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Even with the great success of GNN models in solving various graph mining tasks such as node/graph classification {{cite:388dbaa0804f40063d36b64a45aeb46f7e07c63e}}, much less attention has been yet paid to the study on explaining GNN models. As an earlier attempt, the application of existing explanation methods such as SA {{cite:6560b0aa7d7bf634f8d9866f284d90d2b214d505}}, GBP {{cite:7ad9934b5d1163e7de0ab000ab9746b223a67179}}, and LRP {{cite:225ecc0b15d570fbb9b558926990f6bdf1522ba0}} to graph convolutional network (GCN) {{cite:f5d647c1923fa2ff8e72b2eb2058ff819876c13b}}, one of the first and most popular models for GNNs, was studied in {{cite:4d2bcae263780e7d0e855bd8877931103a744370}} for both node and graph classification tasks. However, such methods have inherent limitations due to the fact that models suitable for data with Euclidean or grid-like structures (e.g., images) cannot be straightforwardly applied to graph-structured data in a non-Euclidean space. For GNN models, explanations as a form of subgraphs rather than heatmaps would be appropriate. As a recent study, GNNExplainer {{cite:04a4fa19a59efb1336c44a75d4ddb37f2af28cf7}} was developed to discover a subgraph, including the target node, to be explained by maximizing the mutual information between prediction values of the original graph and the discovered subgraph. GNN-LRP {{cite:0b185bc04f1590d03a504376e8e1c66c6c907334}} extended the idea of LRP to GNN models to produce higher-order explanations via relevant walks contributing to the model decisions. CoGE {{cite:30ed9510280edb5ad3ef737a8e65a5bf6be6c1e9}} was proposed based on contrastive explanations by finding similarities to graphs with the same label and dissimilarities to graphs with different labels. In {{cite:20e5e8ab57105ce38f52a3e9b7c8abc8020b1f63}}, SubgraphX identified the most relevant subgraph explaining the model prediction via Monte Carlo tree search using Shapley values as a measure of subgraph importance. On the other hand, instead of directly searching for subgraphs, several studies {{cite:12917fbb1dfbf9eee4436e22ccc5cf44ae22e4e9}}, {{cite:2bba958fb1f1495c811fc8d149188af9902d9d45}}, {{cite:228ca5541a9e1d16efb203e3d800f52781d01fd6}} were shown to learn parameterized models for explanations of GNN's predictions. PGExplainer {{cite:12917fbb1dfbf9eee4436e22ccc5cf44ae22e4e9}} proposed a probabilistic graph generative model to provide explanations of multiple instances collectively. GraphMask {{cite:2bba958fb1f1495c811fc8d149188af9902d9d45}} also proposed a post-hoc method that interprets the predictions determining whether (superfluous) edges at every GNN layer can be removed. As a causal learning approach, Gem {{cite:228ca5541a9e1d16efb203e3d800f52781d01fd6}} presented an explanation model equipped with a loss function based on the notion of Granger causality {{cite:efa84d7ea25530e7498399c57c3b3af8ddb06164}}. Furthermore, PGM-Explainer {{cite:755419e3a1506ad83b6231251293541fa805610d}} presented a probabilistic graphical model so as to provide an explanation by investigating predictions of GNNs when the GNN's input is perturbed. In RC-Explainer {{cite:2afc17f322bcdd3340be783393abf3cae85d9c75}}, a reinforcement learning agent was presented to construct an explanatory subgraph by adding a salient edge to connect the previously selected subgraph at each step, where a reward is obtained according to the causal effect for each edge addition. Most recently, CF-GNNExplainer {{cite:8d3c9549d19b4a8cf388c5e845c6df5a6bb158bb}} presented a counterfactual explanation in the form of minimal perturbation to the input graph such that the model prediction changes.
| m | 753c53225a430e0d257a6dfa2e733a88 |
In words, we are assuming that the dot product of the {{formula:f6377141-5d58-42f8-b984-6cde5dcb0d38}} row of
the precision matrix with the marginal covariance between {{formula:4ed3a424-845b-4f40-a683-a1cec914ee18}} and {{formula:44e4d079-a0f7-4697-84e9-d600560639c2}}
is zero whenever the {{formula:9501fcd5-6d4b-4a6a-b637-9741823a9e61}} element of {{formula:9a75c080-ed63-4a5b-b4c5-6e15378c985d}} is zero.
To illustrate why this assumption fails for genomics problems, we
examine a motivating counterexample. Using mRNA measurements for acute
myeloid leukemia (AML, the same data examined below, {{cite:6129052890a3924ee354c9fdf29d39700f301d8e}}), we estimate both {{formula:bee3cdb8-2d79-4be3-82ca-7a824e95e507}} and {{formula:bdfd6b9d-7d63-46a9-a130-0c3a774f0dc5}} and proceed as if these estimates are the population quantities.
To estimate {{formula:e3db4a31-6304-4b5a-916e-b6560323bb0a}} , we use the empirical covariance and set all but the largest {{formula:51acbc39-e68f-4a8f-b60a-342c6abe126e}} values equal to zero, corresponding to a sparse solution.
For {{formula:0cdd05b2-8ea6-4225-b78a-fe29401cfe93}} , we use the Graphical
Lasso {{cite:ebb0ff0ba31d7a126673c03b5aa1b1d2af38f11a}} for all {{formula:8356a441-c831-42bc-96f6-8e264e9c01b8}} genes at different
sparsity levels ranging from 100% sparse
({{formula:bec245d7-06e5-4f03-b79a-5f257cef91c8}} for all {{formula:212ca4c8-f9e7-42e1-8087-14c053662f8c}} ) to 95%
sparse. We then create {{formula:dfe3586a-38e8-4f20-ad7d-342cbaa4c31c}} as
in eq:assumption. This is essentially the most favorable
condition for SPC.
For visualization purposes, fig:sparse-icov shows the
estimated precision matrix of the first 250 genes at 99% sparsity.
{{table:0bdd9d65-0010-49a7-a432-22ddeccbc1b3}} | m | 8be842490d4be311e5733aeb23fb3d11 |
In this work, we propose to explore the identity factor from the I frame with the pre-trained face recognizer, e.g., FaceNet {{cite:e4eac2c56f57a5eb1936b97c34d29fbfbe742582}}. Their embeddings are remarkably reliable, since they achieve high accuracy over millions of identities {{cite:e8fa9434ee1c51b0b18eb641b64f03f49f280b15}}, and robust to a broad range of nuisance factors such as expression, pose, illumination and occlusion variations. Using the identity feature as the anchor, we can explicitly enforce the marginally independence of our identity and expression feature {{cite:8379ffbbf682b3f79d63c3456a603faaf5ef4b25}}.
| i | 2a6eee23f71197c93c9abb38a9241897 |
The vFWM yield, which, more specifically from the particle physics point of view,
is the signal yield per pulse collision from stimulated resonant photon-photon scattering,
{{formula:85ac0076-fe22-4f05-8043-2f7ee4f637e6}} , is factorized as {{cite:865c74f2cdea0f3d81822102b5ddf4e18ccba9be}}, {{cite:d0672b62a943724a4cf3101538d1c7a97b6fb537}}
{{formula:a47c9d3e-f9b5-4d4f-8d3a-71a3ba11ba96}}
| m | b166da48993d39194b2baa81eede78c6 |
Recent works have shown promising results in dynamic view synthesis (DVS) from a monocular video {{cite:4d6f15fae351e79a9736de3d0e2157dd3a7bd64d}}, {{cite:53ffc0f15c2c2891cd9ffbdd424af617305317a0}}, {{cite:02e807cd62b86235a1a5341b72bc914453f29a78}}, {{cite:b20f366f718da128f7807eac2de6bc896b8c0a6b}}, {{cite:1ae4ddd15356780314d55395b5878144d30e73fe}}, {{cite:72363fb833ea0c7717ab2341370758750403bfaa}}, {{cite:abaa7949f9c1affce8ab26b8e2e99478ee8df761}}, {{cite:ce5814cd49d3eb8ceab3466e86a47d8ff1e3ba23}}.
