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However, there are two issues in current few-shot learning studies. First, mostly studies focus primarily on English {{cite:fc64e8cce6371f02bd9631de9f6d6cd8dc4d3f2b}}, {{cite:9cda1e467c17a49964abc06e8a166304dc2fc179}}, {{cite:1ed639a2ea1059412cd5d905803405665942133c}}; it is unclear how few-shot learning will perform in languages that are typologically very different from English or have much less pretraining data than English. Second, there is no systematic and comprehensive comparison of the different few-shot learning methods proposed in recent years, e.g., PET {{cite:1ed639a2ea1059412cd5d905803405665942133c}}, LM-BFF {{cite:9cda1e467c17a49964abc06e8a166304dc2fc179}}, ADAPET {{cite:b4d0dc96e94f02569b732bcb7a9cb4da79ba2dbf}}, EFL {{cite:6ab9c509d9c07bc6435d55308e3c2ae0de3b5802}}, Ptuning {{cite:eef1893330997988e1e7120e0c6a5c42ff8d7617}}, among others.
| i | cbe6cfd1d3212c4f104f620e0d53a10b |
Problem (REF ) is a standard linearly constrained convex problem, and many algorithms can be used to solve it, e.g., the primal-dual method {{cite:ec0095d60a954c489176bddf668e1e6608c15142}}, {{cite:92b786c2c296c38131b992b14f901f97ac1896f2}}, {{cite:84153e2f3d3d27515145aee9c125acd8b851bece}}, {{cite:6db6de63a63b82a783c0fcd4a53ed7d740127ff2}} and dual ascent {{cite:f8219f6926aeac09fe748b33212777cd452c5965}}, {{cite:83a2ad4d4bdb9f0d970d0e54d52d682a7cdc00cc}}, {{cite:16f820c5eb574542c491ab47e80eeea639eb4968}}. In order to propose an accelerated distributed gradient method based on the gradient of {{formula:84aba81a-1e85-4322-a997-3841ee278c85}} , rather than the evaluation of its Fenchel conjugate or proximal mapping, we follow {{cite:63054a2c119926d40f55338cec1ac645c062f457}} to use the penalty method to solve problem (REF ) in this paper. Specifically, the penalty method solves the following problem instead:
{{formula:964c2da5-d34d-463b-9cb9-f0ab1ce1b02d}}
| m | a7c7b8598d80f7b183a0fe8c6b0ba920 |
A Moebius–Kantor complex is a 2-complex with triangle faces whose links are isomorphic to the Moebius–Kantor graph (i.e., the unique cubic symmetric graph with 16 vertices). Every Moebius–Kantor complex can be viewed as a nonpositively curved 2-complex, in which every face is isometric to an equilateral triangle with sides of length 1 {{cite:19178bdb7880ac2c79a481d2c528958c00feef40}}.
| i | 924c5c8f83276995f444e72e63a8b436 |
These quantities are then combined to generate the final PIs.
In the paper {{cite:7028ee0e7c61fb02c7118b5586aac7697c87f3d0}}, the aggregation is done as follows:
{{formula:940f4ec7-652d-4ba0-8c3b-c1cee825e5db}}
{{formula:26859b8e-6a93-475d-99eb-ed5313d8a9d0}}
| m | 1f1d74e627819b0fe702552785472065 |
We then select the model that is the best fit to the data, out of the above five alternatives. This task is performed using branch length data across different clades on the squamate and angiosperm phylogenies. The best model is chosen based on their Akaike's Information Criterion (AIC) values {{cite:f3d2e796b41b6742de73fc324eebb9bb70dc2ff7}}.
| m | 0f80fc714e755a3d709c934bb09c1ce6 |
In this paper, we conduct a comprehensive evaluation of canonical deep network architectures and data augmentation strategies. Our architectures consist of (1) a convolutional model, (2) a fully-connected model similar to MLP, (3) a recurrent model, and (4) a transformer. For each model, we evaluate five augmentation strategies: original/no augmentation, adding noise at different SNRs, re-sampling the timescales of the training utterances, masking time/frequency blocks in the spectrogram, and concatenating neutral and emotional utterances to mitigate class imbalance. To avoid over-fitting, we fix the network architectures and hyperparameters based on the VESUS dataset {{cite:b16ebf32e49adec48c2f6d28f0ca65fb127fa0dc}}. We then perform a repeated {{formula:6551169e-80d9-4fe4-bcad-b1b7d57b606e}} -fold cross validation of each (model, augmentation) pair on the more challenging IEMOCAP {{cite:3b9d91807e572a27255db87ac0aec5448227a3a2}} and CREMA-D {{cite:1d1603af7441482ef22369c9f22397302e49a50b}} datasets.
| i | c82ccb587364b8ddc9a9e93064c6cdfa |
Now we are in position to investigate the heteroskedastic principal component analysis in detail. Suppose one observes i.i.d. copies {{formula:e3ad1637-812a-4bce-a202-9d2a53f7dec5}} of {{formula:a42ac06d-3c9e-4123-bfc1-4f148f6651cc}} from the generalized spiked covariance model (REF ).
Let {{formula:451f5535-fe6f-4e43-84a5-e9e0440222ec}} be the sample covariance matrix defined as (REF ) (REF ).
In order to estimate {{formula:d5be86e1-a127-4c39-b690-5dc48557f52b}} , i.e., the leading principal components of {{formula:056f2e7f-44e3-4d63-9ae3-121cdcf3b0cf}} , the most natural estimator is {{formula:45bf1d16-0818-4e7b-bacc-8f00a5915ae8}} , i.e., the subspace composed of first {{formula:72506e47-a6bb-45f5-a755-4d8d1461f26f}} left singular vectors of {{formula:07bccc56-34da-4415-8662-13e5aa27a094}} . This idea is widely referred to as singular value thresholding (SVT) in literature {{cite:04dbb0ce6cfc74839e9a427967416024515f528f}}, {{cite:3b0ec8ba945d16944223b238f111f9348b40b5d2}}. The singular value shrinkage is another closely related method that has been proposed and studied previously {{cite:56d29ec84c31bfc73342f777a9f310ae179c2be7}}, {{cite:2444fe10fee7fe9cd312618885997bb463ba470e}}, {{cite:3dd067fcfa9ffa58bdf9354364f8f19fafcc53c5}}.
By the well-known Eckart-Young-Mirsky Theorem {{cite:80c6db1c5430d8133b9723063d36c87768319174}}, SVT, or the regular SVD estimator, is equivalent to the following optimization problem,
{{formula:faed63f4-7ae2-415b-b19e-b3866ee54de4}}
| m | ab0509b97c1c9a637db49294661fc94d |
The first one is the classical Riesz-Thorin interpolation of real functions (see {{cite:72ead13f5c28ab802064ebdeda03b112bec34aa5}} for details on the proof).
| r | 371799062d65b712997a7e11b818af3e |
While related, this challenge is subtly different from the well-known divergence issues of off-policy learning with function approximation,
demonstrated by Baird's famous counterexample {{cite:3d374be291b3d75180d3f3da1f389982f12a2bf4}} (see also {{cite:9a36e01b927659fbe2d4be44e895888ff6e9ec6a}}) and conceptualized as the Deadly Triad {{cite:57978e87143ce0b766373f612a9b387d5da92443}}, {{cite:9f8705394c8cc3594d2af7bd4f57cb7d239ae604}}.
While these depend on bootstrapping as a mechanism to cause a feedback-loop resulting in value
divergence, our results show that the offline learning challenge persists even without bootstrapping,
as small differences in behavior cause a drift in the `test distribution' itself.
Instead of a training-time output drift caused by bootstrapping, the central role is taken by a test-time drift of the state distribution caused by the interplay of function approximation and a fixed data distribution (as opposed to dynamically self-generated data).
| d | 47010439fd4e54f862841ca64b815020 |
Sampling and counting are related problems. For many counting problems, approximate counting and approximate uniform sampling have the same computational complexity {{cite:0900eb3824b9431e4c66e370acc8fb4d254beb50}}. Therefore it is natural to consider the problem of counting the solutions to the edge {{formula:3846d4e5-145f-434c-abfc-953fe98d6f76}} -coloring problem.
It is easy to develop a dynamic programming algorithm to compute how many edge {{formula:6e903ed8-1a11-406a-a62e-8c23bca3e1c8}} -colorings are there in a graph with {{formula:f5549804-e771-42a7-baad-eaa63e6c6550}} . On the other hand, computing the number of edge {{formula:60cdaa77-fad8-4d57-ac5c-4805655be536}} -colorings for {{formula:8474905e-4d88-4121-9de1-4fc4a93fc5c2}} -regular planar graphs is #P-complete for all {{formula:5a35c5f5-17a6-477c-b58c-aec37b295f6f}} {{cite:89450f903d08c86dec13e7c4fd7fb6f77862574e}}. The complexity of counting edge colorings of bipartite graphs remains open, although it is natural to conjecture that this counting problem is hard for bipartite graphs, too. Indeed, there is no known easily computable formula even for a very specific case, the number of Latin squares, which can be considered as edge {{formula:893f6254-0395-4941-b0bd-a2abf55ee818}} -colorings of the complete bipartite graph {{formula:b6a70e5b-8fe9-4672-87ba-165abd4f3fdd}} .
| i | 8d0a7d2c3e6f65018e8b4fbf0175d782 |
We then generate an alignment path through this matrix using fast-DTW {{cite:6ab5a91f4830d3513f40ee83b258fce1d27b7ff0}}, through a readily available DTW implementation in Python https://pypi.org/project/fastdtw/. We test the performance of our model on a subset of the Mazurka dataset {{cite:3bf6d709e71dcfe9e1640094dbd6b04e3df50782}} which contains recordings from various acoustic settings. The results obtained using both methods are given in Table REF .
{{table:08076041-492a-4a45-88d1-17916c1ad9af}} | r | dc4f53b1942e74d6438461307263be76 |
For all datasets, we first calculate the set-2-vector embeddings for all baselines and SWE. Then, we apply Locality-Sensitive Hashing (LSH) to the embedded sets and report Precision@k and accuracy (based on majority voting) for all the approaches on the test sets. We use the FAISS library {{cite:d458b6579c1321319a7c3d5725f9381fe735a58e}}, developed by Facebook AI Research, for LSH. For all methods, we use a hash code length of 1024, and we report our results for {{formula:deac8425-2074-48ca-9d1c-b6b023d29c31}} . For SLOSH, we consider three different settings for the number of slices, namely, {{formula:eca2bbfa-ff72-4ff9-8011-0c95cb0cf7cc}} , {{formula:a1412f2d-455d-467b-b5f5-2d50e3343e49}} , and {{formula:f27eb2ec-d12a-4b04-9987-697b5fa4ff59}} . We repeat the experiments five times per method and report the mean Precision@k and accuracy in Table REF . In all experiments, the best hyper-parameters are selected for each approach based on cross validation. We see that SLOSH provides a consistent lead on all datasets, especially, when {{formula:8aa11d0f-8a58-41b4-8000-385be2c07f35}} . Figure REF provide set retrieval examples on the three data sets. Next, we provide a sensitivity analysis of our approach.
| r | 3f86ab12a227a23db083de4139aaf216 |
We compare our method with the following five methods.
Following the recent studies {{cite:966aebbbda94818990164e705ce1b0b4e88d74f4}}, {{cite:989cf0a0c84a418253cfa5e58293d6a8dca0dc62}}, {{cite:07eaf735dbabbfb9ace94c88b84060af8c349ad8}}, {{cite:4b90ce35433ddc03b578f265b2f711493dcfba3d}}, {{cite:93b17b858784143faa4c207f06047bb3d76b9ae4}}, {{cite:ec562fd56445cfcba1ca836e1d2d29d93f575cb6}}, we confine ourselves to the methods that do not need explicit OOD samples for training, if they are only a few. An exception is Outlier Exposure {{cite:0e6eaabb56155b0297e0593ec4c7a640fc8acfda}}, which uses OOD samples for training but does not assume the similarity between them and the real OOD samples we encounter at test time.
| m | 5fc5681da0e8c54bae28e9e6f0a95195 |
The solution of the weighting method is weakly Pareto-optimal under no additional assumptions. It is Pareto-optimal if the weighting coefficients are positive, {{formula:211faf14-f917-49a4-8f97-b4719f34ddc8}} . The solution of the weighting method is properly Pareto-optimal if all the weighting coefficients are positive {{cite:a0128fa379042a49890fc572095cdfcb9b0e5123}}.
| m | f7a64cf7354565d8f3554e38569f4c14 |
Literature search: To get a comprehensive overview of how dashboard is evaluated in healthcare, IEEE Scope, ACM Digital Library, Google Scholar, and PubMed were first searched. A combination of the following terms (including terms obtained through affixation) was used to search in titles, abstract and keywords: dashboard, evaluation, measure, and health. At the same time, we adapted the forward and backward snowballing approach {{cite:3c5a560e9677294f9cf60ba4a85a072747f65298}} in order to follow the references of identified literature and the works cited them. The initial search resulted in a selection of 260 articles.
| m | 392b7cd35e158fa13368c7dbace7551d |
Hofmann et al studied the four-partite entanglement in the {{formula:6dd9e6c9-e061-480a-a10c-f68a58abc4b7}} chain by using the genuine multipartite negativity, and found that the entanglement disappears when the distance between any two spins in the four-qubit subsystems is larger than 2 {{cite:7d76799bf7dd3c76301faba1f6fe0063b40130b9}}. Moreover, by means of the four-concurrence {{cite:4dbaba3ea22e17c8903af315b7b9edd7403413ae}}, Osterloh et al analyzed the four-particle entanglement in the {{formula:1dd5ebee-bec1-4733-8245-09b9dfdff291}} chain, where the entanglement changes to zero when any two pairs of spins are next-nearest neighbor {{cite:6c754aa96c157742c23fa85c13294e69176b7fb9}}. It is meaningful to further investigate whether the four-partite quantum correlations have the larger spatial distributions. Based on the monogamy property of squared concurrence {{cite:f61dbc1bc6a5f480358397e5bf58bf48b3b5c714}}, a multipartite quantum correlation measure is presented in four-qubit systems {{cite:9ea881c3ced11fed56d1f91290a7800208118664}}, which can characterize the multipartite entanglement in cluster-class states {{cite:87404fd5f08add77ce1962b9580c4a5563bfa9e2}}. Particularly, the MQCs utilized in this paper can be easily extended to the four-qubit case and are computable for an arbitrary four-qubit mixed state. Besides the {{formula:f652ef7a-2dff-4344-9007-0fc0efe77c39}} model studied in this work, it is worthwhile to investigate the MQC modulation and critical property in other kinds of many-body systems such as Heisenberg spin chains with the alternating-field or Dzyaloshinskii-Moriya interaction {{cite:df7aa567944338373a22707249f3b264dfb3aebc}}, {{cite:1280707ed54c9117ef2dff5c4b3a2ccd69a07242}}, multipartite quantum systems with topological quantum phases {{cite:2f8542aff452d9244d1b692432bd511be44891a4}}, multi-spin systems with long-range interactions {{cite:a350edccb343003514e9f51fbd04958e4773b3e7}}, {{cite:6879e61bdbed26b9feeb819d9be1fc976f3e2a57}}, {{cite:ff342ad0f138f28b97116b16ad56ed909c5b339e}}, and so on.
| d | efeff0723871b03e3c9b143c932bc473 |
where we used (REF ). For {{formula:b5fef9d8-390e-4fc3-942e-4ef506bd2bb1}} to be a valid zeroth-order approximation in the Solovay-Kitaev theorem, the following condition should be satisfied {{cite:0a963df768e184cd7126bd5d96bce0c6902d5ab1}}
{{formula:42c34ac8-a6a9-4ede-8a1f-db3e4599c3d6}}
| d | 07b3149aecb9d0ce6ba9dc44e65a19b9 |
which have much smaller uncertainties than the world average {{formula:0b5a7a45-530f-4529-a0c0-c13eeca4727d}}
{{cite:5dd82e735b4a52c06f44f03cca455e22c4d98539}}. A renaissance is expected in the
study of weak decays of singly charmed baryons.
| i | b668b7231b40c8c3175eab3f6c2954ae |
We then state the results from {{cite:243a195b32fcf2edae22773aa1f7f5b31dfbf34c}} under our notations.
