SVR, and LightGBM with various loss functions that are shown to perform well in various forecasting tasks {{cite:b5ff6f389d7d4cd3bbed38000ba96b26cdd677d0}}, {{cite:9c2810e0e8fbb4132d27dc732088c1090f35554e}}, {{cite:5f16abf8c67de4076fe1039bd3f9105889e06519}}, {{cite:3ee55c8f4f56ca915e6abada76f40cd4c173ff98}}, {{cite:a885201bb65888c14954450ce4983d9ff82fa0e3}}.
| m | 13441eec8e86f41e8c0dc0ac69ff2aa7 |
We first investigate the kinds of networks where the bimodal distribution of cascade sizes can emerge. In particular, we consider a vital property of networks, the average degree {{formula:d3007dd4-0ac4-4b6e-a3f0-e9156737dc2a}} , which tremendously affects the ability of networks to withstand failures. As for information and disease transmission, it is easier for networks with a higher average degree to have wider propagation.{{cite:58841568da6efa8eacd343487852f96dac4fc42a}}. However, cascading failure dynamics is different. For example, a network with a higher {{formula:48dcee0f-d4a6-4867-9c80-dea0b9788198}} , in which more nodes can share the redistributed load of the failed nodes, is less inclined to trigger a large cascade. Therefore, we first study how the average degree of the network impacts the distribution of cascade sizes. The relative size of a cascade is quantified by the ratio of failed nodes after the initial attack in the network. We stimulate the Motter-Lai model on Erdős–Rényi (ER) random networks, Small-world (SW) networks and Barabasi-Albert (BA) networks, respectively. In each realization, we attack one node (delete this node and all edges connecting to it) and stimulate the Motter-Lai model to calculate final cascade sizes in the network with a fixed {{formula:e4882ad2-9a42-49f0-9aaa-553b31e085d0}} . The size distribution of cascading failures is recorded, until we have attacked all nodes of networks separately. The results are shown in Fig. REF . The redder the color, the higher frequency of such cascade sizes within the corresponding interval in networks with corresponding {{formula:957782bd-980e-447a-ab6e-d4e9746b77dd}} . We can clearly see that there are bimodal distributions of cascades in all synthetic networks, shown by two redder regions longitudinally at a fixed {{formula:aa006ec3-74e1-4aa7-8114-3136fa28c882}} . For the ER networks and the BA networks, the bimodal distribution of cascades is more likely to occur in networks with a lower average degree. In networks with too small or too large {{formula:82880288-0244-4e7e-b80c-a000abcd8db3}} , cascade size distributions are unimodal and cascade sizes are mainly at a low level close to 0. This phenomenon is resulted from that a network with too small {{formula:ad9c5b7b-f10d-4854-980f-3095d7441787}} is prone to split the network into some separate connected components that can prevent the propagation of failures and those with too large {{formula:42ef585d-b011-48af-87ff-b829a4bee912}} have more links to share the redistributed load of failed nodes{{cite:3f9008d4f3b76a47cf5a1145f69257a9624e0985}}. The SW networks, however, exhibit different characteristics that the bimodal distribution always exists, even though the average degree {{formula:062b0ee8-f9a0-48e2-ba9f-18cb3de43e51}} is large. This indicates that the small-world property might bring more cascading risks for networks.