However, upon close inspection, we found that there is a discrepancy between the problem statement and the experimental protocol employed. As illustrated in Figure REF , the input data to these algorithms either contain frames that “teleport” between multiple camera viewpoints at consecutive time steps, which is impractical to capture from a single camera, or depict quasi-static scenes, which do not represent real-life dynamics.
| i | c62cc3fe6fbf587331d7df372a3c915b |
We wish to make high fidelity 3D reconstruction and control of complex facial movements with a simplified camera setup and little or no manual annotation. A high-level summary of our method is shown on Fig. REF . First, we capture fine-scale transitions of facial movements during a semi-structured expression task. The recorded video is then processed with an automated facial action recognition system {{cite:c1ccec80ed8ee01ae66ca2b9ec4569663aa11c2e}} {{cite:cd68358f143568448890fefc7fd2b64c3836bd51}} that provides anatomically correct action unit (AU) {{cite:01006d13fd9b5a49b4b8aad3a472060ad1e556f6}} intensities and facial landmarks. From these, semantic facial masks are generated automatically and frames are sub-sampled to build an AU-balanced set of training data. The selected 2D frames, semantic masks, AU intensities, and camera parameters then used to build a face hyper-space, that can be used to synthesize novel views and unseen expression combinations.
| i | ec4f590c8d3f9d89fae07efad98d87e2 |
established by Mordukhovich {{cite:8794092887ca09f09a0907aa55249c3691c63f8a}} via his limiting coderivative (REF ) and then labeled as the Mordukhovich criterion in Rockafellar and Wets {{cite:6ea8b52da29ad5669fe14fb614d39cb1306cb328}}. Broad applications of this result are based on robustness and full calculus available for the limiting coderivative; see the aforementioned book by Rockafellar and Wets as well as the books by Mordukhovich {{cite:c21c940c145eee31a3029c2d6ea86e302e52fafb}}, {{cite:8d0fdc89de57b3713be25e532ef3f88406f87d85}} with their extensive commentaries and bibliographies.
| d | 12708032813396e9278566c500514eae |
As in previous works motivated by probabilistic inference {{cite:3c6f8fd352e4c5ab74fa9b59c5b5a52974bdc13e}}, {{cite:f38a0ee05f35bcb16e1c7b5ae6a4044a44840d94}}, we introduce to the standard graphical model of an MDP a binary event variable {{formula:3abf6647-5595-4d59-899a-2eaf2eab06a5}} , which represents whether the action in time step {{formula:c1d6de15-f21e-4824-88f7-560eecae16a7}} is optimal or not.
To derive the RL objective, we consider the marginal log-likelihood {{formula:eb05c626-053a-40ae-ab5e-dd45101af17b}} , where {{formula:5ceafcd7-dc1b-44ca-b729-5fcefed13a00}} is a policy.
Note that {{formula:eb91ffff-fca1-4dfe-bca0-78f03c549457}} means {{formula:eaae3d68-ba1c-4c64-9ead-8f841322e476}} for every time step.
As is well known, we can decompose this using a variational distribution {{formula:709261f2-0e71-4ed5-9ebc-57f1c6242cbf}} of a trajectory as follows:
{{formula:104309dc-49dc-402a-b428-1d39849b99a0}}
| m | ce7218a7bf8d20011a0dc0bc5e683935 |
In the proof we inspire in a Lindenstrauss compactness argument (see e.g. {{cite:3619e74edcad74ee96800d4b841b413a8af12a82}}). Let {{formula:764120fb-50a8-4ddb-8163-fcd98a8b0c58}} be a finite metric space, {{formula:8aa1b28d-580e-4530-a6e7-2ff0e23b7b85}} and {{formula:549d3ace-cd21-43e5-a33e-2ebd4a9af47d}} be a Lipschitz function. Let us find a norm-preserving extension. To this end, define
{{formula:b03ef6c6-6d06-402f-8892-dd291fcb56bb}}
{{formula:e822f915-7e5f-4b58-803c-4d0fb643552c}} is a directed set with the order {{formula:724f742b-0493-4c57-a654-e12b686a7b42}} if {{formula:e907417c-cce5-49df-9f90-6810f3287332}} and {{formula:bfc85731-0d1e-4685-82b8-be0ea8ba31da}} .
Pick {{formula:75f9e33d-484d-4338-8008-91c9defa9bcf}} . For every {{formula:d25ee466-58c5-45bd-b317-e7dd621e7cc6}} we find, by the Principle of Local Reflexivity {{cite:d598889b52973481682ca6e5400cf4eb7a20c070}}, a bounded operator {{formula:9052cc06-2c81-4bf9-b45a-8c1478170a41}} so that
{{formula:a43e0681-f765-411c-8c61-b598a76e077d}} and,
{{formula:e848d726-34c3-47b7-ae62-5967e8901e9f}} for every {{formula:3402e3fc-3ab8-48e6-9658-a117e4082264}} and every {{formula:a09b991d-8b7b-4fef-8d03-60934183198e}} .
Consider {{formula:165856fc-2eae-4e9c-aa83-73a6dba59d8d}} . By the linearity of {{formula:151b0577-f3b3-4a3f-9c87-3b9e8a266640}} it is inmediate that {{formula:4b61f3f2-de67-4156-8cbf-5e2186e23a92}} . Since {{formula:648dd429-8b2b-4304-9c00-cf64456c4724}} has the {{formula:123bb88e-a35d-4424-9bd6-11e948ef6b46}} -finite extension property there exists a Lipschitz mapping {{formula:eb17c74f-d1a1-4ba3-81c5-1611e6e525d6}} so that {{formula:2254c55b-f69d-4eda-ab05-6710b73d754a}} and {{formula:f3406f80-1452-442e-8dbd-74349515505c}} . Note that, by the construction, there exists {{formula:32d4348f-a96e-4c6c-ae70-77ef4d6bb20d}} large enough so that {{formula:b6f75788-31d3-4faa-9e48-c152f2892eaa}} and, consequently,
{{formula:1b0b41f8-9be4-4167-a300-966735ed268b}}
which is a compact space under the product topology. Consequently, pick a cluster point {{formula:bc28f440-99a9-4277-891c-8d8addc34490}} of the net {{formula:350d6459-364a-4d2d-9261-ce79663bb130}} . Let us prove that {{formula:34011b7e-9300-4a6e-b068-6411cb25aa29}} satisfies our purposes. First of all, {{formula:430c1e60-f575-47fb-8afc-786488f53bdb}} . Suppose, on the contrary, that {{formula:c120581e-5d26-4c6b-8ea3-5324805ab1a8}} . This means that there are {{formula:a859f6d8-d857-4a8b-93f3-93eafa80a5ce}} and {{formula:9142a4f1-19d2-4249-8296-d17419b2f2ea}} so that
{{formula:136abf52-caf3-4488-bffb-ab5cffe49ac9}}
and so find {{formula:7162d28c-2c4b-4548-a800-a9aee62e9ddc}} so that {{formula:a8a1c0dc-e93e-4980-bd76-d82a6c239e40}} . Since {{formula:7898247e-40c2-44a2-970a-d7f239f9cd23}} is a cluster point of {{formula:40f2195b-6645-4856-9e3b-1b45ab48ad82}} find {{formula:81f3ae45-2e57-4f28-b205-e53fa3b63aeb}} such that {{formula:922d0791-1502-43ab-b676-61c8de14b751}} and {{formula:96a6f7e1-960f-4ec0-95e7-97c72aaaeac3}} so that {{formula:58771e57-496c-40bd-b9f5-a6d2db9e77db}} . Since {{formula:9fe05e3b-1c04-4a22-96b8-eba72e44481d}} we get that
{{formula:ffcde24a-651b-4c86-ac27-0ba75936c155}}
which entails a contradiction. Consequently, {{formula:5a3bb578-c1c5-4dca-84d3-1b402d6c914f}} .