Suppose the following conditions hold:
| r | d7e7a6f2d0a85993da1e2b41d72eee16 |
The work of kim2014temporal was seminal in the sense that it is arguably the first one employing prediction-based word embedding models to trace diachronic semantic shifts. Particularly, they used incremental updates (see below) and Continuous Skipgram with negative sampling (SGNS) {{cite:f328dc0b5c92dad6ad7c9f66041e8948bd3af8e4}}.Continuous Bag-of-Words (CBOW) from the same paper is another popular choice for learning semantic vectors.
jurafsky2016 showed the superiority of SGNS over explicit PPMI-based distributional models in semantic shifts analysis, although they noted that low-rank SVD approximations {{cite:adc6fa39b5143a4da8f8b6ec506eabe11e7b68d0}} can perform on par with SGNS, especially on smaller datasets. Since then, the majority of publications in the field started using dense word representations: either in the form of SVD-factorized PPMI matrices, or in the form of prediction-based shallow neural models like SGNS.levy2014neural showed that these two approaches are equivalent from the mathematical point of view.
| m | 65f309ee4a5b573a8a69fa4e3c536874 |
Despite the recent successes of MARL, learning
effective multi-agent coordination policies for complex multi-agent systems remains challenging. One key challenge is the off-beat actions, i.e., all actions have pre-set execution durationsIn the RL literature {{cite:fbbe8e9d8c9aee2b1bf6b43023aad834cb1d79c0}}, {{cite:dfbd1088b62772c79961f98740cd5a1cf4539f6b}}, action execution durations are called delays of actions. In this paper, we use the term execution durations, which is self-consistent with off-beat actions defined in Sec. . and during the execution durations, the environment changes are influenced by, but not synchronised with, action execution (an illustrative scenario is shown in Fig. REF ). However, Dec-POMDP {{cite:6c91ca2beaafba8cd17896e319f7d0abf09ddf39}}, which underpins many CTDE-based MARL methods, hinges on the assumption that actions are executed momentarily after inference, leading to catastrophic failure for centralized training on various off-beat multi-agent scenarios (OBMAS). To fill this gap,
{{figure:a53a5edc-da95-4f2e-8cfb-6b162758b420}} | i | c8a8736b0fea686412deecc7b784ecd7 |
It is reasonable that emotions have emerged in biological life forms for granting some evolutionary advantage and Darwin already noticed this in 1872 {{cite:146f405bf9df24a07be0e6a75b82c1c31e1c559e}}.
For instance, some emotions are useful for self-diagnosis purposes, e.g., anxiety and disgust, while others may help in combining a large number of complex stimuli, e.g., fear or joy.
However, the reason why we communicate our emotions is less clear.
In some cases, emotions are triggered instinctively and the communication is based on some sort of automatism.
For instance, a ferocious animal showing its teeth is probably trying to instill fear in an opponent.
In some cases emotions can spread among a population of individuals as an epidemic.
As a consequence, we often say that things like laugh or panic are contagious.
| i | 9cc4a384663715e30c13afef0f35b988 |
The accuracy is usually measured in the following two forms.
The fidelity of two quantum states {{formula:2114cd98-aa68-475a-b0d2-dbedf6e141e6}} is
{{formula:5e97b3ab-3583-409d-b0cc-a0195501bddb}} , then
the “infidelity” is {{formula:7705d4c5-5e00-4119-a054-a33fb6531e7e}} , represented by {{formula:56bf0714-9458-4670-9013-77315b56255f}} , and
their trace distance is {{formula:f7129691-cf67-46ed-9c51-e345d3bc46e9}} , represented by {{formula:e0915bbd-93de-4ef1-93cd-13fabd341242}} .
These are related by {{cite:12e54e1761666723dfe99352f7b2fb761a5ce9e6}}.
{{formula:78445d50-b9f1-4260-999a-5eb5c689caeb}}
| r | 699a218b9e77d2edbc2a1eb7912f5637 |
We evaluate our model through qualitative examination of the generated videos (Section REF ), analyzing color change over time (Section REF ), computing the FVD metric (Section REF ), and ablating the key design choices (Section REF ). We compare with StyleGAN-V {{cite:160a238b98130e5c7a135efe51b4b2a6166dc6ed}} on all datasets. Mountain biking, horseback riding and ACID {{cite:5fa15a33039c7f6c4675331d8203093ad86cb6ec}} datasets contain videos with a {{formula:a2a3a96d-ee7b-40d2-afd3-034b4d96a824}} widescreen aspect ratio. We train at {{formula:3b2d0364-e61e-4b4e-968f-c105b5ba2631}} resolution on these datasets to preserve the aspect ratio. Since StyleGAN-V is based on StyleGAN2 {{cite:9e937db1a2fc3dc4f5a78fe716564dbf5f591370}}, we can easily extend it to support non-square aspect ratios by masking real and generated frames during training. We found it necessary to increase the R1 {{formula:3215fcde-0a00-4ceb-9903-2b618994ac55}} hyperparameter by {{formula:fa5ba113-c488-4330-986c-fc2d1e467ed9}} to produce good results with StyleGAN-V on our new datasets that exhibit complex changes over time. We compare with MoCoGAN-HD {{cite:b6cf2fe63b1d8a22d961b388e282539a8ed80329}}, TATS {{cite:9e126c1ed65cf82479e0681f7caa4120a8a7d5ce}} and DIGAN {{cite:a62ea3242b5168bcaf9cd08e0359fdcae3fd53c4}} using pre-trained models for the SkyTimelapse dataset at {{formula:27346dc2-df54-40ff-a8ff-1325c0f944c8}} resolution. For these comparisons, we train a separate super-resolution network to output the frames at {{formula:1a4dd08f-053f-4a71-a4e0-27419aa1e0c9}} resolution, but use the same low-resolution generator as in the {{formula:5e1e7ca1-7d7f-43e1-b323-36436342365c}} comparison.
| r | 2b8c9dc4a5a2549183de4d7db206cf67 |
Human Pose Estimation (HPE) is a fundamental problem in computer vision.
HPE aims to obtain the spatial coordinates of human body joints in a person image, with a wide variety of applications such as action recognition {{cite:f3d714a4f4088ef6c7a845ee045053bcb96a43d7}}, person re-identification {{cite:4922c52a98b9533cf6705307232fbbb8b66843f7}}, semantic segmentation {{cite:b9e94c7853b8a5dae7a32ca56ecfd97eba75ec8d}},
human-robot interaction {{cite:c9ce474697e1ef6562bc80a8fa5bc3c905c4e96a}}, etc.
It is challenging due to heavy occlusions, varying clothing styles, poor lighting conditions and various shooting angles.
Earlier HPE methods {{cite:c83d22685e1704de8cb3d45d51a8c4788c158df9}}, {{cite:0feae7e25e22d17ddad9ccc984022d042064c2c6}}, {{cite:75ff53a986a5c5cda62fd226c39104893c005da6}}, {{cite:c3bfe37e7967c0c67a671c59ac368c1cdc009151}}, {{cite:e3a87ef06fc9c8a114b051a558f8b0d446417475}} adopt hand-crafted features to describe human body.
Mostly, these methods aims to learn the underlying relations between different body parts, e.g., using the seminal pictorial structure model {{cite:c83d22685e1704de8cb3d45d51a8c4788c158df9}}.
However, they are limited in accuracy especially under severe occlusions and complex lighting conditions, partly due to
less expressive representations.
| i | c83e0c686d607c549376e5910d98aae8 |
where {{formula:2f75c84b-fd7d-44e5-971a-f86b90cc8bdc}} Now, using Lemma 2.9, and the proposition at the page-92 from Marshall et al.,{{cite:eafc60cace0dae6d02e5dac968ae4ba3c1f52f9a}} we can conclude that {{formula:41518654-1544-49b9-b26a-f167eac5f58e}} is Schur-convex in {{formula:d1d55011-450f-4734-b791-2b902af69297}} . Hence, the theorem follows.
| r | 9462d09ef0f490722222825aa0360d88 |
Occasionally, the need to account for certain truly multi-physics or nonlinear phenomena brings up opportunities to develop our understanding of wave physics in temporally inhomogeneous systems: for instance, in order to realize bench-top analogues of relativistic phenomena early attempts were made to tap into time-modulated classical wave systems {{cite:aad61157d3eb6951ee22e3a4fe0389fffca0844d}}, {{cite:8482554a6e051acc2b1f8370ca2f257a803fdd86}}. However, the critical mass of research efforts needed to accomplish sizeable advances in this direction has, until recently, been lacking. On yet another front of exploration, time-crystals have been proposed in condensed matter theory for almost a decade as a stable state of matter capable of spontaneously breaking continuous time-translation symmetry while preserving long-range temporal order {{cite:52c213ec80c13c657de0d53bca0d73007150c804}}: their very existence has been questioned and revised {{cite:14bc7dcd34a1a09d7b8068b90ba1d5379be848e6}}, and several increasingly successful implementations have recently been accomplished {{cite:9b0e0b7c2d60fc59b208c4f38c8645e958cdc69d}}, {{cite:2b25330c0d53ae13a544d2ef1bea25b9539bb409}}.
| i | e8ed1ada7cbcdf23f8d79bab72f06603 |
where {{formula:82cc31d2-5591-4be7-9ed6-cb9b20ba875b}} is step-size, {{formula:2e24c09c-7b2b-4831-952d-3d53c7388908}} is a stochastic estimator of policy gradient {{formula:c7aa9a5e-2004-49e2-8b7c-87c5243b3690}} .
According to {{cite:f4e8e09ce925717c872507f31d0ed95620b55d3b}}, we present the well-known policy gradient theorem as follows,
{{formula:b2901cb5-32fd-4ea1-89e5-633bd022d7f2}}
| m | 89ffb9409539cae3f96db3a7fbbab6cd |
ANN to SNN conversion (ANN2SNN) {{cite:80f11a626980488686eb81e5fc1ea876121ede3a}}, {{cite:4eb8dca24988f5d693f4b894373fa751282654e3}}, {{cite:f16ae7594070f8ac36185223c015005c7e644209}}, {{cite:303a794d0b4d1d4e0cde7e6e1afc8403b149d9f5}}, {{cite:c4de8c27b060cce2d4e95ceb42825fe5418b793a}}, {{cite:d1c9c154dc9a71c8dab07509ae39a85d0cbfc700}}, {{cite:437f679b551ebbabd5e2f5aaac3118c2f5f2ef5f}}, {{cite:9239f5e4e97fcb55be17e638976c0b24014b507a}}, {{cite:85cd9856be8bc1203645a2a14d0fdd4984fe2333}} and backpropagation with surrogate gradient {{cite:c0f4c7003a743a76f4af886a68bc6098058f377b}} are the two main methods to get deep SNNs. The ANN2SNN method firstly trains an ANN with ReLU activation, then converts the ANN to an SNN by replacing ReLU with spiking neurons and adding scaling operations like weight normalization and threshold balancing. Some recent conversion methods have achieved near loss-less accuracy with VGG-16 and ResNet {{cite:c4de8c27b060cce2d4e95ceb42825fe5418b793a}}, {{cite:d1c9c154dc9a71c8dab07509ae39a85d0cbfc700}}, {{cite:437f679b551ebbabd5e2f5aaac3118c2f5f2ef5f}}, {{cite:85cd9856be8bc1203645a2a14d0fdd4984fe2333}}. However, the converted SNN needs a longer time to rival the original ANN in precision as the conversion is based on rate-coding {{cite:f16ae7594070f8ac36185223c015005c7e644209}}, which increases the SNN's latency and restricts the practical application. The backpropagation methods can be classified into two categories {{cite:9290a1da27afc6d149e614693b4cedb7d630b205}}. The method in the first category computes the gradient by unfolding the network over the simulation time-steps {{cite:6c98037bbc210f5605072940607dd32415354d18}}, {{cite:c2e8b3c167a38b76253555b6487cf23dbbe6ab3f}}, {{cite:9c8c821283422f1587d5b39736ce894656822403}}, {{cite:7f650a0dba476af4c66d315d6ac8d84864f2decf}}, {{cite:097c5fb911ff053706f4a2c6cc38ef35a35e52b8}}, {{cite:c0f4c7003a743a76f4af886a68bc6098058f377b}}, which is similar to the idea of backpropagation through time (BPTT). As the gradient with respect to the threshold-triggered firing is non-differentiable, the surrogate gradient is often used. The SNN trained by the surrogate method is not limited to rate-coding, and can also be applied on temporal tasks, e.g., classifying neuromorphic datasets {{cite:9c8c821283422f1587d5b39736ce894656822403}}, {{cite:8afc585dac4529b877fc1ba9249a915ab821726f}}, {{cite:528d69fdc6075797f0f7b0f0dbff750f0ac168b4}}. The second method computes the gradients of the timings of existing spikes with respect to the membrane potential at the spike timing {{cite:be8b94a728eb52b399d6c95865543b0ea4539208}}, {{cite:56f2e18eb5ef0a57410ceb67a669802deb21c525}}, {{cite:7c78e07b3a478205fa562a8da28a970053680217}}, {{cite:d5baed820a92746cfed49c92f8e26bf9d8277ad9}}, {{cite:f595235892277a2c920a9b124f1a675d4102cd8f}}.
| m | 997455b6cdf181bf4ace2a004a1a5eeb |
Theorem REF allows us to show that the distance between subspaces spanned by the {{formula:0c1f835d-3d4b-4fcc-a5e1-9fb0645faa97}} leading eigenvectors of {{formula:6f28ca48-66aa-463e-a9dd-f903ca3d55ca}} and {{formula:6ba4ea15-e0f5-4f04-b461-5da6aac36b2f}} is bounded. The well-known Davis-Kahan theorem {{cite:ccb4b9265d5acec92da4ba50162443512b995beb}} of matrix perturbation theory states that the sine of the largest principal angle between the two subspaces is upper bounded by the perturbation amount: {{formula:a57d8f28-51b4-41f1-b01c-f34da25eed5b}} , where {{formula:16490c75-f25e-4578-9bc9-53351b7d8b90}} is an eigenvalue separation parameter {{cite:c488ecc388fc033d0d2cbac21c153ae602944be6}}, {{cite:6a7ec532f0d3504d3eef922d02076f6af6ba89a3}}. Therefore, the quality of the Nyström-based spectral embedding improves by reducing the kernel matrix approximation error {{formula:5e46e500-685f-4f4c-a583-2a5c21eb8308}} .
