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Our results for the form factors of {{formula:4d135bec-1c7d-4213-8978-cfcba924b8ae}} and {{formula:14e9a11a-ade3-4cc4-aeab-3ca3730372f6}} transitions are collected in Table REF . Our results {{formula:9a81a55b-3a4f-4273-a4c1-140e4bd4f032}}{{formula:725628f1-2155-4156-b483-20f2db472193}} (S2) and {{formula:1a0611f4-d892-4d89-b108-7c4a3bee37cd}} (S1) are a little larger and smaller than the traditional CLF results {{formula:242e3124-b944-4728-ace2-a6d75303f10a}}{{formula:1900c65f-69c2-440f-87ac-1cf170af0708}} (S2) and {{formula:7ee8f358-b97b-45ca-98d7-d015ed2a9c38}} (S1) {{cite:74bd5a165325665f50a5fec671d0d62a92fd2fa7}}. The results for {{formula:d67a7672-095e-4311-ba40-afb61a61a0f2}} transition are first obtained in this work. The previous results for the {{formula:b180286e-9af3-401b-a307-a1adfe78fc67}} and {{formula:d7781d23-9820-4fb3-acdd-1fc6757a7d2d}} transitions at {{formula:9a43caf2-dbd2-4baa-b15f-1216c9fa4788}} obtained via other approaches are collected in Table REF for comparison. It can be found that these results based on different approaches are generally consistent with each other except for the large {{formula:2cbfa50a-3e7f-4375-bc53-52c203036821}} predicted by LCSR {{cite:bbdeef46c9ab2300c4528900e1cd539e02392525}}, {{cite:8d55477cbdbc756e2fcd02bd8cca3c8b8a0ab119}} (relatively small results {{formula:020eda36-b278-4fc0-a61e-60dfda0a82dc}} are obtained in Ref. {{cite:1cdd9fb913a3a8aea0d149296463dc5a52606218}}). From above discussion and Table REF , we can roughly conclude that the uncertainties of form factors associated with {{formula:3bfe34b3-6980-4eb6-a352-1d733faf2c04}} and {{formula:eea19c33-b5da-40d7-8805-d32e13062d62}} decays caused by different approaches are less than about {{formula:1e1b6bdf-a9cd-4055-be08-c677ff692d69}} and {{formula:60c5d32d-1750-43bd-849f-9bb01aa6e128}} , respectively.
{{table:bc508dd6-6a34-4926-8bb8-02de4b47382a}}{{table:69ebbaaa-8b27-4522-9528-a8e1593f657c}}{{figure:7e05e5a4-92db-4e5a-8061-15c8c5f05207}} | r | 4781deb277a62848b7b150fd968ecb75 |
There are several versions of the EnKF. In this work, because the state space has relatively small dimensions, we use a classic implementation called EnKF with perturbed observations ({{cite:d586a47c692091893d1be7b22c566a7cab9fd808}}). Because of sampling errors and unrepresented model errors in the prediction state ensemble, the prediction sample covariance is underestimated, so that the EnKF ensemble usually has a tendency to collapse, i.e. underestimation feedback between prediction uncertainty and posterior uncertainty. To mitigate this effect, the common methodologies are multiplicative covariance inflation ({{cite:d61299337fc213a279e9c9485a49a2fabed27940}}, {{cite:ea62edb4103657069a6c01c722e9795932a8c2bc}}) or additive Gaussian noise in the state variables of the ensemble member updates, i.e. additive inflation. After some preliminary experiments, we found that the intrinsic stochasticity of the SEIHRD ABM results in forecasts with enough spread so that covariance inflation is not required. In other words, the stochasticity in the ABM gives a reasonable representation of the model error. The initial variability of agents populations is given by random sampling at the initialization of agents attributes.
| r | 7cad18fd0cfa9b9d6b5c7e925b1b710d |
In this paper, as down by {{cite:11a65c7cfb4204d52733a34a5ede374ce166654b}} and {{cite:e5fa92d4a48ee8b42dde6fe9d1050e5bfd581856}}, we set {{formula:2b055818-1ff6-4841-99a1-d4cdc7d7009c}} for {{formula:67a9881f-9904-4c2c-81c7-f4104e79b95d}} and {{formula:216278d2-6a2d-482a-bedf-2795698d1f87}} for {{formula:f0556c4a-3811-4958-82ff-aa5aab9439ea}} . In {{cite:f984f8bb41218c277e1f8b118335f40e959ddbba}}, they set {{formula:50230355-b02f-475b-b9c1-29a39e620331}} for entire range of {{formula:fd9bb34f-94d0-498f-b93c-22231b963d95}} . {{cite:f3e65bea086c28f3e6e0db7fe3422800dec04db8}} compare the results of the two methods. They find that both of the mass flux and the velocity of winds differ roughly by a factor of 2. However, we note that both of the two methods are arbitrary. In this paper, the scattered and reprocessed photons are neglected. In reality, the scattered and the reprocessed photons should also affect the properties of winds. For example, {{cite:8b16dcc87121aaeedaa2283fc71ba1bbba4fee37}} find that the scattered photons can also ionize gas, which can make the gas too highly ionized to be driven by line force. However, we note that radiative transfer and hydrodynamics are decoupled in {{cite:8b16dcc87121aaeedaa2283fc71ba1bbba4fee37}}. Therefore, in future, it is necessary to perform hydrodynamic simulations with radiative transfer to study the effects of the scattered and reprocessed photons.
| d | 96bd792b9121377156f54bd4fe9aadc5 |
While the higher accuracy on observed languages could entail an overlap between LangID and contrastive loss pre-training, the robust performance on unseen languages suggests a more broad rationale. We believe instead that the observed 'critical layers' are locations where speech sounds (phones) become most distinct during pre-training. In related work, Pasad et al{{formula:d5d918a9-c547-454a-a40a-794f62fc121c}} {{cite:16ce5fe530f956856ab463c355e312ae5ed4d5cd}} saw medial layers of wav2vec models exhibit high accuracy in phone identification. Their results roughly correlate with our observations over which layers are optimal for LangID. We note that ranking n-gram frequency of discrete segments is one of the classical methods for LangID {{cite:a051f50a71d1dd8e111d86330a8e47393ae1fd3c}} and this task can be accomplished by a single feed-forward layer {{cite:2f113050f9e9449352025e58b93b62c3f53f2fe8}}. From this point of view, LangID for speech could be seen as functionally equivalent to learning a language's phonemic distribution.
| d | cc04608baeff806d3fa4dba31b6e5279 |
In this section, we first revisit the FedAvg {{cite:14658adce1c6471da085d8c4fa9e462da807027e}} and FedProx {{cite:f0bb2cdf52fcf895280f8139d683c826bec53ebc}} methods which are widely used in FL tasks. Then, we adapt two optimization methods from the multi-task learning literature to the FL setting: dynamic task prioritization and dynamic weight averaging.
| m | 83d9556cc6d6cb1ef1c8eca386bc2848 |
Metrics. To measure the anomaly detection performance (classification of anomaly slice and normal slice), Area under the receiver operating characteristic curve (AUROC) and Area under the precision-recall curve (AUPR) are adopted. In addition, we also provide the segmentation performance based on the dice similarity coefficient (DSC) because previous anomaly detection approaches evaluated the segmentation performance {{cite:3e25a443c1a88d6bc63773b8a01a9bfc3cbe4ad6}}, {{cite:5f28432664e6b435fdf114fd6e0a278b67ab8835}}. Please note that our method more focuses on anomaly detection, not segmentation.
| r | 642bdeb6867023d94fa5fcdf90277b30 |
CNN:
Proposed by {{cite:7b24098dd4445e5023cf90ba8b059e66a7e905e9}}, we perform convolution and max-pooling operations on Telugu word embeddings to get a representation of text that is used for text classification.
| m | d59b05b4bb3132ed797d9f8bc9240f7a |
Seemingly strict limits pervade cognition, from the so-called attentional bottleneck {{cite:b20fc8a2c0dfbf1ea3f71cac345a2a3a7f93274f}}, {{cite:da7560d97846cf9e9dbc7025f64af5e1ec4b20fa}}, {{cite:bedfc23e33329e920c232250f73f0f20f3598f9f}}, over working memory {{cite:7c26350f1bd8831baf297ff98a28c7b5a21c08e7}}, {{cite:86801ec0e11f40b33926c30894829cdb8c169056}}, {{cite:430056991fbf94a5a75bfd738a56188216667010}}, {{cite:1b4122916ddf9e6d75a0cfbfc1f0b4bb75b93e30}}, {{cite:ef8d6ce8baab019b93862aecda3a789d9da8ea13}}, to executive control {{cite:cbc129174f440254c7b7dd1c0b001714fb5c926d}}, {{cite:4258015bba1f3196d88d85434fb56a5d09cb36aa}}, {{cite:f9fec5c110e7015ac17756f94e4a4f676c811cbd}}. These limits might result from using scarce neuronal resources or from using them inefficiently. However, a likely alternative is that bottlenecks reflect strategies that make optimal use of limited but large resources.
Indeed, past work has recognized that some apparent limits, most notably dual tasking bottlenecks {{cite:e0e4a6b8c4d34fc98ba2458cbe3afc44b0b70773}}, {{cite:676eacd7a08bd74fc676f0f59dab594d7fa4a2ef}}, could be the result of optimal allocation of finite resources to avoid overlap and interference between the different representations needed to solve the two tasks {{cite:676eacd7a08bd74fc676f0f59dab594d7fa4a2ef}}, {{cite:075a3e4d23909fda6c716507b04b0ecf803165f5}}, {{cite:5db0ed8d855f0c487a1454a3e2b5c861c5e77846}}.
Further, it has been recognized that the narrow focus of attention could be at the heart of solution to the the binding problem by integrating separate features into a coherent object {{cite:d49dfbe695be1bc0be7a144fdd02c3e4e262aeda}}, and thus its narrowness might reflect a function more than a limitation. Our work follows this line of argument and provides for the first time a quantitative account for why it is optimal for an agent to consider a handful of options in the face of uncertainty, well above two but well below 10. In addition, our results shed light on why people might ignore hundreds of accessible options and focus resources to a very small number of options {{cite:03f4a079f73d1c553c9b23078ae216e64750f04d}}, {{cite:78789773ebe6a66c22670b716b663a9ddc0824ab}}, {{cite:3370cae4f14d49c0a72a70cbb485ee7b711a0293}}. Thus, some of the seemingly strict limits in decision making can be the result of optimal policies that favour depth versus breadth processing of the options.
| d | 4959d78eee7c1a1b13192bf932913204 |
Besides the classical macine learning metheds tested above, some popular deep learning
methods are also tested.
(1) Seg-Net is an open source project for image
segmentation {{cite:26d8659fb166da9f0847bcb993f9e39bb4087e8a}}. The network is identical to the
convolutional layer of VGG-16, with the removal of the fully-connected hierarchy and
the addition of max-pooling indices resulting in improved boundary delineation.
Seg-Net performs better in large datasets.
(2) U-Net network structure was first proposed in 2015 {{cite:60319c7f05b523523b1f897a3a34eec12aa25c16}} for
medical imaging. U-Net is lightweight, and its simultaneous detection of local and
global information is helpful for both information extraction and diagnostic results
from clinical medical images.
(3) MedT is a network published in 2021, which is a transformer structure that applies
an attention mechanism based on medical image segmentation {{cite:272ea049fc05a0e0d07dae1d075f59fb1b0d3fd2}}.
The segmentation results are shown in Figure REF .
{{figure:6bb681fa-a474-465e-a2ec-6950d7ae4e00}} | m | a2ecb95cca828d75b7905c3094271b5a |
with {{formula:3ed75099-36dd-4211-9b66-d57b80104344}} for a total surface density (stars + gas) {{formula:7e4b0522-c58f-49cd-86c1-2788bbada335}} and {{formula:c4e8a483-167e-4fc5-84aa-a84e97f2a869}} otherwise;
the metallicity derived from (O/H) by using
{{formula:8e1b3f80-05b2-40a1-aee9-95743308a66b}} so that {{formula:8dd2da56-6948-43a0-b7ab-4ccbf1224f89}} for the MW disk environment (assuming it follows the Solar mixture). Equation REF further assumes that the characteristic surface density of molecular clouds in a galaxy and in the MW is the same and equal to {{formula:18ac6264-29a5-4033-8cff-b6a2e915888f}} {{cite:9db3fb11f793c27520116c74e06a96e419dd8eef}}.
| m | 6781f9894158c97f4b3e63d6e3cfe7c4 |
paragraph4
.5em plus1ex minus.2ex-.5emBlending Pasted Objects.
For composing new objects into an image, we compute the binary mask ({{formula:4f41c9a3-f94e-4b9d-90f3-7378b12d1357}} ) of pasted objects using ground-truth annotations and compute the new image as {{formula:00ce27c3-3866-455f-acfc-6de2057e8149}} where {{formula:927b5c15-9c2e-4849-8501-8ed56be6abc9}} is the pasted image and {{formula:0349b40c-6f6a-4a5d-90bb-ac772b4b822b}} is the main image. To smooth out the edges of the pasted objects we apply a Gaussian filter to {{formula:04ff23ba-e144-43d9-bb7d-8d18c51177a8}} similar to “blending” in {{cite:ca1ed44f68524a2dbf972c47b810d8646b7c50b5}}. But unlike {{cite:ca1ed44f68524a2dbf972c47b810d8646b7c50b5}}, we also found that simply composing without any blending has similar performance.
| m | 62b8babf668afe1981b68eaa5ad86326 |
First, we calculate the key rates of the asynchronous-MDIQKD protocol with a short time interval {{formula:7567e62b-4a4f-4894-a039-30eae062ff7e}} . The detailed formulas for simulating our protocol are presented in Appendix . The statistical fluctuation analysis formulas are presented in Appendix . Fig. REF shows a scenario in which phase tracking is removed. The time interval {{formula:39dc91c6-1a97-4da5-8970-9c13ac3f04d0}} {{formula:705d7bbc-4da9-4577-8f6d-c30aede78ccf}} , and the system frequency is {{formula:477c3374-95c0-4904-9c8b-0c22255cd0ce}} GHz. We assume that the angle of misalignment in the {{formula:1e3097ac-107a-409d-9196-fe86756f57d0}} basis {{formula:55d13d8c-ce68-4f9c-ac91-f21247195a86}} rad. The key rate beats the PLOB bound at 280 km under the condition where the data size is {{formula:99d3eb46-b309-4124-9806-5f9e72aeada1}} and the transmission distance reaches 450 km. One can also transmit over more than 420 km and overcome the PLOB even with a data size of {{formula:9f8ef6a7-b4ac-4303-ba39-542e04d3d0f0}} . The key rate in the case where neither phase-tracking nor phase-locking techniques are employed is shown in Fig. REF . Here, we set {{formula:955951ed-c8e0-41b0-b84c-07c2e26a88a0}} and {{formula:32bbdaa8-577b-4771-9ad7-686160903f79}} GHz. The simulation results show that the proposed protocol can overcome the PLOB bound at 270 km. The secure transmission distance is larger than 380 km, and the corresponding loss is 62 dB. In free space, if the Micius satellite {{cite:1557c6ee9c2d0ef53d88fc715e41cd45b77c02a3}} is used as the intermediate station Charlie, the key distribution between two ground nodes with a distance of approximately 1000 km can be realized. At an intercity distance of 300 km, the key rate is 0.15 Mbps, which is sufficient to perform a variety of tasks, including audio and video encryption.
{{figure:3482f88d-546a-4a08-9180-adeef9d8e4f8}} | d | ee176b5e137bd764f0ff76314677a4cb |
where {{formula:e23e176d-631c-40c8-b4cd-7a02f086eaed}} is the density of a crystal. The calculated value of density {{formula:950e3de1-683e-4b21-bec7-a78ff1e14541}} is 4.94 g cm{{formula:be5f43c9-d431-420d-b8d6-f086b7835764}} . This value is in good agreement with the experimental value for pure CdSe {{cite:3ed9ad722d91105cd2ffd2ace487433ed0bec3e3}}. The calculated acoustic velocities in different directions are presented in table REF .
{{table:dbdabccf-3bc4-480d-b3ee-fd1a137dab4e}} | r | 9e8ff5a45ed178b565f66be48abcf445 |
as the corresponding world average, which has an amazing precision of {{formula:36db8a17-8dae-40e3-871c-77437d3eddf3}} parts per million.