We will derive actually the equality of norms when we have proved that {{formula:af68ad38-ff1a-40d9-8535-90e60cd0fe9c}} coincides with {{formula:7164cd6b-d728-4f42-9881-32fb9719399a}} on {{formula:249f2dd8-7eb9-48f4-a0cc-32d6c12cd7c2}} . To this end we argue again by contradiction. Assume that there exists {{formula:557e24d9-2fe9-45b7-ac21-a67f9865c6e1}} so that {{formula:954b4d31-9cd1-4217-8fec-6ad1d3375f5f}} . Then we can find {{formula:3ea1ca48-8766-4d40-8c82-9c59251f3c0e}} and {{formula:82408831-d3b0-4b4c-88eb-5fce6f3381cf}} so that {{formula:d45f062b-b1a1-4c85-8259-d7d293bc7ac6}} . Since {{formula:ee10a44d-e5de-4fdf-aa88-ca513f0137ad}} is a cluster point of {{formula:a5919703-2431-4c06-b2fb-564a29ebad23}} find {{formula:ee784b25-1117-4377-8034-14becf8b75ea}} so that {{formula:ee5064d6-f7a6-4da4-98dd-8c197ccf6a17}} and {{formula:356dc403-8857-4327-a432-6cea690fa545}} . Since {{formula:004093f3-ab9c-45a1-8878-1e012090be73}} we get that {{formula:eb7fb791-b241-42cf-89b4-87b03ebc7910}} and, since {{formula:0520b90c-68c8-46ec-9806-449a64a25548}} and {{formula:d98303d1-ac35-4471-a5af-7b1c4aa6f5fc}} , we derive that
{{formula:eab09c45-84cb-4771-83b8-25a450ab9f09}}
so {{formula:c5ff84a9-c8e9-4c2c-a3bf-9cf7070f7f78}} , a contradiction. This contradiction proves that {{formula:09a2bb52-e155-42dc-a305-a7909e15f921}} equals {{formula:99fe319d-e0a5-4fe8-8ccd-65ee347f40e0}} on {{formula:e08c83f2-9fe8-4988-a4f2-efb09ff2ff74}} and the proof is finished.
| r | 5da5f33aeda60e76d1936ebe723b1d24 |
Change-point problems range from the simple situation of detecting an alteration in the regime of a random sequence to identifying a structural break in multiple linear regression with possibly correlated errors. Although in the second case the change-point can assume any value, in the first situation it must lie in a discrete set. Generally, the limiting distribution of the likelihood ratio statistic for detecting a change either converges to a Gaussian processes or can be adjusted to converge to a Gumbel type distribution {{cite:ae8d1df489acb0ce4e96650d689de82f3272d7d1}}. This technique was first applied by {{cite:4101b112b5ac2e70952b1d37009b066265625229}} to derive the limiting distribution of the maximum of independent random variables, and has further been extended to depedent data; see {{cite:e65f47d9d2afa8a2684d42ae2bce99aa3ee68ff6}} for a review. Approximate critical values of the test statistics can be obtained from Bonferroni’s inequality, by using asymptotic arguments or simulation. In some situations the likelihood ratio statistic for the unknown change-point is unbounded.
| d | 6f903187493e2c3b745f63b4688b226a |
In this work, we focus on the problem of CT image reconstruction from incomplete data {{cite:884d78834eaf14f631492af8e50287b5f28c0ede}}, i.e., sparse views and limited angle reconstruction problems. Traditional CT image reconstruction algorithms include filtered back-projection(FBP) {{cite:884d78834eaf14f631492af8e50287b5f28c0ede}}, algebraic reconstruction technique(ART) {{cite:0bef8d82a1930dd75ee8aec6c9c44be446413afd}} and model-based iterative reconstruction{{cite:70cd6125e7318939f6c954b1e65bf40066873332}}, {{cite:a460f3d430a27ceb3fa1b687be362738057999e0}}. However, these traditional methods cannot effectively utilize large image data sets, which limits their performance in various image reconstruction tasks.
| i | 3a8480034fcf8bb5189a0543bac02182 |
A promising direction for improving the sample efficiency of reinforcement learning agents in complex environments is to pre-train low-level skills that are then used to structure the exploration in downstream tasks {{cite:1672b2f8a5f5fbde10a7dfe6d2be2d5ef1f6938c}}, {{cite:962fe25d65632e95cf72855e98c22ed9f6958c2a}}, {{cite:9568c0ad1b42071d064e6696a88916f374d4917d}}, {{cite:4c540e575a3df5dece75a0476c4a9be3d90fd8de}}, {{cite:e175320cb78cc238f31d099fb415e7b11122b53f}}.
This has been studied in particular for the control of (simulated) robots, where there is a natural hierarchical decomposition of the downstream tasks into low-level control of the robot's actuators with a skill policy, and a high-level control signal that specifies a direction or target robot configuration with coarser temporal resolution.
The large body of work on unsupervised skill or option discovery in hierarchical reinforcement learning (HRL) for continuous control relies, explicitly or implicitly, on prior knowledge that low-level skills should control the center of mass of the robot {{cite:6852c9bd1c67d723befb9b9e11f6c7f4a65b6b5a}}, {{cite:2bf24da4692eb41e129c767594140dafedd643e9}}, {{cite:4c540e575a3df5dece75a0476c4a9be3d90fd8de}}, {{cite:6b12cce636094772c76257ecc0ef0c034bb4802e}}, {{cite:423d183411f4a684b9592c3055a2dbbfbe986d8e}}.
This nicely fits a wide range of benchmark tasks that are variants of navigation problems, but the benefit of such hierarchical setups outside this problem class is unclear.
| i | 82e9aac860a8d71eb583f196efd746ad |
The structures and kinematics observed for these UCHII regions cannot, with the one exception of W33M2a, be satisfactorily modelled by a single embedded star either moving or stationary.
Each UCHII region can be simulated by a range of lower mass OB stars, moving relative to each other; the stars, the winds and their interactions interweave to create the complex kinematic and spatial structures seen in the data.
The total stellar population suggested by the simulations is dominated by the lower-mass stars.
The total ionization of the suggested stellar population slightly exceeds the observed [NeII] result, suggesting that some of the proposed 'stars' are density clumps or low mass stars, rather than ionizing OB stars. The worse discrepancy is in the complex source W33M1 and we think it possible that some of the 'stars' in the outer regions of that source are in fact non-ionizing. It may be that the central stars and gas are interacting to produce gas arms rather than the usual cometary shape on which the simulations are based ({{cite:df4342c7a8347d7230e233e9063204bc4b2185f1}} or {{cite:454fd5d658c997e033da09b00917a29f145e3fe5}}).
| d | 65dcde5f1f55546c236f1f980735595f |
UCDCC {{cite:37166ee9dde777d31c0fcf3175cff049a9a62561}} is a Siamese LSTM model exploiting Glove word embedding features. It achieves the best performance on SemEval 2018 Task 3 Subtask A. The method has designed a lot of rules in preprocessing Twitter data.
THU-NGN {{cite:987ae9c071bbda8655a0c6a87f48b69ad62e1579}} ranks second on SemEval 2018 Task 3 Subtask A. The model consists of densely connected LSTMs based on word embeddings, sentiment features, and syntactic features.
Bi-LSTM {{cite:a98139d587eecfb5cd4746c1e50a387e81df586d}} is a variant of RNN, which could learning long-term dependencies and bidirectional information.
AT-LSTM {{cite:d1463a05e9349aa31aedbb95e1faada43cf718d1}} is an LSTM model followed by a neural attention mechanism. It uses weight scores to attend the important part of the input.
CNN-LSTM-DNN {{cite:f811162aba7d120e3969c03251de8daa50feef23}} is a combination of CNN, LSTM, and Deep Neural Network (DNN) via stacking. It stacks two layers of convolution and two LSTM layers. The output then passes through a DNN for prediction.
MIARN {{cite:a80e0edabc883fd39ef55b2339644dcc4d1d31f5}}
could learn two representations. One reflects the intra-sentence relationships of word pairs. The other represents sequential relationships of a text.
{{table:08c692b1-6433-4d82-bb18-6cd697ea260a}} | m | b15f337148cbef7b04df12a731d387d3 |
Results
In Fig. REF and table REF , we show our main result, i.e. that our model consistently outperforms the SOTA {{cite:2d676fbba05cc2998740f95e7f3a7da75925d922}} by 5 to {{formula:722ce307-49c6-48c6-b14f-ae76f8262e06}} depending on the task, in terms of test accuracy, despite having much fewer learnable parameters.