{{figure:95642ac5-bd64-4e84-a139-800b03238801}} | r | f285936312f20ddf3650d714ccc186a2 |
According to the same jargon, when the differences {{formula:0e6f7289-a8d8-4d1f-a36b-2708b09c1991}} AIC and {{formula:69891e59-580f-4e08-a4f1-34d2dc63aefb}} BIC are both above 10 one speaks of “very strong evidence” against the unfavored model (the {{formula:4dcc9bd5-5e85-4afe-87ae-3b612c13461e}} CDM, in this case), wherefore in favor of the dynamical vacuum and quasi-vacuum models. It is certainly the case of the RVM and {{formula:6e0d75d7-3e7d-4a4b-b452-8427f0d3882e}} models in Table 1, which are singled out as being much better than the {{formula:7568f3ea-a8a6-4dd2-b834-ec0641f6e9a0}} CDM in their ability to describe the overall observations. From Table 1 we can see that the best-fit values of {{formula:3923d026-6009-485b-bf9d-54c7d08617fd}} for these models are secured at a confidence level of {{formula:399e7d35-07ce-457c-b9bf-f0ab60bd011d}} . These two models are indeed the most conspicuous ones in our entire analysis, and remain strongly favored even if {{formula:d58e1dd7-b42b-49b0-8460-a8d225e0a10c}} {{cite:6b2bab36d28e38592260bef4c457e6301ebdab7f}} is included (cf. Table 2). In the last case, the best-fit values of {{formula:a4b5c61e-cfd5-4976-8d11-3be3eeb8c68e}} for the two models are still supported at a fairly large c.l. ({{formula:782fa526-ff5d-4295-a38f-03d98de40b91}} ). This shows that the overall fit to the data in terms of dynamical vacuum is a real option since the fit quality is not exceedingly perturbed in the presence of the data point {{formula:e99b5a75-e671-4720-baab-797319c3a91b}} . However, the optimal situation is really attained in the absence of that point, not only because the fit quality is then higher but also because that point remains out of the fit range whenever the large scale structure formation data (LSS) are included. For this reason we tend to treat that input as an outlier – see also {{cite:aabe0117171e76aa954ad3641d5c263078899891}} for an alternative support to this possibility, which we comment later on. In the following, we will argue that a truly consistent picture with all the data is only possible for {{formula:f6ea49c7-3acb-4978-b03a-b736e1011267}} in the vicinity of {{formula:7bc7be96-5dfe-44ae-8398-e970c8d4a9cd}} rather than in that of {{formula:c90bd539-e2c3-4006-8ec1-080a77d62828}} .
| d | 5dd7c321cb7a906aa45ab47ac76b3fba |
Using high precision arithmetic and the re-orthogonalization algorithms described in {{cite:1d648730370638a4a68ee438df69f00d103a73fa}}, we computed the Lanczos coefficients associated to operator (REF ) for various instances of XXZ, see Figure REF . Then, following the discussion in Section REF , we plot in Figure REF the time-averaged transition probabilities {{formula:8f7b03d7-118b-4e02-a3ed-0d80d4bba45d}} for several XXZ systems with different numbers of spins {{formula:aff17c72-872f-4f3e-bc36-e55e3e56fa98}} , different magnetization sectors {{formula:cdec445c-e7a9-4aec-88c4-d61ac439fd5c}} and various choices of the {{formula:c4adf258-b822-41e3-84e9-03fcc69d7a6a}} coupling. The weighted average of {{formula:9d60b396-40f4-4379-9911-575bc5befa83}} , which is equivalent to the long-time average of K-complexity via equation (REF ), is plotted as a vertical line for each system. In each case, we plotted also the transition probability and {{formula:342471be-f060-4873-938e-c08f78371e13}} for a similar sized complex SYK{{formula:65675689-8fbb-4667-bb20-2f002d124df9}} system studied in {{cite:1d648730370638a4a68ee438df69f00d103a73fa}}. To make the results clearer we normalized the {{formula:a78ac3b1-921e-400a-adca-30f97d317ac7}} -axis with respect to the Krylov dimension {{formula:3f62f4d9-c41b-42f4-9d8f-7f94616c86d5}} for each system separately, as well as normalizing the transition probability in the {{formula:b202a06d-8a73-4ac0-9783-368909fe075a}} -axis with respect to {{formula:d066ae3e-d75c-49b8-b87d-9486ed1d9919}} .
We find that for XXZ the transition probability is biased towards the left side of the chain, whereas for SYK it is almost horizontal and of the order of {{formula:0b4f2982-4638-45ef-ad94-c999fa983ad4}} . The left-biased transition probability for XXZ moves the saturation value of {{formula:720bd51a-221a-476c-9d75-6a6e93815f13}} to a value smaller than {{formula:116b8d34-2e61-47f4-90bd-7d1c36be3945}} , while the almost flat profile of {{formula:489d016f-185c-4853-aa85-0508e6aec5eb}} for SYK gives {{formula:2e223154-d03e-4708-b4a1-9820200dc49a}} a value close to {{formula:15d2da59-6576-4f6b-8c3c-bec7bafa0f1f}} .
| r | fb8dd289c916e4d49ac5b025a27b5f35 |
The numerical explorations in this paper have opened up interesting questions that can be investigated in future work. These include a better understanding of the onset of oscillatory behavior of the expectation values as functions of the Barbero-Immirzi parameter {{formula:daf7c52c-271f-4d94-ae80-2dcffa14f104}} , which we have found to be foreshadowed by the oscillatory behavior of the absolute value of the partition function. We are also interested by certain features of the absolute value of the partition function, for example, its oscillatory regimes and its maxima, which seem to be independent of scale. Knowing how this behavior can be explained will help us to estimate whether such behavior is stable when one changes certain details of the model, and whether a similar behavior can be expected also from other spin foam models.First steps to generalize the results of this paper to the Lorentzian case have been made in {{cite:4b47a1e0fa06367c100e0bcdf65dac7c2f4aa66e}}. One should furthermore allow for triangulations constructed from constant curvature simplices, which are connected to the cosmological constant, infrared finiteness, and course graining and renormalization flow {{cite:53d4a1ec99cb589fb4c4b720827e8dcd9f2148ab}}, {{cite:7a76ff0f40894c0e81768b8a24a417c97dae37b2}}, {{cite:a80d97efa9c5862aaab0daa95cb94a1dc77ba8ed}}, {{cite:e7576e515d8b01e6f2fe95b211a7009e8a58a747}}, {{cite:ddab5e03f562688016822782f9ad5cc2ca45bf40}}, {{cite:0a7431b41bbb9b9a5773dd47dd52492f956cd572}}, {{cite:ed36b6f0a5f320dfc8f638a92c16cad1a5a74855}}, {{cite:3ff53a17a21b4bb984b8062c154f2a0e2a9544f5}}, {{cite:c21fdc522df4c4a39d9d3812516441e7b2396536}}, {{cite:3ee9ec97d3cb8e43c013abbf76dc9360d228da47}}, {{cite:908331b4e4b8e3224dcb7771efd787d6a615b742}}, {{cite:4f2e4ed0c8702cc687029e05b4b89f431704fa71}}, {{cite:7d2b1d8ea0d2b751a089515a93bd5fc6663113f4}}.
| d | 8f5139841342144174009aca3359c9a2 |
This section presents qualitative results on one scene from ADE20k {{cite:32967f56eaf8aa7f6dc2ef78aaf270f63e72eee9}} in order to illustrate the impact that different class orders have on the final predictions and how the foreground-background class-balancing can mitigate some of these problems.
| r | 976a62a19fb695550f8c1ba44bb697de |
A prevalence of (1,1) modes in this star, and in {{formula:a9d23a77-61c1-49ee-a45c-50ca026696bc}} Doradus stars in general, is beginning to emerge. This includes two modes in
HD 135825 {{cite:811d129f1c7e122d39235eb7ca72f9fe88bcf3f8}}, two in {{formula:0983d4bd-a6b7-4c35-90a0-edda93aa5970}} Doradus {{cite:d6fc88b123c643582ef17d7e14847ea3fea40b4f}}, {{cite:2fa9634ed72902672eec003eca8734bf7fdfc35f}}, one in HD 40745 {{cite:dfd956cdd61f003e080dc7ca9fa7aa1e9c579efc}},
one in HR8799 {{cite:996a4c90e54f539206a7fe23449231af8f38193a}}, two in HD 189631 {{cite:0c7235e411dc0c9ff611cb4313d4a98e1cf06658}} and two in HD 65526
{{cite:cce14048fd0f8255f01f5cdc0f0625f1a29bb65a}}. This is possibly due to the large surface area covered in each segment of a (1,1) mode, meaning pulsations have larger amplitudes and
large changes in amplitude across the stellar surface. This indicates an observational selection effect. Additionally
{{cite:492553aae643cdaf7d0d6e4d0c2e2878872d7e39}} discuss the prevalence of {{formula:2c361ce2-b9a9-49de-b1b6-a90fc91b72cb}} modes in a sample of {{formula:f32ddb2c-b73d-4f05-8f73-9f7ca5282679}} Doradus candidates from Kepler
photometry. These authors assume the dominant frequency to be the rotational frequency and they then show further frequencies to be close to this
value. This
constrains the light maxima to once per rotation cycle, requiring a {{formula:50e841f0-92fb-471b-927c-7d9dfc49ed00}} mode. The occurrence of five of these such modes
in this star suggests some physical linking between them. The identification of several (1,1) modes in this star led to an investigation into the
period spacings of the six identified frequencies (Table REF ). The asymptotics of oscillation theory {{cite:cd383dd01b9ed58808c7fb817af6f0fc6a8eaa10}} predicts a
characteristic period spacing for high-order g-modes of the same low degree ({{formula:8f019528-c169-4c42-b211-d6f7ca7982b7}} ) for sequential values of {{formula:180ddf45-9fe8-4e35-9ef7-eb1e9a22863e}} . An investigation into the period
spacings of the PbP identified frequencies shows that the spacing between {{formula:6d06c33d-5a14-468a-a296-050789dc8ace}} -{{formula:91bc8c46-6dc7-4c11-bedc-ca9178d6e193}} and {{formula:b3bd7286-a253-4b5f-8068-f418bde2f6e1}} -{{formula:f8dbcfa9-d68c-47d8-b733-34afbcc99631}} to be close ({{formula:8bed4291-9330-43d5-a86e-761ecf143bea}} d and {{formula:230fde26-b6ff-4e2d-97aa-5bc40fccfb16}} d
respectively). This suggests they could be subsequent values of {{formula:a1a72532-1ea6-4745-979d-5d35e7aa3485}} if we allow our frequencies to vary by {{formula:838def4b-7b09-4cf1-b134-338d09cef70d}} d{{formula:8fd715fd-dd05-4281-98cc-02085ccf04eb}} . The frequencies
{{formula:b438ae9a-1b04-4add-b17e-b15e48fc67bd}} , {{formula:f5f8c0b4-a39f-4133-9ebd-a68c50906d37}} and {{formula:43e342b3-d9bc-4280-b6e6-94a9809ede7d}} however do not fit with this spacing and additionally it may be that the close spacing of {{formula:b6dc79a7-a7b2-4d2a-84bb-5b2307bcf760}} and
{{formula:1d30fd07-ac95-465c-b4bb-5e34d7562f62}} is inconsistent with current theoretical models. The identification of the frequencies could be further improved by photometric studies to
confirm this. Ultimately the sequencing of {{formula:2a85d21b-58a5-4471-816a-847b9dace41e}} -values could provide us with direct information about the stellar interior.
| d | 38eacb5890800e77fc687276f994fc6b |
where {{formula:9bf486e1-b6a8-4fdd-b4d2-950d0687f0b1}} is a fixed entropy term so the temperature term {{formula:1e2f8015-5381-4998-b3b2-207ee543e7ac}} is
generally decreasing such that the degree of exploration is reduced as the training proceeds{{cite:db4dca708f8f6541b100b1e26f14b8be04888435}}.
| m | b0c378b291e8ef265c0182747c819131 |
Feature subsets – We then evaluated different feature subsets to assess which ones had greater impact on the final performance. All the results presented in Table REF used a the small model of two layer, 64-6-3 feed-forward units. The three statistics (arithmetic, geometric and harmonic means) of morphological features account for most of the accuracy while using the individual morphological features under-performs. This is probably due to that the small nature of neural network used doesn't allow it to effectively learn these statistics. The difference in the performance of inflectional similarity features may be attributed to the differences in the two pre-trained word embeddings used. The vocabulary of our "Morpho" embeddings is almost as twice as big than the fastText {{cite:5946428e4f6a524b78bacdb6990864647301f4f3}} one, even though they are trained on the same corpus and both are based on the Skip-Gram model {{cite:a54945b4a768f708d26caa3f9b528e4e39374590}}. So, comparing them requires carefully setting proper hyper-parameters {{formula:5c2bb41f-0278-49f8-9263-c847e8a7008e}} and {{formula:3ee77864-b605-4f3e-88d3-2d2b0aee4f40}} for the normalizing function {{formula:cf06c0b3-962f-4a6a-b604-11f79679789c}} in equation 4.
{{table:f579b6f9-e87a-4567-bf9b-8e365ea8242d}}{{table:79fd999b-a733-4e72-ad54-1aa3415f67fb}} | r | 86ceeb9ece2526573db34e7fd421d46f |
The present work demonstrates the compatibility between microwave optomechanics and ultra-low temperatures. The next generation of experiments will incorporate a TWPA (Travelling Wave Parametric Amplifier) in order to open the detection bandwidth, potentially down to the phonon relaxation time, while reaching the quantum limit {{cite:be097ffe31b0f81e1e9b5d4719866c6f152004ed}}. This would enable the detection of single phonon jumps in-and-out of the mechanical mode, similarly to electrons in an SET (Single Electron Transistor), which represents the "holy-grail" of quantum thermal transport experiments.
Besides, the microwave circuitry is fully compatible with standard quantum electronics; which means that future developments will also incorporate a quantum bit {{cite:d733bc574f0c3cd573534b8838f6a70dfcbf79cc}}. This would enable experiments directly focused on the study of quantum mechanical decoherence, as proposed e.g. in Ref.
{{cite:7ef48a58b5369eca8309c0106b967ba1abad8852}}. Such proposals that rely on macroscopic motion can only be implemented on low frequency devices {{cite:799ef248596815d7fbaf9b3444773f15d30500b8}}, as opposed to GHz modes.
| d | a3ac2c2113792a7bd362458d59e13c2e |
Next, we focus on the interlayer symmetric exchange interactions and our DFT+DMFT results show that significant antiferromagnetic (AFM) couplings exist in bulk Fe{{formula:f523a286-9688-44ba-af23-7c77365e976e}} GeTe{{formula:29298b5b-8085-45da-9828-7d36613258fb}} , as already discussed in the literature{{cite:77fdb48ad6cdca148655f46ea61da2867d0abf92}}, {{cite:e46b298b04ebc680ff72ea92f86357465ad6e47a}}, {{cite:0025523ec1562ad4053ee0ac92e77d9584c83075}}.