{{figure:5b4c5f2c-c335-47f0-8f66-2b91942f45dc}}{{figure:4c81d550-76e3-4528-8558-f24dd44b65dd}}{{figure:af15de17-3e26-42f3-87da-83d246e8d69c}} | r | 2d0d224c22dae900dd852d7bd02807ee |
Recently, the combination of Monte Carlo optimization and neural networks has gained increasing popularity. These approaches include both using MCMC processes to find optimal weights in ANNs {{cite:1684e8a8e420d88f6a5f2e7bc281f7027a43a39b}}, {{cite:8ed9c2d818bd2c6bbe2fa2f4e0d41708733a74ab}} and using ANNs as parametrized proposal distributions in MCMC processes {{cite:24af7cc5bb6eb71513b6a2987e9c77674b3acb43}}, {{cite:60071473b125a4a013dc84841fda111072fce7fb}}. While our approach is more similar to the latter, the important difference is that in such adaptive MCMC approaches there is only a single MCMC chain with a single (adaptive) proposal to optimize a single task, whereas in our case there are multiple adaptive priors to initialize multiple chains with otherwise fixed proposal, which can be used to learn multiple tasks simultaneously. In that sense our work is more related to mixture-of-experts methods and divide-and-conquer paradigms {{cite:99293cf7b4f7c5a116c08506a86308bd42ef5a0f}}, {{cite:051acbd85ea969958b1661c4b4fa349874082feb}}, {{cite:27cf663bbfb091c2c9ebcd708a4abb77e8a113d8}}, where we employ a selection policy rather than a blending policy, as we design our model specifically to encourage specialization. In mixture-of-experts models, there are multiple decision-makers that correspond to multiple priors in our case, but experts are typically not modeled as anytime optimization processes.
The possibly most popular combination of neural network learning with Monte Carlo methods was achieved by
AlphaGo {{cite:dd08dc88047caa95b59298504c22146205eeeac4}}, which beat the leading Go champion by optimizing the strategies provided by value networks and policy networks with Monte Carlo Tree Search, leading to a major breakthrough in reinforcement learning. An important difference here is that the neural network is used to directly approximate the posterior and MCMC is used to improve performance by concentrating on the most promising moves during learning, whereas in our case ANNs are used to represent the prior. Moreover, in our work we assumed the utility function (i.e. the value network) to be given. For future work it would be interesting to investigate how to incorporate learning the utility function into our model to investigate more complex scenarios such as in reinforcement learning.
| d | d886bed4088d89bd2b4d914ed35863ab |
For details, see Da Prato & Zabczyk {{cite:ac1b79bcefb92d4ba67f0ce10ec0ba545e9039a6}}.
| r | 53f214099159daa9dcb19431a621d9e5 |
Large-scale crises, such as pandemics, natural disasters, and social crises, drastically shift and reshape the physical and mental well-being of millions. Understanding emotions that people increasingly take to social media to express during large-scale crises can have wide implications for a deeper understanding of the society as well as to inform policy makers and first responders about the emotional states of the population {{cite:416d0849d8418c59396342b9b36757e5da721d83}}, {{cite:59bb8b61d92951bc4fafe385d2c487051c6341cf}}. In NLP, multiple datasets have been proposed to detect emotions on social media {{cite:cdd109ddec9f10f4b3a4008ff63b137849342ad3}}, {{cite:8ee34b0f632691d3321cc73a591dd86841f916b8}}, {{cite:886567d5dab84a111620e0a56c7625aadb648d76}}, {{cite:d0da32112d91eecacfe779c6e63f53620b533fac}}, {{cite:3ce37d431b0dd246972a6bad51e98d58b99158b5}}, {{cite:88fc7350e502553bf298a00995ce67a79cce7137}}, including from hurricane disasters {{cite:71eab998a592424f881b64cc8ac29ed35f4422d1}}, {{cite:879061f7abf6f992d264c70d58b1bc883dcee0f7}}.
| i | 53b0130e697e6d84965b9e6d51697eb4 |
The data set employed for this analysis is the atomic database of the National Institute of Standards and Technology (NIST) {{cite:69862a7ed57fd5c7a495a9793cac2026ec98aca3}}. Complete data for all transitions were downloaded and a computer program was written to apply various criteria to identify transitions of interest for AO. We examined all excited states that could be reached from the ground state by at most two successive excitations using wavelengths greater than 300 nm. For species in which no such transitions are possible, two-photon excitation was considered. For every such state, all possible downward transitions were examined, and the excitation fraction {{formula:c9742de5-90f0-4408-8933-dcb23e935594}} of the excited state was computed according to the methods presented in Appendix B. A specific energy density of {{formula:0bc0d1e5-6bea-4db4-9561-2cb3c4449556}} J m{{formula:db2577c0-56f3-4371-9228-b18b460de74f}} Hz{{formula:282188fe-d93a-40f1-89a1-33066c065444}} was assumed for the laser excitation. This is at the high end of range of energy densities that can be achieved with current AO lasers. A complete listing of all such transitions that have {{formula:43bc0112-5e31-45cd-9e6a-6f5bd3e8c398}} s{{formula:9640edd1-d63a-4da9-a98e-a303ea1c88b1}} is blackavailable from the authors upon request. From this and the data of Table 1, the return flux coefficient was computed. For PLGS, the penalty factor {{formula:36ee4bb5-a2fe-4212-913b-0fadfebdbc3b}} and merit function {{formula:13975438-deb1-443b-8fa4-735573c20785}} were computed for all downward transitions.