For comparison, we also report results from the expert approach {{cite:dace1466c55ab1cad9a82e41e5b437711167abc0}}, which nearly matches the GNN baseline.
| r | b916fdb5aa0df2efd6ec44c0c36ff8b5 |
where {{formula:9106ba38-9b6a-4438-918d-44b30526e07a}} is the photon energy. The total photon flux modulated by the non-interaction probability is given by {{cite:7defed718398a9ebccbf20063b6f94562279868d}}, {{cite:89c7397470894ae2a2db032f0469c0df9355f63b}},
{{formula:3272a318-c47a-41fd-b30f-159bb7695c04}}
| r | 41a99eb5dc5f4ceaf7f5979b33a41121 |
By the classical open mapping theorem in functional analysis, if two Banach spaces coincide as sets, we obtain the equivalence of norms immediately. In {{cite:1f046d0de1f2603952fbfa2981acb4664902d814}}, authors only studied the case that the base domain is the unit ball {{formula:9db32032-682f-4f77-897b-e6b81811ad38}} . Since unit ball is a bounded star-shaped domain for {{formula:f4cd28bf-9d34-4df9-b573-4a2b832cbb4f}} for every {{formula:3b735704-fd6d-4e9c-8c5e-ccac88545ea0}} , the result in {{cite:1f046d0de1f2603952fbfa2981acb4664902d814}} is only a special case of our result here. By the classical result due to Hajłasz {{cite:31682f9b8c2d4d1aa43dc0ce2f5aadcbec7c659e}}, {{formula:994b3183-6ce8-4603-9f57-10f3126fe9ff}} on a {{formula:32b0c4f5-1507-4059-bff2-9b90bf102e51}} -extension domain for {{formula:6c3ec130-f94c-4313-ab49-ecae6d8e8257}} , we have the following corollary to our theorem.
| i | 9aa53cee48b12b8171bc64e9223cd655 |
This result was refined in the pioneering works by Bramson {{cite:1d618d78fd912bf7814cff538669ae3bc49513a1}}, {{cite:e8883097e8952ba92659d6498459099f97769552}}, who
used probabilistic techniques and the
connection of (REF ) to branching Brownian motion to analyze the front position {{formula:e1369e10-3390-4a24-9a0a-f0fd2c232a12}} .
In particular, Bramson showed
that there exists a constant {{formula:506643f9-c312-41bd-9650-727721a525d8}} that depends
on the initial condition {{formula:96998d03-90e4-4583-b29a-369435b28627}} for (REF ), so that
{{formula:57c398d0-1c00-489d-a948-2df64873125a}}
| r | 349e6793d7b2e768a061dca5418a7a72 |
Most of the literatures are confined in using a particular type of image sets for the analysis of corresponding denoising algorithm/s {{cite:82e93263b2f6a68a78952db6868b0f9fa241bd6a}}. Moreover, the image quality assessment (IQA) measures such as: Peak Signal to Noise Ratio (PSNR) and Structural Similarity Index Measure (SSIM) {{cite:fd8d377e47e74f85c8979205815d622c81c05a74}} may not completely evaluate the performance of several image denoising techniques {{cite:def8d6a91e105c205ac4850b715a7816fc70d337}}, {{cite:be25f5fcb68649fd4ce8d79b78a9c089799a2369}}. Therefore, for completeness, in addition to the PSNR and SSIM indices, authors have considered the edge keeping index (EKI) to measure the edge strength (in terms of its magnitude) retained by the denoised image {{formula:9e2002cd-b73b-4282-8ab9-1ffbd0e34b31}} compared to its true edges in {{formula:1ad1ab9c-a013-4620-b6d8-f98ad5e38075}} as {{cite:86eaaf05e7f28146d78e6115b68b530f21d91182}}:
{{formula:bab05984-44f3-45fd-bdb6-2723ef6834cc}}
| r | 9e2d4b30e4c01ce49b6a1b1be0db3ca2 |
Previous studies have concluded that Bot-like accounts stir conversations in differently politically aligned belief groups rather than concentrating on conversations in one belief group {{cite:4dc22eceb40a612d636703dea5ead8a54f04d0a2}}, {{cite:e40871bf2c8cce352f200da800c919a6c98b95f2}}. In this study, we further provide evidence that Bot-like accounts were similarly active in sharing conspiracy related messages irrespective of whether they showed activity akin to a Disbeliever or a Believer. These bot-like accounts aim at widening the divide between belief groups and pose a danger of creating confusion on scientific facts {{cite:e40871bf2c8cce352f200da800c919a6c98b95f2}}, {{cite:34b24e87d5af30f1cd96b3c2cb81137fb360096e}}, {{cite:aa5f852320110c46973321a4053736affa0187b8}}. As more and more people consume information via social media, it becomes imperative for these platforms to identify and remove bot-like accounts.
| d | 8f010cc17df2f23714cf4d94a9db5c53 |
The Leiden algorithm is an improvement of the Louvain algorithm {{cite:af290727786befb2d58c1f1dc15ebdc58b2b9d73}}. The Leiden algorithm consists of three phases:
| m | 343459da45a9a773b85c59714122a223 |
We use birth/lifetime coordinates rather than birth/death coordinates. Lifetime coordinates provide a more interpretable feature, and simplify the description of partial Wasserstein metrics, as the distance to the boundary is simply the lifetime coordinate. Birth/lifetime coordinates have previously been used in the description of persistence images {{cite:98e9b7184e298658efaf85dd8d5feebba1152b31}}.
We use bounded persistence diagrams, supported in the space
{{formula:054a988e-3a27-466b-a90c-0b1f81d4ef18}}
In practical applications, this is a mild assumption since we often work with finite metric spaces built from data. The boundedness assumption allows us to provide stability results.
| m | 2d98c5794eceb87afb0e34e1a1368600 |
In order to emphasize the input variable discarding step, we use a similar approach to the momentum method {{cite:bd36f0d4569b36669d30e57f3e7cfd4a8ebbf48d}}, which is a technique for accelerating gradient descent algorithms by accumulating a velocity vector in the gradient direction of the loss function across iterations. Our iterative process is summarized in Algorithm REF .
| m | 9190eac1f2668ccf54794cfeeaf7a99d |
Timescales in the neural activities are hierarchically distributed across several cortical areas {{cite:5392f9b3462a2cb0cd790d7e8e2e39be16250d7e}}, {{cite:690cb82a3933bfd3e006f6ede735de4c007c2fa6}}, {{cite:ac34575d92af0a7524e889887ee6743967edb1f8}}, {{cite:57eb42b7f7e29cb76b97313035699921fbdc5d3b}}.
For instance, consider the hippocampus (HPC) and the prefrontal cortex (PFC), which are coupled by mono-synaptic and di-synaptic connections {{cite:32c3fba2b20455129d1a9d9aa1d18574993870cc}}.
HPC neurons respond to the location of animals {{cite:2bb5357df9db961028c10db07408b3ac8251fd33}} with faster timescales than those in PFC, which has the slowest timescale among cortical areas {{cite:ac34575d92af0a7524e889887ee6743967edb1f8}}.
Experimental studies {{cite:69f35b51182fb1b35c04e9ad39adb8f1549b0d98}}, {{cite:32c3fba2b20455129d1a9d9aa1d18574993870cc}} revealed that PFC neurons are necessary to differentiate HPC dynamics depending on the context and previous experience.
Similarly, neurons in the orbitofrontal cortex (OFC), whose timescales are considered to be slower than those in HPC, are necessary for concatenating the sequences in the stimulus-reward response {{cite:0860a5ff9b8493454caa8468bcdf44f75894a300}}, {{cite:d62968fa60862ea4117c933c0bcb05f874cf583b}}.
Accordingly, it is suggested that the area with the slow dynamics is necessary to generate and concatenate the sequences.
| d | 2842f6620a65ab04d6a4361ba0f15bf9 |
Furthermore, in our graph neural network approach, the embedding vectors for the vertices are fixed through time. This limits the capability of the vertex embedding module to capture the evolution of the vertex over time. Alternatively, we can try incorporating a time dependent embedding module into our graph neural network {{cite:6e464e613a848091f291176cc9d7773a40af555e}}.
{{table:ac86ec9e-fde2-4548-98a9-222f35980851}} | d | d7b8d193835470f856bb0141d6478104 |
Unfortunately, the application of this powerful concept for the estimation of {{formula:4ac60f94-8114-49f6-95f9-877bb4b3a7f7}}
is limited by the fact that AC is a non-computable quantity.
Even if the minimal theoretical program that generates the sequence is not
achievable, there are compression algorithms which can over-approximate it.
Among them, asymptotically optimal algorithms are the ones for which
the ratio of the length of the compressed and uncompressed files
tends to {{formula:71c963e0-6442-4cc0-a627-d73302dccef8}} when the length of the sequence tends to infinity.
For sequences emitted by finite-alphabet stationary ergodic sources,
a famous optimal algorithm for 1D sequences is the Lempel-Ziv algorithm (LZ77) {{cite:3068fe26c7af52bbce822024a815f07f54748d23}}.