Fig. REF (a) and (b), (c) show the side view of bulk Fe{{formula:28ec5840-8f9c-4b74-80f0-001360bd38f8}} GeTe{{formula:5dd1e17b-cdd9-4ae8-ac4c-17008323e89c}} and the interlayer symmetric exchange interactions {{formula:208aa07b-e7fb-40ba-8715-86ac03294da1}} for {{formula:4ff452de-e384-4bbd-b686-a9ab48455e12}} and {{formula:e56eb8bf-b9ec-41a7-ac81-e323c9654620}} , respectively. Bulk Fe{{formula:97c09209-ad17-42d2-9843-3bd8a33342de}} GeTe{{formula:20b8877e-bcb0-4dbb-bb5c-d9ada30b0d8e}} has the vdW gap of 3.47 Å and the out-of-plane lattice constant is 16.33 Å. Note, the unit cell of bulk Fe{{formula:a419f971-1314-4e61-89b4-3cf3ff55377b}} GeTe{{formula:115d5471-2375-4f4e-a87a-d49d76f30853}} and Fe{{formula:3d1f9ccb-f149-431b-8862-52b39f2a3142}} GeTe{{formula:fc9c52e8-6281-47b0-adbe-72e5b00d3dee}} contain three formula units along {{formula:708e0108-685b-4704-9351-5c90be9672c5}} direction with thickness 29.08 and 29.20 Å, respectively{{cite:dd8c40bf3d17cdbd8ddb72e443ca5e59352fb866}}, {{cite:163700ebe83702edf3156dbc8d0cd7dc3d152bed}}. Fig. REF (b) and (c) significant interlayer AFM interactions are present in bulk Fe{{formula:e4f2e6fc-156c-43bb-99fb-ed431712f8c9}} GeTe{{formula:15bb3078-a055-4175-ac9b-caa839630ea1}} . Though these interlayer {{formula:283bdfd4-1dc4-4fda-9b07-872c4a115064}} interactions are weaker than the intralayer interactions, such exchange couplings are enough to tune the {{formula:aabc00da-0ce2-4f65-9ed2-167122aa6b2f}} . As a result, the Curie temperature changes from 260 K (monolayer) to 205 K (bulk), and this value of {{formula:39d45ae4-17e8-4539-8ab9-7886040abd42}} for the pristine bulk Fe{{formula:728a8ed3-fd8a-4418-b805-f1a75c2354d6}} GeTe{{formula:121e0098-2c52-433e-b551-8da5bad279b1}} is in excellent agreement with the previously reported experimental findings{{cite:a13b6347964ddc1a1eaeedc315ae41068ce5f37f}}, {{cite:bd740cb682d83ed91752a983847ea167dfd98810}}, {{cite:dd8c40bf3d17cdbd8ddb72e443ca5e59352fb866}}, {{cite:23329d5aaef68aa84d46559379af03016d77bd10}}, {{cite:3cc06060e82c89569bb370fee0164bdfa706ec4e}}, {{cite:1d8bc6abd95fc729c1e11ed3a3441dd4244f9807}} and computed values of {{formula:799984c7-d7a5-483c-a3cb-c326e6ed6468}}{{cite:1f75be5c823cd698606ebb58b73c8ad7fd9dc07b}}, {{cite:dd8c40bf3d17cdbd8ddb72e443ca5e59352fb866}}.
Note, from standard DFT calculations the value of {{formula:69154b65-ed0b-4538-b1d5-685bd717fc62}} for bulk Fe{{formula:03086e97-e504-49e7-9d27-a05a4565abf9}} GeTe{{formula:c2728f78-f49a-48f1-9c0e-382801b8f4da}} is found to be 410 K, which is hugely overestimated compared to DFT+DMFT and also w.r.t. the experimental reports. Fig.S13 shows the comparison in magnetization ({{formula:d857d980-4602-40a7-a49e-f7e050155439}} ) vs. temperature ({{formula:56f56c42-f388-4d98-bbcc-8a2e6db9196c}} ) behavior for bulk Fe{{formula:29786834-ed0b-486e-9734-587e8eaaf824}} GeTe{{formula:0444c1bd-c5b3-4e4e-a5af-d97d10979aa7}} between DFT and DFT+DMFT.
| d | 241869398add3415d059b92f6eb9d834 |
A technical aspect of the LMBJ potential and its parents BJ {{cite:11346f875933f2dae8346bd6fc2d525d650836b8}} and MBJ {{cite:80564eff690d075da04554da902d88a2f5f92a3f}} as well as AK13 {{cite:9470945b71057fc7181388bacbb5e227c4130e6e}} should be mentioned. As discussed in Refs. {{cite:11346f875933f2dae8346bd6fc2d525d650836b8}}, {{cite:7925f2bfdba26bc5a793b92dd931b9d9af9f8b4f}}, {{cite:e2ea086190ad510f91e664c3961fe69934f94ace}}, these potentials do not tend to zero in the region far from the nuclei, but rather to a system-dependent constant. Since it is customary to set any xc potential to zero or to the LDA value where {{formula:428ba35c-b5c6-476e-afc2-61c51fe65c88}} is very low (below some chosen density threshold) to avoid numerical instabilities, one has to be careful not to do it in a region of space where the CBM extends. Otherwise, the CBM will be artificially shifted to a wrong energy, which would also lead to a wrong band gap. Thus, one has to use a density threshold that is small enough to avoid this problem, but also not too small to avoid numerical instabilities. A value of {{formula:e76f3438-9a31-4165-8ae7-c926f8e39700}} e/bohr{{formula:5a01f2cf-edda-4c1f-b81c-7576173a506e}} seems appropriate for LMBJ.
| m | ecc8fa38dc10d11692fa16579a207a15 |
Keypoints Regularization. Ensuring a shared representation and temporal coherence is important, but not sufficient to ensure the encoded keypoints capture meaningful information about motion.
Specifically, the keypoints might collapse to a single point without any relation to the object itself. Therefore, we suggest additional two loss terms based on the terms used by Suwajanakorn et al. {{cite:84dfa336cd94f7b5629e4ac6949435fc165546ca}}. First, we use a separation loss which prevents the keypoints sharing the same location, by penalizes two keypoints if they are closer than some hyperparameter threshold {{formula:5a4619fe-b177-49aa-8bbc-cd0207a46c48}} :
Lsep = 1K2 K-1=0 r ( i=0NA - 1 (0, - ka,i- ka,ir2) + j=0NB - 1 (0, - kb,j- kb,jr2) )
where {{formula:715b7747-b095-448a-bdd4-36f41a6e67c9}} are the extracted keypoints from frame {{formula:3b4d0e9c-96a2-441e-9f48-668d90fe5f4f}} . Second, we use silhouette loss to encourage the keypoints to lie on the object itself:
Lsill = 1K K-1=0 ( i=0NA - 1 -u,v sa,i(u,v) Ha,i(u,v) + j=0NB - 1 -u,v sb,j(u,v) Hb,j(u,v) )
where the sum {{formula:3f30b624-2003-4932-a44d-67c7d46a5180}} is over all image pixels {{formula:6a56cd40-4f9d-46a1-8c06-506c000e99fb}} and {{formula:c75accf7-dc80-4ee6-a3c1-8610e58d794e}} is the heatmap generated by the keypoint extractor for the {{formula:d7be3098-4de3-4392-98a7-6230d7d53938}} th keypoint from frame {{formula:cbec07a2-a191-46e7-b0d7-d8bb244c99b6}} (see implementation details in Appendix ). Without this loss, the representation might focus on meaningless regions of the image, rendering some of the points irrelevant.
| m | ee410b9e84881e6d0d968c414a0abf1a |
If at {{formula:186fa596-c7d7-462e-9613-de6694a7bd99}} an initial distribution of {{formula:44e8553e-c0b1-4270-95d9-03d9e517dadc}} walkers {{formula:3e63b1aa-1ee2-4619-9d3f-f1e43eb73fc6}}
is generated to be equal to {{formula:b743bec5-a389-4f16-a398-6b929810ff1d}} , within a
generalization of the importance sampling algorithm of Ceperley and
Alder {{cite:cbaf51510dc38f03671d81d6d3ccd99aade5929e}} (see below), {{formula:89ff3a58-d5c4-419b-842f-b26316dbfe50}} should evolve
in imaginary time as
{{formula:22057523-71c2-41f7-9894-a5d5b469bdf3}}
| m | 8552c5579f0be314f42039709d88f8a6 |
An important question is whether it is possible to define a matrix {{formula:fcdbfa59-b115-4b31-a063-426f292c3def}} of {{formula:83c2fac5-e7f9-442d-afd4-df3972c3b7e3}} such that every graph becomes {{formula:b42c7f83-d32b-4ae5-b608-ee75e366cf04}} -DS.
In {{cite:833623467483671e19bf55a6ac9b5f6e66bbf322}}, it was shown that the answer to this question is positive. However, in this case it is more difficult to check cospectrality of these matrices
than testing isomorphism.
If there would be an easily (polynomial-time) computable matrix {{formula:8e8b7444-a479-410d-8d65-9dd5aa81fac1}} for which every graph becomes {{formula:3938aeba-0350-4089-a580-088a38ed4155}} -DS, then the graph isomorphism problem would be solved.
One can say that {{formula:ba2dae08-d0de-45b8-94e7-9efecf12c5b9}} is not such a matrix for which all graphs are {{formula:d55cc592-0e9c-43be-b9c6-aefd1677e9ae}} -DS
when {{formula:9f8e3dfa-1ad7-4e34-b146-e24d21f2cdd3}} is one of the commonly used matrices associated with graphs (adjacency, Laplacian, distance matrices, signless Laplacian, normalized Laplacian), since there exist many examples of non-isomorphic graphs that share the same {{formula:6da61e1f-9dd4-42e9-8e7b-ec660aca3cad}} -spectrum.
This leaves open the possibility of amplifying or replacing spectra with the use of more refined representations for obtaining more faithful graph information.
| i | 69ba565dcea220d3633c94d17c9a0f49 |
Cheng et al. {{cite:b318e837bcb4d075bf98308dfe0029ac52d78173}} proposed an alternative MILP formulation
which uses a variant of the Big M {{cite:f6556c1c86cc5b25eae7009f5fdefc6e83f7940d}} encoding
method for the ReLU activations:
{{formula:f3eef812-5277-4fdf-aa7c-de754f5d0f1b}}
| m | f154e58357aa7a7d14d214b372cc7e5b |
For a graph with {{formula:1c845078-e243-493a-b499-da0008cddafc}} vertices and Laplacian spectrum {{formula:e097719c-502b-494d-8413-5babdb6aee6d}}
it has been proved {{cite:84c521ffa8b7fba6267b672da80362ee80b7b8af}} that:
{{formula:92d00f65-009c-411a-b652-130ab8cb7d30}}
| r | 3c59467b54b91bfff01f7475d8f962c3 |
Canonical correlation analysis (CCA) is one of the most important tools in multivariate analysis for exploring the relationship between two sets of vector samples {{cite:e1a9765ee3727fb1f54ff6b8d1033d4b3d8e3a3f}}. In the standard procedure of CCA, the core step is a regular SVD on the adjusted cross-covariance matrix between samples. When the observations contain heteroskedastic noise, one can replace the regular SVD procedure by HeteroPCA to achieve better performance.
| d | d35cb6d2649f0654beb08df07d907fb2 |
Automatic dataset filtering has been performed to ensure that the training data only contains the optimal observation, action and reward triplet. For this we have utilized the reward signal provided by the simulator and ensured that the subsequent reward only improves from the previous value. This aids in removing the error that creeps in due to human-expert based data collection.
We have iteratively arrived at the optimal network architecture and the corresponding input image preprocessing. While Canny edge detecion enables Sim2Real transfer, it also help in overcoming issues like reflection on the marble floor which was causing the network to select the wrong action. To overcome the low-end spec hardware in the DeepRacer car, we used MLP-Mixer architecture ({{cite:d67ad613438b72152b570a1f12dd2632487b7104}}) which gave us a runtime of {{formula:dd884ca8-2df3-42db-8ca4-24ba058d8946}} ms.
| d | c17c5d6358e5f2497dfd8e31593b86f2 |
With the connection of non-negative orthogonal sparse coding to the ReLU function and convolutional neural networks clear, the derivation of the convolutional neural network forward transform required little extra work. The hyperparameter {{formula:2545c12d-a2fe-4658-b923-8949844b2499}} for each exponential distribution of each sparse coefficient {{formula:e0d1dd30-acb4-4143-8310-7f3113d650c7}} was allowed to vary as the parameters {{formula:7d962c9b-c894-4d1f-97ca-080bd2dd8c9e}} in order to let each coefficient {{formula:38956259-293c-4225-8799-569a6e22eeb4}} (output neuron) have its own bias neuron input (with value {{formula:fabe1645-a92b-432c-9447-b3d5eb9a6df0}} ) instead of having one bias neuron for all the coefficients. The model of {{cite:c732f286c826c2ef8180a3720227f1ae9c35e2d8}} also allowed different {{formula:e4a4978c-535d-46cd-85fb-8cab9624624a}} for each coefficient {{formula:57966bbe-36d2-4a7a-9778-598250342cb3}} (computed as a nonlinear function of latent variables), but here the change was made to make the connection with convolutional neural networks. The derivation proceeded the same way as that for non-negative orthogonal sparse coding (see section REF ). The difference between the findings of {{cite:52b1e386ee8d38e151350864fbcba0ddb91539e5}} and {{cite:15929f890cc5f9fdeb57d37dd602fafa8a0233cd}} and this derivation of the convolutional neural network forward transform was that {{cite:52b1e386ee8d38e151350864fbcba0ddb91539e5}} and {{cite:15929f890cc5f9fdeb57d37dd602fafa8a0233cd}} provided links to closely related problems. Both provided models with sparse dictionaries that directly applied the basis functions as filter vectors to the image {{cite:3474b11c7b4ab51708f6def3ce2782861db9e4f2}}. Here, the base model for this work was that of {{cite:983db770017ac30b769041e6fcf5aee329e8ee50}}. The prior (exponential) distribution parameter {{formula:e88f4f23-608f-4565-b1f7-e2609fa51978}} was varied for each coefficient {{formula:19e08ee1-d339-446e-8907-00cff3eb5938}} in order for the solution to match the forward transform of a convolutional neural network exactly. This way, the output of a hierarchical orthogonal sparse coding model and a convolutional neural network can be compared more directly.
| d | efc05d2342b64129e4c29886a02bb8cb |
BERT
A pre-trained BERT model can be readily applied to the NER task, by reinitializing the output layer size to match the NE labels and fine-tuning the model on the NER data.
We used the case-sensitive version of the multilingual BERT model within the Hugging Face Transformers framework {{cite:047332ff4df50e9d3a7e17c1da0ec7384e21ac81}}.
The model consists of around 110M parameters and was pre-trained on 104 languages with the largest Wikipedia content, which includes the Kazakh language as well.
| m | bdd6a40915d684cb3bb36f20813c65e6 |
Using one-hot encoding does not provide any useful information about the relationships between the tokens since the method simply assigns an arbitrary vectorial representation to each token. Therefore, pre-training the language model to learn vectorial representations would allow the relationships between tokens in the DSL to be inferred (i.e. learning word embeddings such as word2vec {{cite:3f8ac27b570c2de432aa4f1483524e9f234e2f7a}}) and as a result alleviate semantical error in the generated code. Furthermore, one-hot encoding does not scale to very big vocabulary and thus restrict the number of symbols that the DSL can support.
{{figure:ed55a757-a617-45b2-b242-39709a6d0866}} | d | defdb6387aa4a9db455d58b2ae727995 |
Limitations
Our work is the first large-scale evaluation of many CNNs and many methods, which we cover three main sets of representative methods: gradient-based, perturbation-based, and CAM-based.
Yet, there are naturally other methods not included in this study.
Furthermore, we tune the hyperparameters of each AM for each CNN separately using grid search heuristically (Sec. ) instead of a large-scale hyperparameter search.
That is, we only sweep across a limited range of values heuristically chosen from multiple rounds of tests.