On the other hand, the outcome of the Muon g-2 Theory Initiative for the Standard Model prediction of this quantity {{cite:629b469d55832c500fe66840c025e5b6325d65a5}} This result is based on Refs. {{cite:b277a0582e839342c4efa5d4d6ffa845f69cf0e9}}, {{cite:127b98ac0d2902371626ba1c75f31b881275c7f5}}, {{cite:e395128a7e3eaf75b08c1402e4cc74f6a1bdb333}}, {{cite:a08236bfbcff3418e0137d35eedcd3d395a548aa}}, {{cite:249f3d066934ac228330cd5a4119f20d01027131}}, {{cite:e37e49e865124be159c44d6450438dacc3041a6c}}, {{cite:b3544880226d4243e0bb200f3e7f38fee0458e74}}, {{cite:3f78432a3c5c37142d02088c397919c92f9f290a}}, {{cite:07f6a1328955a6acbeeb30b82d94f6e93859b7a1}}, {{cite:f3adeead9db478f0d4396ea5db7425acc7a928e9}}, {{cite:36f39d7991a5c002ae4486dfad1ad2d60c9001fe}}, {{cite:69b66c86f212ce8179149a7aea3446e3b89dab48}}, {{cite:08609313a8583dc9b9cd474e4376247321f55304}}, {{cite:3c1cbf40bb2c3f3ac7150bf4accb1198d0e57cec}}, {{cite:cc71e7bb1e56814e3df6c5d6138308f57cbd9fc4}}, {{cite:92e6c1780e671b46ed63e22e7befd0acf661e967}}, {{cite:30d16ac3c632a871ccbf98a6cca05554bae0b99c}}, {{cite:6b5770a31a97c21d238ad39bf5c275577da98532}}, {{cite:36c264ecc8be1897fa4892e9ecc98a3865a55b3a}}, {{cite:1e15d7de974fe18c3163cef02abfda2f94030040}}, {{cite:da0fd3c729242c242a0ca12a5c97400672f3419d}}, {{cite:68ef395b9456cd7f996e91cd58cacf9a022ca061}}, {{cite:98b80a6cbc44cff481ed06fac1f74d5feb03cb33}}, {{cite:3fede7dce9658cd39bc1fd4cb1c3d4ec45f82f82}}, {{cite:e198e2c709cdace139957903395ee9675713b00a}}, {{cite:0ad8acf698cd2d673cff8544ec7d6428df1a04b4}}, {{cite:328c0ad9492140c07cf7958fb3722efcc21a3bd8}}, {{cite:0715c6a8fe716063758b8d225e5bf4977da35a47}}, {{cite:273bd9c76df47094ba6fe98be0cdbb191fe4c0fd}}, {{cite:76a028bdbf6b7404369901b6bee56bf919c6f808}}, {{cite:4088e072f4fbbc4a95eea08dccf78711be863d92}}, {{cite:20776efa143a03bb641b307643520fe21e056d60}}, {{cite:0db409740500ad6039a955065f65419ccf1b1bd6}}, {{cite:7f07d38ef26ba0fd0523c62ccfbefecc813a7b63}}, {{cite:8b0533b164d40eb8c5c788d696ccf848dd441113}}. Later developments, after the cut for inclusion in the White Paper {{cite:629b469d55832c500fe66840c025e5b6325d65a5}}, include Refs. {{cite:d5376abd4fffa0190e22460b71c17726faa6b953}}, {{cite:84d0174c5425eaac4f2234f0086f25fb89e033b3}}, {{cite:dbedc6fc595430b91166eab5c42ec883a13ef654}}, {{cite:438b43acccbc488ee3858ab2146f92937490ec6c}}, {{cite:66cd13c4f7a6eff52753daad5d2e9902e2057978}}, {{cite:e85b811d7898a5b75b25657f207a7e73db9ce19b}}, {{cite:fc873a8a2f79fa6786fc10bbed5b3c034af74655}}, {{cite:cfc984cf5e75396234e46d2d3fae467485381fe0}}, {{cite:842b5cc32eca0594e0fc6203f77cf522f0ad6b47}}, {{cite:5361fa21fe816ec90e1d7c8402fc10220e9dd938}}, {{cite:a42b060da13ef436df8faa88e058eef0c27bc39a}}, {{cite:3c328d64d4079203d6875f6b76dcbd4c53032a0b}}, {{cite:e559d87694edffd27e6bf9beb948b09f797dc21c}}, {{cite:a6d4ff88cc52fb175324d671112b01092a4a2911}}, {{cite:5e20b237101cdb081deea254da750fde72b13ea2}}, {{cite:f8869c7914b5e5023513951bd88a907338d9834e}}, {{cite:f220ff0a3f3fe6c8040b672bee8f00d7936e88e2}}, {{cite:f00a2cfd390812c200a63b4b11e725254a6ffe7a}}, {{cite:f3cc119442db73ad3bfe2bbc04a64bdb45449279}}, {{cite:c704ef74831357c65b78c6b8315e1ce275227552}}.,
{{formula:af581816-3229-4126-99db-ffe1b5519d92}}
| i | b189e60f38ea116ab7018549826b2e61 |
The same as the classical Gauss hypergeometric equation, the Heun equation has several confluent forms. Indeed, there are four standard confluent forms when two or more singularities merge into one or more irregular singularities (cf. {{cite:ca3093ce4dfa226a780a36e5f71b34891d586ff2}}).
| i | 3a54fbc4585b1a5a118210d6c3db286f |
The Intra-Modal Regression module leverages CatBoost {{cite:8663fa17d9504cc3d0d8b530468a76b7e9ff90e4}} that uses gradient boosting on decision trees for intra-modal test query regression. For each model pattern, we use all available spectral bands as the input features and the output query band as the regression target.
| m | 6c02dc859ac27d0aec17f592d0fe0f8d |
By combining the two aforementioned directions, we believe that the active–interactive segmentation model is the future which aligns beautifully with the life-long learning paradigm {{cite:a244b239afa7490696a4dc7a959f13297ab1cba2}}.
| d | b4b23c67e400433a8457ebab0b78d45a |
Is PALMER less expressive than standard deep Q-learning: Two important premises of deep Q-learning {{cite:e2bb3b4e2e0fa581c24f19efdba8ed46c6aa931f}}, {{cite:64b1773b169e5d90d106f8af7c3313315e7fa493}} are: i) minimizing Bellman error through temporal-difference (TD) updates can restitch observed transitions in new optimal ways {{cite:99fc876b754d4cf93895d22b1cdad6b6632d43cc}}, {{cite:7e88fbae2722bfc6df492b0819a7dc81bb43f07e}}, ii) a neural network can learn to extrapolate Q-values to unobserved but close-by states in high-dimensional spaces (e.g. images) {{cite:4ecd28efa433e3b4ce2600d0d9005c3fd238bece}}. Both arguments are equally valid for our approach, since it can: i) restitch transitions at arbitrary resolutions (i.e., anywhere from one-step transitions to multi-step trajectories) by virtue of sampling-based planning, ii) group together close-by states through {{formula:8b6829f8-736b-4525-9ed1-a9434fac7b90}} . Therefore, PALMER is an RL algorithm that: i) optimizes Bellman error through sampling-based optimal planning rather than gradient-based TD-updates {{cite:4ecd28efa433e3b4ce2600d0d9005c3fd238bece}}, ii) performs extrapolation between states using a perceptual-backbone {{formula:257c11cf-48f2-43fa-bd34-baaa768ab559}} rather than a deep Q-network, and iii) replaces the greedy-policy {{formula:af8cb90c-fc1f-4510-96d5-b485c1d4b0bc}} and value estimate {{formula:4bd4dc13-11a4-42f4-9feb-70a04b9bd92e}} with {{formula:a2cff8db-fbb8-47e9-ac20-27086852c8ff}} and {{formula:26fe68e8-f4d9-4b1a-988f-addccf2e37c7}} respectively. The key benefits of these alterations come into play when {{formula:db577ba1-c554-4e73-b0f5-d0e8e175b89d}} and {{formula:ee04e791-4d8b-4ee0-a4f5-260db4ec912c}} are far apart, and these benefits are: i) the PER mechanism in eq.REF that prevents hallucinations in {{formula:1a599d02-9675-46aa-a891-b47a0db37510}} , ii) global propagation of value estimates by virtue of employing sampling-based planning methods, which are known to be particularly proficient at searching high-dimensional state spaces across long-horizons {{cite:7fbdcc8fd311105972857052cbe8c65dc209a09e}}, {{cite:747aa73d971999c5b026467c6b729ca91c369511}}.
| d | 89bc5b6ca92514cf26744d5d47f31688 |
We report the results of the models trained on MS1MV3, and tested on various benchmarks. The results are shown in Table REF . As observed, on LFW which is saturated, our proposed methods achieved top accuracy along with a few other methods. On the pose-sensitive dataset CFP-FP, our part-fViT has obtained the accuracy of 99.21%, surpassing the other state-of-the-art methods of VPL {{cite:c0d3deac68502912915c1126149a9ee5ed8e69cd}} and Arcface-challenge{{cite:d776555d2ab7e573f67e558d12bf4d56150441d7}}. Similar results are observed for IJB-B and IJB-C benchmarks: not only does our part fViT outperform the other state-of-the-art methods by significant margin (97.29 TAR on IJB-C, 96.11 TAR on IJB-B), but even our baseline fViT is the second best method (97.21 TAR on IJB-C and 95.97 TAR on IJB-B). Similar results are obtained on MegaFace evaluation, where our part fViT is the top performing along with a few other methods. The only exception is on AgeDB-30, where our part fViT obtains 98.29%. We need to mention that the loss function used is CosFace {{cite:a2ae56e5986f0ace8c2fa161f6f02724b336d966}} which was chosen for its simplicity and stability. It is possible that using more advanced loss functions for training, including VPL {{cite:c0d3deac68502912915c1126149a9ee5ed8e69cd}}, ArcFace {{cite:394186247352d765855a570a1768bfb580ebfc00}} and Sphereface2 {{cite:9a08392d8eb148c57275a251a3d181ac71c390ea}}.
{{table:6463758e-6a7f-47a5-bdb8-240d5f45412b}} | r | 9d38ad987ad87bfafcabb707c19ab440 |
To this end, we have conducted a large-scale psychophysics study using a fast-paced animal vs. non-animal categorization task. This task is ecologically significant and has been extensively used in previous psychophysics studies {{cite:6b531a8288ef558dbc8d93020baf8f1640f5e192}}. We have considered 3 state-of-the-art deep networks: AlexNet {{cite:88ecbe19b1a5e29fc0f590abd716dcfecf854b4e}} as well as VGG16 and VGG19 {{cite:22dbc41b5c284a6eca812714bb1cfccb01c034d5}}. We have performed a systematic analysis of the accuracy of these models' individual layers for the same animal/non-animal categorization task. We have also assessed the agreement between model and human decision scores for individual images.
| d | ba738b0348d5e66da4bfd0faf4c25554 |
Copy methods stem from Pointer Networks {{cite:058503dd118d090b50cd0bb30db51ad2b5bbf4be}} which use the attention distribution produced over the input sequence to choose an element from the input at each decoding time step. While at its core Pointer Networks only allow copying elements from the input, Copy Generator Networks {{cite:534a278402ba29476c1cddc488754b23dd9ad4bc}} support both generation of new tokens and copying relevant tokens from the input. Our code generation task benefits from having many tokens in the input sequence in common with the output sequence, such as variable names and method identifiers. These are notoriously troublesome for sequence generation tasks since they are often very rare in the small code-descriptions pair collections. As such, Copy Generator Networks provide an effective method to emphasize tokens regardless of their frequency in the dataset by copying them from the input.
{{formula:c2c4fab7-009b-4960-9091-fb5f4d4c36df}}
| m | ea80434e2ad65f8fcb98444e672c2eff |
Here, we demonstrated a possible connection between the near-critical branching dynamics of the NALSM liquid and the edge-of-chaos transition (See Appendix REF ). The critical branching transition has been extensively used to model critical dynamics in brain networks {{cite:e7c5ab3944488961cbd28d21f2ecd10df1405a34}}, {{cite:bbc813bba70a41a8d267480229643b8d4790a209}}. Focusing on the computational benefits of criticality, machine learning has mostly examined network dynamics at the edge-of-chaos transition. Although the presence of one transition does not guarantee the existence of the other, both transitions are well connected to the same result, an improved computational performance {{cite:6e573b3412d18518f8ce4e4892651329112639b9}}. Indeed, the computational performance of systems poised at a critical phase transition has been widely studied both experimentally {{cite:600b69dffac63688346d759a74b4d380f6ee28bc}} and theoretically {{cite:90f5db30fb48a5348ce5fdc9df3a19886f8fa2e3}}, and are well-connected to both edge-of-chaos {{cite:0250b0e46fcc3223d83ed6e415121504b9adcc7f}}, {{cite:ecb42b2df9554975a1eeb154a823477ee9678962}} and critical branching transitions {{cite:6e573b3412d18518f8ce4e4892651329112639b9}}, {{cite:2ba4f2e84d8ec1bd8aa9a2d14245c5a1fc36e94e}}. Networks operating at near-criticality are believed to have simultaneous access to the computational properties (learning and memory) of both phases, which results in 1) maximizing their information processing capacity {{cite:600b69dffac63688346d759a74b4d380f6ee28bc}}, 2) optimizing their dynamical range {{cite:d90c9feacd2fd3b8a60123adf82674788f9a9937}}, {{cite:dfb8869b05950107be502de7abbb3461165aa2c1}}, and 3) expanding their number of metastable states {{cite:6e573b3412d18518f8ce4e4892651329112639b9}}. Hence, it is not surprising that the NALSM's astrocyte imposed near-critical branching dynamics resulted in improved accuracy and generalization capabilities as observed in LSMs with edge-of-chaos dynamics {{cite:0250b0e46fcc3223d83ed6e415121504b9adcc7f}}, {{cite:ecb42b2df9554975a1eeb154a823477ee9678962}}, while adding the benefit of a neuromorphic compatibility and self-organized criticality.
| d | af40c53a0783196c521a306197788761 |
The robustness of modern NER models has received considerable attention recently {{cite:90e730dbc8efd60d89d9fd4980eec3a0652480a7}}, {{cite:5e71eec322d953da140fd180ecd34780bf82db2a}}, {{cite:dbba66a33d5d3029234b54ced25bd4294d0c7aa9}}, {{cite:63f93fc00045277bc86aea84aa3a798f8dcdb23a}}, {{cite:4f44b1970d5e902f68cf39e3d5e0ce5321b2f0f4}}. Name Regularity Bias {{cite:09593c32c16c90d03b7fd548895e61681b2e1987}}, {{cite:bf351eac3bcf938b4f0fd3632b1183c8a0769809}}, {{cite:63f93fc00045277bc86aea84aa3a798f8dcdb23a}} in NER occurs when a model relies on a signal coming from the entity name, and disregards evidences within the local context. Figure REF shows examples where state-of-the-art models {{cite:469c3211925983b1ef0cb9706e6a4a275ca76a53}}, {{cite:2422264d0578847191c2524944f6830c2387fa95}}, {{cite:876777b0ac343f0f490ef0d661fc4ba9539d2b54}} fail to exploit contextual information. For instance, the entity Gonzales in the first sentence of the figure is wrongly recognized as a person, while the context clearly signals that it is a location (city).
| i | dc64271077a3ffca8cf2608b0488a5ad |
That means non-local correlations are certainly relevant whenever spin, charge etc. fluctuations are important. An obvious regime where this is the case is the vicinity of a second-order phase transition as already mentioned. Here the magnetic, charge etc. susceptibility diverges and significant changes to the DMFT solution are thus to be expected. For low dimensional systems we will get corrections also further away from the phase transition. The Mermin-Wagner theorem prohibits long-range order with a continuous symmetry breaking in two-dimensions at finite temperature. Hence, antiferromagnetic order is restricted to zero temperature. However, above this zero-temperature antiferromagnetic phase, we have now strong antiferromagnetic fluctuations in a wide temperature range, even with exponentially large correlation lengths.
DMFT has been developed with the limit of dimension {{formula:efc0776c-c132-4610-b708-026be590eb91}} in mind, see {{cite:2e1b346dda9a042c214652b874f36bf050c516f9}} and Chapter “Why calculate in infinite dimensions?” by D. Vollhardt {{cite:02972b494eb4dc3a84473614a008629162175acf}}. Hence, also from this perspective it is not surprising that we need to expect larger corrections to DMFT for low dimensional systems.
| i | bd5d79697943e1888115a4c64fac504d |
Since the quantum average power {{formula:f5563265-0559-4e85-aa7b-62adc7495cfa}} , in all approaches, is expressed in terms of the population and the coherence correlation function {{formula:aee8b272-daf0-4e5a-9815-aa0e09e59551}} and {{formula:4e558177-27ff-4ab5-89e1-fffeda7a3a79}} respectively [see (REF ), (REF ) and (REF )]. We write their explicit for {{cite:bd02e9eafb64da6cead46b6681b3787c6a30efd1}}, {{cite:1f85a0bb4beb2b754324e5f30a34b0a9fada4717}}, {{cite:2efaf8a29b8653db539f443ecd14351a39eaf50f}}, {{cite:a437057f62dc27015e6ed0b8baf87ece0a1a4aa7}}. One has
{{formula:96023a3b-c1c7-4054-8657-25d6b555ad1c}}
| r | f41f1fc066fde5b003328c7f948b6f04 |
Estimating the generalization error of a pipeline {{formula:b30dbd20-3c8e-4671-879b-17e38c46d31b}} practically requires to restrict the CPU-time per evaluation to prevent that one single, very long algorithm run stalls the optimization procedure {{cite:7c2c990940db8a22dc26b5ba05c856ab7faf9d4a}}, {{cite:84ba19040d03ab2e8fa8edaad62a12b4ee2d09df}}. If an algorithm run exceeds the assigned time limit, it is terminated and the worst possible generalization error is assigned. If the time limit is set too low, a majority of the algorithms do not return a result and thus provide very scarce information for the optimization procedure. A too high time limit, however, might as well not return any meaningful results since all time may be spent on long-running, under-performing pipelines.