The convergence to {{formula:af69615c-f294-42da-ac9b-2aa78afd4110}} is slow, with corrections behaving
like {{formula:6395dd0a-ae78-420b-9de3-c04df445b2d0}} {{cite:cccf43375914da4156847fe9e2b238fdf36380e4}}.
| m | e494b004ff6be4192cec13f9b7e4ba08 |
We propose to employ CNNs as feature extractors similar to {{cite:8ce70951182aa5e32b1a55e7b332d9d2482b46ab}} to facilitate comparisons with traditional texture features. We also propose to use a well-known machine learning classifier, to evaluate performance of different feature sets, thereby eliminating the effects of having soft-max layer for CNNs and a different classifier on traditional features as our likelihood functions.
| m | 83c652e1f9dc7dd5489a3bcadf6da725 |
We first show that semantic fusion confers additional robustness against existing LiDAR attacks; traditional, naive FP and FN attacks are intrinsically limited against certain fusion architectures. In fact, we leverage that naive LiDAR attacks on camera-LiDAR fusion generate inconsistencies between the camera and LiDAR sensor data to outline a lightweight cascaded camera-LiDAR defense framework that processes sensor data sequentially and eliminates nearly all (> 99%) FP attacks from the state-of-the-art attack introduced in {{cite:ac29be5d1b2c84f03df2968f3083916285920943}}.
| i | c7eed779ce76dcdcef4e2a9b150113c6 |
The renormalization scale is taken as {{formula:8353adf4-10fe-48e1-9abc-4159150a3aca}} , and the bottom
quark mass is taken as {{cite:c6d99dd3b4a1d9a9f26b882b1efef5503fe8e383}}: {{formula:b354e1a8-cbe3-4bd8-a8c5-b9cc3326a3de}} .
{{formula:7a597232-ca4b-46bb-ba50-9897bf2af943}} is taken from {{cite:8826f045c20498653a744008cd742e72b8505d9c}}.
| r | 19c811e919914b5fa3ebed2ee603cd4e |
Analytical calculations in Section and Appendix were made using the Wolfram Mathematica system for technical computing and the package {{cite:fc864db768296f7800610868dd6304beb7a5c0fd}}, on the parallel computing server Theor4 of JINR BLTP.
| i | bf112077ebc6d52298b0c2791016245e |
Starting from the state {{formula:11872668-50ce-496c-a835-61253f0be0fd}} , prepare a superposition over the first register
{{formula:5dbc83d0-c5a8-48e9-9489-3f77fdfa2952}}
If we allow for error {{formula:0a127d15-e8b4-4b71-8fef-7ec45c031c7d}} , the complexity of this step, in terms of T-gates using the QROM is {{formula:df54d353-c323-4c0a-802f-65b3c9381ae0}} {{cite:b8670a873d1a4ddfe034b70b6c459837b58e476a}}. The {{formula:9d4960c3-de6c-42ac-88c4-0768e8b3c188}} dependence is due to the Uniform operator preparation, that requires to use two controlled Z rotations, at cost {{formula:651ef115-6ece-476c-ade6-c5c04d435604}} each. On the other hand, the Uniform preparation requires {{formula:93ac548a-376e-459a-8d8b-5386f51a74f7}} T gates as can be seen from figure 12 in {{cite:b8670a873d1a4ddfe034b70b6c459837b58e476a}}, which has to be added to {{formula:2512f7e5-4bcb-4513-8395-1a77809ddeb4}} T-gates due to the controlled-swap operations in Subprepare. The value of {{formula:a3cb4001-5388-4afa-bb01-a0db723bfffe}} can be taken from equation 36 in {{cite:b8670a873d1a4ddfe034b70b6c459837b58e476a}}.
Perform a Hadamard in the second register and another on the third, controlled on the first register being {{formula:7054dc00-a222-49e0-8e2a-cc6a52fb8d4b}} .
{{formula:0c6f654d-85f1-4cd3-a7bd-7a496630a0f3}}
The cost of this step is negligible compared with the following one, and can be performed using a multicontrolled Hadamard.
Prepare a superposition over register six with amplitudes {{formula:1b8c8ad4-a849-4340-864a-8983643beeae}} if {{formula:d523048c-8759-4d3b-9b14-b6cf2e5239a2}} or {{formula:ab8432fe-f770-4a6f-abb0-2ec48bbcce0f}} if {{formula:eee3b7b8-c332-4152-8a41-d1c1988edeee}} .
{{formula:296b3a67-bd6a-4be6-8ba4-fe671b23a6c1}}
This step and the following have the largest complexities, since we need to use the unary iterator and Subprepare circuit of {{cite:b8670a873d1a4ddfe034b70b6c459837b58e476a}}. We have to iterate over {{formula:a742040c-939f-4ebc-b054-80bb42f23374}} , {{formula:d1616dcd-f43a-4127-8867-7fdd0a66e682}} and {{formula:edea6a33-6db1-40dc-8628-a14b4ab73e17}} , and that gives a Toffoli complexity of {{formula:244fa750-c769-4509-8d0d-28b97494eada}} plus the cost of the comparison and the controlled swaps from Subprepare.
For {{formula:788f1ba6-aad0-484a-a398-659853061e46}} , prepare weights {{formula:a161b081-2085-41ad-a051-0a542f0428fb}} in register 7.
{{formula:6d81f1b9-71dc-461c-9de9-ba712564ea59}}
In this step the Toffoli complexity is also {{formula:e677b0a5-080e-44d0-ad36-1c3de09d02ab}} plus the cost of the compare and controlled swaps.
Finally, use the QROM to output {{formula:d5811677-d3b6-4545-86c6-9295d46fc60a}} and {{formula:75571f0d-e61a-47ca-a614-67971658c241}} in registers four and five.
{{formula:35cc88a8-1fe0-4a32-a94e-3950b00e1caf}}
| m | 7f54234d8b233675f4a5eda0501581e8 |
Also, the effects from passivating hydrogens, known to be commonly present at the edges of experimental
nanoribbon samples {{cite:6e2f5d99385cb93a104461afd6bfd6f2f7c326e3}}, {{cite:5f8934af51c780fc55274702cf8093c30d5060fc}}, {{cite:fd3acb5232e22fd0c436ea5a71b96efcd0c48c36}}, {{cite:d016694804bf076f71158282379c154cafa7f0fe}}, may influence the dynamics of host
nanoribbon carriers. This factor can be naturally included into the above developed Hamiltonians and
resulting GFs, to be possibly an object of future study. At least, an experimental check for the suggested
effects, for instance, on carriers mobility and its collapse under definite external factors should be
of considerable interest.
| d | afafa60d0c62c67be2c74088ebd510a0 |
DeepLIFT (Deep Learning Important FeaTures) is a technique based on decomposing the prediction of a neural network for specific input. The entire backpropagation process is observed along with observation of weight and bias on each neuron on every layer of the entire architecture. Based on a variety of weights on neurons specific scores are assigned to each feature of input {{cite:a31af210fcb00f1e05fbef013253ea7b3d830724}}.
| m | ca8f1d3a09c366c69e6df5bd6e524d49 |
Another motivation for using BEV features to perform perception tasks is that BEV is a desirable bridge to connect temporal and spatial space.
For the human visual perception system, temporal information plays a crucial role in inferring the motion state of objects and identifying occluded objects, and many works in vision fields have demonstrated the effectiveness of using video data {{cite:c8ab22c1b4a562ae82552602d5f971f8f8e1e3eb}}, {{cite:c348cf64e18be3fa33149b81d51e7baa53e40856}}, {{cite:464d3bc731e9679e967611e58b3f9b824f8d81c0}}, {{cite:a3e3ec2f043c2a99da954b73271d3bf3d5bbd068}}, {{cite:aedab905c2a45662105f4ee58acf03cfacdbb3aa}}.
However, the existing state-of-the-art multi-camera 3D detection methods rarely exploit temporal information.
The significant challenges are that autonomous driving is time-critical and objects in the scene change rapidly, and thus simply stacking BEV features of cross timestamps brings extra computational cost and interference information, which might not be ideal.