We choose to include WSL, Pointing Game, Deletion and Insertion, which are representative of localization-based and score-based metrics.
However, some explainability conclusions may change when tested on ROAR {{cite:8726701adb1f499c1ac4298ce37ac1dfc25a4b4a}}, which however is not included in our work due to its excessive computational CNN-training cost at the scale of our study (i.e., testing over 9 AM methods, 12 CNNs, and 2,000 images).
Therefore, we leave ROAR for future work.
| d | f951c5fd860267c9fcf2be6954ee5749 |
For the data-driven control of unknown nonlinear systems, a common approach is to derive a data-based representation of the dynamics. If the controlled systems are of certain classes, such as polynomial systems having a known degree, the monomials of the state can be chosen as basis functions to design data-driven controllers such as presented {{cite:b12aea14fdd550f7c8c1d62d519c6ce89dc85c64}}, {{cite:dad4bf830af91312dc656893d869e0479455536b}}. By integrating noisy data and side information, {{cite:d756e71423136ef117105b1cd02f2c91907ef988}} showed that unknown polynomial dynamics can be learnt via semidefinite programming. When the nonlinearities satisfy quadratic constraints, data-driven stabilizer was developed in {{cite:d98e5236eb83b3520d4e8b8600b5419c6d01b541}}. With certain knowledge and assumptions on the nonlinear basis function, systems containing more general types of nonlinearities have also been studied in recent works. For instance, under suitable conditions, some nonlinear systems can be lifted into polynomial systems in an extended state for control, such as the results shown in {{cite:553636be2c08afe534d6db6938549c37f8a6f0d8}} and {{cite:e1d2b1c1e80b76fcd15c1417178841787078e539}}. Using knowledge of the basis functions, {{cite:2c1cb821930a5eb8220f5281250b58e18936dd3c}} designed data-driven controllers by (approximate) cancellation of the nonlinearity. When the system nonlinearities cannot be expressed as combination of known functions, {{cite:2c1cb821930a5eb8220f5281250b58e18936dd3c}} presented data-driven local stabilization results by choosing basis functions carefully such that the neglected nonlinearities are small in a known set of the state. On the other hand, if the knowledge on the basis functions is not available, approximations of the nonlinear systems are often involved. The previous work {{cite:56fac8797ec6e777944aa36a576c43a594e600be}} tackled the nonlinear data-driven control problem by linearizing the dynamics around the known equilibrium and obtaining a local stability result. According to these existing results, it is clear that the efficiency and the performance of data-driven controllers can be improved via pre-known knowledge such as specific classes of the systems or the nonlinear basis functions. Nonetheless, there is still a lack of comprehensive investigation of the more general case where the nonlinear basis functions cannot be easily and explicitly obtained.
| i | e26304fe60fee0f98fa7a7973a31702b |
New Paradigm of Designing GNN Architectures. We bridge the gap between discrete regularization framework, graph-based semi-supervised learning, and GNNs, which provides a new paradigm of designing new GNN architectures. Following the new paradigm, researchers could introduce more regularization techniques, e.g., Laplacian regularization {{cite:1ac29c44f0609712a564ce1559806270b1ddf3c4}}, {{cite:9d7e1b1d93aa324f2bb807e6d23e94768734549c}}, manifold regularization {{cite:0aeec4617029e05f592764e8933213bab34ef0bc}}, {{cite:a5b90ff019e21deb4e13ac02306c5814a4d01fbc}}, {{cite:7e461910f233341a23aa5db6c137672ee9aa2026}}, high-order regularization {{cite:86d4e7194869780d5a579c29892c386ab460ec36}}, Bayesian regularization {{cite:3b292b266ec26a4a77a22363ad2aaabf6837ca72}}, entropy regularization {{cite:4290e0f4aefd4820ed2ac7adaa3872be6657d86f}}, and consider more explicit assumptions on graphs, e.g. the homophily assumption, the low-density region assumption (i.e. the decision boundary is likely to lie in a low data density region), manifold assumption (i.e. the high dimensional data lies on a low-dimensional manifold), to develop new graph convolutions or message passing schemes for graphs with specific properties and generalize GNNs to a much broader range of graphs. Moreover, the paradigm also enables us to explicitly study the behaviors of the designed graph convolutions or message passing schemes from the theory of regularization {{cite:3bce04c88529a0d06b75b59a53eafdfb383bd5f5}}, {{cite:7e461910f233341a23aa5db6c137672ee9aa2026}}, {{cite:f488d08fcc008bfb37e3ea0f3bacce347972c203}}.
| d | 881984a01b9b460d2f7f5c322b019e82 |
Since the objective is linear and the constraints are either linear or linear matrix inequalities,
dual problem (REF ) is a semidefinite programming (SDP) problem, which can be solved by using the standard CVX toolbox {{cite:37fc628e5125ce22e51855629e01aeb05abeb5b7}}, {{cite:eced806fc0a680a157d1bab0ea381cfa4baad8a1}}.
Having obtained the dual variables by solving dual problem (REF ), it remains to obtain the optimal beamforming {{formula:b0a61dbd-8b6b-4dbc-a3d2-b8ddf07fd351}} and transmit power {{formula:94e9d36e-da16-4d11-b4df-e2d7d76e9ade}} .
To find the optimal {{formula:31fe185e-b25c-4011-bf4e-2b3c732383b0}} , we calculate the gradient of the
Lagrangian function for problem (REF ) with respect to {{formula:049200b0-fd78-431a-bbb5-3a4a86a2dd10}}
and set it to zero:
{{formula:b811cd75-a26e-43e6-8646-daaa14c2fa75}}
| m | 291c42a2a984e2f9712bcedb6e5373be |
We take {{formula:338e5e0a-b7d3-48b4-8750-5a713cdaedb6}} by fitting to the total width of {{formula:46f1b25b-7b23-49d8-99a4-fb40cafa4167}} as the {{formula:6fa2aaf0-b51e-4592-97de-47d74ed5a27e}} state. The decay widths of {{formula:39f70830-b7cf-4a7a-9688-0a2c8a358e03}} as the {{formula:6c4795d6-f5cd-4b77-a930-909a0b20c8ce}} state are listed in Table REF . According to our results, the dominant decay mode of {{formula:09f771dd-4a3c-49e6-a7cc-783ee8a34f44}} is {{formula:57443f7e-e6cf-46a6-9b48-99bb044d9ad5}} , which is consistent with the experimental data {{cite:ca04bc23f0c9b8bdfb2218dcfbea185d5adfc425}}.
{{table:dc426d43-bb23-40b9-b95c-e0001cc62069}} | r | a2d09316569441eb505f4c55ed14dca6 |
We evaluate our framework on Flickr30K Entities {{cite:bdbd3104185abe248785863bd462532316deab9a}} and Referit Game {{cite:c2fbefe4971745686424a49959a04cdeddede1b8}} datasets for phrase grounding task.
| r | 029edf4bad76f6b94991a993a87c4953 |
We evaluate the performance of our proposed FW-based adversarial training (FW-AT) against standard training, and PGD-based adversarial training (PGD-AT) {{cite:1072b743676a36861a03dc5058804e540642abeb}}.
All networks were trained by fine-tuning a standard model.
| r | 192a00fe146663dc1abf6902fded48f9 |
We evaluate our approach on the open-source RL Unplugged Atari dataset {{cite:1fd9075dd3c3059cad3f00b1206d89f35b3a76a0}}, where we show that {{formula:76276038-5694-4681-9771-3dcd80e49400}} -{{formula:b267a422-e68e-4861-876c-eb3e7f812763}} outperforms other offline RL methods. We show that {{formula:15af2229-aa1d-49d8-83e7-6b1a07924381}} -{{formula:bb25466e-0b39-4124-9950-a09d16d1ace0}} performs better on two more datasets: bsuite {{cite:e43f0b73f56ddc587fce51c55bc68f5bd97b2325}} and partially observable DeepMind Lab environments {{cite:dd4a776a966f8e103f596ee95979ad49ee02c92f}}We released these datasets under RL Unplugged github repo..
We provide careful ablations and analyses that provide insights into our proposed method and existing offline RL algorithms. Empirically, we find out that {{formula:466ecf6f-db48-4a56-b258-a7d9b5dcf719}} -{{formula:410be3bc-c461-474b-b7bc-b66f0ba52c41}} reduces the over-estimation from extrapolation by orders of magnitude, and improves sample-efficiency significantly (see Figures REF and REF ).
| i | f1e92a43661b3445d175adcdb52f7942 |
In this paper, we quantify the science prospect of extragalactic HI detections based on a planned large-scale survey, namely, the Commensal Radio Astronomy FasT Survey (CRAFTS). We use FAST commissioning data to estimate parameters including the beamsize, the gain and the system temperature. We make a mock catalogue based on the HIMF derived from ALFALFA by assuming the HIMF doesn't evolve with redshift, and HI galaxies are distributed uniformly in the nearby universe. We also study the potential impact of confusion to CRAFTS survey using model in {{cite:3516912b8c111870bbe9c2fd404a690e2e752250}}. We summarized the expected results from CRAFTS as the following:
| d | 61d111f6cf700123f93250febdc577c1 |
This paper presents the first attempt to derive a generic and automatic algorithm for optimizing the control depth of QAOA, which is more efficient than random search and more generally applicable than existing empirical or analytical selection rules. Since the control depth is a hyperparameter of the model, the depth optimization can be taken as a model selection problem. Therefore, any model selection method {{cite:0fdbb9f9f1b96f9e4988e02add86172c36bb78a2}}, {{cite:b71f847f47902e4990ba1dfa6bffdfcc55e18879}} can be considered to solve this problem. In this paper, we employ the model selection method with {{formula:46a58e35-f591-4f31-81dc-7e17a59e94af}} regularization (by additionally minimizing the {{formula:1e932906-89c6-4f49-86b6-67d797c28adb}} -norm of a parameter vector) {{cite:966adc23df43ab381e3b38eb9a605fd9472c98ff}} for mainly two reasons. First, the regularized model can be optimized iteratively, which makes it very efficient. For example, regularization techniques such as LASSO (Least Absolute Shrinkage and Selection Operator) {{cite:966adc23df43ab381e3b38eb9a605fd9472c98ff}} and its variants are often used for the automatic model selection. LASSO imposes an {{formula:7d28a349-0121-4b19-b2c5-b660f3cdc7f9}} regularization on the parameters to be estimated in addition to the objective function, which can effectively shrink the number of parameters of the model during iteration. Second, an {{formula:4d883c69-7689-4107-8e44-e1b75c6fec60}} regularized optimization problem can be solved by fast algorithms with optimality and convergence guarantee. In particular, the commonly-used Proximal Gradient (PG) descent method can be used to solve a linear and convex problem with a basic convergence rate of {{formula:b01f7faf-bbe7-4f11-aba6-a2fa1be9d0bb}} {{cite:f942cd787da941fe75d95d0ad82e067540f8e7e7}} which can be further accelerated by a line search {{cite:a46c525d909f4f15ff226ca6168e7f21a8b168d0}}, where {{formula:93c81256-3955-4e3e-89b1-e6a0ba86d72f}} is the current iteration step. Since the objective function in QAOA is possibly non-convex {{cite:3d37478012c8b6671bc0cad1ca7a84013e4c37c6}}, we also have to consider an extension of PG descent algorithm that is compatible with both convex and non-convex problems {{cite:22188c4c3c90c8689ee11274588be6e2507ccf4f}}, {{cite:368d81aaa8f35a75a39e8f2a81f6ed0f6dd93725}}. Other regularization terms can also be used as candidates if certain assumptions on the correlations between the parameters are made {{cite:7cd7c6ccec4e9f3de9e746bfcc5b5b824b372fc9}}.
| i | 885ad77d7a3a071a4e59d984fcdc8f34 |
We examine the activity detection performance and the channel estimation accuracy of the proposed algorithm through computer simulations. As a reference, we compare the proposed FAT-DL algorithm with the AMP algorithm {{cite:f222dce824c00ed724e3cf29f28aafb4907561f0}}, the LAMP algorithm {{cite:840d2f2fb76705857de7bf377ea68980be323948}}, the LVAMP algorithm {{cite:840d2f2fb76705857de7bf377ea68980be323948}}, the FISTA algorithm {{cite:2840426818a4511970527a95749712e7f7242de3}}, and the OMP algorithm {{cite:5761656529d1b182ddb8ea2cf7b5a2a386579d21}}. We use the activity error rate (AER) to measure the detection performance and normalized mean square error (NMSE) to measure the channel estimation accuracy. The AER is a sum of the miss detection probability, defined as the probability that a device is active but is declared to be inactive, and the false-alarm probability, defined as the probability that a device is inactive but the detector declares it to be active. The NMSE of all active devices is defined as {{formula:fba0871f-42f2-40b9-b140-a8c3e82207d0}} where {{formula:6c6ec35d-168d-416a-8e55-a37c81266b6b}} collects the row vectors corresponding to the active support {{formula:8feac7c5-91aa-43f8-b506-5fb38ccbc62e}} in {{formula:13f0f640-0c68-4f00-9c09-f8acfba2fec8}} . The SNR is defined as {{formula:d456e320-30c4-4f56-8889-779a69bc53fc}} .
| r | 508fd1e3cd7d907e7ad071db281cb04c |
where {{formula:a2abd6ce-d0a6-4ca7-85c9-9ab5f56d5bec}}
The above error estimate has been proved rigorously; see, e.g., Wong {{cite:ca47722ff6d9c0818ec55473995350a2cd208e89}}. Thus we have the following result.
| m | 33792248eb59e3255b6b008b54cb761e |
We have noticed that our DSA module gets global context information from features of all snippets by global average pooling, which is same with the squeeze operation in SENet {{cite:fb08437c47efdc10912aa9356c644e5971e2ca1e}}.
However, there are essential differences between SENet and DSA as follows:
| d | 6e2da1e6dfe717d43aab9c556faa7275 |
A central question in graph theory is to understand those graphs containing no copy of some fixed subgraph {{formula:6a4eb4a3-15e9-490a-a6e0-fc084fc88cef}} . In one of the first applications of the probabilistic method, Erdős {{cite:e50f255ad8b6c4dd09dfd9870e0e1328ec8ffee7}} showed that there are {{formula:e08f6947-413c-4833-b287-16b3a21c7cdc}} -free graphs of arbitrarily large chromatic number (so long as {{formula:f5d9f258-366e-4f47-ad97-d91243948a2b}} is not a forest). However, Erdős's construction is inherently sparse.
| i | 60b8300a4842ab225aa148634638378d |
All of these systems can be approximately described by a Hamiltonian of Richardson-Gaudin type {{cite:38369014bc7a8a55617e70af50a98edf940ad4cd}}, {{cite:0f7099a38368e24fc1dcfb5578b2ef00a72edf0b}}, {{cite:cba3885e3b08689b7ac948f6ebb6a301de81c25a}},
which is both classically and quantum mechanically integrable. Quantum integrability implies that the many-body
spectrum can be obtained from the Bethe ansatz {{cite:38369014bc7a8a55617e70af50a98edf940ad4cd}}, {{cite:0f7099a38368e24fc1dcfb5578b2ef00a72edf0b}}, {{cite:cba3885e3b08689b7ac948f6ebb6a301de81c25a}}, {{cite:7fb94d9d582f61086fccb772afc450734096026c}}, {{cite:7bbf870775a5c32e06c69e5443b68820538c42df}}, {{cite:ca5ff5a66a6c6b66403149591bb2c3cf07b65433}}, {{cite:661ebb668310e703a97866eb8a08e1895d50538b}}, {{cite:811fff86b256ad07919906d22989845e2cc49a13}}, {{cite:7efde3e49cc2d4752daf222c879ce2cc36efcdfd}}.