| r | 1d597015bb60bc5587bcfd278b6a877e |
To address these issues, several authors have proposed methods for adapting zero-shot models to a task of interest using labeled data {{cite:21f2ec40c8f2336d53c98e3454c0283e0aa8ad8b}}, {{cite:658a56be9d408a5d3676753af4844d88f6694f66}}, {{cite:50146ed1c87ad8e5f3b89ea2dde6579df05abfb2}}, {{cite:0771db6868b511ac0b0b4acce91725f96b367765}}, {{cite:fbe6f15c7fb022ccd5ea075ab6e54006d3076a50}}, {{cite:5c80b58d4811e952a8f90a03635189c14aa992d7}}.
A common practice is to fine-tune the zero-shot model on the task of interest {{cite:21f2ec40c8f2336d53c98e3454c0283e0aa8ad8b}}, {{cite:68fadbba08fb4867fb51a979480f2bf21bf2e79b}}.
However, fine-tuned models can suffer from catastrophic forgetting {{cite:4e90cb07f4675037bf9c2330ea1ed837ce2d728c}}, {{cite:de585133233afc757abbbf8be3c9b7c4f61c369c}}, {{cite:dfe76b26de00b92cfad787034cf607928e8a3966}}, {{cite:9bccbde856a92c47a3fae3cc84922357dd5fe6af}}, performing poorly on tasks where the zero-shot model initially performed well {{cite:dc69ff27a02bde1c11b4be5b5f8cf0e59a2d48bc}}, {{cite:21f2ec40c8f2336d53c98e3454c0283e0aa8ad8b}}, {{cite:68fadbba08fb4867fb51a979480f2bf21bf2e79b}}.
Additionally, fine-tuning typically produces a task-specific classification head, sacrificing the flexible text-based API that makes open-vocabulary models so appealing.
Whereas an open-vocabulary model can perform any classification task in a zero-shot fashion, a fine-tuned model with a task-specific head can only process the specific task that it was fine-tuned on.
This specialization can prevent knowledge obtained by fine-tuning on one task from transferring to other related tasks with different classes.
| i | c61995f8701fa5ed50b7ec8cd6193362 |
Notice in the beginning of discussion of small gaps between primes, we consider the indicator function and pick {{formula:ebb74de2-d31b-4d00-89a3-e05de731b091}} to satisfy
{{formula:58586cd8-9beb-4233-ae58-e2b518b56c64}}
which basically is a weighted sum. The things we really want to show is {{formula:615d7086-f365-4dfd-9382-df3a7a0b12e9}} for some n. The most natural way of thinking would be improve our choice of {{formula:5980226b-16da-4a2b-8b2a-dc7e9ee71da2}} or our technical of estimating sum. If fact, both of them can be quite difficult like {{cite:cbe943a49d4cbf2d5c7d25ca7cae71ae6a347549}} and {{cite:43bd83c8783594e7b8797a372f018e5c52a8edda}}. However, in order to obtain {{formula:9bfc3b72-3447-4a0b-a91a-933ee2bd7743}} , it is not necessary for us to use sum or weighted sum. Instead, we can use following
consider
{{formula:f91fd25d-9f2a-43aa-a16a-0a53ebbb9587}}
Since {{formula:9f166113-423a-418a-a83f-701628a43ee7}} are integer, subtract {{formula:155c233d-5bd1-4609-a306-bceb1a6aebf4}} does not change the sign. Also, for the same reason, each term in the product would not be zero. So, if we can prove the product are positive, there are two cases to consider:
if one of {{formula:3b90b810-9f89-4738-9205-8b473c482bfa}} , then we are done for the same reason we said before.
if all of them are negative and due to our {{formula:2686a9d1-14da-4301-914b-1e84252d9c3c}} , there are even number of negative term. In this case, we can product over either {{formula:c2a550a5-0233-4521-8d20-354afbb151e6}} or {{formula:3cf65a6e-1abd-4b75-88ed-e13ce96a2d67}} . there must be one them that only contain odd number of choice of n. Thus, we do not need to consider this cases and suffice to show the positivity of product.