Inspired by recurrent neural networks (RNNs) {{cite:26430951f25ce2afedde5e852b9bca6e2033df11}}, {{cite:fb4628375f95d72fde6791b23c240841ed443f17}}, we utilize the BEV features to deliver temporal information from past to present recurrently, which has the same spirit as the hidden states of RNN models.
| i | 6112d98d081506713983592cd5c0f59f |
Classical penalisation methods {{cite:47f2bc7b7f4c7106389817c0b9f17185f43bfb3c}}, including lasso, ridge, and elastic net penalties, can offer sparse solutions to the linear regression problem. They are deterministic approaches that employ constrained optimisation schemes to achieve sparse solutions, in that they add a convex penalty function to the usual least-squares objective and shrink the small weights to zero while leaving out a few large weights. Another popular deterministic method seeking sparse solutions to the linear regression problem is the sequential threshold least-squares algorithm, which iteratively solves the least-squares problem while zeroing out the small weights in successive iterations. This algorithm has been used in many works on equation discovery of nonlinear dynamical systems, including {{cite:6d366ccb1ea876eef175eeb3d3e30fa3bd9f653b}}. However, a common drawback of the deterministic approaches is that the results are sensitive to the choice of a regularisation parameter, and its tuning is required externally by cross-validation.
| i | 7e70530611d5957492a75c4263c6ee22 |
To realize the real-world environmental impact of Data-genie, we discuss a typical weekly RecSys development cycle
and its carbon footprint.
Taking the Criteo Ad dataset as inspiration, we assume a common industry-scale dataset to have {{formula:db366742-c265-4ea3-a84a-43f5fb9f93a5}} B interactions.
We assume a hypothetical use case that benchmarks for e.g. 25 different algorithms, each with 40 different hyper-parameter variations. To estimate the energy consumption of GPUs, we scale the {{formula:c4750105-9b0d-4b78-981c-0879c958a416}} minute MLPerf {{cite:31973bb88838fe9362b0e9e4b84d840a1658bc1f}} run of training NeuMF {{cite:b59b046a370298800f6effd6d20a440859ffc4d4}} on the Movielens-20M dataset over an Nvidia DGX-2 machine. The total estimated run-time for all experiments would be {{formula:5fe09442-134b-4eec-ade3-fa2871d75e0c}} hours; and following {{cite:ba984b4571d2bf664d5c5f3fd771ec632d2c67cc}}, the net CO{{formula:f48c0cae-50c9-4dae-a68e-7f421452e818}} emissions would roughly be {{formula:33b2bc63-16c2-4a79-9061-07a751c0948c}} lbs. To better understand the significance of this number, a brief CO{{formula:ad3f6476-d398-4d63-b737-f39f4e208f18}} emissions comparison is presented in co2e. Clearly, Data-genie along with saving a large amount of experimentation time and cloud compute cost, can also significantly reduce the carbon footprint of this weekly process by more than an average human's yearly CO{{formula:2d463822-6df2-4908-b42b-9d98d46b8b9f}} emissions.
{{table:0a6b64b0-4313-4571-b881-e3a99149a87e}} | d | 00feb94685299fdaad5d963d35ab7a64 |
That being said, the various applications mentioned above may yet be guaranteed to
run efficiently by exploiting various restrictions. Our results to date suggest that it
is most important to restrict the environment. This can be done either directly by
restricting the available features and actions in the environment ({{formula:0089d28b-6ceb-428b-91e4-d8593a34ed85}} ;
Result J) or indirectly by restricting the structure of the given demonstrations
({{formula:1a2a1c88-16e1-48c4-a83b-f83d913763c5}} ; Result K). The latter is particularly exciting, as it
shows that LfD can be done efficiently relative to few given demonstrations as long as
these demonstrations are also small in the sense of having few environment-state /
action pairs which invoke few features and actions. Given that it is desirable that
LfD be done efficiently with few demonstrations, i.e., when {{formula:b287d4a0-dadb-4e55-b23c-81eea26df06d}} is restricted
{{cite:af23dce8cea37c00bae9695667ef8c6ae5a46ca8}}, it would be very useful if fp-tractability held relative
to a small subset of {{formula:7ae19979-0603-4f47-8d2d-c4c25aa7aa17}} that includes {{formula:a7305eb4-3ba8-4c83-92d8-4f9c49a2a22a}} (in the best case,
{{formula:8d7d9925-a73b-451f-b399-a73a357ae7c3}} by itself). Parts (c) and (d) of Results E, F, and G rule out the
possibility of fast LfD relative to many such subsets, including {{formula:d7b8274c-9a96-4357-a269-68a967ecbcd2}} . Just
how many (if any) of the parameters in {{formula:a869ad4e-2684-45a7-bec3-beb2b0f236f2}} can be removed
while retaining fp-tractability is thus a very important open question.
| d | a7c85b020ef0c69ca6fc3209ed1f11c8 |
Corollary 3 (Dirac, Corollary on p.73 in {{cite:d289fd5863e8fced0e8d2aef87569ce3bd56b1aa}})
If {{formula:c13e987a-a5cb-49a7-939e-5cd1f85e753b}} is adjacent to a vertex {{formula:d0e7c9c9-6c4d-4df4-b6f9-f842278cea62}} of {{formula:662006a5-76f5-4cf3-b9ae-b772ff934196}} , then the graph contains two
paths connecting {{formula:46c02a6b-e22a-460e-a182-f11c2a65b8f4}} and {{formula:60da8129-3cd1-44ee-95c8-ffc802278464}} such that they have the properties (i) and (ii), and
one of them goes through {{formula:de9bb2c3-0cc5-4da5-9555-a2522dbfee76}} .
| i | 8b9cad43f67571b3b1870a75cf9d9616 |
On the other hand, the study of quantum many-body systems has lived an explosion of results. This is specifically true in the field of Tensor Networks. Recently, "Matrix Product States", and more generally
"Tensor Network States" have played a crucial role in the description of the whole quantum systems {{cite:313fee8ba6cc58829f162f59c07731f55a6352e8}}, {{cite:d534edda4584d13665a0d9c80898322442825241}}.
We point out that an interesting mathematical approach to quantum states on tensor networks has closely
tied up with QMC on tensor product of matrix algebras {{cite:d718b6b66c952e13472a348740e89fefe8e0d9f2}}, {{cite:f7f832d0b7efabbf33964a68ba78367e2711ffe6}}. Therefore, QMC have found massive
applications in several research domains of quantum statistical physics and information {{cite:e3cd05dddfee264315d0246a06daa5abc9bbc51c}}, {{cite:759c0798df6dad45e8ab12893e9ceec8fdd71dd5}},{{cite:531de6230294d4446c0722f7f9d76ae42b3d1479}},{{cite:c611cec47377de72468694493467d61b1f904e1d}}.
| i | 6010d7ef71d6c77a74069530d63c2bbd |
We use three different methodologies for training the cross-lingual word embedding models on all the language pairs with Hindi as a pivot language (Hi-Mr, Hi-Bn and so on). The first methodology uses the supervised method named MUSE {{cite:b4cd87eaf801a35c1082cee1930dd85daafeb77f}}Link: MUSE - GitHub which utilizes a manually curated bilingual lexiconLink: Bilingual Lexicon for alignments. We use Hindi as a pivot language due to the ease of computation and availability of resources (Corpora and WordNet size). We use the monolingual models described above and train 13 cross-lingual word embedding models (thirteen language pairs over 100 dimensions) using this approach.