To mitigate this risk, for algorithms that can be trained iteratively (e.g., gradient boosting and linear models trained with stochastic gradient descent) we implemented two measures. Firstly, we allow a pipeline to stop training based on a heuristic at any time, i.e. early stopping, which prevents overfitting.
Secondly, we make use of intermittent results
retrieval, e.g., saving the results at checkpoints spaced at geometrically increasing iteration numbers, thereby ensuring that every evaluation returns a performance and thus yields information for the optimizer. With this, our AutoML tool can robustly tackle large datasets without the necessity to finetune the number of iterations dependent on the time limit.
| r | d1116c975010fc260d23a145bd3588b0 |
The 87 datasets and 99 low-precision configurations in experiments are listed in Appendix .
The datasets consist of natural and medical images from various domains.
Apart from CIFAR-10, the datasets include 20 CIFAR-100 partitions from mutually exclusive subsets, based on the superclass labels.
They also include 50 subsets of ImageNet {{cite:8e087e3c74849f8dad0ce0eda3aad0ca95b5f544}}, which contains over 20,000 classes grouped into multiple major hierarchical categories like fungus and amphibian;
each of the 50 datasets come from different hierarchies.
Finally, we use 16 datasets from the visual domain benchmark {{cite:df3815580a5a33af7ab153ac531ee3e15fb3df35}} to increase the diversity of domains.
| d | d906503acae020d0574db2a148f750ba |
Conventional approaches {{cite:6e71af80bed2ac9a533925d9518abe477e077236}}, {{cite:77ff43683cf52f280bbaf9567a5b14f97c7bd52f}}, {{cite:48e9678fc6f018e08bf2fea6ebc2c5cd13b740cf}}, {{cite:7b7105f7ca9bb00879c4edd906077ca4b1068c34}} typically discard unnecessary channels from the original over-parameterized network. Distinct from previous backward elimination methods, the proposed PEEL addresses channel pruning via reallocating parameters in a predefined architecture, usually an over-pruned backbone from the original network. The resource consumption of this predefined structure is smaller than the target value and the remaining resources are stored in a place named resource pool (Fig. REF ). The intuition of PEEL is that those informative layers should be assigned more parameters to amplify their positive effect on the final performance.
| m | 4787e9fb1c0212e314439b57ea100745 |
In this paper we provide a general framework for comparing generalization bounds for deep learning, which complements two other recent large-scale studies {{cite:041497d970d8d1080790a5996fb6f63390ea36af}}, {{cite:02459685121bae71483bde1427b4b6221aa19fd8}}. Our framework has two parts. Firstly, we introduce seven desiderata in desiderata against which generalization theories (including the bounds we focus on here) should be compared. Secondly, we classify, in generalizationtheory, different bound types by the assumptions (if any) they make on the data and the algorithm. This classification is summarised in tab:multicol.
| d | f4d441238f2e77a71d5ac17c92303da4 |
For more details see {{cite:4f9f9524e7e90a398a8f2484817c06d6f1ee6f36}}, {{cite:5b1c55afc38a3207e678b9693f0b9ae0a101b728}}, {{cite:d19a8bdf94b3b2eba3030e5dab5eb9268daab793}}.
This proves well-posedness of the WRM for {{formula:c86b127a-74fd-4345-b11b-8f3395b67941}} and {{formula:149b79bf-bdd4-4b43-8502-6765617d5ea5}} . By iteratively applying the previous arguments is then easy to show that the WRM is well-posed for {{formula:61264527-e3f5-4402-9422-a4eced19a239}} , because {{formula:ecf5af1f-cee6-4b56-abe6-1585b9678d76}} .
Theorem implies that (REF ) admits a unique solution {{formula:5b0319aa-0622-4176-ae2a-dff2f1680a81}} for {{formula:5ccaa42f-4796-497f-8912-f01865b0b23a}} and {{formula:b8735b9c-bb16-4e0d-9a3e-a4ce97a2d824}} . Note that, at each iteration of the WRM, the solution at iteration {{formula:e6ab41af-a47f-4738-afe6-1022901c398f}} depends on the one at iteration {{formula:8b324523-18bd-4941-a924-0a230660371e}} . Therefore, we can define the solution mappings {{formula:de92bd13-0545-441f-aa8f-039ea5220886}} for {{formula:cc5f6017-3d44-4c21-a4b8-9802a45ac393}} as
{{formula:6c02ac12-c0e7-4f56-8704-c45c781491f5}}
| m | 7d116700fd02606cf91e455f1ecef796 |
Generally speaking, our results imply that, even with the truncated heavy-tailed noises, the function {{formula:6f72ce19-bb97-484e-a367-8b3bfbd6aa14}} needs to satisfy certain regularity conditions to ensure that SGD iterates avoid undesirable minima.
This is consistent with the observations in {{cite:fdb7e51c6a32111c3c8f201f631172952a1d7046}}: the deep neural nets that are more trainable with SGD tend to have a much more regular structure in terms of the number and shape of local minima.
| r | 03aa2a3f24693e6fa78f59504a81f745 |
the minimal dimension of the Koopman-invariant subspace that approximately captures the limit cycle attractor for all three {{formula:a473459e-edc0-498f-8ff6-089afcc4218f}} that fall into laminar vortex shedding regime {{cite:f5660d6765467b646809048081c66ca66fa9cedb}} is five, cyanwhich is consistent with previous multi-scale expansion analysis near the critical {{formula:48f1fc67-eb08-4b9e-9c1c-c3bbfea6b5ca}} {{cite:a0fc9663c4dc24a139144602da39ed165fac67ea}}.
the lobes of stable Koopman modes in the type-I cluster show an approximately 50% larger width than those in a type-II cluster.
similaritybrown/colinearity among Koopman modes within each cluster is observed. cyanSuch a finding is previously reported in the theoretical analysis by {{cite:a0fc9663c4dc24a139144602da39ed165fac67ea}}. A similarity in spatial structure exists among the Koopman modes belonging to the same family, even though the structures are clearly phase lagged.
as {{formula:4879adbc-f88d-452f-8cb2-6fe1bc18e2fe}} increases from 70 to 130, mode shapes flatten downstream while expand upstream.
at {{formula:c09e2fad-e840-49d1-b995-dc1c64b54f7e}} , the shear layer in the stable Koopman modes continues to grow within the computational domain. However, at {{formula:945fcd4e-5ca3-415f-9435-1c89ae12ac81}} , the shear layer stops growing after a certain distance that is negatively correlated with {{formula:a335a232-9bc9-4f24-814c-7bb64f5ffcdb}} .
{{figure:5e3d87e3-57f2-48ef-ae05-b9b54239be78}}{{figure:1ef4fee7-c79f-4ce7-a11b-0e64a9fd70ad}}{{figure:d834894b-fa30-4f3f-9ebf-e9b99c02a089}}{{figure:6ce919f1-df2b-4153-91f6-3353d3ca00f1}} | r | dc6dc596949a9660a86bc8eaff76ee98 |
To estimate the empirical upper bound of the classification accuracy, we approximated how fully-supervised
models with access to all data would perform. To accomplish this, we used all the data available within the
datasets from which the few-shot tasks in the meta-testing phase are sampled and trained one classifier per
meta-testing task in a fully supervised fashion. We evaluated the classifiers on the same query sets used in the
few-shot setting, i.e., query samples are fixed, but the support set is replaced with all data available in the
original dataset. To investigate knowledge transfer, we trained independent classifiers on the support set of the
meta-testing tasks and evaluated them on their corresponding query set. Negative transfer occurs when the
performance on meta-testing tasks is negatively affected by knowledge transferred from meta-training tasks
{{cite:0f36048367cf00f37a2d9da3270da4c26e70f35c}}. Therefore, if the independently trained models outperform models that utilize knowledge
transfer, it implies negative transfer. We also investigated two strategies to utilize knowledge transfer:
pre-training using contrastive methods and learning-to-learn strategies. For contrastive methods, we
aggregated support and query samples from the meta-training tasks into a unified dataset, pre-trained a GNN,
and then fine-tuned it to the meta-test tasks. Finally, we investigated the effectiveness of the proposed encoder
by comparing the performance of the meta-learning models with and without using it.
| r | 001e5ac090d782275a1225eafa3022dc |
Lastly, we investigate how the structure of the SF network affects SOB. Specifically, we are interested in the influence of scaling exponent {{formula:62c1825d-892e-4910-b239-1de4a1fd3547}} since this parameter regulates the prevalence of highly-connected hubs in SF networks. The latter units play a principal role in the first-order transition and, consequently, the emergence of an SOB in our model. Earlier, Coutinho et al. {{cite:abb10dd4e2288f1787cbbbd3ac0fea57eb79aec7}} have developed a theoretical framework to show that in the frequency-degree correlated networks, the first-order transition is present at {{formula:1104197b-7e5c-47b7-a961-f321a0898a13}} . Recall that this particular range of scaling exponent is the most common in real SF networks {{cite:e95b8166cab685d2612dbf7327a986e7e8f1f5f0}}. For {{formula:a513477f-86eb-4eef-928c-286ef5862b3a}} , Coutinho et al. have predicted the suppression of hysteresis that determines the continuous type of transition.
| r | f950dde2f0a68847468bd3d2c6cfb893 |
We consider different combination of ID and OOD datasets for different architectures. We compare OOD detection performance of PNN with existing works including state-of-the-art approaches such as Deep Ensembles {{cite:481ad2c2800d8dfae1e779ac9153662033afe383}} and BayesAdapter {{cite:041dcccc53f9affdb83a8122f3f7355a5afc0898}} along with ODIN {{cite:7e8d45ab838fe11ea867eaec5e3f413079c5af12}}, MHB {{cite:a0fce0a329f0544030df0621b95e2b45a9ff9a6a}}, and the Baseline OOD detection approach {{cite:e4b826f53021ca20085146167af4b8658a8e98f0}}. For ODIN, we pick {{formula:8446f51c-b5d7-4c25-832b-160ddebe4864}} for temperature scaling from, {{formula:5f36c966-7e93-48d8-8f01-7efd474ddb8f}} and {{formula:139547f7-90d3-4997-ad54-77026e99f496}} from {{formula:82f46013-3a68-4244-a7d8-499968c8986e}} . In Mahalanobis distance based OOD detection (MHB), we use the features from the penultimate layer and the layer preceding it. Similarly for Deep Ensembles, BayesAdapter, and the proposed PNNs, we considered two siblings of each for a fair comparison. It should be noted that, no method including ours, is adapted to OOD data or calibrated for uncertainty using proxies of OOD data, as in a general scenario, the OOD examples can come from any distribution which may or may not be known during training.
We use False Positive Rate at 95 % True Positive Rate (FPR at 95 % TPR), Area Under the Precision Recall Curve (AUPR), and Area Under the Receiver Operating Characteristic Curve (AUROC) as the performance metrics. The results for FPR at 95 % TPR and AUPR are shown in Tables REF and REF , respectively. AUROC results are provided in the supplementary material. It can be seen that, PNNs outperform the previous works in most of the experiments and achieve comparable results in other, particularly in terms of AUPR. It is noteworthy that since AUPR is a threshold independent measure it can be of great significance when it comes to comparing different techniques for OOD detection. Higher values of AUPR reflect better performance on a large number of thresholds. To understand the capacity of the proposed PNNs better, we further test them against corrupted and adversarial inputs, and present the results as follows.
| r | 80a9171b99a8c49add165ad96a27695a |
As we mentioned above in the phenomenological
approaches the parameters of the model, {{formula:a1a2d116-75ed-450a-b860-5b856ab48fdc}} ,
{{formula:24ed91e9-614f-49d6-94b5-f756d9d34b71}} , {{formula:952cfff2-4e2f-4294-bea0-39f8f504019b}} and {{formula:47bb0ad7-1105-445f-b0cd-7c2b60a0e528}} , are fitted to the spectra
of experimentally known charmonium states.
For example, the authors of Ref. {{cite:d6a67cb247ad128dda26814d801990399b2717a7}}
proposed the set of
potential parameters given in Table REF
(see the model referred as NR).
{{table:834aa775-6289-40dc-944a-68daa105aa61}} | r | 9188f093b4a91fe4b5d8545f55317cbf |
The explicit derivation of {{formula:b1421ae3-ae36-4d20-82c1-4f47b0a1dfcb}} constitutes the primary reason for studying the complex zeros of (REF ). The main device for treating {{formula:d760d8c4-ee64-4923-b99f-17febae21d51}} throughout the complex plane is the Rice formula. This remarkable result provides a representation for the expected number of zeros of certain random fields. It is reproduced below from {{cite:d7fc452ec2a9cf688c42d53391f871c0a82487b0}}. (See, also, {{cite:9e8cf6431dadd19f4211ca45623276821efbc02c}} and {{cite:56b2eeb0f8bfb5e01698946accba92433b0d62cc}}.)
| i | 6ad33c413672adaa21b992bad42f35a2 |
For the CIFAR100 results of average incremental accuracy and average forgetting are presented in Fig.REF . Three groups of methods are shown: non-exemplar based (FT, LwF, EWC, MAS, E-MAS+SDC), exemplar based (iCaRL-CNN {{cite:bd30fa2f9c00023434427c37223bef6a1491e6f5}}, iCaRL-NME {{cite:bd30fa2f9c00023434427c37223bef6a1491e6f5}}, Rebalance {{cite:a69d94e613754d4ec54682f627962b2c5167d14a}}), and joint training. From the average incremental accuracy, we can see that our overall best method E-EWC+SDC beats all the other non-exemplar based methods by a large margin, with a minimal gap of 27.6% compared to EWC. It also surpasses two exemplar based methods, namely iCaRL-CNN and iCaRL-NME {{cite:bd30fa2f9c00023434427c37223bef6a1491e6f5}}, by 7.1% and 1.1%. To compare the preventing forgetting capability, we show the performance of our method and exemplar based methods in terms of average forgetting metric in Fig.REF . Our method (in red) suffers from less forgetting than all the exemplar based methods, obtaining a 13.9% gain over the best exemplar method (Rebalance {{cite:a69d94e613754d4ec54682f627962b2c5167d14a}}). Experiments on ImageNet-Subset outperform all the non-exemplar based methods and two exemplar based methods as well in Fig.REF . The conclusion is consistent with CIFAR100 on average incremental accuracy, 35.0% higher than LwF and 15.5% higher than iCaRL-CNN and 2.5% higher than iCaRL-NME. For average forgetting, our method has 3.5% less forgetting than Rebalance method.
| m | ce8aaa9b10bf12931150398b836149a3 |
{{cite:624437488dd825c3f0deb25165411f7ba9f961d9}}, based on 22 years observations at 15 GHz found that the jet of OJ 287 is rotating with a period of {{formula:7b400c51-2fad-4b68-ab78-b453730cbcfa}} 30 yr. Modeling of OJ 287 radio data showed that this rotation can be explained by a combination of jet precession and nutation. The physical cause of the precession can be driven by a binary system in OJ 287 center, as well as by the mechanism of the Lense-Thirring precession by the tilted accretion disk of a single BH {{cite:cad49242443a2c67a68e570c97e4ac913fb7e3e1}}, which in the case of OJ 287 provides realistic parameters.
| d | bc295f663f9ee12834f5499b3f80ac66 |
There are some interesting and surprising technical twists to our results, but given a definable hypergraph {{formula:83ff342d-705f-4a35-b366-d2b8d59caafe}} in finite fields (or in the difference fields {{formula:14882735-53a8-47cc-8f72-4f5fb99a7bad}} , as discussed below), we find some {{formula:8583821c-9cdb-49b7-adce-113b3e20b38f}} not depending only on {{formula:63386026-1eac-49dc-9cff-b4cc4a865ecf}} and a partition {{formula:9559c18e-1e50-4757-938f-210402e22d5b}} of each set {{formula:f61581fe-b621-421b-9ee2-16ec345b13ce}} where {{formula:c66e8b49-1a12-4b98-ad41-30ad257973f1}} and {{formula:8ff2adb8-afb5-49ef-bb7c-a03a9ea13adb}} such that {{formula:17c65417-69e7-47e1-b311-1fba55a7155d}} for every {{formula:86cfa301-4833-4fd8-ab59-bff7fd445fb3}} and such that restricting {{formula:290b59da-b2e0-48b6-9ff0-e91aac10cda0}} to any family {{formula:ddc4d738-077c-4d62-b641-de241c9e3218}} with {{formula:a3b9c808-fbc2-424e-b5e3-b695fbd2f5f0}} gives a {{formula:26fc98c4-ef24-4fdd-bfab-b44dad30b450}} -regular hypergraph in the sense of {{cite:b07d42dbfdb08d8a3021e362cbb2a008d8091bfb}}. See Theorem REF for a precise statement.
| i | 772e2eb590bc077a9c9db36ae2126068 |
Without loss of generality, let us assume that {{formula:5f7d62a9-cf1f-4704-b015-2867c0c58be0}} . As in {{cite:abe1afcb9c9dff58f5d99d90a7c6a55d9d89c7a9}}, the input image is then divided into {{formula:71304b8e-54df-42bc-ab10-b173631722a7}} patches of size {{formula:f50112b8-0b16-46ca-932a-2a076e0557a5}} , where {{formula:b4c43c10-bbbd-4ef6-9654-1bcf6be15e6f}} .