More generally, as we did in the sum, we can add some 'weight' {{formula:60cb1bd0-0d94-4d67-a981-5dcf7d727fbe}} to the product to make the calculation easier.
{{formula:0609930d-d7bf-4bd9-ab04-2d5a6505cd30}}
Moreover, there are nothing special about product or sum. Let F be a function from {{formula:19590bed-d502-49e5-bb15-ee978652a1bc}} to {{formula:716cb056-b890-431d-ba8f-14dad6c47044}} satisfying: if {{formula:da176945-ccf5-4e0d-9425-6b9468f6a060}} , then {{formula:9e517c4c-0d48-441b-95d1-66d1135b924f}} for some {{formula:8886ecec-f537-4c41-9514-f3a39d71d658}} . For such F consider
{{formula:d2a75eff-c28a-4232-94fe-7f450349cde7}}
if we can show the expression is positive for some {{formula:15882fa9-6f0e-4c24-ad68-7ecaa56f9d17}} satisfying the condition we require above, we are done. In this case, we have more flexibility in choice of F since we input only one constrain to our function {{formula:30f88be9-fb3c-46a9-a37d-c55f7b9ea4ae}} . As a special cases, weighted sum clearly satisfy the condition we impose on {{formula:2feb7f66-e382-4c2c-adc2-274e95fac093}} . Thus, weighted sum would be a special cases of {{formula:d3c686e8-4989-4b20-bbab-b7a40acc47c3}} .
In small gaps between primes, Zhang and Maynard focus on different aspects and did the improvement independently. Zhang improves the result in arithmetic progression, whereas Maynard modify GPY sieve. Zhang's result allow us to have a better bound for the estimation and Maynard's method allows us to have a more subtle and stronger results. Thus, is it possible that combine the two results together with some necessary modification to have a better conclusion? For example, using Maynard's sieve, we somehow modify Zhang's results in Arithmetic Progression to have a better bound.
In the studying of primes gaps, the question we are dealing with is about {{formula:e7238580-23fa-4859-bae4-e6c6a0f96200}} or {{formula:4ec9d908-b13d-40f0-9071-13bea2e8cec0}} , which basically are question asking infinite often. However, this kind of question has been studied for a long time in Analysis or Probability. Having this in mind, is it possible for us to model the distribution or primes gaps for all primes, so that the results from probability might give us some new way of thinking. Moreover, if we convert problem in prime gaps to probability, we are able to use theorem like Borel-Cantalli lemma, Strong/Weak Law of Large Number or Central Limit theorem. In fact, in the proof of Erdos-Kac theorem we state in the beginning, Central Limit theorem play an important role. The classic version of those probability theorem above require the random variable to be iid. However, there indeed some stronger version that only require independent, which are much easier to obtain by only considering a sub-sequence if necessary. Since we are studying infinite often question, prove the statement on subsequence would gives us the result.
For example, we could set random variable to be the number of primes smaller that {{formula:6161ef9c-00df-41fe-8bfc-caf2e471ccbe}} or number of primes divide {{formula:e190e5db-6db1-4b83-91ea-149ccc1a4cd6}} . If we want to study {{formula:1d13e3bc-058e-48f2-8706-202b2610f02e}} , we consider the number of k in admissible set. We might set event
{{formula:4464ce60-7dec-43b4-8641-4f5a43c5e09d}}
From construction of {{formula:e45bc481-15b6-4f20-973a-91c94b7039b3}} or Kolmogorov 0-1 law, we are able to see {{formula:c051eabc-9be3-46b8-af43-2a981cc8aa25}} = 0 or 1. So we can sum up all {{formula:4c041754-00c5-40ad-a728-64c2fb0b58a5}} ,
{{formula:8fa4b8ac-d39b-40a2-95f8-3d719c45b91b}}
once we have a result of positive number, the {{formula:17e34682-5fdc-422d-a052-ad8feed41f92}} would be the number we are looking for.