Instead, here we focus on the thermodynamic (infinite-system-size) limit, where self-consistent
mean field theory can become exact {{cite:0d1a611155f0ab645134bcf38230a1f04488a75c}}, {{cite:dfdc30ff508a44db9299416b98eca47e74258ae9}}, {{cite:a9881417c99e66cbdd2729628b25417b7e27bb4a}}, {{cite:be253f9990f266b7c43f5e0a861ffb0aa2f4affb}}.
In this case, the system resides in a pure BCS-type state at all times
(with time-dependent coherence factors), and the dynamics of generic observables (Green's functions) can
be computed exactly by exploiting the classical integrability.
| m | 7e95b680c3a27535005b4bdab99006de |
MAE: We use the ViT-B and ViT-L weights pre-trained on unsupervised ImageNet-1k from the authors of {{cite:9046fd02ce57d1a58f423b5e072958b0fae1f0a1}}. These models were pre-trained for 1600 epochs using normalized pixels as the target.
| m | 4770fff88c7a558157c5c7d0eed09b3e |
We designed a set of four perturbation functions, also called confusion probes, that operate by systematically transforming multiple-choice NLI instances in four publicly available benchmarks, which have been widely used in the literature for assessing machine commonsense performance. These four benchmarks test the ability of a language representation model to select the best possible explanation for a given set of observations [aNLI {{cite:c90a3fa86c054f9fe85facfe8cd7760729620cec}}, {{cite:0cc385d27346f61bd7cc18e15fb97446f2b5eb7c}}], do grounded commonsense inference [HellaSwag {{cite:c769b043380a75b2a12291625a2993946a06eea7}}, {{cite:d75d0b74df9a1cf922ebe3bf0eea12b348a7f0cd}}], reason about both the prototypical use of objects and non-prototypical, but practically plausible, use of objects [PIQA {{cite:9c6e17303ca64bfe0f4ce687c791190617c4e1ad}}, {{cite:26b75b532ece3bb1a4ad3ebe882b83e421a0aa79}}], and answer social commonsense questions [SocialIQA {{cite:e8b7f6a663cad606b570aac11b2407714f3b48bf}}, {{cite:ce23406bd7f11db1e97e565f6ea055ba4f5a90ce}}].
| m | 639db4486255f1009ab2f4fbfa2ade09 |
Furthermore, the dynamic communications between IoT devices, EDs, and the MEC server and the migration of IoT data tasks across the MEC network potentially cause security vulnerabilities. blackRecent works {{cite:bd217059b64efc9d3f104b74354a8174db84d05b}}, {{cite:54c7eb186c2c23cfafa1bce36916cca8dbd02edc}}, {{cite:5803385dc3e0c5b8d67f2dda44759acd4a2d0c9a}} have mainly focused on computation offloading designs for task scheduling and resource allocation, with the lack of considering security aspects in MEC networks. Fortunately, blockchain has been envisioned as a strong candidate to enhance security of MEC systems {{cite:b9ce8e849413a656362672176e3a120e2ef0491f}}. In fact, blockchain is able to provide high degrees of security and trust for MEC by employing the community verification among edge nodes via mining mechanisms such as Delegated Proof of Stake (DPoS) {{cite:b9ce8e849413a656362672176e3a120e2ef0491f}} without requiring any central authority.
| i | 0bddc2e76c2112192a1aee9de2fff386 |
One of the objectives of the hypercyclic spaceability theory is establishing sufficient conditions for an operator to admit a hypercyclic subspace. This is the case of Theorem REF which can be easily reproved with the theory developed here: for any operator {{formula:1c073746-f799-4f8d-b2e7-90f76596b279}} with {{formula:ca367af4-c973-4d66-b024-22a180568ec5}} we have that its essential spectrum (which is a subset of the spectrum of {{formula:11f162ff-7da9-45a8-9305-017ac0a03dec}} ) is included in the closed unit disk, so any weakly-mixing compact perturbation {{formula:32393d7b-c99e-4a5e-a64c-1d5ca21e1f7c}} of {{formula:2dbc31d8-2e08-41a2-bebf-6e390a7e93e7}} admits a hypercyclic subspace (use Theorem REF for the real case). We can also recover the following well-known result (see {{cite:a952371fe2f423bbf4e2bca03329f97d1992d70b}}):
| r | 2344c1db12f849f78d3933212485fd59 |
Next, let us recall the findings of
{{cite:ae6fbf0a6be7811db613dcae8406dfb35292f175}}[Proposition 2] (see also {{cite:c9fa49bc65af4b0fd8b43a1b9124378c7ec8e6d0}} [Theorems 3.1-3.3])
for the asymptotics of
{{formula:3d738952-803a-4432-a09f-c50a593fc554}} , as {{formula:8a0bbfb3-9327-43d9-b893-61dc6c0b5173}} , which will be a useful benchmark for the results
derived in the next section.
Let {{formula:e6a3d8b5-5ea5-4a7e-8422-a025f89b47e0}}
stand for the asymptotic inverse function of {{formula:18c9c3d2-e6d1-4bb4-9117-48988340d754}} ,
i.e., {{formula:88206579-f234-4647-9e20-ecaaecb3998c}}
(for details and properties of the asymptotic inverse
functions see, e.g., {{cite:8f5569d1c3c3430b48d521556058fb7ec5cfbfd0}})
and let
{{formula:fb060122-8a9d-4567-b03d-aeed86ffa948}}
| r | b9f95a2c108675416413ed7ef5f52072 |
Unlike LASSO, ridge regression has a closed-form solution without the orthogonality assumption. The solution is a linear function of {{formula:c650b9fe-22e3-42db-9681-3d19371c7034}} and {{formula:dde5a54b-8968-456e-890f-0b0b835d21d3}} given by equation REF . Under the orthogonality assumption, the solution is also a linear function, but a point-linear function (linear function of {{formula:c83ab649-b5d4-4044-8831-dab42fe3acf0}} ) given by equation REF . It is likely the case that a similar reduction in transformative power occurs with LASSO which is what made it a point-nonlinear function. In fact, the orthogonality assumption almost reduces the orthogonal LASSO (orthogonal sparse inference) solution to the orthogonal ridge regression solution except for the rectification step in orthogonal LASSO replacing the {{formula:ca09e99b-3fd1-4651-b057-0425b292c216}} linear scaling term in orthogonal ridge regression. In other words, it is likely that important transformations are lost under the orthogonality assumption. A similar effect is seen for orthogonal L0-regularized least-squares. As mentioned before, the solution to the L0-regularized orthogonal least-squares (sparse inference step of sparse coding, see section REF ) is the vector {{formula:eb666011-71ee-450a-b26a-0862ca2f1cee}} with the {{formula:e91e4700-1783-4c54-ad2c-9464627efc4a}} largest components maintained and the rest set to 0. So once again, the solution is a point-nonlinear function of {{formula:73debbe0-5a7a-43b5-8ea4-7f4c1796130f}} . L0-regularized sparse coding may be explored to improve neural networks, but since solving the L0 norm is similar to solving the L1 norm for large {{formula:def58826-ac7d-4180-9ff4-dc22573661ed}} {{cite:9eb044822235886c10d0987153a035713a5c8589}}, {{cite:9439343b334872b11b8fd52117d4e58f1eea24d8}}, {{cite:50e754afdd771d748459e8f5f831f5c40a05c9d9}}, {{cite:6cc61e340d1449b2564784796c7dac4571acb6a1}}, the L1 approximation may be preferred for highly sparse solutions.
| d | 434331e0271dd6dd7f5ba6bf5309bd90 |
Consequently, several extensions are available which include the use of 2nd order information such as preconditioning and optimizing with the Fisher Information Matrix (FIM) {{cite:966da46e6bab7b775b0c294c066dadb7bf077700}}, {{cite:ed4700ebd3d552a7de71b3c924802e92059a021b}}, {{cite:99d45d760581250b6a1e138a47d406ccf6c31ca1}}, the Hessian {{cite:2db54361804dac2f89ccaadc37ee2084f4f0903f}}, {{cite:ff88af784c69736f353678ae8748e185cf31963a}}, {{cite:e805739130e5d1b732ef903531480d3cecc300ea}}, adapting preconditioning diagonal matrix {{cite:260a30a7c0d5809003a94bbcd3148141bff2c705}}, generating samples from non-isotropic target densities using Fisher scoring {{cite:c8c3a091fc4fe69fd135d29d4314a34c7b9816c4}}, and samplers in the Riemannian manifold {{cite:cdb18dc1cf113d5b2183198b5fbda24e7ec34973}} using the first order Langevin dynamics and Levy diffusion noise and momentum {{cite:941b04bd264c6d2ab86b4caa7fb534fbf477b8e7}}. Within these methods, the so-called parameter dependent diffusion matrices are incorporated with an intention to offset the stochastic perturbation of the gradient. To do so, the "thermostat" ideas {{cite:bddd17abd8f669f62d10c19a0a6c3db9603a1a8b}}, {{cite:28145cbf77d3502d7b2f504da4b28c7be0f43629}}, {{cite:24b9a57e28213e866c576c07c31ac2ce5bcaea9a}} are proposed so that a prescribed constant temperature distribution is maintained with the parameter dependent noise. Ahn et al. {{cite:72282cfcf649f1d5dfe4abd060ab3f70f945661b}} devised a distributed computing system for SG-MCMC to exploit the modern computing routines, while Wang et al. {{cite:a4a9e8912abb69b2cc640cffa4db7d8e0fba64dc}} showed that Generative Adversarial Models (GANs) can be used to distill the samples for improved memory efficiency, instead of distillation for enhancing the run-time capabilities of computing predictive uncertainty {{cite:64a2482b2684b3c3475771f018e284451e738222}}. Lastly, other recent trends are techniques that reduce the variance {{cite:d513bc9d262a8a3597106baaf79870de7932af23}}, {{cite:9ca4582f9b657155f9aa2c360ab5cb9c5c48e01e}} and bias {{cite:a119e579e75ecc6d2d3d3fae6ba5a0aa2fa0f0fa}}, {{cite:0e6b41b26f2da52205e8962c33cd963b981ddc75}} arising from stochastic gradients.
| m | 5cff1a05ae0fd1125d221ab04c4667e2 |
obtained by substituting (REF ) in (REF ), and implied by (7.16)
of {{cite:4f364204333a200b5c9087a726cb6bc4c5e8120a}}.
| r | a4b1badba0b8581bbb84125b4004ac7d |
Let us apply the above mathematical tools to study the energy of fermions in graphene, which is a hexagonal lattice with two Dirac points that are inequal {{formula:2815c709-eba4-47aa-9651-048173c2bfab}} and {{formula:34c4f14f-9b00-4e9c-aa0a-1c4ebc945c0a}} at the zone corners {{cite:201c52f85895d7d40677a14b985bac8c1137e308}}, {{cite:3bba7699f7e4876a21e4a25b8bef1f1e4e1dcbd7}}. Both valleys {{formula:3da4eea8-e29e-4a75-8109-470a12e6b93c}} and {{formula:8ff7cc70-92e7-4f94-9f33-aa77c10d8682}} have linear band crossings in the band structure.
The mapping with the spin degree of freedom {{formula:1ce1a5b0-ed9c-4595-b38b-939a3e0ed39a}} results in the basis {{formula:c92cd41f-76ef-4eda-93f4-c4316caed4d8}} for {{formula:3d592a3b-a4e0-4bf3-9a31-2b08342c03d8}} and {{formula:7d0c2927-3cc8-4087-ad9f-7befa4c51cad}} {{cite:4161260dd5505abd6c5cd6a53681e74a3d90dc92}}, {{cite:b90b772dc6aa4ee71f62372313b481e2cc65768e}}
A As=A |s
| m | cd352adcac6e0a460cecebc8e8ec7e6f |
Classical multi-view methods such as canonical correlation analysis for dimensionality reduction estimate joint information shared by all views {{cite:67bd419dafc1c89308754b883d2e81edaed88c27}}.
Similarly, many multi-view clustering methods assume there is one consensus clustering (see Figure REF below) that is present in each data-view {{cite:15df962544e7884fb7292e5f63f602ddd3e6303a}}, {{cite:55da27e6bb1be5bc5d2c7b5888fa9145bc486698}}, {{cite:48d4df959818f37f065a5fd53011c1e582d51143}}, {{cite:345f1b2911f1de1e9474915e5e1adf85d3eb0fbd}}, {{cite:a5da074836d61c68a576120f42639f3f985e3403}}, {{cite:a5769b1b4b0b4ad0c26d6ad51874db2b4f86f326}}. A singular focus on joint signals ignores the possibility that information is heterogeneously spread across the views.
For example, environmental factors might show up in a clinical data-view, but not in a genomic data-view.
Contemporary multi-view methods examine how information is shared (or not shared) by different views.
Recent work in dimensionality reduction looks for partially shared latent signals {{cite:2e45d3ab9366e881ed90dc98f15f969eb6e9f15e}}, {{cite:ae1f4d9023dc710a8f1710bc28240b49534a213e}}, {{cite:3138b276cd9a11ea1fa874e0df5b7089a333ae89}}, {{cite:52f50f6b3c5adb70894d3e2eb3b1a85e3bd14aba}}, {{cite:460b2b3512c3df9c4846d06eeb57ab185b5703d2}}.
Similarly, recent multi-view clustering methods investigate how clustering information is spread across multiple views {{cite:6f636c81a364978b08611bda018b0af077f51174}}, {{cite:a3c6889663c93d6b6d98f7a9875878e0db875d71}}, {{cite:5f658372eddbe91f06499057a2bad190025dfcff}}.
| i | cc3ea764eb941c50ac385fdf2eb72cf8 |
In (REF ), {{formula:4f4abcdc-04a2-41a1-a50c-b14363dabbd9}} is greater than 1, indeed:
{{formula:982d213d-feaf-42d9-9cef-ff760347caf5}}
which is satisfied by (REF ).
Remark 3.10 Here are some connections to existing works where variance reduction techniques are used.
Linear convergence in expectation of the primal-dual gap was established in {{cite:c51eaff37845a7c35eb49380fa09affab83e4411}} for a different stochastic variance reduce algorithm.
The authors in {{cite:cc709ff2e1e684a5fe27ebcc0535f00d2cba572e}}
also proposed stochastic variance reduce algorithm for saddle point problems with the linear convergence in expectation of the iterates.
In the context of solving empirical composition optimization problem, the
stochastic variance reduced primal dual algorithms with the Euclidean norms were in {{cite:4b889b46b879d4f5661f408778c68dc61f0dbd54}} in which the linear convergences of the iterates in expectation were achieved.
For a special case of Problem REF where {{formula:0b453735-4d4f-4d5a-8fe5-f1099692e2a9}} and {{formula:25a24245-9885-4e69-b8f7-b4101587ea30}} , under additional assumption on the linear operator {{formula:90c6709d-4ee9-4c2e-8886-965b7c835b8d}} , the method proposed in {{cite:dbacb5cc6fe184168cd2be45611ab81fe3a1cee2}} with the Euclidean distances achieves the linear convergence rate even when the strongly convex-concave condition is not full-filled.
| r | 1197c103ef7300345bc5e8757bd490fd |
the mean lifetimes {{formula:503c9c7a-2fea-4d17-aa7e-6dd9fe81320d}} and
{{formula:23761dcf-3df2-4003-8936-972fd95af929}} {{cite:b933226800d0591d72104509a2a5a99ad2fcb82c}}, {{cite:99ac2db0a2ac3c98411e30256ed6589e05d47208}}, and
the values of the Wolfenstein parameters in Refs. {{cite:b933226800d0591d72104509a2a5a99ad2fcb82c}}, {{cite:99ac2db0a2ac3c98411e30256ed6589e05d47208}}.