As a result of this procedure, an input image {{formula:c5d464c0-8423-42ec-a01d-0a62fedd906c}} becomes a sequence of 2D patches {{formula:2000f418-7ad3-4da8-9579-148901b4a65c}} {{formula:794c747a-8bad-4207-b382-cbb3c9a2c542}} {{formula:c2d7cc14-3d85-428c-8100-1c93547e5c6d}} with {{formula:31035d95-1960-46ff-b8bc-6a7a22e15ae4}} being the channel dimension.
The 2D patches are then flattened into vectors of size {{formula:e5bedcf3-7f05-42d2-9775-ffaf352c6afb}} and projected to an embedding space of size {{formula:7b80e1d2-e573-488b-8b6e-2297be9de053}} , obtaining a sequence of token embeddings. As a last pre-processing step, learnable positional encodings are summed to token embeddings, producing the actual input data sequence to the transformer.
| m | 3645807b047777f92d5f7bc9bbafb8fd |
We have investigated the possibility of detecting these objects and discriminating them from BHs with current and future GW detectors. We find that ET and LISA will allow one to detect and potentially distinguish exotic binaries from BBHs (with total mass {{formula:ce809479-65da-4098-b4bc-014ea6220811}} and {{formula:41e669aa-f07e-49a4-ab39-b16b8ddfec5b}} respectively) throughout the observable Universe, as compared to up to {{formula:ea2132bd-9714-4a65-88cf-d675de7f6b8a}} for aLIGO. On the other hand, we find that up to {{formula:0914de60-64cb-476f-865c-534d70808ecc}} of the SNR could be lost when using BBH templates to search for these exotic signals, thus affecting our chances of observing them. Finally, we have estimated what the post-contact signal would have been like if the events in the first GW catalog released by the LVC were ECO binaries as the ones considered in this paper. We have found that, for the loudest events, the post-contact signal would have been sufficiently strong to be detected by wavelet-based searches, thus making this hypothesis unlikely. Our analysis could be extended to the second catalog released by the LVC {{cite:fd3f2f782b1fe94ccacc7798ca4f8aeb6efe0fe7}}, including the noteworthy event GW190521 {{cite:09d8930b439ea863d46323b088b52e85d058edd9}}, which has been suggested to be compatible with a BBS signal {{cite:667dbfbab68bd14b24de3471e435b6f82d50ceb3}}.
| d | e83c9519b0441b217c2ffa0286d6b234 |
The reference values for {{formula:93ddfbb1-0e32-4178-b404-c7cbd4a3da2f}} , {{formula:6c38425f-138b-46fe-b736-40b684007020}} and {{formula:1e0ce80b-4798-416f-8f9d-cbc5eee8ec85}} are assumed to vary freely between ({{formula:05001f4c-cc2b-46c3-b968-8a5e871f496e}} ). The reason behind this specific limit ({{formula:511a7927-e6c0-4193-a5f4-dd49cb7b7b76}} ) is that all the values obtained using our reference experiments i.e. No{{formula:df13b73a-93b8-4069-ad8a-608d7b48f194}} A, MINOS, SuperK, and IceCube-DeepCore vary between this similar range so instead of taking a specific value we have taken the whole range in our model.
After performing the Monte Carlo simulations we estimated the texture of the correlation matrix ({{formula:2ea75532-3bb9-408b-a2fc-51bc2a8748ba}} ) for two different values of {{formula:bb5cbb51-85c4-4574-961c-8fcba72d7a1b}} {{formula:53de4501-3200-472a-a4ee-3261f795ebd6}} {{formula:81836791-2c41-464c-a6dd-fc8b555f2e0b}} {{formula:6edaaaf8-208b-4d73-8552-bfa32d594abf}} (where {{formula:8a82b1c4-54bf-40a2-b5c7-31b136bf9ce4}} is the mass of {{formula:a814f25f-38e0-40e9-b23c-2c134db80fd9}} ). We implemented the same matrix in our inverse equation and obtained the constrained results for the sterile neutrino parameters.
Thereby we have obtained predictions for CP-Violating re-phasing invariant and {{formula:6e6af018-971f-4863-9834-b3a457165823}} and {{formula:8adbd2c9-4084-4832-878f-511f48648b3d}} , then compared our results with the current experimental bounds are given by No{{formula:918437de-d1a5-4fcb-9834-f65a4855b06e}} A, MINOS, SuperK, and IceCube-DeepCore experiments {{cite:63177944306dc1a3649aeb3d0f04dadebe5d9215}}, {{cite:6b936953da3ed36eb534c7cb5b1a19094992adec}}, {{cite:bcb61ec3e1622cf2ee4e70c5b8433ed86d21152d}}, {{cite:2e03eb7a54b4ccc801bc0c0858032acdd983d7c4}}, {{cite:a9552a7cb4e5ca22a1f0a46f9e533953368e47af}}. It has been found that the entire analysis is very less sensitive to {{formula:dd4277e4-a914-4e3c-a8b3-f8e9a37cfc06}} , which is constrained to be small by reactor experiments {{cite:cb45b520df433cd0397d0a72b412551d4bbc45cd}}. Also in the QLC model analysis the value obtained, is lesser as compared to the other two sets i.e. {{formula:1e2c094d-5ca4-40df-9680-90508f8b7490}} and {{formula:1b395e7e-4dfa-4fcc-a49a-d09dde6e7bf6}} .
| r | be29ac97880cc854500710115c7dc1b6 |
For a robot to grasp and manipulate any object in its surrounding environment, it is essential for it to estimate the position and orientation of the object relative to itself - often through the use of its vision sensors. In recent years, advances in deep learning based approaches have used powerful convolutional neural networks (CNNs) to process the input image data and generate a pose prediction {{cite:8bc301da6e94da759eb2e00de07a481e21b1d49e}}, {{cite:d664b747db119366fb914466d33506054716f45f}}, {{cite:ece08a2488c8efbe4b0b357aa10043844b8a3efa}}. The networks attempt to learn a mapping from the high-dimensional input feature space to an output space where the learning process is generally needed to be supervised through a set of labeled samples. To avoid overfitting of the network on the training dataset and achieve a good generalization, the domain space needs to be sufficiently sampled meaning that the labeled training data points should consist of enough input feature variations. In the case of CNNs designed for detecting pre-defined object keypoints in the input RGB image {{cite:52a37a5eb74b83c1fb4ac1dc077ba751a6b28245}}, {{cite:dad2c8e88892c1a6c676035e8e5f5ffce3e93862}}, {{cite:ece08a2488c8efbe4b0b357aa10043844b8a3efa}}, {{cite:d664b747db119366fb914466d33506054716f45f}}, {{cite:89412230b285437ffc7b181dc06f21bf4bdae87f}} this implies that the training dataset should be composed of annotated images of the object in many different backgrounds with varying lighting conditions and surrounding environments. Hence, the required training dataset quickly grows huge in size. A central problem, then, is the generation or accumulation of this labeled dataset with minimal manual effort and time consumed {{cite:52a37a5eb74b83c1fb4ac1dc077ba751a6b28245}}, {{cite:fae64157cb55512d2d14c656e5de8715976f84e4}}, {{cite:749cbddd6c4e85e9a97bc875a837c6829f1a9430}}.
{{figure:aa23593c-87f0-487e-9cb6-1988525bf6f0}} | i | 7cd8f7b16401fc868ec7875a0dd76ea8 |
Humans usually read text by row or by column, but how do you “read" a 2D image?
We first look at the area of greatest interest and then the other areas or patches.
And how the DNNs do with the image and text?
Arguably, regardless of the text or image, many DNNs read it as text. Recently years, inspired by the Transformer extension successes in NLP, Convolution-free architectures, in particular vision Transformers {{cite:fb0a9ea8461786b8bbccf56fec811f44f8907367}}, have become the model of choice in computer vision.
A series of works try combining CNN-like architectures with Transformers, some replacing the convolutions totally {{cite:06d69362ebeb3314076ef446bdbe56f1c5b67968}}, {{cite:1c585df6d68fc6795ee959262482960c73287a84}}.
{{figure:8f08ecad-8e85-4b89-bf10-17bcffc7d729}} | i | 2ed88794aae007aebb0264827524d3ce |
Let {{formula:0e88f79b-fee7-4246-bddf-aea903b6b3b6}} be an unknown joint distribution over instances {{formula:54f7014d-6436-4aae-b77d-6a6270c860b1}} and responses {{formula:bfc7d2b9-357a-46f2-acc3-6c8192bd7023}} , where X, Y denote random variables, and x, y are their instantiations. A common goal shared by many predictive tasks is to infer certain properties of the conditional distribution {{formula:e215b849-e068-4cf5-9294-bc6e05f09895}} . For example, in a standard regression task, we are given a training set of {{formula:587cf3f2-bb26-45f1-996f-23bbd3934514}} sampled i.i.d. from {{formula:95b4eab8-1d58-4de9-be1d-8f07997e2033}} and a new test instance {{formula:082a37f6-a19c-42fd-b6bf-1c6f419c607b}} sampled from {{formula:a60491d1-560e-4d12-9b52-dc364a511110}} , the goal is to predict {{formula:83013a6a-0887-4045-865e-5ebad0297604}} , namely the conditional mean of Y at {{formula:21656328-a8d0-4f58-93ff-905a289a0fb0}} . Although estimation of the mean is highly useful in practice, it conveys no information about the predictive uncertainty, which can be very important for improving the reliability and robustness of the predictions {{cite:d5a1d59d2aee8d53c0f286c49b59192c4ed69fdd}}, {{cite:0ee9faf132a813ce0bd7671428dbdb8a89a9f101}}.
| i | 271c492a48d30bb8c10a04859504bb7d |
Static nonmagnetic random disorder is most simply characterized by a broadening {{formula:c5d76ec1-799e-4b51-a5fe-32f4fa60d617}} (where {{formula:8d3548da-0dd0-4932-af61-7fa48ae02fdd}} is the Fermi energy) of the electron spectral density {{cite:b035551e89c18f7b6c9269eabe0bca59d5217e83}}, {{cite:8fc28b6ff2e99bfbaf86cfbd60411f96f86c5081}}. Microscopic calculations generally use on site or zero range disorder with a Gaussian probability distribution of its strength related to this broadening. The effect of disorder on electrons is mostly implemented in the Born approximation, where its only effect is to lead to lifetime {{formula:ac78b0f9-1a3f-4f22-82a1-eefa92ede2b6}} of electronic states. Such a treatment neglects Anderson localization effects{{cite:feb757bda928b8a076829747478eff8d1fd51b72}}. In this approximation, it is well known that in the so called dirty limit, i.e., {{formula:cefdc1f5-e56b-49fa-b56d-f627f664c3e6}} , {{formula:1f67f448-4504-4f1d-8b20-a146d6dec4ef}} at {{formula:c71354e6-bae0-4184-bf10-6033356ee1e6}} scales {{cite:8fc28b6ff2e99bfbaf86cfbd60411f96f86c5081}} with the dc conductivity {{formula:10a0b722-dfeb-4bf7-9bb7-98e2a8b178dc}} (where the relaxation time {{formula:bf345ea4-8da5-4fae-a393-c62538160aba}} ) in the normal state, i.e., {{formula:d9b5118e-e80a-4833-af93-24075878ed52}} , where {{formula:27be0c04-9ca9-4100-a634-52a1ac3fb0e2}} is the electrical conductivity of the system and {{formula:b35982b2-f486-423c-b7fd-e4e529f6359a}} is the gap at {{formula:d5a65810-4094-49a7-8ab3-5958e04ab32c}} . We note that {{formula:7f6ef738-9fa0-4983-84d2-301c1e3c1b7b}} is independent of disorder, according to Anderson's theorem{{cite:defbcc43008201e4705d28794906dcae82c3e3bd}}. A phenomenologically generalized form of this zero-temperature superfluid density at finite temperatures is often used for analyzing experimental data; {{cite:e601c3ff8d1b616f23fc068ea9b2f993dfec84d3}}, {{cite:ad69f6b0dd4c3456c9f323a6cc081ca3d92c4668}}, {{cite:ce3f11a53aa1e49b0751c92b63cc3b05b0192615}}
{{formula:736230e2-b1b7-48a7-a765-3b8b4bd19b31}}
| i | a670407d1910466b444165e6518f6a3f |
The programs FeynArts 3.9 {{cite:4f23d82201d26fe264fb6b59db4e3709972a2bbc}} and FeyCalc 9.3 {{cite:8b8986d5a77a7814a224938a00330753f0eb0b45}} are used to generate the amplitudes and do the algebraic and numerical calculations.
| r | e631351d46d819bc8230fbe913eff3da |
One tempting question: is it possible to reach the maximum mass of approximately {{formula:e51286c1-e90c-4106-b91a-65de98d06d61}} while keeping the results still in agreement with the canonical mass observation data? After systematically studying all possible combinations of {{formula:1668df3e-b717-469e-8887-0aff1fcc220d}} and {{formula:f8c272bd-4e9f-4339-9c45-eb571ec799e9}} , we have found that the case is only possible if we take the unphysical value of {{formula:709759f8-7b98-404c-a494-2bc4624046af}} , i.e., it should be negative and the {{formula:af41926d-a24a-4ca9-8fa6-bea35998294b}} absolute value should be much larger than {{formula:a163a7d2-ba2c-43e2-acf4-87dfc070bdc9}} m{{formula:9083d307-123a-4081-af6c-e4b2706ae74d}} . The reasons are as follows: Increasing (decreasing) the value of {{formula:309a70f5-2bed-4506-b86a-479849e47431}} affects the “tail,” corresponding to the MR curve on the lower right. If {{formula:90a70008-bc4d-48a4-bece-a83076e2ce55}} , then the tail goes to the right. If {{formula:26cf1d29-7cca-42ed-a50f-5a25d9b407f8}} , then the tail goes to the left. For {{formula:f8133d9a-8af4-4c87-a6cb-e58f3554cdfa}} m{{formula:19b73007-a675-4a2f-8ab2-59974ed3778e}} and {{formula:75ee59fb-7bce-43ee-932b-1431a1363e27}} km{{formula:c50fde0b-a5c4-408d-be52-72f4da315c0d}} cases and for both EoSs (WHSS and WoutHSS), the results of varying {{formula:2bbea4c4-97bf-4798-93b8-3143a623907f}} are shown in Fig. REF . Clearly, the impact of varying {{formula:c453b723-8413-4c8d-b900-aa16c0a491d8}} on the radius is greater than that of the {{formula:4d9822d2-6678-4a65-9c12-4a38e91672fc}} variation, except when near the maximum mass. A positive value of {{formula:9beb19cc-0cfa-4767-b51c-47e820231be5}} tends to increase the radius, whereas a negative value {{formula:ffaf64b9-5eec-4f46-845d-0e593a5f0c96}} tends to decrease the radius. We compare the EoS G3 WHSS and G3 WoutHSS by comparing the plots in the upper and lower panels of Fig. REF . When we increase {{formula:60b55ced-fe35-4861-9f4d-366ccf257550}} , {{formula:6a3d3b22-3f1f-47c5-8604-2998e7bf2172}} and {{formula:ff7520f8-e8fc-429f-9083-6b19d0221cfd}} increase and vice-versa. The plots show that for {{formula:4680cb87-293a-46b2-a8bb-482c03efbab0}} m{{formula:f44ba4e4-732a-483a-9a6b-41796b6dbaaa}} and {{formula:bed390f7-f07d-43ca-a7f9-ceb3cf994f84}} km{{formula:ba0298f0-a854-45b3-87dd-87a711d7739b}} cases, the range of {{formula:d797edc7-ceca-4986-912b-c824ab0179a4}} of the G3 WHSS and G3 WoutHSS EoSs can be constrained with NS of approximately {{formula:5b82ebe3-f4fe-4604-a6f2-76ad9fcf9529}} and canonical mass radius observation constraints {{cite:615fee827b105fe1d9835ef57392df8934f37c05}}, {{cite:f6c92b6ea4e4e180e5e84152a656c18a7eb563aa}}, {{cite:756021deaf7480178d4db204e7088cd46d2b3151}}, {{cite:75a2023d61e350804710afa54a197f83c69e5730}}, {{cite:e746a086b7e04c969d855565c777adf53206771d}}, {{cite:52afeeb8fe6daa7f4977ffb2ca854bae7ddb1ca8}}. The range for {{formula:0ae3a8bc-a855-4ed1-9b57-7ca72c1d380b}} m{{formula:78cea092-6f20-439a-b104-edbe62b20b1d}} is quite wide, i.e., {{formula:469fbdd8-018d-4eef-8dbf-42fcda8b06f5}} m{{formula:783d1a59-3c89-4602-9415-3841321768d3}} , and this range is relatively wider than that of {{formula:33ac2154-72db-412d-b38d-0d7cd0af8b24}} km{{formula:7ed88ed6-09ae-4d54-b3a1-315e1a083665}} , i.e., {{formula:9dcef4b2-872c-4e88-967a-ec0a7080b71e}} m{{formula:a683d402-e8e2-474f-86b9-2cd524ea739f}} . Thus, it is possible to have a relatively large maximum mass, but the radius is still retained small by increasing {{formula:036c9060-046b-4c84-a87b-bfbd8f1a8591}} value and decreasing {{formula:dcde8cbd-3b6d-44b1-bd9c-4960666cbeff}} value. However, for large {{formula:70b2c688-1af7-4bd1-bb25-61315b9d7eda}} values, the range of the {{formula:4a06adcd-42c6-41bf-bf25-b8cbcab3074e}} value becomes narrower. As a result, we can obtain the maximum mass of approximately {{formula:5d0684a0-acc3-4958-8453-7aca43c71dd1}} and satisfy the radius constraint for {{formula:396745fb-8090-438f-a4b1-2eeb0e198aec}} NS from the observations if we set {{formula:de3c2c66-325f-450d-96e3-f888cb5bce5a}} km{{formula:e3a94476-a7a9-4678-b5d1-ba1d08c6c136}} and {{formula:de8331ea-afc0-47b2-a6aa-5222e2fc6631}} km{{formula:63b05d7c-7ea0-4b2c-8ab1-120c00f1f59c}} for the G3 WHSS EoS and G3 WoutHSS EoS, respectively, with an unavoidably large and negative {{formula:bc49c25e-3571-4b06-9c85-b39c235ab13f}} but with a narrow range, i.e., {{formula:4eba379b-c6e3-45af-b46f-0d89e351b987}} m{{formula:0ece83b8-231d-43fa-b493-ec8c8ce0e3ff}} . Their M-R curves are shown in Fig. REF . Of course, the combination of {{formula:b9886644-05c1-4a59-9fb6-a514e81b38cf}} and {{formula:6e044876-1c34-4ac0-bc96-9bb88c1e43c2}} values can be chosen quite arbitrarily, but canonical mass radii and maximum mass constraints cannot be satisfied simultaneously when {{formula:0189e957-124c-483b-a37e-b6d5ed99bd55}} 0. Note that the WHSS EoS yields a more significant radius shifting by varying {{formula:0675f6bc-aef8-4561-86cc-f2803d1f11e5}} than that of the WoutHSS EoS. The reason is that {{formula:e45af7e6-9378-4e11-a8ae-fae022eecde3}} is usually not by itself in the equations but rather in the form of {{formula:fe9aa0c3-c22e-4af1-818d-af5c3f257b13}} . In Fig. REF , we show the sensitivity of {{formula:46688842-b9da-4000-8f75-364b3094a0f2}} and {{formula:9883a873-5b7d-42c9-9e61-456154b3a642}} variations around the narrow region where the M-R curves satisfy the radius constraint for {{formula:12e75b8e-3949-464d-8898-919dd0232648}} NSs from the observations {{cite:615fee827b105fe1d9835ef57392df8934f37c05}}, {{cite:f6c92b6ea4e4e180e5e84152a656c18a7eb563aa}} and {{formula:4f6f3f28-1cd1-4d37-a035-f7ec22223e87}} from GW190814 {{cite:d1c39ed05f13f4e3d681bf1125f6f4583532b276}}, respectively. Evidently, from the lower panel of Fig. REF , the radius is quite sensitive to the {{formula:ff264625-8d31-43dd-bec7-c8c82ccc8ae9}} variation. For completeness, we show the impact of the {{formula:ad0455de-189e-4f9e-8780-a5bd648dd7d1}} variation on the moment of inertia and tidal deformation in Figs. REF and REF . For this case, the moment of inertia and tidal deformation are not too sensitive with the {{formula:4f93b75d-6658-4e7c-bdda-5a9291722a7a}} variation, and the results are quite compatible with the NS results of the tidal deformability observations from Refs. {{cite:39fb46839f2920d40de1914759e14ed5da2d133c}}, {{cite:615fee827b105fe1d9835ef57392df8934f37c05}}, {{cite:f6c92b6ea4e4e180e5e84152a656c18a7eb563aa}}, {{cite:76a486445c22128ceb2bfc0ccbd435953c18bd3a}}, {{cite:4708cb978c01b8cf4e6f202444aed69378b5d4b9}}, {{cite:d1c39ed05f13f4e3d681bf1125f6f4583532b276}}.