In probability, there are a noted inequality called Azuma's inequality (See {{cite:36a273e485665e65697d32d91d86480da1e7c38b}} for example). It states that for random variable {{formula:2b9d9b6a-b49c-4122-80c6-5aa8ce8856c7}} and function {{formula:0628ff7b-c420-40ec-81ab-25c9bcd5fb68}} , suppose {{formula:ca94b7ad-c686-4eec-9a0c-d27e6efe3380}} exist and
{{formula:c64b262b-0678-47b1-b4c8-98c37b151f4c}}
for any {{formula:967cafd9-3327-4746-92d8-44f123256d36}} take value in the range of random variable. Then we have
{{formula:a6870957-b021-4dc8-bb62-8ad46c0ff30d}}
One of the application of Azuma's inequality is Erdo-Renyi graph. In Erdo-Renyi graph, one considers graph {{formula:38acc3fa-6d42-4fa8-883d-2eb13ec7218a}} with n vertices and each pair of vertices are represent by iid. Bernoulli(p), {{formula:99f90e40-cfdc-4dcb-96e7-8597ffd329f1}} , where {{formula:5d14d6e1-a365-49f6-8f9b-bab1ba80bb46}} if edge {{formula:83ad71f2-7975-4b4e-acea-24ff594244cf}} are connected in the graph and {{formula:a427e0c7-00d7-4fe3-a7db-edf86a4f083c}} otherwise. we send a coloring to the graph {{formula:df4139ff-9dc1-4ae1-acc5-4a5b2596c4a3}} and the graph is called admissible if 'color of i {{formula:c43725c7-8295-41f8-8a5d-38b8e71f7266}} color of j if {{formula:2a6e9468-3304-4341-9c4d-3c19f9819205}} '. The question people interested in the chromatic number of {{formula:6b041f40-7abd-4983-8ac8-eee44b069216}} denoted as {{formula:a01fbef9-607f-4073-81d0-dc916c8005d2}} . One important fact is that the expectation of {{formula:c17e6329-a110-42ee-94f1-dd6d8d82a1ff}} is in the similar form as Prime Number theorem. i.e.
{{formula:08533ed7-1f78-4abe-8d05-ac3d9c1871f3}}
In probability, people are trying to improve the expectation above by substitute the {{formula:47165c41-1977-4493-b678-cc3b2d86691a}} with expression like {{formula:b573451f-1fac-4dfc-b0b4-86e18afbb321}} and etc. However, all these have lots of similarity with primes gaps and in fact, we have already lots of results looking like {{formula:5c646d7c-9b17-4623-8b90-bc70f943f640}} . So, if we are able to find some connection between chromatic number of Erdo-Renyi graph and primes gaps, we are able to witness a new way of thinking. Even though, at this time, Erdo-Renyi graph might not provide some stronger observation in prime gaps, like what probability sometimes did to Analysis, the intuition and simpler cases are very helpful and enlightening.
| d | b3bdf183ca8068fe3316c5d0aa21a1db |
Other features that were added in the current feature set characterize user behavior in a community earlier, before the current state. Furthermore, we added modularity {{cite:7b4b51bb244ad34e3b388626e5f4b53ac9efaa10}} of a snapshot where a user appears to the set as well. The list of features can be found in the Table.