Choosing the Gegenbauer coefficient as {{formula:24a0b03a-b93f-4d30-a3b7-334a3f0b8eb8}} , we extract the parameters
from the LHCb data {{cite:3d394775f2103e696240699742d2fe0ab5d3a303}},
{{formula:864fdae7-3edb-4d89-ad00-f36471410fd7}}
| r | cf5633ed27a8761f046707a7be67c2a8 |
The present fundamental particle theories are based on Poincare
invariant QFT, and, as noted in Subsec. REF , for solving the problem why a particle and its
antiparticle have equal masses, those theories involve local quantized field {{formula:4fd44668-b242-4cc3-adbe-dc31f78e2c58}} where {{formula:57579dc7-9591-421f-b970-ab99b998df94}} does not belong to any particle and is simply a parameter arising from the second quantization of a non-quantized field.
So, the physical meaning of {{formula:82fc9602-9e04-4bc1-8cea-a77186cd7823}} is not clear. Although QFT has many successes, it also has problems because,
as noted, for example, in the textbook {{cite:8831f1c6e23747937ccebb0be83e6c604d338e81}}, {{formula:8c4c27b9-ce46-436c-9bdc-69f7646fcf56}} is an operatorial distribution, and the product of
distributions at the same point is not a well defined mathematical operation.
| d | 79bc4a3f1ce6eda76aa44299018ca8e6 |
However many methods removing bias from data fail. Removing the column containing the protected characteristic is clearly insufficient due to the presence of proxy variables. A number of methods go beyond removing the column containing the protected characteristic and attempt to de-correlate the other characteristics from the protected ones. However, these approaches generally cannot account for non-linear, non-binary, and/or multivariate relationships between the characteristics {{cite:3281c8bb1dc7f9832243fc977868c0006136970e}}. To counter these problems this paper has introduced FANs.
| d | 1ec0f1271e7e0f5c214c612e902e93e1 |
To reduce the amount of computations needed when solving the chemistry on-the-fly, alternative approaches have been attempted. These include a large grid of pre-calculated astrochemical simulations which are then tabulated and used during each hydrodynamical timestep. Although this approach may limit the ability to study properly the chemistry in turbulent regions where the gas mixing timescale is comparable to the chemical time needed to reach chemical equilibrium {{cite:8f660598616ab5e97d9bf183a4a94a1987abc614}}, it may well be used to estimate the average abundances and diagnostics in the large-scale ISM. Such a methodology has been adopted in the works of {{cite:12c46f0c8d83a68dfcc6683ea8c7fe079db56e16}} and {{cite:6bea8a0c1708e5114a17631b3fc9ce27c3c5771b}} using pypdr and cloudy {{cite:dd4124af9475bb7a8f0d569cc14b18bafd6a9e54}} pre-calculated grids to study cloud-cloud collisions and whole galactic-disk ISM, respectively. Recently, {{cite:624975a8d4af0afae1e6cdf90c4d26fecd40b61f}} performed a great number of PDR calculations (also using cloudy) which have been tabulated in publicly available datacubes for usage in hydrodynamical simulations for ISM studies from local to high-redshifts. Such a methodology has been also used in steady-state calculations of large and high-resolution three-dimensional clouds on pc-scales {{cite:4a3f0de45b0885c1da84640bc42852f4196b4fb1}}.
| i | 02dca0a8e24d51f578ae1c4d78f97781 |
Table REF shows results of our proposed methods against baselines and current state-of-the-art methods at ETH-UCY datasets. Our proposed method Ours-ViT with ViT{{cite:72098b42936316277e4c2d69ed07991cc3f071ac}} feature extractor achieves {{formula:8286bb12-9385-4f25-8460-d226517b0442}} boost performance at FDE metric comparing to previous state-of-the-art method.
Table REF shows results of our proposed method against baselines and current state-of-the-art methods at SDD dataset, Ours-patch method achieves superior than previous SOTA ADE results.
{{table:fb48bc19-73e3-434a-a615-f2e7ed2ba841}}{{table:bd483d1f-ac0f-4f5a-8347-8d6ea739090f}} | r | dc2892b4284e83d0aed5c7ebad74f695 |
Diagnosis results of different methods: We conducted several experiments for fault diagnosis problem. Our proposed model is trained and tested using two different settings. First, we use Border-SMOTE {{cite:a2d564356e76b2b6c160d5b59ef0df4f43928a1b}} (B-SMOTE) and other resampling techniques to traditionally resample the minority class instances and simultaneously applied our discriminator to find the represented class for each instance. Second, we use our proposed mixture data distribution (including minority and majority class samples) to generate minority class samples and then our proposed MoGAN is trained on the new dataset. As suggested in {{cite:2ac9fc639d31f2355b1f45ada6a3e129a004e74a}}, we used Recall, Precision, and FAM (average of AUC, MCC, and F-measure) as evaluated metrics. The results are given in Table REF .
| r | 662c7af03082df1ba54381da899f20d4 |
The correlation matrices {{formula:bb01036d-e2f4-48cb-9b25-03d5d588abe1}} and {{formula:c8d5eaf9-8171-4ac6-804a-3d09bade18cd}} are computed according to {{cite:30553f14d6b9c4f7fdb8766403fe87052b41f226}} and {{cite:4a6ad0a4b31cdd3508923fa56f652f17b1e721d2}}, respectively. The size of each RIS element, required by the latter, is given by {{formula:25643d72-b7bb-497a-992a-2f21a04be250}} . In addition, the path-losses corresponding to the BS-to-RIS and RIS-to-UE {{formula:edcc6f97-802f-4ba1-a0cc-ac7533a3c54f}} links are given by {{cite:df2e6135db399b09922c667015b82efdff9639f1}}, {{cite:c2b8c9bcdcb823f59fcf86bd5f69d930ac1ae773}}
{{formula:dfc0ff5d-c085-4534-a926-63df963bcd7c}}
| r | f792731a337f1457817ea5d17d711c3d |
Matsumura-Nishihara {{cite:d5395e0df7cb669ef639b48720f04cd4256e2f18}} showed that the viscous shock wave is stable if {{formula:ef4c1b72-fc8e-415c-b0d4-b5ce4a217eba}} , that is, when {{formula:c05bed81-b088-4a60-89ec-fb771446cdff}} , the strength of shock wave could be large. This condition is later relaxed in {{cite:9db286f1a652dec1996b8e291dffc79fa6ac326b}} to the condition that {{formula:3daa9a7a-017f-4167-bae4-8e6548d4e350}} . Recently, the restriction on the strength of shock was removed in {{cite:d500c942baff2648d84db789fef95631036d1f4f}} by an elegant weighted energy method as {{formula:169fd9d7-e903-4329-a265-b0bf93d11ec7}} . Vasseur-Yao {{cite:8e0a702d3e3726129d08d6dc0cb26135d84c12be}} removed the condition {{formula:57dc2367-b8ce-45ce-adbc-14e66ae53ccf}} by introducing a beautiful variable transformation. Moreover, He-Huang {{cite:810c0c2a6e76c82232f058db90f09431a627a570}} extended the result of {{cite:8e0a702d3e3726129d08d6dc0cb26135d84c12be}} to general pressure {{formula:72de2f43-7904-4a6c-bdd3-8b191e4006c3}} and general viscosity {{formula:f8589f88-4c86-4b51-9b90-6540b66cf038}} , where {{formula:ce7c3379-a433-41f5-a37f-9c0e9d6235cc}} could be any positive smooth function.
| i | c18419e9293ad0352e3ac462cd907517 |
Baloglu et al. 2019 {{cite:5aa0f14c317dc03b3141e88dfc8ef5f745904560}} CNN+LSTM Epilepsy Normal/Ictal, Interictal/Ictal, Normal/Epilepsy, Nonictal/Ictal, Normal/Interictal/Ictal From Andrzejak et al. {{cite:679219f58a4afe9b829b1e90079bfe77e3a88236}}, 10 Participants (5 Healthy and 5 Epileptic Patients)
| d | a0c545e9c6eb9928beccf51d5bb206c3 |
which is nonlinear and ill-posed (cf.{{cite:ec72cd4eaa65c1b9ab2a7cbeb0020490c12358c6}}).
| r | d787b9cc3b9ce05e53194b3291c8f311 |
is the Krylov space of dimension {{formula:c8dbe57c-232e-4644-bc68-f47c66a7b999}} for {{formula:3df21dfe-b917-4a67-9ebe-9bc0ccf341f5}} and {{formula:898c3403-98cf-41d3-9dbc-8b184567276e}} .Notationally, we let {{formula:fec31cb5-a28d-44ac-870e-5f7bd1e2359e}} be our coefficient matrix throughout, but note that this need not be a Hessian matrix. The update
{{formula:90656fdd-3a75-44a9-965b-beb17304d721}} comes from a projection onto the Krylov space, and its computation, as well as the choice of {{formula:bd01fbcd-1ca1-426f-8031-05cc6655810b}} , is
specific to the method. We note that {{formula:c7b94899-f4c4-429a-b814-6503b38f9631}} is never explicitly computed as in (REF ). For the methods
employed in this paper, MINRES implicitly builds an orthogonal basis for the Krylov space and iterates such that the residual
{{formula:745a39d6-b38c-435a-b468-ff8f18f63100}} is minimized. CG does so such that the residual is orthogonal to
{{formula:0ce97565-009e-431d-8997-353a77c9d481}} . Other approaches, such as biconjugate gradients and error minimizing methods also exist (see e.g., {{cite:c9ca5115246b05aeab3a39ecfc74662fb5a788ff}}). More details on the Krylov methods specifically employed in this paper are given in Section
REF , and we refer the reader to {{cite:c9ca5115246b05aeab3a39ecfc74662fb5a788ff}}, {{cite:9c6b1e732098826273a478597b73d279955211e3}} for further details on Krylov methods in general.
| m | 10964b822b706e7263025a9c6f0ed47d |
Universal quantum computers are expected to efficiently solve several hard problems that are intractable for classical counterparts.
However, to exploit their full potential, quantum error correction (QEC) is necessary.
For current technologies, QEC is highly demanding because it requires precise state preparations, quantum operations, and measurements.
That is why the potential of quantum computation without QEC is being actively explored.
Such non-fault-tolerant quantum computation is called noisy intermediate-scale quantum (NISQ) computation {{cite:f9b3ae3d3e84023fca636d6e5b1e26af4c747cb1}}, and several quantum algorithms tailored for it have already been proposed {{cite:26ef926fd5f9fab035401e269311f858d6c10fe4}}, {{cite:e48528d5c7158a89ee4200140b7b54b263225c0e}}, {{cite:9307e3a1faaa2431400da64a422b3860671c5c5a}} and experimentally evaluated {{cite:0448a4ef9330109e8f6efd7df4a3f538e7d587e4}}, {{cite:5fd80fe777932d9d52c338bcdedd604f5c9f9f6e}}.
| i | 0763e9c9c030784fd441afee3b8e4c5c |
Adding Groups of Classes Together:
Next, we test our method in a dual task scenario, where {{formula:5f70b38d-c2fd-4fe8-8256-ab833c93d64a}} contains one set of classes and {{formula:15d623ca-194d-48ef-8a0f-090ae4f88fc4}} contains the remaining classes. We consider {{formula:0b79668a-2f06-41e0-b685-a6bae2d92e71}} , {{formula:14a7c52f-2120-4455-9905-7f8928895760}} and {{formula:7e8712a1-8525-452f-a6f1-3180c333674b}} settings for PASCAL VOC.
Tables REF , REF and REF show the corresponding results. The second row in each of the tables shows the upper-bound when all class data is available for training. The third row reports the AP values when we train and evaluate {{formula:604ebae5-c063-4158-b24f-8eae2642fe6e}} on {{formula:68b46467-c33d-4dfe-8a3e-58432a4c6011}} . When the second task {{formula:f3d24df4-96ad-47aa-9c9e-e4cf820058ec}} is added with standard training, we see that performance on classes of the first task drops significantly (fourth row). This evaluation is carried out on test examples from all 20 classes.
In the subsequent rows, we report the accuracies of our proposed methodology when compared against Shmelkov et al.{{cite:f11bee469dd52b0798cf0524107a7bd2e3ca91d9}}, Faster ILOD {{cite:9fc48426c1cf2e4a24b573e1578def6b889a6796}} and ORE {{cite:294eeb4728213c3ba564149d4f5769d78ced4032}}
. We see that our approach comfortably outperforms {{cite:f11bee469dd52b0798cf0524107a7bd2e3ca91d9}} and Faster ILOD {{cite:9fc48426c1cf2e4a24b573e1578def6b889a6796}} in terms of mAP in all the settings.
ORE {{cite:294eeb4728213c3ba564149d4f5769d78ced4032}} has a slightly better performance in the 15+5 setting.
ORE's capability to model unknown objects explicitly is orthogonal to our work and can be incorporated into ours. We will explore this direction in a future work.
Class-wise AP values are also reported, showing our improvements on majority of the classes.
We compare with DMC {{cite:66c12408f6e0185989e7b85660e0e72f37508b75}} in the Supplementary.
Qualitative results are showcased in Fig. REF .
| r | 033696e4cab2a5e37309d01458bf7e5a |
In REF , we compare the performance of the proposed JCEDD scheme with different modulation orders, where the power gap factor {{formula:01ba4d23-424b-42c7-ad69-b79ab6d9b7d7}} dB.
It can be checked in REF that the BER increases gradually as the modulation order becomes higher.
Take {{formula:29a3a3e5-049d-4bdc-bf81-78ce05ed8df1}} dB as an example, the BER with 4QAM modulation is slightly higher than {{formula:3800ff4f-9834-43e6-8af7-f81a1559287c}} , while that of 16QAM modulation is still very high.
This is due to the inaccuracy of the estimated CSI for 16QAM modulation shown in REF .
However, when the SNR goes higher, the NMSE of the equivalent channel gain with 16QAM rapidly approaches to that of 4QAM and BPSK.
With more accurate CSI, the BER of 16QAM modulation also decreases substantially,, and reaches {{formula:b7a2db6d-16d7-4f6d-ad22-ff4b693c2006}} around {{formula:1698ded5-8300-41a3-bfd7-5b7c2fa58b85}} dB.
Besides, we further compared the BER of the proposed JCEDD scheme with the designed receiver in {{cite:69d0437327a7618d4ece033a2a580482447fbdd7}}.
Note that the BER of the receiver in {{cite:69d0437327a7618d4ece033a2a580482447fbdd7}} is based on the knowledge of precise CSI.
It can be observed that the BER of our proposed JCEDD scheme is gradually approaching that of the receiver with precise CSI in {{cite:69d0437327a7618d4ece033a2a580482447fbdd7}} as the SNR increases.
This is due to the fact that the channel estimation is getting more accurate in our proposed scheme and can achieve similar BER performance of precise CSI receiver when the SNR is high.