| r | ec2cab10cb48a1e469db8dd3f018663b |
One important feature of stochastic gradient-type algorithms is that the noise drives SGD to escape
from sharp minimums quickly and hence SGD prefers flat minimums {{cite:f91ad3c62d75e7e1c892e03d3924c82c051f53ea}}, {{cite:3d07444477bc85b472447e2dd9736befd97f8cc4}}, {{cite:e7277cd014b2a6332ad7e9d2da93661e4118ada8}}, {{cite:e178805c306cb6f8889de51641d4eeb51780f5b5}}, {{cite:f8507b1cd3242f273c2c8678ae7aae36b1cf2060}}. Such a bias towards flat
minimums leads to better generalization properties for problems such as deep learning. However, when
the ultimate goal is to identify the global minimum and the landscape around the global minimum
happens to be sharper compared to the non-global local minima, this bias is often not desired as SGD
often misses the global minimum in a sharp valley.
| i | 2f46ac28630a99bfd6e3541318ecc62a |
We have found 113 cluster within GAMA. For this sample we have estimated positions, cluster redshifts, velocity dispersions, cluster sizes, and cluster integrated luminosity. Our algorithm has been tested using the GAMA mock catalogs ({{cite:0e10bf13f537db0e384ad6e1b9d7897cf72b698e}}). The calculation the cluster luminosities have been generated by using the individual cluster-galaxy luminosity functions (LF) corrected for completeness. We have evaluated the cluster selection function by the application of a simple halo occupation distribution (HOD) model. We want to stress that the density of clusters found by mass selection methods (e.g., the Atacama Cosmology Telescope (ACT), {{cite:f0e7450c5cf2f058d3ac33a7c4db7e8860b9d77c}}) is comparable to one found in this work; however, we have covered a larger mass range by more than three orders of magnitude. In addition, we have generated the two-point correlation for clusters of galaxies for our sample. We find broad agreement previous observations and predictions ({{cite:30c6c79d806bf5930498f26f588569cd7e6c48ea}}). We have generated the mass-to-light ratio (M/L) for the clusters and BCGs in our sample, we find that a single power law {{formula:5daf12a4-b742-40f9-847d-66f239da6979}} can describe . We found {{formula:f0056dd9-ad22-4f9f-8766-b04221ae5d16}} for clusters and {{formula:b2e6bc5c-ab1f-47cc-9048-f7496fb019f8}} for BCGs. These relations agree with the results of {{cite:67385abcd35dd2130d1da1c121424046b1da1f05}} and {{cite:e3f7379e8d54725c3f0cbeb38a8ebe73d0ec2c77}}.
| r | 7181e74586af2bbe13d6400c04fe8eaf |
Also the fermionic definition of the topological charge, via the eigenmodes {{formula:8b61b6c6-30f9-4eef-a444-62e4bfc82557}} of a chiral Dirac operator, has been used to explore the IR structure {{cite:988bf7db6964019dd09af84cdb1f72a2bad3c394}}. For this so called Dirac filtering one truncates the sum in
{{formula:a1debfeb-09d1-4fa6-bbe8-5ccc0e85d245}}
| m | 98c75bc3c15fce8faf4331791a893026 |
Designing submodels based on the main CL models to regulate information transfer. The CLS theory states that the hippocampal system exhibits short-term adaptation and enables the rapid learning of novel information that is played back over time to the neocortical system for long-term retention {{cite:28a95a3bcc74a40eb5fdaf64373acd3d69c1ac61}}. The interplay of hippocampal and neocortical functionalities is crucial to transfer different memories. The cooperation of different areas in the brain indicates that the expansion of the structure of the model is not necessarily restricted to the original one. In fact, more concurrent submodels can be designed to regulate memory circulation in combination with the main models.
| d | 76956b383083660bc0d74bfdb96af5e0 |
Formally, in computer vision, given n images ({{formula:92516a72-17a6-4e59-b51f-cab1cfe978cc}} ) of size {{formula:f6486e76-dab2-47b1-9fbb-279f37c94e5b}} , k kernels of size {{formula:4bf49490-1839-4158-bddf-406cdd968b78}} are set. For each kernel patches a small image({{formula:0c632fd8-9ed8-4e1f-a579-5fb757c38e7b}} ) in the large image ({{formula:fccc4726-ebae-4293-9e08-ee668da33ee2}} ), {{formula:88fd21a6-dd59-4b1d-b4dd-73f609683643}} is computed, where {{formula:34d431c9-0f87-4ece-9618-a52fb988f0ba}} is the kernel function, giving us {{formula:9fc36e12-589e-4d6c-b1cc-e2c8dd031040}} array of convolved features (more detail,see the tutorialhttp://ufldl.stanford.edu/wiki/index.php).
Max-pooling is the key module to help training deeper model. It works like this: Expect that there is a {{formula:4284eb4f-d1f7-45b1-9fd5-b6dc0dfba9d2}} matrix. Let's set pooling size {{formula:3108b9d0-3e25-47c1-87d7-849051aaf575}} , then the {{formula:37f4761f-4497-454c-9b2b-c52822625ed3}} matrix will be divided into 36 small matrixes of size {{formula:692915ea-c8da-40e8-9ebb-0305b5b76999}} . Just pick the biggest value in each small matrix and combine them together. At last a {{formula:97bd094b-8e99-473b-96d5-fa209e219cbf}} matrix instead of {{formula:97206713-16db-469f-aa96-67a6c4a11153}} matrix is gotten. Extending the implementation http://deeplearning.net/tutorial/lenet.html#lenet of the lenet5 {{cite:6e062b40704f8ff7cb5872c1b01c392e09a1a8d6}}, the convolutional layer and max-pooling layer are merged as one layer. The structure of ConvNets used is shown in Table 2.
{{table:88a6a1e5-069b-4384-91ca-2fcb564b4d5f}} | m | 1dfb1f321a92a27b7334e4e020a3d402 |
The relation extraction (RE) task aims to identify relations between pairs of entities that exist in a document. It plays a pivotal role in understanding unstructured text and constructing knowledge bases {{cite:188e04322b1548610554ab57f593b131158716fe}}, {{cite:fd5846a9bcf7d9b7e895634ddd5d61c9f943208e}}.
Although the task of document-level relation extraction has been studied extensively in the past, the task of relation extraction from dialogues has yet to receive extensive study.
{{figure:b088ae6f-6c2d-48cf-bef2-66afabbdee2d}} | i | a29baf4c57aa69c1d1fbc57fb0ce654e |
To the best of our knowledge, most of the SSL SOTA methods are validated on multi-class downstream tasks and only few SSL methods {{cite:e4d54a6228cf41829d77c0f6430e9bbf7c159f72}}, {{cite:de524e473774722bb8e36a3cf545c359edb8a36b}} involved multi-label classification as a downstream task where simple CNN architectures, like AlexNet {{cite:85122b9ac792d2a7ef857ab6068c7693419004cc}}, were employed.
| r | b669b00853dae9bde3f7c881ec65bf22 |
For the ShanghaiTech dataset results in Table REF , our MIST far outperforms other RGB-based methods {{cite:a5e347b737e293caa8967e2a557af75b243017d8}}, {{cite:81a20768173a8046739090638661510f0132c860}}, {{cite:69c061757987f83c92d87626c446cad9b268c708}}, {{cite:f664080c61a78803bc078d1a280aaaa43263dba7}}, which validates the capacity of MIST. Remarkably, MIST also surpasses the multi-model method of AR-Net {{cite:f664080c61a78803bc078d1a280aaaa43263dba7}} ({{formula:42d4d360-4f7a-461f-8cc8-c9f626ad405c}} ) on AUC by more than {{formula:2fb414a2-085e-4752-8e6e-1cb85ff9a297}} to {{formula:002d0580-a551-484e-8f0a-1f3f8258cdf4}} and gains a much lower FAR of {{formula:206ff398-cbc4-44e7-a2b8-b212755fc5f6}} .
| m | b108f4624467441174a0e70282de5d51 |
The classical mirror symmetry summarized in Section applies to the so-called (families of) lattice polarized K3 surfaces replacing the Kähler cone with the ample cones {{cite:390fbdc020f7e838c4b182fe56e048f48af68c6c}}. In our case here, we consider a primitive lattice embedding {{formula:f8cfa69c-ce8c-4c18-a1cd-d8282a4493a6}} with a fixed decomposition {{formula:2d6f5f9a-c7b7-4898-af51-2a433cbc2251}} . Then {{formula:926a3f69-783f-4eeb-945a-c2e27f17975a}} is a member of the {{formula:54a4001b-011d-4749-915c-c844d6d801a0}} -polarized K3 surfaces, while the mirror {{formula:09a37d27-64c6-4049-83b7-c6fc6d040ac4}} is a member of {{formula:90930984-93dd-4d53-9afe-701b63d95813}} -polarized K3 surfaces (whose transcendental lattice is {{formula:4d34b4ec-ff6d-432e-a734-ea95d1307ced}} ). The classical mirror symmetry in this case may be summarized in the following isomorphism:
{{formula:32d3f026-c6c3-46b8-b56b-f26b630ab604}}
| d | fead537a2f93cb2736b2998bfd3c4be4 |
where weighting parameters are set to {{formula:3173ef59-7515-4f4f-a272-25121ebe23a8}} to achieve a balanced training. We use a decoder-encoder network with 9 residual bottleneck for our generators, and a 3-layer CNN for our discriminators. For segmenter, we use a default setting of a 5-level UNet with concurrent SE module {{cite:2beeff5e3f3d2ce632b5025429f7bc2ea5ea1f4f}} concatenated to each level's output, named DuSEUNet. The segmenter in AccSeg-Net is interchangeable with other segmentation networks, such as R2UNet{{cite:fa210fa121b069ba47ee0d174844d3725d618670}}, Attention-UNet{{cite:992173da07e50962ec01d6c32f09aee13017ebe3}}, and UNet{{cite:c4475d3c9749151b45b62950ef1cc412cda7f40d}}.
| m | 67694dd7e5bd1a648517bb13aa63f767 |
Further, the new practical version of minimization using (REF ) mentioned above will be combined with (REF ) to establish a new ANN framework, based on deep residual-type architectures, for the approximation of solutions to (REF ). The approximate solution will be, therefore, expressed as a sequence of ANNs {{formula:e47140b1-d16d-42b6-b282-3eeed0f08664}} , each representing the approximate solution in the time interval {{formula:43594e78-4cdd-42c9-82e7-025a135836df}} . This point of view has several potential salient features compared to the generic `monolithic' space-time residual approximation proposed in {{cite:c79c8a04fe430282e334441775074c250df97d9a}}, {{cite:e9c6407892975a16e9822f24c791b23a2f09fc31}}. In particular, the minimization takes place in the natural {{formula:f6d9e3f4-5c58-40bc-98bd-9e4751f11980}} -norm setting, and the boundary conditions are treated weakly to alleviate numerical stiffness. Furthermore, starting from fitting an ANN approximation of the known initial condition of the PDE problem, not involving differentiation of the network, the method progresses iteratively in computing {{formula:6296891d-4370-4b04-97a6-a8dd13a7a218}} , {{formula:0d3107e1-4344-4bef-ad00-cb8dd4ec87ca}} , having the same architecture as the initial condition ANN. As such, we can use the ANN parameters fitted in the previous timestep as an initial guess for the optimization in the current one; this leads to a significant reduction in epochs needed to achieve a given accuracy. The ANN architecture used in the numerical experiments follows the residual architecture proposed by Sirignano and Spiliopoulos in {{cite:c79c8a04fe430282e334441775074c250df97d9a}}.
| m | 42b175931a2acc91223d509c7ca605a1 |
As we discussed above, the collocation points for residuals are usually randomly distributed in the solution domain. Furthermore, all randomly sampled point locations are generated using a space filling Latin Hypercube Sampling strategy {{cite:0cc4b1308411c4f5a4b6fec6b53fa0d0c4bd2f74}}. This sampled method works well for many equations, however, it may not be efficient for some PDEs that exhibit solutions with steep gradients {{cite:044ca73d5bd340b00edfb5a1d1d4f5d16ed4d836}}. For better results, we use a RAR-PINN algorithm to improve the distribution of residual points during process. The modified algorithm structure for solving Eq. (REF ) is shown in Figure REF , which also applies to other coupled nonlinear equations.
{{figure:3efd1c7b-ed6f-480e-b56c-a899e5ead028}} | m | 10c3f95957c47f949a12eb99fc2df0f9 |
Using lower weight CNNs (less than 5 million weights) was necessary to prevent over-fitting to the small training set (less than 500 images). Regardless, due to the large number of weights in the CNNs relative to the small training set, the two fully connected layers before the output layer required a 95% dropout to combat over-fitting (Table REF ). Since dropout is typically set to 50% {{cite:259099e54e4d9ffadc921ce6fc1f0b08bb4b4d00}}, it may be that too many neurons were initialized in the fully connected layers thereby resulting in strong over-fitting. Model 15 was trained on the augmented training set of 1000 images to see how a CNN model with less than one million trainable weights, and a more standard percent dropout of 50% would perform.