| m | 82c8e9d793cf36e06180468aa8fac31e |
The mechanical characteristics of light in optomechanical system {{cite:be6df29446df9581553171dc498f255f773b4fba}}, {{cite:5b5f88d979b25f19b712cb42029394d4646dbdda}}, {{cite:3f146255f49abaac1d7159cf0d3f84d26d39aca4}}, {{cite:346957629df3cf0bca2c87749f4ea7a6fa8b645b}}, {{cite:c7f2b606d381743c057b844c957c0c3a6ba57d98}}, {{cite:4a72787454b9c88cc48b8dc16009e1e9a0104cce}}, {{cite:63afe45ae5802d447e44c56bceda6fdde0699ad9}}, {{cite:5cc8717b333ec3532f0f8c75e49935c9276b266d}}, {{cite:a6fad112a36936f38c7fd456129a0b6d98b6d568}} yield to phonon induced transparencies {{cite:7e3caeebec83939e63d02355e19e6eba274f2324}}, {{cite:34ff7c434f69bd4604617e5dcce9328a756a86e2}}, which can be referred as optomechanically induced transparency (OMIT) {{cite:01fe870ce7794e5c7060e95e12747403d041c1a8}}, {{cite:c9971fdc25597a9686d3dcf0c6ad15e8baa814c2}}. The coupling produced by the mechanical effects of light between multiple oscillators, notably mirrors and ultra-cold atomic states, further lead to the concept of multiple EITs {{cite:d39d7bb0e536a91fd29a9ed171a97c104eda8b35}}, {{cite:2ff478aa5cfea0908a37b005ab7cbc0197f4506f}}, {{cite:688c7f7a356e1179d51a0eaa0f5b5fbba2407377}}, {{cite:929fe0e5bb10128ac6e9577ec8f9933a888cfdf0}}, {{cite:180a322c8f377314c28eee94e60a9417ef7db7b9}}. These transparencies occur because of quantum interferences in multiple transitional pathways at intermediate states of the system. However, the recent discussions on Fano resonances – a phenomenon of quantum nonlinear interaction that consequently occurs because of the off-resonant interference {{cite:c6eff1cc631872f3de6b23f47c7e759c30b4d3c9}}, {{cite:2d2ce4ce58df7087f97288398a885be16d4a9ccc}} – in a four mirror optomechanical cavity, with two vibrating mirrors, have raised another aspect of engineering hybrid systems {{cite:c6030fc0b47ed1a8aba851b8d3b686bfd82860e0}}, {{cite:a0faedc734ccbf87c35cf580132bef49f15c1e0a}}. Although, the phenomenon of quantum nonlinear optics has been discussed in complex systems {{cite:efcef6ab4ab65c7c50e6dbaa21e277bb5707b917}}, {{cite:11f0ff63cd33a772e0e591d4cf2b47f46fa3cde1}}, {{cite:84ca6ea89e87fa29d56b23dcdc4b103fc716341d}}, {{cite:6423e704738da35851e57d4bafd92b654b22b327}}, but the demonstration to configure ultra-cold atomic states in such multidimensional hybrid system is essential, especially with respect to quantum nonlinear optics.
| i | 8311090d4bb4eae32b6cccfff7cb89be |
is free from IR divergences for the scattering problem with a potential {{formula:3ce69e37-ef45-4b4f-9bf6-d2da1e50f76b}} , see the last section of Ref. {{cite:939b58c3c8d6a317b05f7e5c0ffd3deed38f8f46}}.
Regarding the value of {{formula:785ad5f0-ef51-4d95-a59d-f96ee6988939}} , it is important to stress that Eq. (REF ) is actually a resummation of the soft exchanges of photons under the assumption that their momenta are clearly smaller than the momentum {{formula:734e24a7-8da7-44de-9fbd-3fa11087f86c}} of the external particles.
However, as a resummation one could use it for convenience with finite values of {{formula:656691d6-28f0-4228-9487-78fd5c86a8e5}} as well, with the pertinent extra contributions accounted for by the dependence of {{formula:fd82c8ac-ecdb-4fc7-8553-81c16b65e7ec}} on this parameter.
From this perspective, one could then naturally consider {{formula:37c87675-8983-4aba-ab2c-8e17aa3558a3}} as a number larger than 1 but with a finite value. Indeed, it only enters logarithmically in the problem and we will take in the following that {{formula:81cabbce-9b0c-4f60-8b0d-7c951b06e68e}} . Later, we give the value of {{formula:3cbe895e-ebea-4dda-8daa-ce9cfa287ef9}} by comparing with the known exact Coulomb {{formula:9175695d-35da-4fa8-8bd6-34250143e384}} matrix in partial-wave amplitudes, as similarly done in Ref. {{cite:7da376590f0542769955d6566c8f46e58c57d454}}. We advance that in that case one has {{formula:3faf2f06-2756-41a8-8a69-d4b70ac93a85}} .
| m | 06a86a16b44e1404e7f2931771f7a50e |
where {{formula:57a34437-e5d5-4809-9d2f-0a6f96ac782f}} and {{formula:ac8111c6-4b72-402a-8620-fc692f8dc02b}} are numerical constants of order 1 (see
{{cite:575fc4ae1e545742eb55396ebf5807143ff462b1}}) and {{formula:42106adb-014e-47d1-9a4e-d329b0612b43}} is the number of times the estimation is
repeated (here we will consider {{formula:a30b6a6d-095e-49fe-a744-a65a650de5b9}} ). The first term in the max
expresses a quantum speed limit {{cite:a4da06a2a387ac91622db06c39152456e2ea10b1}} and the second arises
from the time-energy uncertainty {{cite:578a2c9da9ec52c66d329af4d47924f76b52d249}} (our choice {{formula:a3f63431-6e69-403a-9403-9db1cc207b14}}
follows from these results {{cite:575fc4ae1e545742eb55396ebf5807143ff462b1}}). Eq. (REF )
implies that any energy beyond the standard deviation will be wasted
for the estimation: if {{formula:1b2169c3-07f4-467c-87ae-3322033b503c}} (with
{{formula:edcacdb0-519c-4404-86e8-e8b87cce55b1}} ), then the error {{formula:1e264b5d-43f4-4db4-a999-b8afdd93cab8}} is
dominated by {{formula:439782bc-502f-4c69-af08-37d8a295828b}} : “too much energy” strategies. To avoid
wastes, we should choose {{formula:c3468062-002f-41ed-b9e2-05220d6a5c1b}} (“good
strategies”), where the “{{formula:53a83a41-c459-4ec5-8383-78b04ebd681d}} ” sign emphasizes that only the
order of magnitude of the two terms is important since
Eq. (REF ) is not a tight bound {{cite:575fc4ae1e545742eb55396ebf5807143ff462b1}}.
Eq. (REF ) also implies that estimation strategies that have
{{formula:260b4913-a3cf-41b1-b284-ece5de50d10d}} (“too little energy” strategy) have error
{{formula:16acceb9-6fed-4eea-a4d3-9ce51bd3ce24}} dominated by the energy: they cannot achieve the error
of Eq. (REF ), but are limited to
{{formula:59832ed3-94b1-42cd-993a-e6fd76a70e61}} .
| r | feb32d8d889c902362fcf15c6c955037 |
Finally, our work highlights how computational solutions that appear in humans can be fruitful for approaching related problems in machine learning and AI. In recent years, models that capture human reasoning have received substantial attention {{cite:d7db93d999d124bb43ac1cfa81b92c72a1040bc8}}, {{cite:380347392b2e4f9cc14435363de9265e319bb97f}}, {{cite:18611ffdbd1ca03b9fd03e41e70ee960ab08be19}}, {{cite:882d25a7b837a9d374047032196e8dfae9dd55ce}}. By understanding how humans leverage representations of their cognitive processes to create more nuanced and accurate representations of the world, we may also be better able to design human-like artificial cognition.
| d | 06be242494120300732bb0a6c944f891 |
In this section, the DRL-based algorithm is simulated and analyzed. To evaluate the proposed method, the minimum rate among all users is used as a comparison benchmark. Furthermore, the proposed schemes are compared to the exhaustive search method and the random pilot assignment, which respectively give the upper and the lower bounds of performance for the pilot assignment problem. The performance of the DRL-based scheme is also compared to that of the soft pilot reuse method in {{cite:cd5fee10439fe9675973c2a4ce9807134f52bb91}}, which necessitates using more orthogonal pilot sequences than the number of users in each cell, resulting in high system overhead. It is assumed that the system is composed of {{formula:dbe2495a-aa64-44ad-8b32-c52024c8ff64}} cells each containing a BS with {{formula:2c359d6b-4941-4735-8fab-f0badcfb84dc}} antennas serving {{formula:f51e155d-63c7-4656-8eee-88e122e8df23}} single-antenna users. Also, the path loss coefficient is set to {{formula:700942b9-3b20-4cd9-a933-c673b4106b4c}} . The QNN structure utilized for the deep reinforcement learning is a deep residual network (ResNet) {{cite:5592ee2253eb9507861b612d575bbf269ceb17bb}} with six hidden layers. This QNN structure is depicted in Fig. REF . In this structure, each hidden layer contains 128 neurons. For the sake of simplicity, we refer to the realization of QNN by ResNet as ResNet. Furthermore, each item in this ResNet structure is referred to as a ResNet block. The ReLU functions {{cite:4e3944726ad39ab2d6868ce9a5ca7cd28d71d16a}} in this structure, are considered as the activation functions for the neurons. The first two hidden layers of this ResNet are completely connected to each other and they are followed by two ResNet blocks.