{{figure:ff72d77b-9051-459e-9661-2d03f76a817d}} | r | 06854a2ed94dce7f947d97df48330e08 |
{{cite:6629ab8762bf33f50e9cc1b3cbf3a5d36b7f113f}} have suggested that {{formula:17759ac6-e8bd-4132-9cb6-fb74d01984d9}} is a BLR metallicity indicator for SDSS type 1 AGNs. {{cite:e729af1888654ad3d273f435695d69aaa843cd0b}}, {{cite:9cece8e12e7056ff854e1082c143f57e9e625cf0}}
have suggested that {{formula:3b3eb492-6b0f-44fa-8a66-6056061935f5}} is associated with the BLR metallicity. {{formula:ac04a441-06e4-4200-9c43-061e68666f1b}} increases with the increasing metallicity. The BLR metallicity can influence {{formula:9c7706ac-f870-4a65-b237-8e8d042935d3}} due to the line-driven force dominated by the metallic elements {{cite:a2059ce4c59c7994ede43b45db098cd426826b2c}}, {{cite:a192061eb677016846d8df4739173749a81d1c38}}. Thus, {{formula:d0e57632-5838-4891-8d6e-0624adb78d54}} may influence the virial factor. Three positive correlations exist among {{formula:f0886a42-0752-4d84-9247-109ec4859bcd}} , {{formula:11ea91c1-b437-4c94-9487-5256e3ddd415}} , and {{formula:db5c21d8-9da0-4cbd-974f-57e3fcb787ea}} (see Table 2 and Figure 5). Since three correlations exist among them, there should be a correlation like as {{formula:99207fd0-6444-4355-85f1-9d9d891cba89}} . In fact, there is a positive correlation at the confidence level of {{formula:4c01ad6b-7ffa-4428-b69f-7f4ce8fd434a}} , {{formula:650e753c-be83-4b87-8f1d-b9d0151f1687}} . Thus, {{formula:d5a9a3a5-00e6-47e4-af6f-c377c65fc484}} is dominated by {{formula:cb01cfef-1a4f-423d-a669-95d4637e4ac7}} and {{formula:9ec1edec-aad5-4c91-ac23-fe4c636efd27}} (or the Eddington ratio). This should be easily understood that {{formula:0d3cb811-9c3c-4a90-85e1-edd3ac87b6e3}} exerted on the BLR clouds will be larger as the BLR metallicity is higher and/or the radiation of accretion disk is stronger. Thus, the observed envelope delineating the data should be a consequence of physical effects, such as the Doppler effects, the gravitational redshift, and the line-driven force, which depend on the black hole mass, the bolometric luminosity of the black hole, and the BLR metallicity.
{{figure:2eb4be35-974f-4c83-997f-6c37b8ce94c4}}{{figure:ed739d42-216d-4818-89b2-87035b438777}}{{figure:1cb624cf-437c-4812-a90f-d6e4353900d5}}{{figure:f2c195d5-d365-47e9-b994-e6ef014d5818}}{{figure:5b6421e1-5678-4fef-a648-17dd6dda2b69}} | r | 2f7843006e93e6c140dd13db448b4039 |
It is straightforward to see that for {{formula:2f584b05-fe46-458c-9812-ce943751996a}} , {{formula:836ab529-aee6-4bc6-bec1-dc67066eb831}} reduced to {{formula:ebb4fa2a-4d18-4bd1-8288-be0f2f476ae5}} by using {{cite:a60e8f38332dd4293c2b0fbb2f196b389404d6f5}}
{{formula:e1ccd61b-b23c-43c8-8dbe-70fcab7636c3}}
| i | 17de8ca3a468422e66ed0204008629b7 |
On that path, SLAC is planning the E320 experiment, and DESY is planning the LUXE experiment {{cite:4dfd250fe64b18f50f3fb73098372d0ff7069fc8}} using conventionally accelerated [10 or {{formula:805fb323-0237-43dc-b91c-7c04ece66784}} ]GeV electron beams in collision with tens of TW laser pulses. The University of Michigan ZEUS facility will use two laser pulses (with [2.5]PW and [0.5]PW), one to accelerate electrons in a laser wakefield accelerator (LWFA) (to either [{{formula:91675ea1-8a7e-494b-9377-dd35f31ff57b}} ]GeV, or several GeV) and one to provide the EM field (with intensity [{{formula:981d6e77-d79f-486c-bd90-edd59dc972b8}} ]W/cm{{formula:0b372a55-ef8c-40ae-9e13-966c04084e2e}} , or [{{formula:02a1b61f-ba69-4cd0-a541-bdb8b5a458fe}} ]W/cm{{formula:cb71f7dd-81b3-40e4-8622-b708ae41b053}} ). Other laser facilities with active SF-QED study programs include J-Karen in Japan, Apollon in France, CORELS in Korea, CALA in Germany, ELI NP in Romania with interaction chambers with colliding [10]PW laser pulses {{cite:7acf2a5f6d785081b3c94671ff4443833255f7d5}}, {{cite:dc16208e3713762950d6a9f8dbbdfe2226f025df}}, and ELI BL in Czech Republic, SEL in China {{cite:10be0e1985d13221fcf4371dc14a544613b022c4}} (for an expanded list see Ref. {{cite:bb3fbbf3562c4ef03b24e2ad56f97b6548f2c79e}} and {{cite:173a135cc0780a5a1a4364f20dfc1a9b6833d690}} for PW laser facilities).
| i | 9e20074c24bc61e8dbdf7f995a912c97 |
If we consider the back-projected pixel-level features as pseudo 3D points, our loss function is similar to PointInfoNCE {{cite:a932b2a59d8799d1206dceb06151990dd0d7e31e}}. We both apply contrastive loss on point-level (or pixel-level) instead of global instance level, which is commonly seen in 2D contrastive learning. However, our PPNCE is applied across 2D and 3D features encoded by two different networks. PointInfoNCE is applied across features of two different point cloud samples extracted by the same 3D network. Additionally, our motivation is different. We propose using the contrastive loss to minimize the relative distance between the point and the pixel representation to transfer the 2D knowledge.
| d | f8a319349503f63fd8e1878b583cd7b2 |
Black-box evaluation: To evaluate ATD under the black-box setting, we generate adversarial perturbations by attacking the introduced baselines as the source models and transferring them to the ATD as the target model. This test can also be considered as a sanity check for detecting gradient obfuscation in the model {{cite:f0a88039fd69444e527603603ec4326823b60a2e}}. Since the single-step attack enjoys better transferability than the multi-step ones {{cite:9292be1784e9de46ef931cb6d310b14eb969a7e1}}, we use FGSM for attacking the source models. Based on the results in Table REF , ATD is sufficiently robust against all the transferred attacks.
{{table:f0734558-6bf3-44cf-a411-ff7f096cd0c4}} | r | e64ce6f443e5e1e750470151183d223b |
Fe{{formula:bd8b65bd-c92d-4790-9108-1bd5fa2817f1}} N{{formula:001ed26e-5b38-4334-91d5-f30274216116}} has a body center tetragonal structure with space group I{{formula:3c835263-ca70-4adf-a11b-d17da3812f32}} (number 139). Our PBE optimized lattice constants a=b=5.68Å , c=6.22Å and position parameters, x{{formula:ef8f1600-4d21-442b-8e2c-59ae1026ad28}} =0.243 and z{{formula:027edd76-e79a-4a77-9720-423a4f7e09d4}} =0.294 are in good agreement with the ones measured by Jack et al. {{cite:657a741c4f17f2d986ec482f6202b2ad7f115bfa}} (a=b=5.72Å and c=6.29Å ,x{{formula:5682fa8c-f818-479b-990a-8eb6f437a4e8}} =0.242,z{{formula:e139959c-f531-4608-9247-7de753738f29}} =0.293). For comparisons, we have considered other two variations of PBE, namely, PBE-sol {{cite:51180b22e16086d733c23371ba355fe23404c14f}} and revised PBE {{cite:e1d6390d2b0eb656d56b8cbd187f3e2c6a649d83}}, which also yielded similar results. The average magnetic moment per Fe being respectively 2.43{{formula:449acc40-5bcc-47da-8bd6-9701b9c97765}} (PBE), 2.45 {{formula:23784b2b-84d8-456f-8968-fc1bc945f48a}} (PBE-sol) and 2.48 {{formula:6bda11dc-50ba-46f3-9285-43cdb7bc8f53}} (rev PBE). As the change in magnetic moments are in the second decimal point we carried out other calculations with PBE functional only.
| r | 0e1b0eaf4298088363909db91a372117 |
This phenomenon of low stability must also be present in other finite
geometries, like cylindrical structures that have been proposed
recently {{cite:e5f4b755bc2b2e79462024140cb7fe6da4cf72f6}}, {{cite:be2a63ec84b6cfc3bd138fe8e1a28e7c2b6dac45}}, {{cite:35c85c012959732007213c0fa97fda02272aef7c}}, complicating any technological
application of these systems, at least at room temperature, since at lower
temperatures the energy barrier can be significant. For skyrmion based
technology to operate at room temperatures, we need to find systems with larger
energy barriers for skyrmion destruction; other DMI hosting materials such as
those with a bulk interaction, or those of increased thickness may have larger
barriers. This claim is only speculative since modifying the parameters
involved in the system, such as adding thickness to the sample or applying
external magnetic fields, changes the energy landscape and different paths
would be encountered with the NEBM relaxation, which would require a proper
analysis in a different study. On the other hand, a recent theoretical
study {{cite:4c8f447232f5d29951d766730ff6d10ee52b05d8}} has proposed taking advantage of edge instabilities for
the creation of skyrmions through the boundaries of a track, avoiding other
larger topological energy barriers from different energy paths.
| d | 18c151a9b61a314af97c79949813fcc2 |
where {{formula:f00df8e9-2150-4bbc-b8f9-30b9acea44a3}} is the estiamted number of people, and {{formula:171cbd2b-a4c7-423a-876b-34e543e3166b}} is the groundtruth number. We pre-train the front-end on ImageNet {{cite:cc687745cdf3ab0c11efc006ea6b12701d89e966}}, and then train the benchmark network on the crowd datasets. We use a stochastic gradient descent (SGD) optimizer with a batch size of 50, set Nesterov momentum to 0.9, and set the weight decay to {{formula:f2a150e0-5101-4656-b3f8-0063bf85f52e}} . The learning rate is initially set to {{formula:60905890-e664-4119-8eae-12accd144a7f}} , and then divided by 10 every 3 epochs.
{{table:2c127474-5743-46ce-82bd-dca42fd8ab35}} | m | a8d9fec10ca28e554e4f417a7906a8b5 |
Writing {{formula:28fa0b74-5b7b-4b69-a427-7961c99f98f6}} for the set of discontinuities of {{formula:2b664727-20d4-4b09-966a-c31437503c77}} , we have {{formula:53cf9bec-4809-4b7c-badc-b550ff80e8a3}} by assumption. By Skorokhod's representation theorem {{cite:b384df7a8580ba32271f90802f65e712921c82f9}}, there exist random variables {{formula:281a62db-4e05-4d48-ab27-5ae9e6f394c1}} defined on a common probability space such that {{formula:dc241489-187d-4eb8-a9fc-0fddd66c4e4a}} , {{formula:22842917-939d-4a6d-88fc-be5cd44eaca6}} for all {{formula:f4011b8e-f6f1-49f4-a53c-1a3c2a62f93f}} and {{formula:368f1575-1b92-4d76-a6c4-85596ae63ef5}} almost surely. Then {{formula:81104313-3404-44c7-a194-0a22e8a2dc6d}} almost surely on the event {{formula:0281dfc6-d8ef-4fac-98e8-83368c73a7e8}} , which has probability {{formula:89bc29ee-0a18-4b67-a47c-00ce63515f3d}} , so an application of the dominated (or bounded) convergence theorem shows that {{formula:95230900-feb3-4764-9888-6201e810635a}} , as required.
| r | 8c6b21af80bd327bcb65baafb9c79cd6 |
We study different versions of local search on variable orderings. In contrast to previous work that defined the local neighborhood of an ordering as all orderings that can be reached via one operation, we consider parameterized local search {{cite:7766c6b47d938791bb9c7bd130011c6e0740d7d0}}, {{cite:a24b07e64cfc4c48b7b702a68a3da02fcd9c1e5f}}, {{cite:068181dd6434705d996f6232c8487f974aa68a55}}, {{cite:e7a50fa39a4bc57b9ec3f1c74d9a2e184881eee5}}, {{cite:b7aa4e0c9957b8ee6109885359b1598aafe88c79}}. Here, one sets a parameter {{formula:9e0815ff-9c6f-478c-80a7-cb52b3e77375}} and aims to find a better network that can be reached via at most {{formula:ca23e1e3-34a0-46e0-882c-cbaf774e4a52}} modifications of the ordering. The hope is that, by considering such a larger neighborhood, one may avoid being stuck in a bad local optimum. We consider three different kinds of operations in this work. We first study insertions, where one may move one variable to an arbitrary position in the ordering and swaps where two arbitrary variables may exchange their positions. Recall that local search strategies based on one insertion have been studied previously {{cite:c00cdf5212a3e7ff70bd3ddb1e650b12e84923be}}, {{cite:06b536bb81054ddf578d720922388408bc697587}}. We observe that the local search problem can be solved in polynomial time for both variants if {{formula:cfe4af96-e9aa-4bf4-b980-58b60e1a658a}} is constant. The degree of the polynomial, however, depends on {{formula:be5a53f0-4b0a-4c1a-b41f-5d7e0961b8d7}} . We show that, under widely accepted complexity-theoretic assumptions, this dependence cannot be avoided. Afterwards, we study inversions, which are swaps of adjacent vertices. Our main result is an algorithm with running time {{formula:c64f2d92-5012-4b42-8d2d-07c9c2b0f332}} for deciding for a given variable ordering, whether there is a better ordering that can be reached via at most {{formula:1c407468-bb0d-461e-b248-dba83d96b2b2}} inversions. The distance that measures the minimum number of inversions needed to transform one ordering in another is also known as the Kendall tau distance as it is an adaption of Kedall tau rank correlation {{cite:f900b0c898267b0ea7f8df0e16e37e07fa0e5398}}. We then introduce a new distance that we call inversion-window distance. Intuitively, given an ordering {{formula:76f5c708-2d88-497b-9aff-e90794fea246}} we find an ordering {{formula:159de80b-1a66-4ad8-ba8b-99a217d5cd1c}} that has inversion-window distance at most {{formula:e1f63c12-9a3f-47e9-8691-c576b764415e}} by partitioning {{formula:47b95f95-68e4-4cc1-9db0-f76d8f390053}} into multiple windows of consecutive vertices and performing up to {{formula:4f3faef5-441c-4ddc-a0e2-0f6530452ae7}} inversions inside each window. This new distance extends the number of inversions in the following sense: Given a search radius {{formula:9865f958-7044-4941-9466-bfcdd22db727}} , the search space for orderings with inversion-window distance {{formula:a0e13292-9022-4baa-8f50-451ab511cd70}} is potentially larger than the number of orderings one can obtain with at mots {{formula:7bce8f45-1d23-4b1d-9e8b-c1b726899384}} inversions. We provide an algorithm with running time {{formula:478b0580-d3db-4f9d-8bca-c0e91c2faa3d}} that decides for a given ordering, whether there is a better ordering that has inversion-window distance at most {{formula:23c48c16-6cf3-490d-82dc-9aa9d34a1010}} . An overview of the distances studied in this work is shown in Figure REF .
| r | 4578e8d31365efd097d564ac32eca1b8 |
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