{{table:9a635dc5-43e8-4af3-a803-782f5a279420}}{{table:01f2bcde-dc79-4b0f-a5fc-2b3375c99429}}{{table:10a4c9fc-80b4-492d-8939-9eff234a815d}} | r | 7a0531c33e4621441f0ddebc2112ea39 |
We experimentally demonstrate the reasonableness of this formalization of side effect regularization. In the ai safety gridworlds {{cite:40d114ca90f694c052e5c412ae4d66655acec9b8}}, we generate several held-out “true” reward function distributions {{formula:13a753f4-f461-4303-8aea-9460814b2b7d}} We consider two gridworld environments: Options and Damage (fig:method-levels). In both environments, the action set {{formula:396af88c-718c-4891-9cfe-900fc14393fb}} allows the agent to move in the cardinal directions, or to do nothing. The episode length is 20 time steps.
{{figure:40718214-5c65-4a95-aa99-7e0707d10474}} | m | 769bdf24a58bcd8c67760bc0357dfd97 |
Of particular interest is the characterization of ABP in the dense regime, see e.g. spontaneous flow {{cite:9113caf16372917fe8611dba39d7f121dc6a3ee1}} or glassy behaviour {{cite:aeaa7594efa12f1d8a7c7760570f75c6a3d655fc}}, {{cite:d751418d6d2f3a6ebd47dc45dda5dbadb4c5e34a}} in biological tissues, biofilms, cell mono-layers {{cite:405a2f9957db4e58090df92dee8920d316b48611}}, {{cite:b7bd29070589be9cae1546b68ec81a75159a42cb}}, and can be considered a target
for the development of new materials {{cite:f77f8a8194d9802dbccab9ce2360f9ae5de08d87}}. In two dimensions (2D), ABP present ordering phase transitions when the density of the system is increased {{cite:95538ceecd895b0a7c1ab548da5a1a00b777ef06}}, {{cite:adea657fb635dac7f782366f8074e4a1b5537b02}}, {{cite:bd0a1a50db81c81028649cec02ded5f83a57e1ea}}, {{cite:3b9db0e34cb0c127685d4783c3fc1d6ecf005fc1}}, which are connected to those encountered for passive hard colloids {{cite:bfb3a89634597901ef4f8d1d5f796524bdb88183}}, {{cite:a696432270d432ef7c997642ea08090b2c232ff5}}, {{cite:2fc6135def1d080866a877012179259b099a3913}}. At intermediate values of the self-propelling force, a liquid-hexatic critical transition is followed by a hexatic-solid transition, where the solid phase has quasi-long-range (QLR) positional and long-range (LR) orientational order, the hexatic phase has short-range (SR) positional and QLR orientational order, while the liquid phase is homogeneous and has SR positional and orientational order. This scenario is very similar to the theoretical Kosterlitz, Thouless, Halperin, Nelson, and Young (KTHNY) two-step scenario{{cite:38cbc2a501a2347bbbe8fb62f310a200806aaae0}}, {{cite:f11a18d69151b6fa4863e7dbf4ae8899d462013d}}, {{cite:e51bef1905247d540fb9c27500bb8c343c37212e}}. If activity is high enough, instead, MIPS takes place, as a phase separation between a dense phase and a gaseous one {{cite:adea657fb635dac7f782366f8074e4a1b5537b02}}.
| i | dd42bb1041a0f8d21485ad4ab9903bdf |
We also experiment on the YouTube-Object (YTO) dataset {{cite:2702d1d3e04afc51889a451ee1b0724fba2110d4}} to show the effectiveness of our method in segmenting objects from videos by simply evaluating the results produced by SONet.
Following prior works {{cite:f27e453e89edc20e65c8eaba88d1f9b4a21c38d0}}, {{cite:ffb8511ec2233bb42533d3ca64c22fcbe2fe139e}}, {{cite:2265f652d44110959126a980938752867c1e0c6d}}, we use the groundtruth segmentation masks provided by {{cite:2cbed6132d97b06d0daeeed5285d134b168d20af}} to evaluate the performance of SONet and also compare our method with recent video segmentation methods with weak supervision in Table REF . Note that all the baseline methods are explicitly trained on video datasets and use temporal cues, while our method is trained on static images without temporal information. Our SONet method outperforms the existing methods which use different levels of supervision. This may be because objectness-driven pseudo-labels provide more fine-grained localization with sharper object boundaries than coarse bounding boxes. Samples of the predicted masks for the YTO dataset are shown in Fig. REF .
{{table:ff1bab0d-147c-4a0e-8258-cb2ef6392d61}}{{figure:e8e2f776-5330-40e1-b968-7b6219af511c}} | r | 9ede83c9df62d609c2b3db01db5efba1 |
When cooled down fast enough, a liquid can avoid crystallization and form a solid with a disordered structure. This phenomenon, termed the glass transition, has been widely observed in many natural and industrial systems but still lacks a satisfactory fundamental understanding {{cite:0a0cbc82b171e342f3eea17d0f206ef571300ca8}}, {{cite:ed24bee9a6671dce7bc47aec258a93cba212ef18}}, {{cite:63716020f2a38c92c4c5cfab45ac7b7ea97e299d}}. Direct spatiotemporal information of particles in glass-forming liquids is highly useful for investigating the physical mechanisms leading to the glass transition. However, in common glass formers, such as metallic or molecular liquids, the relevant dynamics of the individual atoms or molecules is on the scale of nanometers and picoseconds (or even smaller) {{cite:bd34cf918ef19761c3a2d18c257a878f6e413165}}, thus very difficult to access by current experimental techniques. In contrast to this, colloidal suspensions not only share typical features with normal glass-forming liquids but also have the big advantage that the trajectories of the constituent colloid particles can be directly tracked by optical imaging, therefore allowing a detailed analysis of the system's dynamics on the particle level {{cite:bd34cf918ef19761c3a2d18c257a878f6e413165}}. As a result, in recent years colloidal suspensions have been widely used as model glass-forming systems in experiments and have provided insightful results on the physics of glass formation {{cite:3382f3d6a3749d9e858a8c5187e638a6bb553537}}, {{cite:9e9d3f61dffd4daace39fcaf2869252a68e8bc3f}}, {{cite:bbada2feadba72792b46192b75d7360952f6a462}}, {{cite:cd4e5013527538f8f98f67214535bc19135e4583}}, {{cite:dbb7e877025b4a32facb6d46cd25b95e951ac99c}}, {{cite:71fc7dad469972ab6e279403257dd69659f8df61}}, {{cite:750b65eac7cac1f207475635cf455c3636709b73}}, {{cite:28896e1704a6630200c0928dd667f3a06aed136d}}, {{cite:e58f5007792412f07bb472c28e57d5137a9237a7}}.
| i | fcdda9b0db870509d917f2013b052d26 |
To ensure global convergence (i.e., to ensure convergence to a solution from any initial point), suitable modifications of the Newton method are needed. An example of a globally convergent variant is the so-called Levenberg-Marquardt method {{cite:6d69f6556243edc69386ad60a5eb61eb687b0808}}, {{cite:e35f9be6173581bb2b6572ed1415a7e4110b0d0a}}. This involves a modification of Newton's search direction at each step of the method. Without this modification, however, quadratic convergence can only be ensured when the initial guess belongs to a quadratic convergence region, namely a region from which every starting point generates a quadratically convergent Newton sequence.
| i | 27741dfacff4becd6357dcc43ab58071 |
Overall, our study can provide a characterization of the topological order through the response of the entanglement spectrum, on a local scale. This may facilitate the experimental sought of topological order {{cite:595dcf85354cfa4bb29e7b10cf72142783d75775}}, {{cite:d8055124aaf83be8f2f2147288d623bdd2a31727}}, {{cite:0bcaae61e5e3ad4bd39395fcf09cb0646ac858ac}}. On the more quantum information side, our results contribute to the questions on whether topological phases universally encode more computational power than non-topological phases.
| d | 561c803ef176a5f9f4344df64b1a75af |
By (REF ) and using integration by substitution for operator-valued functions {{cite:59eefdeb418b48ab503ddb8d45755eca19145a88}}, we get
{{formula:bbabe653-298e-4720-9427-b29e811b8f38}}
| r | 10f8dad5af6beefbacee33ee2f6991bf |
Polynomial neural networks {{cite:880260a45ffcc7c0fc81d06aa56a187128531aeb}}, {{cite:3774d5a92b858c7e97833767e5b5309cb11ef7be}}, a special class of NNs-Hp {{cite:a7956b15e708ecdd8d495e98c8b3026506cb4dbe}}, have showcased remarkable performance on a broad range of applications.
As a step for analyzing NNs-Hp, in this work, we derive the NTK for PNNs
with high-degree multiplicative interactions and present a rigorous proof for the equivalence to the kernel regression predictor.
This analysis enables us to further examine PNNs in a theoretical perspective.
This NTK analysis can be useful for investigating properties, such as the extrapolation. StyleGAN and {{formula:bff710ae-3ba1-4136-a3e1-6fe3ed19a9b4}} -Nets have demonstrated stellar in-distribution performance,
however implementing networks for real-world applications requires the ability to extrapolate to unseen data, e.g., for medical imaging.
Neural networks have demonstrated weaknesses in extrapolating simple arithmetic problems {{cite:53c8eb1c1453ff34cdc900b1b8a6a7d7e07f4313}} or learning simple functions {{cite:6889fa5820db4a294ac5573e72dd2097f8a16d3d}}, {{cite:60605f706c14273158f44ca7301738602979f0d1}}. Early works demonstrate that fully-connected NNs are unable to achieve exact extrapolation when fitting low-degree polynomial functions {{cite:6889fa5820db4a294ac5573e72dd2097f8a16d3d}}. {{cite:7bccac7e41833466b9e0919bbe23fbc143528087}} theoretically and empirically point out that 2-layer fully-connected NNs with ReLU can only extrapolate to linear functions. However, data in real-world scenarios usually lie in highly nonlinear manifolds {{cite:f5ea9b37c481b8c8ca944248347b052af957b634}}. Our findings extend these results and highlight that PNNs
can extrapolate to unseen data in a non-linear way.
Besides, studying the NTK of
PNNs
also allows us to investigate its spectral bias.
| i | 1072b1bd83380c8e6e5e22593280afd0 |
It suffices to show that {{formula:64b12741-5690-4f49-bfd0-fd35e409fb97}} is free over {{formula:f8df62d3-600b-4f53-b1b8-f036c6c4e525}} since free modules are faithfully flat modules. Note that {{formula:98c5473b-5e82-4b93-86a6-8b20e65a2d8c}} is injective since {{formula:08310cff-d9ae-4656-b542-93a0492cc3d6}} is a regular sequence. It follows that {{formula:12ffabcc-98cd-4f53-9450-e1eef6ed8ae8}} . So we identify {{formula:672249a0-3785-4be4-ba57-ae17cbde7be7}} with {{formula:f3773cc3-0ba8-4aad-b59d-00305002c179}} and show that {{formula:5f2e16fe-ef76-47cf-b530-2f308dd1710e}} is free over {{formula:4193fc6f-3f55-42e3-8994-fe9fc004cd7d}} . Since {{formula:c5283144-473b-465b-902b-c966cd43ea22}} is a maximal homogeneous {{formula:c0df410f-449d-4ca5-95cc-7fed65992ef6}} -regular sequence, it is a homogeneous system of parameters (sop). The reason is that every regular sequence is part of an sop and because {{formula:e80f8e44-3192-4e47-8d67-e8f66c0b5650}} is Cohen-Macaulay (CM), every sop is a regular sequence ({{formula:9b84ba7f-22b9-4cb5-9fe2-de9ce1bcffd6}} ) and so if {{formula:c5e57e7d-2ba7-4d41-a0a1-c5ce148acaab}} is a maximal regular sequence, then it is an sop. Since {{formula:f9ecf50a-745a-4a07-abad-c084c104f1ce}} is a positively graded affine {{formula:5ec23ee4-ff30-45f4-ba96-5190705d1a3c}} -algebra, the fact that {{formula:0a357246-21b8-4d14-9374-9754b4d85bf2}} is a homogeneous sop is equivalent to {{formula:ab179530-db51-470c-9320-b6e829115636}} being a finite {{formula:8ad95f51-4bd6-40aa-bf03-2571db15e124}} -module by {{cite:3a9f39ff84cb9a7bb0a78265b8315cd75f2044d6}}. Since both {{formula:35813958-7941-4ebe-aa7d-c79dda836ff5}} and {{formula:791e7193-96e4-4dea-b1f3-024312f9bf0e}} are CM, {{formula:6d099101-715e-4c54-a413-ae6d61b8c131}} . By the Auslander-Buchsbaum formula {{cite:149dc6ff99d2911626f4e3a43488d04346066595}} {{cite:cf5fc837dd19f71d27db3789447a510ee9ea07b2}}, {{formula:bd973985-0e94-43d6-8ddb-3b9d813185b6}} . It follows that {{formula:6cfefb1e-631c-442d-a7ad-981e4525f703}} . So looking at the minimal free resolution of {{formula:9c59f95d-019d-4d2d-8b7a-92f65330f43f}} as an {{formula:632f18d7-0730-4bdf-b14f-4723ec41285c}} -module, we see that {{formula:33cfbd7c-1fe2-4515-9215-6de92550762c}} is a free {{formula:37063909-b92f-4841-8fec-92a950bdf448}} -module. Therefore {{formula:d620f310-24da-44e5-b12c-50aa59c26a27}} is a faithfully flat {{formula:959d94f7-31b8-4a7f-8bce-16c6db4d7e8e}} -module.
| r | 8b24d0bb6697d5441b04b97e88bfb9f1 |
It is interesting to compare the results obtained in this paper
for the cover times of RWs on RRGs
with the corresponding results for RWs on regular lattices with the
same coordination numbers.
For example, the coordination number of a hypercubic lattice in {{formula:665254bc-79c0-486c-a668-5da12c16e565}}
dimensions is {{formula:e79c8197-6f2f-4faa-b77a-0911a381a30b}} . Thus, in terms of the connectivity
the {{formula:e622b934-067f-4cea-a82a-734a74502d3c}} -dimensional hypercubic lattice is
analogous to an RRG of degree {{formula:19c7e2bf-bc21-4348-b0fe-07c61dc593ec}} .
In the case of an RW on a one-dimensional lattice of {{formula:b188adc5-20b4-40fa-8877-c723dcf7b595}} sites with periodic boundaries,
it was found that the mean cover time is given by
{{formula:4450bb78-2b91-4971-8502-5e700850bcdd}}
{{cite:88322eb56932fd9fcbad73fcff9a515a113ca5ec}}, {{cite:ef5d97addb129d8262941c5fb1444ba698ee69f9}}.
For an RW on a two-dimensional square lattice consisting of
{{formula:e2e4df81-3ac4-4762-917e-72deb200260f}} sites with periodic boundaries (forming a torus),
it was found that
{{formula:ba079dfe-9495-4eba-97a2-99492a1cba44}}
{{cite:88322eb56932fd9fcbad73fcff9a515a113ca5ec}}, {{cite:a33c8f33d3b14aebfeee2d636470335d72d3c610}}, {{cite:7bb003c65d16ee5c238d27e4d3b91f0373a669e2}}.
For dimensions {{formula:de38efbb-e957-4a49-bbdf-003ac8b0969f}} it was found that the mean cover time
of an RW on a cubic lattice consisting of {{formula:cadbabda-0dce-41c7-9eac-13824efb7be8}} sites with
periodic boundaries is given by
{{formula:22eda859-a89b-4f7c-86dc-f4350e8a734a}} ,
where the coefficient {{formula:d2054a43-93dc-4f7a-a1cc-50e4680ee49a}} depends on the dimension {{formula:e2080089-5003-459a-a8d4-ab8412fbb0eb}}
{{cite:88322eb56932fd9fcbad73fcff9a515a113ca5ec}}.
Thus, for {{formula:679c1b90-c48b-4b2c-8ca9-0ab8a5fca7b8}} the leading term in the expression for
{{formula:fa72ebc6-abef-41e1-b5f1-b6607bd434c6}}
on regular lattices has the same functional form as
in the case of RRGs.
However, the values of the coefficient {{formula:abbf5dfe-f2b7-4222-b9cf-36981dc8cc17}} , {{formula:defb5b44-01a5-446c-a7a8-1d415dbeb8f7}} ,
for regular lattices are known only approximately from computer simulations.
For example, it was found that
{{formula:cdb1f930-58b5-4549-8244-b8cfa43e7c90}} and {{formula:bea03b0b-a3c1-4ff0-8a93-e0875a0d2b75}} .
These values are larger than the coefficient obtained for
the corresponding RRG with {{formula:0593fe82-2dc0-424d-b798-bd1a436aeaf0}} , which is given by
{{formula:e34cb608-e9db-4f3b-9113-4bfb2ba96446}} .
This implies that the cover time of an RW on a regular lattice
is larger than the cover time on an RRG with the same coordination
number. This is sensible in light of the fact that the RRG is a small world
network on which it is less likely that the RW will remain for a long time
in the same neighborhood and revisit the same nodes again and again.
Interestingly, beyond any differences in the prefactor of the mean cover time,
the limit distribution of cover times on RRGs and lattices with {{formula:e4520298-a906-4a26-a292-b37a28f0c4f8}} is Gumbel in both cases
{{cite:61f865a033da8b3fcb51dc860c59fe0732bbdbd9}}.