{{table:7aa066a5-db61-4542-8656-a973aafe35f8}} | r | 596ee6a75c6e7b92d42f25099d1a9c66 |
Interestingly, The Depth Contrast pretrained model, which is fine-tuned in a semi-supervised setting using only 20% of labeled data in experiment 6, achieves a comparable F1 score of 0.65. The proposed method, Depth Contrast, clearly outperforms by 11% on ImageNet {{cite:5f91a5a4aa4c3bc31a69fe3096441ecce90c4921}} pretrained model in the same semi-supervised settings mentioned in experiment 4. This comparative study showcases the representation learning ability of the Depth Contrast method to yield performance generalization on unseen data even when trained on significantly reduced labeled data.
| d | 8c571d055635191e85ac6f973d8a3a5b |
where {{formula:bfa0e5a4-6b89-4d0d-bc85-af25279e80d8}} is one time series sampled from {{formula:b89e9cab-1638-4409-83ba-bdc9e63ee306}} with probability {{formula:69faebe3-32e5-4e96-8eec-26627c16bd4e}} .
We also sample {{formula:c7353cb4-0ebd-4553-b319-e521059ddad2}} from the nearest cluster {{formula:1ef6b806-ee56-4b2c-984f-cdc1c6304d11}} .
We repeat this process for each of the {{formula:e875b58f-ddea-45de-b99d-e4b1727c724e}} classes, accumulating the replacement series into respective matrices {{formula:4c414a6b-cb6e-4060-b3e1-76639b7309aa}} , denoting two replacement time series {{formula:213acdfe-74c2-4f0c-b5b0-adefb5d55a74}} and {{formula:e1039edf-77f3-4225-8fab-889bf66f8d45}} per class.
We employ epsilon greedy-based prioritized sampling {{cite:8d283d08fdfcdb4b766cc255a826344fdcd6ce55}} to explore and learn which replacement time series sampled from {{formula:ca08f8cd-b2f8-40cd-8e2c-59eb20b6f519}} are best for instance-of-interest {{formula:af3d9051-ad38-4ef7-a5cd-fd67e1e1a673}}
| m | cff81aeae8abc4d378c72613eb6d05ba |
is positive and grows in {{formula:b8f5aec0-1436-4fb3-a286-7cfcd1f5c942}} . Since {{formula:d23c1749-104e-44d6-b52c-63357a3a65ee}} and {{formula:17aed44f-2afb-46a9-b263-4602642e5e8c}} become negligible compared to {{formula:79614bc0-dcb3-4797-9e18-19a18282e5af}} as {{formula:e96db563-4772-41ad-8b0b-8ffa8ae5ff5f}} gets large,
our protocol thus achieves the asymptotically optimal rate by {{cite:c33729d2240b32f7c409dca08bfe9a1deae9ff8c}}, with {{formula:833e0345-4313-42ee-88d0-710b502134ca}} .
{{figure:c6a3c83b-3b42-438b-ba17-fa22bc32ebda}} | r | 2dc5098348090143ecc92652e44f2127 |
In this paper, complex networks are expressed in the form of simplex complexes. The purpose of this paper is to derive the adjacency matrix and obtain the reconstruction model of the complex network by estimating the probability of edge connection between different nodes using the maximum likelihood estimation (MLE) and expectation maximization (EM) methods {{cite:b9179dd7135482d99e5ae22b49cbdefdcced9ea0}}, {{cite:81548c08960d370a0864c209bc9298926e35df04}}, {{cite:77d6dc872000b57c54a0c4a03d874c9d9cc2abbc}}, {{cite:0303e1b40196609d916c51cdfd38a122d7d3d2b4}}, which is based on the binary time-series data {{cite:24080b3980a5e2fdd26df6d88a7b391193062d47}} generated by the susceptible-infectious-susceptible (SIS) information propagation model {{cite:013807d725078e0d0beceb5e867ef5f6de3a8777}}. On the basis of complex networks, we introduce high-order networks and use the form of the simplex complexes to infer the information transmission between communities {{cite:b401ece37e964f306b488daa59aa403b3cddac88}}, {{cite:a04ce013ac84d21ff1e3fbd8b622025558bd1f89}}, {{cite:d4445e386152b358cb969aea34311cb2b4f77e45}}, {{cite:3a92305df77273ff918b947ed4a79c673056bba5}}. The generated probability is compared with a threshold to determine the existence of the edge between two points. Then, we use {{formula:147bf9a1-ae76-4ffe-bb13-92d8eb8d0f67}} criterion {{cite:dbafa5234398f69700f4da3b1676349858cce38d}}, which is a judging criterion based on the joint calculation of the existence of real network connections and the prediction of reconstructed network connections, to evaluate the effectiveness (or the accuracy) of the reconstruction.