Based on the experience gained in the study of other problems on RRGs
{{cite:755fcd7cfa5185e53461a820d4b4e5a01f48ea7c}}, {{cite:1e1730f9d0979cc7ae44554d8b49d4e295a787ed}}, {{cite:df56fbeaa1ab3167437ef03cd603132b83b95b5f}}
we expect
that the results for {{formula:5bfbdf35-c4ec-49c0-8a87-40f013b720ea}} provide the asymptotic large {{formula:ecda22f2-ea59-49b1-916e-5d82f25be6a5}} behavior
on regular lattices.
More precisely,
we conjecture that for hypercubic lattices of high dimension {{formula:ee1246de-1734-420f-bc42-b98ff4645479}} the coefficient {{formula:5b49d092-fbe5-4935-ba71-6c9e46dee798}} is given by
{{formula:4ee151cd-742a-4184-b855-f79d6cb6166a}} .
| d | b62dce6646e4c759df545e06d5acfe49 |
Synthesis vs Analysis methods. Our result could also inspire new ideas in estimator design. There are two families of methods in non-parametric estimation. One called synthesis framework which focuses on constructing appropriate basis functions to encode the contemplated structures and regress the data to such basis, e.g., wavelets {{cite:a440a073bbf96b874e6bcaa935601343261750f3}}. The other is called analysis framework which uses analysis regularization on the data directly (see, e.g., RKHS methods {{cite:15a5fadb3289b93db63bcc1808adb4e85ced795d}} or trend filtering {{cite:419264c2ce6f8fa354babd7046cb38d836eb53d1}}). It appears to us that parallel NN is doing both simultaneously. It has a parametric family capable to synthesizing an {{formula:aa8cd042-0e17-4841-ab5e-95d483e348c0}} subset of an exponentially large family of basis, then implicitly use sparsity-inducing analysis regularization to select the relevant basis functions. In this way the estimator does not actually have to explicitly represent that exponentially large set of basis functions, thus computationally more efficient.
| r | f464263e06f5e39e9aa55dbaef19d281 |
According to the BEAMS with Bias Corrections (BBC) method {{cite:15ff6c79f8a36d3a99499515244e10a49bfe35c2}}, the observed distance modulus of SNe can be simply given by
the apparent ({{formula:3ff44625-b580-4cb3-a5ea-10d7da58209d}} ) and absolute B-band magnitude ({{formula:8fc1e061-8782-414d-9b46-6bce7b0cb4fc}} ) as {{formula:f74d0e4d-a3d8-4fd6-a74c-cacba3d44e93}} , with the nuisance parameters in the Tripp formula {{cite:7ac476412789d125f1c2a1f1e3729e0020f6c7d7}} retrieved. The theoretical distance modulus {{formula:55cd7088-b234-4822-a8bf-1dad0388d13b}} can then be obtained by
{{formula:d0e7d15f-5d94-4151-985a-d154f2968c80}}
| r | c1c9889b8617175150c37cf43a6d0ac4 |
We have investigated two holographic models of evaporating black holes. First, by perturbing the 4-dimensional black droplet
solution associated with BTZ black holes on the AdS boundary {{cite:8a847f84aab94ece04baff2fdcf5f89c3441b840}}, we have constructed the bulk
geometry dual to the boundary field theory in a time-dependent BTZ type black hole with the horizon area decreasing.
We found that negative energy flux going into the time-dependent horizon always appears by calculating the boundary stress-energy
tensor. This calculation agrees with Hawking's picture of evaporating black holes {{cite:2c0b7d42b6bc9666ec3d9694e544b893a838e445}}, where the
horizon area decreases by absorbing negative quantum energy flux. According to the energy conservation,
the total energy and the matter entropy outside the evaporating black hole should increase by the Hawking radiation.
Our result supports the generalized second law (GSL) {{cite:2c0b7d42b6bc9666ec3d9694e544b893a838e445}}, {{cite:f76031ca12acdafe3c1cf464bf6448b432827063}}, which states that
the total of the gravitational entropy and the matter entropy outside the horizon should not decrease.
In Ref. {{cite:0c1244f4c38778370f0e865160dde1ee276fc849}}, it was shown that the coarse-grained
generalized second law is satisfied in a holographic theory when the boundary black hole admits a timelike Killing vector.
As a generalization of {{cite:0c1244f4c38778370f0e865160dde1ee276fc849}}, it is worth trying to prove the GSL for more general holographic models
of time-dependent boundary black holes by evaluating the holographic entanglement entropy outside the boundary black hole.
| d | 3107ce7100f4e13867f9f2a96e559b7e |
From Figs. REF and REF one infers that the radiative corrections
decrease rather fast, by about 10-15 orders of magnitude, with
increase of {{formula:32a68b6a-2756-4579-8272-8f4e13f8fccb}} from its smallest to highest physical values. It
means that the contribution of the heaviest {{formula:660d9fc4-629c-4f6f-bf2e-2a8e86c153af}} -lepton to the
anomaly of the lighter ones is much smaller than the contribution
from properly the muon and electron loops. This effect increases with
increasing of order of the radiative corrections from {{formula:7eb46b6b-5860-448f-a375-09de0f0c44be}} to {{formula:92d748e3-64ea-4848-8043-1a89d9c79845}} and depends on the combination of
the internal and external leptons. However, due to the extremely high
precision achieved in the measurements of the lepton
anomalies {{cite:e1ba0b2b3fb812079f71aefdadf982b30ee04aa0}}, {{cite:642d87912d2b4c3e2334bd35b04caa52d5b1395d}}, {{cite:f28714bc64c207d0dd319389e397e5914d36266a}}, {{cite:2cb928534b53eed12e7259dafb42464c99821cb8}}, {{cite:e56a8ece0c4a1e829e79031c8a4c90f4028e38c9}},
the corrections from {{formula:5a0f3a3a-9f48-4f14-af0f-a0c884a2841d}} -leptons cannot be neglected. The horizontal dashed
lines in Figs. REF and REF correspond
to the values of the coefficients {{formula:20b881f2-04ef-44a8-8c11-ff34b9e87cdc}} at {{formula:327bf8d2-19e8-4fc7-9d56-97a15ba16911}} , i.e., to the universal
coefficients {{formula:037005a5-6eb1-4d19-aeb2-06208c4f3b2d}} , Eq. (REF ).
| d | debeb80ef70647fb2cc5149349946a28 |
taking the VEV as (REF ), which has also been mentioned in
{{cite:76eb09ab7b1d90e0f8783820dba18cd7ba64756f}};
rearrange the gauge field as (REF );
decompose four complex scalar (spinor) fields into eight real
fields.
| d | 62f3313cf3f2462387e2831c7761497c |
We consider the problem of rtMRI synthesis as a sequence-to-sequence problem with input text sequence of length n and output rtmRI video of shape n x 3 x 64 x 64. As shown in Fig. REF , we use a transformer architecture to represent the input phoneme sequence. Transformers are an ideal choice since they have been shown to perform well in learning text features, especially in multi-modal scenarios {{cite:67c6b31d733979aebb4ca80be77c7867270c7198}}, {{cite:1459bdd2ccd6cc1f56818d89e4977ba24073d002}}. We then use a custom convolutional decoder consisting of 2D and 3D convolutional neural networks (CNN) to represent the frames. The CNN decoder is designed to upsample the representation to the image size while maintaining the temporal context learnt from the transformer encoder. In the following sections, we go into detail about the encoder and decoder architecture.
| m | f1fbf61649c8ee30c5fa001d7db1f6a3 |
Uniform stability is a representative technique to derive algorithm-dependent generalization bounds based on the algorithm's stability with respect to perturbations on training data {{cite:6348d13f42f48c3127c057db54cc62f129718b2a}}. One problem of the application of uniform stability is its dependency on the {{formula:e8f8f9e1-7d02-4902-8970-4c5a7b1cd667}} -smoothness assumption of the loss function, which is imposed in all such works treating nonconvex loss functions and SGD. Recently it is shown that gradient descent on DNNs cannot be analyzed using (even local) {{formula:8ceb87a0-38af-4bbf-bbdd-993c9ff49f99}} -smoothness at any reasonable step size because the sharpness hovers just above {{formula:86f842ab-1cc7-45a3-bee0-0a793b39e050}} {{cite:89bfc19c0ab41a4750bad3ade8e39d9c4c78693d}}, {{cite:11f50338977e5e240e717d472c40f9d8105ce180}}.
| r | e39d2f1f0a1f5a00402ed6982200a3d3 |
The embeddings themselves are character-based, trained using the skip-gram negative sampling method with 50 negative examples per observation and trained for 20 epochs. Implemented using the fastText framework {{cite:3f35274296da8c713788376613463f6af44a61db}}, these popular embeddings have the advantage of being character-based, which we expect to reduce differences that are caused by morphology or writing system (c.f., Table 1).
| m | 46d30087fd614fad9b7dcfff73460289 |
We implemented several machine learning algorithms commonly used in the field {{cite:a0cb37724207eb3bbb8e9369937a3732cd66c98c}}, {{cite:34efdeb6dc35d50bba9d28679ceae97efa4f93c3}}, {{cite:056555bbd24a7985073873fa67a460f4143e09ad}}, {{cite:aa961311f13eff186ea1b6efc9cc182976e7fb1a}} from the scikit-learn {{cite:fc10c68548fc045433413bfdc2b27784d1e75da1}}. For example, Linear Classifiers, Nearest Neighbors, Decision Tree, and Ensemble Methods.
| m | 924a9cd55f94ef0f1ab404d2475fef36 |
Recent deep learning applications use a semantic distance metric, which enables applications such as face verification {{cite:4bb0700ec9320f374c265ce9b211bd0c86b0774c}}, {{cite:de6a53da75a6f7d06ea56a6ec3b821bb3e897ca6}}, person re-identification {{cite:c905b3df443dc4d2cdefc479537a3196dc7b9975}}, {{cite:a3c578a7ce2a53dca38e98cb9f65189af01487f1}}, few-shot learning {{cite:cb916f2472cdb93c5a5ff9332c567ee6b00ce282}}, {{cite:4ca625586930a6d0e5674ec3fbb4fed7b9acaff9}}, content-based image retrieval {{cite:64b4e89345004d5eecb8d83fc07362a5e15f55e5}}, {{cite:c738147fca968b16efb98260c980d454220b19cf}}, {{cite:835f49a307e3ddb33e14110d40b8a82a9ed8ebb7}} or representation learning {{cite:af8fb0bcc353168188bd1e9f0eaa455fb20cf4a3}}, {{cite:64b4e89345004d5eecb8d83fc07362a5e15f55e5}}. These type of applications rely on vectorial spaces (embedding spaces), which are generated with the objective of gathering together the samples of the same classes while distancing themselves from the ones of other classes.
| i | 84bb537f247397347aa12261f34c3e5d |
Using (REF ) directly as a boundary condition is the classic Nitsche's method {{cite:284cd81d9e5afda88680c0ae811ed4c9d5b2d49f}}. Multiplying {{formula:1d635e1d-2e14-4bf5-aa06-e88fb0976153}} on both sides of equation (REF ), we have
{{formula:42af3b65-cf8b-4019-89bd-e9dbfd61b436}}
| m | 55a0c46f31d28696633c28fef38f23c4 |
Very high flux emergence rate can be used as a precursor of strong flare activity of an AR in the future. Our estimates suggest that flare-quiet ARs do not exhibit flux emergence rate higher than {{formula:a3c085b6-4d08-4411-9194-f59b6e2ae224}} Mx h{{formula:37ea6712-cada-4ae6-b958-4cb805191e7d}} .
However, the number of such ARs is less than 10% in our sample. The most flare-productive AR of Solar Cycle 24 NOAA 12673 exhibited extremely high flux emergence rate. {{cite:e7e7e46e0f806f97ecfca97bacd11cd04eb4f76c}} estimated the averaged flux emergence rate to be {{formula:a340ac09-5e9e-455c-9f4f-170bcad2c0c4}} Mx h{{formula:49b978fe-f821-44cb-91ef-c465957b55b3}} that is comparable to our value {{formula:46466a20-03d0-4936-ab3e-61c21dce4ecc}} Mx h{{formula:ff28baa5-8800-4ef8-b833-b522fe149085}} (see Table ).
We found that similar flux emergence rate of about {{formula:efad169e-bc45-4bfb-a560-b381d5ac99ba}} Mx h{{formula:cf2abe28-dc30-4bff-9282-9fef98fafc61}} was observed in NOAA AR 09393. The AR produced one of the strongest flare X20.0 of Solar Cycle 23. Interestingly, both NOAA ARs 09393 and 12673 were classified as type II ARs: in both cases fast emergence of a new magnetic structure was observed in the close vicinity of pre-existing AR.
| d | d473efc7be0cb250f8a4bc8d0a7ab248 |
Our results, {{formula:3f96c1cb-6c4c-4cf5-a989-0d52b8f30520}} , might be useful as a comparison with the fixed-node Green’s function Monte Carlo results
{{formula:a9cb32e2-1899-4fe7-898f-ce158f733c9e}} {{cite:2c49fa31a202141f421ab61029e5f531783b0570}}, {{formula:9888735b-c32d-435c-8833-1e9f15b74960}} {{cite:ab179419905ec15a7af61201dfc1036d4f03d341}} and almost with recent experimental results, {{formula:66c43014-dd60-47d2-9074-f5f9a446c569}} {{cite:7a0b7fcb4c29c43fb3535f0f9a75529d94d2627c}}, {{formula:2472b422-f153-433a-8eab-5bb5abbdae26}} {{cite:b17df74bbdd0f9827a3046edd0363397b628debb}} and {{formula:ba1138ba-775c-41fa-b0d5-6689a2bef574}} {{cite:7b4475ea8f71ce7dcc61eda66b8fa19648f6d2e1}} within its error. We have to point out that, because we consider small number of particles in our simulations, a careful extrapolation to the thermodynamic limit has to be done, otherwise, it is quite problematic and dangerous to make a direct comparison between the results and experimental measurements, as well as with other calculations. Using wave functions which restore symmetries of the system can reduce the systematic error significantly {{cite:5a95d36ca2dfb5d1df2663e3903f158766748da0}}.
| r | 2d42c2332ec88d5cf2b3ec133c6da47e |
FMNIST Only DCCS is able to surpass our method's ACC and NMI performance. We emphasize that using data augmentation in DCCS causes a significant improvement, since selecting the right type of augmentations for a specific dataset can reduce much of the intra-class variance. However, augmentation with GANs is challenging {{cite:662e76d62f5125d9970d937b0489dc66f8965e0f}}, so we leave this for future work. The refinements still had a positive impact over the raw split only experiment.
| r | 932c70282353a3dc1c03b8f1daf768e6 |
Faced with an obstacle in proving global well-posedness in case {{formula:438c7bed-d74c-419e-871e-af0cbe83fb5e}} or 3, a natural strategy is to investigate its criterion following analogous works for the 3D NSE such as () from {{cite:657de669fdc2de2a6ae2886671ff779d7426dd63}}, {{cite:339da6706f52cdaf78eec3db3537b2feacf2ad34}}, {{cite:f78babc03466918c0d13973457e90d0dcb9382cb}}, {{cite:88ffe8a7da9bf92be96779d84a5a14572646f8f7}}. In this endeavor, we first obtained criterion that seemed to be natural extensions from those of the NSE (see (REF ) and Remark REF ). To our surprise, subsequently we were able to improve such results significantly (see Theorem REF and Remark REF ). This motivated us to pursue another direction of research that has caught much attention in the past few decades, specifically component reduction of such classical regularity criterion (see ()). Despite a large amount of work dedicated to such results on various systems including the NSE, magnetohydrodynamics (MHD) system and surface quasi-geostrophic (SQG) equations, divergence-free property of velocity field was crucial in all of their results; consequently, we are not aware of any example of a PDE that does not involve divergence-free velocity field and yet admit component reduction results. Unexpectedly, we were able to obtain such results by making use of special structure of the KSE, which seems to be a unique property that is absent in the NSE or Burgers' equation (see Remark REF ).
| i | d07c631a778b515342346c27c47f4373 |
Determining the shape of an inhomogeneous object by minimal/optimal scattering measurements has been a longstanding problem in the literature with a long and colorful history; see {{cite:b27d2dc3c42196dd9b7e35d6dd6e3e7530da195a}}, {{cite:9aee92145e4875ade42a65fac885cdc84030bfb0}}, {{cite:2afab873576d8c043f8e0e8125d092d932d7f393}} for reviews and surveys. Recently, several qualitative uniqueness results in determining convex polyhedral medium scatterers were established in {{cite:6159be516db37aff7d4b1638c48c3a0f213408d5}} for electrostatics, {{cite:bac4c3ea4cd58f0ebb95fb478c3a91bbfefe7b14}}, {{cite:ec16a3eee3119ccb301b5dfce8dd4777f5302c46}}, {{cite:74db1e1315101fcb97aba1d63dcd3c5493b715b0}}, {{cite:2d6a4ce96cedc63062a33cd898865eeeb5f16fff}}, {{cite:7d1a89e32f88b37fe55933cbdfb6479753ac7726}} for acoustic scattering, {{cite:f7d6673fd1d20ce33d2a70951b2e85262788a17e}}, {{cite:053c074b3b319976b2d21c8e3315f09a195bc057}} for electromagnetic scattering and {{cite:cb81a2a9ba5133326e130aab86cff644f9dd5ba7}} for elastic scattering. In {{cite:6b0c25b4848e0bc0c96f0b1fb05503673d24e183}}, {{cite:cb7943b1612d8330178205c2a8fccbb75093ab5d}}, the shape determination of medium scatterers whose boundaries possess high-curvature parts was also considered for electrostatics and acoustic scattering. In {{cite:1cda77e15b5432d3e06f8a8f3ff9037aa06f0fd1}}, {{cite:e6f6e9ce5f553d4c69efea0a9f07bc377844800e}}, quantitative stability estimates of double-logarithmic type were established in determining the convex polyhedral shape of an acoustic medium scatterer.
| d | d1f5ec960e7b548156f73ba67639ac1d |
More about Big Model training.