| m | d09bd368a7dd26eaa4ea04561c9056f6 |
In this part, we illustrate more results generated by different methods. The listed images are sampled from nuScenes {{cite:cc343004bd0181da83dfc2f56153218d689d78aa}}, Argoverse {{cite:4f1cf0e09b61ef50539493119a57ed641549154e}}, KITTI Raw, KITTI Odometry, and KITTI 3D Object {{cite:1ae0cdfcea8cbca2a5bb97dc3a067f8ebf766d19}}, {{cite:14ae2799d02ebf83e430f609cbd36b52aef56b66}} datasets. We choose several FV images in these datasets and list the FV image, semantic segmentation map in BEV produced by PYVA {{cite:806c28ec487ad0eba26eebf70e8bd73848a13035}}, PON {{cite:f7846b0a1e3ed0728be255ca39357b355c59fe9c}}, HFT, and ground truth semantic annotations from left to right respectively.
| r | 7b70aeea1d896a3e408bdbb5f85b6816 |
In our work we have followed the augmentations used by the authors in {{cite:255cb49b1fd1b5f16ab397460e8ae873113012c8}}. They are summarized in the table REF .
{{table:58b43686-c42c-449c-97e6-3bfecce7ca89}} | m | b30e5675d49645e445ef53b1378bbb5a |
On the algorithm side, our bounds applies to the practically used version of SGD, going beyond the SGLD studied in most uniform stability-based works. Compared with the anisotropic noise of SGD, SGLD takes an isotropic noise and has different behaviors. Our analysis also works on full-batch GD. On the model side, our bounds hold for any layer-wise neural network models with homogeneous activation functions, such as FNNs, CNNs, and RNNs with ReLU or Leaky ReLU activation functions. On these models, our estimates are independent of the neural network's width, and all terms in the bounds are easy to calculate along the training process. More importantly, our bounds do no suffer from the curse of dimensionality. Lastly, while most previous works studying the algorithm-dependent generalization performance of neural networks are built on the seemingly reasonable {{formula:83b6294d-1075-4a9d-b8f6-bb4689bb5da2}} -smoothness assumption of the loss function (e.g. the uniform stability bounds), our analysis does not rely on this assumption and only need the network function to be bounded. Therefore, our bounds are not impaired by recent works questioning the {{formula:46133d2a-29c4-4c0c-a70a-0ae0c838872f}} -smoothness of the loss function {{cite:89bfc19c0ab41a4750bad3ade8e39d9c4c78693d}}.
| r | 52414ce7cf85ed077c6b147bcdef854e |
The results of HD-VILA on video QA are shown in Table REF . We can find that our model outperforms existing methods on five tasks in all the three datasets, with 1.2, 1.2 and 0.2 absolute improvements on Action, Trans and Frame tasks with TGIF-QA dataset. The limited gain of Frame is because Frame focuses on one frame while hindering the advantage of our hybrid image sequence. On MSRVTT-QA and MSRVTT multiple-choice tests, we achieve 4.8% and 4.6% relative improvement over SOTA methods. Among all the compared methods, ClipBERT {{cite:cf9f2bcd9351aaced1583d5e16b0563f19227012}} and ActBERT {{cite:b705ee0abdf02830260ea10aa5da4aeba6dc7b85}} are two pre-training models. We can see that pre-training with more data will marginally improve the performance. Compared with ClipBERT which is pre-trained on an image-language dataset, videos provide richer information. Note that the language used in ClipBERT for pre-training is more closer to the downstream dataset in both content and length while the language in HD-VILA-100M has a domain gap with TGIF and MSR-VTT languages. This further indicates the generalization of the video representation learned by our HD-VILA.
{{table:68280fef-d9b8-459a-a451-90d8105d3793}}{{table:d124e40c-49f0-412b-84eb-a2a7de500558}}{{table:44970bd2-6d9c-4e6a-8c24-00ed84f3793f}} | r | 4dad221ce7a7b6f176c829970b5a0730 |
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