We can see that resource requirements for Big Model have grown far more than hardware improvements over the past generations.
To facilitate the next major leap in model capacity and performance, it will become increasingly important to co-design training algorithms, models, software, and hardware {{cite:d8942605654e0de8b84ade93a50cddb3141682af}}.
In addition to the technologies introduced in this report, methods for training Big Model include specially architected hardware training platform {{cite:79801952e369750cb597c8662dcef9dfdc8b3eb9}}, {{cite:ec71fd79c752cee494016c1c0acf60bb5aa0a5b7}}, efficient optimizers {{cite:04138a4fbe6fcbd95e47e48d33fc817aed278628}}, {{cite:13fa2f276d1c9bc7979a6907bdd16cf1b79b2baf}}, weight sparsity {{cite:3e3b98350e16397fcf34b53d90f1139c10d4410f}}, {{cite:a04fe2efec1fc4da6a93ce817a88b86ea7f2e638}}and so on.
| d | b52e6007cb7665777e40750b2215bdea |
Traditional deep learning methods cannot be applied to process graph structure data, because of the complexity of it. Graph neural networks are the hot research direction for the majority of scholars. Graph neural networks can treat graph structure data as message propagation among the connected nodes and then the dependence between nodes can be modeled, so that the graph structure data can be handled well. The essence of graph neural networks is utilizing neighbor nodes to update the feature representation of central node. So, the research work of graph neural networks started with how to fix the number of neighbor nodes and how to sort neighbor nodes, such as PATCHY-SAN {{cite:460394471a9e5ca553e5097a4771c4a2d4bdc699}}, large-scale learnable graph convolutional networks (LGCN) {{cite:f634e6e8bf98386ae07dd38a747ce0fe40e57efa}}, and diffusion-convolutional neural networks(DCNN) {{cite:37d098d02d867c956e1130931fa28e8fc6b1697d}}.And now, with the further study on graph neural networks, researchers begin to turn to the research on graph neural networks in various fields of deep learning, such as graph reinforcement learning {{cite:e0ee30fa9267fe74bea4eaed504fa35d69bf7170}}, graph transfer learning {{cite:2dd318a6396e165c63a97e2792bbade0a1af0068}} and the explanation for graph neural networks {{cite:c13f0a9c6c6f6b9235537dd7f9cb159bbb84513a}}. However, no matter which direction graph neural networks develops, it will always be a powerful tool for handling graph structure data.
| i | 79841a17147171f4dd943f26bb3dad34 |
The interactions in the lattice gas model originate solely from the statistics of a MSA. They are therefore not directly related to physical interactions. However, it has been demonstrated that the {{formula:e964c2e9-2bf8-4532-934b-fdefd86c66b5}} matrix as used in this study is a good predictor of physical contacts in native protein structures {{cite:4f62cb8dbde150687555f28b1e93f9c2a95f859d}}, {{cite:02f861ced676a254680ea2f38d79b421cae744c7}}. To further confirm this,
the present results showed that the effect of non-bonded (statistical) interactions was more pronounced in the V-set domain (an all-{{formula:7579f7ef-3f2c-47fa-820d-ee293952d9e7}} fold, involving more nonlocal physical interactions)
than in the globin domain (an all-{{formula:d08e0bb7-8fda-4b64-9876-dc4c55a8f65a}} fold, involving less nonlocal interactions). In addition, the {{formula:4aa7079e-c2f2-4f5f-94a3-32d7683c9d9a}} -only system showed relatively better correlations with conservation for the globin than for the V-set domain, indicating that the bonded interactions also reflect physical local interactions to some extent. This point is also supported by the correlation, albeit weak, between divergence and secondary structures (Figures REF and REF ). Thus, the lattice gas model provides a means to connect the information in amino acid sequence with the underlying three-dimensional structure of the domain. This connection cannot be addressed directly in conventional sequence analysis methods such as the profile HMM. In fact, the very existence of long-range correlations indicates that MSA's cannot be modeled as a purely one-dimensional system where long-range correlations simply cannot exist {{cite:3fec43eb9941aab317b085ffe20d8d198f61172c}}. Considering this fact, it is surprising that conventional multiple sequence alignment methods, inherently based on the one-dimensional system, can produce MSA's
with long-range correlations. This may be a manifestation of the consistency principle indicated above {{cite:474852bac188a11c6a0e65f2d57db530d9327547}}.
| d | 5ba45b56787efee940eabc64e1714412 |
In the case of SDSS J1212{{formula:7dc92c8f-b2d5-405c-bf89-4d81fa499cae}} 0136, early studies suggested that the brown dwarf was under filling its Roche lobe and was more likely to be a PREP than a LARP {{cite:172bf1985859ce169aec8eceeabca442639887c1}}, {{cite:076a55b20cbe7f8df302396479874433554fa14f}}. However,
the X-ray observations of {{cite:36fcb4050d14ef73661ff470390c1bd8df3c3bf6}} strongly suggest that this system may be filling its Roche lobe and should be considered a LARP.
| d | 4add48c9c688671d08e379bc699d3c34 |
where we introduce a coefficient {{formula:b1c5fee8-d334-45e7-8ce7-2f8bd7f36261}} , if {{formula:38fa05f5-b6e6-4398-910e-53bf337a4b5e}} ,
the QCD sum rules can be saturated by the scattering states
{{formula:73a3e98f-94ea-49e6-83f9-6778923b789f}} and {{formula:3b8f160a-922a-4a9b-8ea8-026f0bc13d20}} , respectively.
The input parameters are taken as {{formula:548cbb6d-8401-4f45-adf8-c75e8e873984}} , {{formula:f557c198-a25f-4d56-b405-dcc875975d13}} , {{formula:ade3933b-ba92-4294-9018-4778f1eee963}} {{cite:87c66e802f6c50cbdad5d0643ce23fae26d8abab}},
{{formula:7a1a4095-0d27-4575-9107-d01b1eaed09e}} {{cite:684d650434f0081367a94b6f44531531f32efd7b}},
{{formula:9696b979-d71b-4233-ac3b-7d3e1cb277d8}} , {{formula:44297b82-8567-478a-9585-e2a15632fff0}} ,
{{formula:4ca5928d-c6a6-4d4a-97d0-5f67c28c03e7}} , {{formula:541f0e12-a4b8-4896-8c33-607b992df9ce}} {{cite:e9d7cfa88b591eb497945eaed130d529e3c850ab}},
{{formula:7d9bdeb4-8fd3-4ebf-87d5-99ba7e7ea023}} .
In Fig. REF ,
we plot the coefficient {{formula:31ad55f0-d02d-436d-a656-a36577b04398}} with variation of the energy scale {{formula:38af7336-7dd6-4932-a2c9-f2ab193253ac}}
at {{formula:4868e64a-09cb-44ab-ab90-08ee571a06de}} and {{formula:cc1520ec-330c-4444-af88-34c89dacb802}} for the {{formula:1a3adaf9-59a6-4bfe-80eb-8ed0aec9c097}} , respectively.
At the vicinities of the energy scale {{formula:ed32edd2-eae6-4ec1-b128-3eb3be7d77d8}} and {{formula:a7545884-3f92-45ba-81ee-ccebc102abf4}} ,
{{formula:003270f4-0587-4e10-98e3-49c3c4f95745}} ,
however,
from the figure, we can see that
the coefficient {{formula:2b86df2c-3891-4294-84e1-f5875347034c}} decreases monotonously with increase of the energy scale {{formula:ff10bfd3-ac35-4da5-8753-c4953120bdc8}} .
The reliable QCD sum rules do not depend heavily on the energy scale {{formula:d1054669-559c-4b8e-a1b0-7c2b444629fb}} .
So, the QCD sum rules can not be saturated by the scattering states
{{formula:daeeebfa-e2d1-4cf6-b637-0626d560bf5e}} and {{formula:b33f5f12-c8d1-484d-8123-402619f39917}} , respectively.
{{figure:3c422b97-32e8-473d-ac32-59da622155fc}} | r | a70a6d9d0f6de6decc6955dc02c886cf |
In conclusion, for the first time we have shown that the anomalous intracellular transport of endosomes is described the spatio-temporal heterogeneous ensemble of FBM motions. We find that endosomal displacements and increments both have strongly non-Gaussian power laws distributions. Analysing local endosomal dynamics, we find that it is described by a spectrum of exponentially distributed anomalous exponents and the power-law distributed generalized diffusion coefficients. Such heterogeneity of endosomal transport has implications for sorting and delivering molecules for different biochemical reactions in different locations inside living cells. Heterogeneous dynamics of endosomes in space and time has a huge impact on these diffusion-limited reactions: it broadens the distribution of the first-passage time to a reaction event and increases the likelihood of both short and long trajectories hitting targets {{cite:845c28f0dfcafc10bd4f9dcbb307baea2ab0a659}}, {{cite:2c498f224ab80febb9c7211359bf6b7c6b686c5c}}, {{cite:248cebca4282a85648838c8adadeb0661cd3eb09}}. Both effects haves a big impact on biochemical reaction rates, for example signalling of Rab proteins on endosomes. The dynamic properties of other intracellular organelles, such as mitochondria and lipid droplets, share many similarities with endosomal transport {{cite:ca9f366ba5132ab082dfb2f91b655b8e1c1d507b}}, {{cite:f93972522d408625651c5cbb47e05481c4d60cf6}}, {{cite:4509a835d7b3caba30d292c5ef1a4b842d974177}}, {{cite:0488c65827820a4b3c98cdcf63f8a11ff5714200}} and we anticipate their transport properties will also be heterogeneous.
| d | ecdc2408cf96708a951d84b182b4ea64 |
We present the results of SeTHPose (both SeTHPose{{formula:28a59e4e-1997-4842-a9ce-4b1996df5fe1}} and SeTHPose{{formula:ce1926ca-cd7c-48fd-a4f5-9895685d9cb0}} ) on MuViHand dataset and compare the performances against {{cite:ba5162179ffd263f162e0892b23916b6e59a0ece}}, {{cite:1d66ca745c35b3027a4a9f5383cb4d9659ffad99}}, {{cite:3a58fc73fd29f3a4df07665730c539e241058e00}} as well as two additional variations of {{cite:74b22899de3f74e44ba1fa956c21a2beb0b0abc9}}.
Interestingly, both variations of our method outperform all other existing methods on this dataset, including both multi-view and video-based methods.
A graph showing the PCK curves for thresholds 0 to 50 for our method and other methods is presented in Figure REF for both test protocols. Also, in Figure REF , we illustrate multiple examples of our network's performance on the MuViHand dataset.
| d | 3926cc90c105a829728c8f6deaef781f |
A deep neural network method is proposed and verified to approximate the solution of the Stokes' equations.
The method makes use of least square functionals based on the first-order VPV formulation (REF ) of the Stokes' equations as loss functions.
It has less regularity requirements on the solutions compared with other methods such as the methods based on the original form of the PDEs {{cite:4047e03a1cd9479ba99217ed402e19c6fc4eeb91}}, {{cite:6a65635e48ac39acec206c334802c32b86c3106d}}.
Convergence and error estimates have been established for this method.
We observed that smooth solutions of the Stokes' equations can be well approximated by the VPVnet method using Resnet neural networks
with a rather small number of neurons and hidden layers.
Within a certain limit, a better precision can be obtained by using more hidden layers, more neurons and more quadrature points.
Either smooth activation function, such as {{formula:86d12acd-9f9f-453b-a4a1-8e57fb0414e2}} , {{formula:a4c44aa2-7b43-4a62-b557-9fd89a230779}} , {{formula:8ef95a0d-a37a-4432-ad90-b6e236f50bef}} , etc can be employed and all of them can provide satisfying approximations.
The method is divergence-free and pressure-robust.
| d | 810be3cedc0a4d379bd23e8134f16442 |
The evaluation metric for the Toxic Spans Detection task was an adapted version of the F1-score {{cite:b325f493f1d9442bd20252210e748483a1995df9}} that takes into account the size of the overlap between prediction spans and golden labels.
| r | f160cf98f68c8542322929e59fd62389 |
Natural Language Understanding.
We evaluate the performance of PAD-Net for MoE on various datasets from the General Language Understanding Evaluation (GLUE) benchmark {{cite:1bdb9a4a750bb67e63058126cb2a7096913225d3}}, including linguistic acceptability (CoLA {{cite:a0d2bbeb5ec7184f128a913c94e4e857699f3e80}}), natural language inference (RTE {{cite:6c47cf15d56024c6f8be0d42e873bd306d06c402}}, QNLI {{cite:010de8d4623ddcf4696afa0ca98313f9920480bb}}, MNLI {{cite:4e69866f858d688f97a7462c554c77e729820bbb}}), paraphrase and similarity (MRPC {{cite:01e2f1392a544229e0d03e8709487444a2021ac8}}, STS-B {{cite:ee9ff99c904dbf16bc9ef255eaee82882bd32213}}, QQP {{cite:29b1988aab26bea51ab1b3552be36c00b3ea0fed}}), and sentiment classification (SST-2 {{cite:20dbed5d329da9f551dee725487a00309c91cdeb}}). Following the previous works {{cite:4e63fde948d480ed2cc0c1196ee1c755fa26d32c}}, {{cite:eeb744c435ecc1eb01fe2e7d2631bb967ceacd57}}, {{cite:abaddd8fc096ca4d9d1abbf1822f21db6f75f6ac}}, we fine-tune the pretrained model (BERT {{cite:b8f6127b082619dc4c1ce4c7cdc8c94ecb789a3d}}, ALBERT {{cite:37c3a91d596729890261af784214ba4c6cc06428}}, RoBERTa {{cite:12ca6e4980b63698cfcf892ad81800d6cd1567d0}}, ELECTRA {{cite:24064d9910bce8b43db6fc73ff481f8e9cbfe1c5}}) on the training set and directly report results on the validation set using the last checkpoint, since the test results are only accessible by the leaderboard with a limitation of the number of submissions.
| r | 793738efa22362abb38fbfd9782b8b22 |
The generalists: A fully-supervised framework for training SE models defines a large set {{formula:8a4ecfd8-183a-444a-a01d-e6162f123f8c}} of clean utterances from many anonymous speakers. They are mixed with various noise signals sampled from noise corpus {{formula:90e48f38-7e46-417e-9b2c-bcaee4e133d5}} at random signal-to-noise ratios (SNRs) to simulate arbitrary contaminated speech, i.e., {{formula:720b938d-575a-4fa8-82f9-28c595a3e81a}} where {{formula:7e940a70-f2e0-44e5-acff-628a3662b8c9}} and {{formula:1e0bf885-d447-4a9d-a4b7-af7ab8238a55}} . The SE model is a mapping function {{formula:969baa50-1876-4bf8-8610-cae0dd628813}} with trainable parameters {{formula:0ff3d087-b5b9-4b16-b255-593f0cc35bbd}} that aims to recover {{formula:834cde40-4c49-4ea1-b4bb-715aea0599ae}} from {{formula:85eb8547-8d68-4f14-ab33-09992681e13f}} , i.e., {{formula:5204b533-5fde-42d2-8360-1ac8b2d05e92}} .
Our experiments use negative signal-to-distortion ratio (SDR) {{cite:beb915b7f2362d2b72b26c08de83d017fa41d82b}} as the loss function for the SE system:
{{formula:15628deb-6009-4225-b9fe-d7b95594c3ed}}
| m | 8f8a2440e07d6a38603a1fb0ccf564d8 |
Several variants of the linear ICA model have been applied to fMRI data including square ICA (with equal number of sources and sensors) {{cite:03621595bad11d824d129ad3e580b28bee6bec4e}}, non-square ICA (with more sensors than sources) {{cite:591ee423463e3c66d81781809b832359dba47fe9}}, and non-square ICA with additive Gaussian noise (noisy ICA) {{cite:d70a1710bc97d22c442ac0bcbe6ca03a5e5dc67e}}. All of these models are well known in the ICA literature {{cite:64815f5e9775c2e8c4fb804ac502a3ad17c7c536}}, {{cite:ae97e8d7d99f55c5138b5a2b45a10c4b54d3a64e}}, {{cite:36331d4f2520b8bf725d5fd95d1f3a6d0f60fa07}}, {{cite:0545244102df9e6ad40e8c608a4f67cfdc454572}}. Since the other ICA models are specializations of the noisy ICA model, we will assume a noisy ICA model henceforth.
| i | ae4b28d7ba4d8d09531dfdcf43466f2c |
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