{{figure:5c5631fd-dfec-4ee0-88cb-d6fd777e278b}}{{figure:3c594ecb-94e1-4d39-816d-a4f13b3a9289}}{{figure:1ab319fa-0af2-4234-a25b-d70d64dbdc24}} | r | 13a750fce1aef6956f1a9760ae35260f |
In the unsupervised domain adaptation problem, the source dataset {{formula:64dca346-6f1d-4135-94ff-ae0ee82b0042}} consists of data sample ({{formula:98021307-72c3-4ee8-9212-5c82e52b52d0}} ) with corresponding label ({{formula:3d4f96d4-8c7b-4afb-a5d0-9e28f5f38e88}} ) where {{formula:39b76aef-8f7c-4211-a878-2200d24563e9}} and the target dataset {{formula:543217ec-1cb4-4571-b71a-73f05583873c}} consists of unlabeled data samples ({{formula:153c20bb-5c58-4183-a210-67fe921aab0a}} ) where {{formula:a8339608-a994-4c81-8f2e-4bbfac720a0b}} . {{formula:15755dbc-9424-4833-9b9a-5f44412dfdf0}} and {{formula:3f27e8fd-412a-43b0-b41a-fee7ff123178}} are the source and target distributions. We further assume that both the domains are complex and unknown.
For solving this task, we are following the adversarial domain adaptation framework, where a discriminator is trained to learn domain invariant features domain invariant while a classifier is trained to learn class discriminative features.
In this paper, we are proposing a discriminator certainty based domain adaption model represented in the Figure REF , which consists of three major modules: Feature extractor, Bayesian Classifier, and Bayesian Discriminator. The feature extractor is pretrained on the Imagenet dataset, while both the classifier and discriminator are Bayesian neural networks (BNN). We have followed the approach defined in {{cite:e795056a178d78d08888ef6dacc1712b0158f9fa}}, {{cite:d508b61bf3acb28c8c9a292fee1feb26e865830a}}, {{cite:79d1504aabb595205bf72760e12ff8298648c8f2}} for transforming deep neural networks into BNNs.
| m | 35bdb4d06329ec6cfd4f09f70f02b57c |
Reinforcement Learning (RL) is a machine learning paradigm where an
agent learns the optimal action for a given task through its
repeated interaction with a dynamic environment that either rewards
or punishes the agent's action. Reinforcement learning could be
considered as a semi-supervised learning approach where the
supervision signal required for training the model is made available
indirectly in the form of rewards provided by the environment.
Reinforcement learning is more suitable for learning dynamic
behaviour of an agent interacting with an environment rather than
learning static mappings between two sets of input and output
variables. Over the years, a number of reinforcement learning
methods and architectures have been proposed with varying success.
However, the recent success of deep learning algorithms has revived
the field of reinforcement learning finding renewed interest among
researchers who are now successfully applying this to solve very
complex problems which were considered intractable earlier
{{cite:62ada5671f5b3009319047e38d26a360a03527c5}}. Events such as artificial agents like
AlphaGo beating world chapmpion Lee Sedol
{{cite:aff0bf00a3872b177af8a744540ebf1bd590a308}} {{cite:02ac7e8ae9094d3fad2c4e5b09b5f5e6c6cb3339}} or IBM Watson
winning the game of Jeopardy {{cite:e52de7990f3c01966d279dba04a2412bdd0440a8}}
{{cite:2f6fed5a59402fe9e023c90b0ada70098258f47c}} has attracted worldwide attention
towards the rise of artificial intelligence which may
surpass human intelligence in the near future
{{cite:9010c0800720fd6ecb461bfdcb8e7c86cae24d26}} {{cite:d7522c8cc0522b0431831c6e1947bb524a54ebd1}}. Reinforcement
learning is a key paradigm to build such intelligent systems which
can learn from its experience over time. Reinforcement algorithms
are now being increasingly applied to Robotics, healthcare,
recommender system, data centres, smart grids, stock markets and
transportation {{cite:564f059f091c11136182804d18c9d647fef73468}}.
| i | 29d0e2788d582b104d29992cc8ed09ee |
Given a set of {{formula:8766f9a0-176b-4a71-9121-ddb7273e0f76}} images {{formula:cfb0f03b-b115-4774-a74d-02f43d17ef20}} depicting a generic object in-the-wild, we aim to recover a set of {{formula:1faed72a-d327-4cb8-af87-6d49d4a68f52}} rotation matrices {{formula:ca2ec3c3-fd4d-4423-a581-6c71918aa413}} such that rotation matrix {{formula:1dadcce5-0a45-44d9-888c-01eec85611a5}} corresponds to the viewpoint of the camera used to take image {{formula:6457b443-cdbf-473f-b5a0-2d3835ee1e6c}} .
Note that while we do not model translation, it can be easily initialized using object-facing viewpoints for 3D object reconstruction {{cite:4afcc1a9b9ced9b681d2852390cee9d490266199}}, {{cite:5c784ea258cdd27f18ef80a4dbfa8482927531e8}} or a pose graph for SLAM {{cite:a2999ccb36623dcc6f9848ceaa377be4c46ce379}}.
We are primarily interested in settings with only sparse views and wide baselines. While bottom-up correspondence based techniques can reliably recover camera pose given dense views, they do not adapt well to sparse views with minimal overlap. We instead propose a prediction-based top-down approach that can learn and exploit the global structure directly.
| m | 8517a76ae75ce7e83303b81a50bb107c |
Among WiFi RSSI fingerprinting indoor localization approaches, the probabilistic method is based on statistical inference between the target signal measurement and stored fingerprints using Bayes rule {{cite:15df3a2a851f1431d49b79a61849bd98ebdc1ea0}}. The RSSI probability density function (PDF) is assumed to have empirical parametric distributions (e.g., Gaussian, double-peak Gaussian, lognormal {{cite:088206a523db19aa33ccf4580414ecee8fa74495}}), which may not be necessarily accurate in practical situations. In order to achieve better performance, non-parametric methods {{cite:934ee9a4db23701d95013b01867675171424d262}}, {{cite:944002a235ea59d7796114167708d1faddffa55d}} did not make no assumption on the RSSI PDF but require a large amount of data at each reference point (RP) to form the smooth and accurate PDF. Beside the probabilistic approach, the deterministic methods use a similarity metric to differentiate the measured signal and the fingerprint data in the dataset to locate the user's position {{cite:cc167a3658b87d3b273052f556a1a994b75e6449}}. The simplest deterministic approach is the K nearest neighbors (KNN) {{cite:0f0d9744a91d79b4add9d6668ca0070ba938bd73}}, {{cite:1a0e843aafb43684f6f521babdd42a8c01ec2bb7}}, {{cite:14810b3bf0de7aa22d98ed18136c547299107eb5}} model which determines the user location by calculating and ranking the fingerprint distance measured at the unknown point and the reference locations in the database. Moreover, support vector machine (SVM) {{cite:c4be2bfd7bfa2a3cb2260999f29511eb31bcebda}} provides a direct mapping from RSSI values collected at the mobile devices to the estimated locations through nonlinear regression by supervised classification technique {{cite:aed2e4cb08515f56d510092cfc5ea8b06d0bfc3f}}. Despite their low complexity, the accuracy of these methods are unstable due to the wide fluctuation of WiFi RSSI {{cite:1a0e843aafb43684f6f521babdd42a8c01ec2bb7}}, {{cite:14810b3bf0de7aa22d98ed18136c547299107eb5}}, {{cite:c4be2bfd7bfa2a3cb2260999f29511eb31bcebda}}. In contrast to these algorithms, artificial neural network (ANN) {{cite:0df6a483d99d1e82d830e60e897713c4eab920f0}}, {{cite:1e51c145721966b21a3032ece3f4251017e208eb}} estimates location nonlinearly from the input by a chosen activation function and adjustable weightings. In indoor environments, because the transformation between the RSSI values and the user's locations is nonlinear, it is difficult to formulate a closed form solution {{cite:aed2e4cb08515f56d510092cfc5ea8b06d0bfc3f}}. ANN is a suitable and reliable solution for its ability to approximate high dimension and highly nonlinear models {{cite:0df6a483d99d1e82d830e60e897713c4eab920f0}}. Recently, several ANN localization solutions, such as multilayer perceptron (MLP) {{cite:be3ae99c30a2f9be2176a4fe14e33feabd81cbf4}}, robust extreme learning machine (RELM) {{cite:b9e098f7a7ca136b315d0f7ca076d85a10c36b83}}, multi-layer neural network (MLNN) {{cite:14c2ac3e9e5cfaf826dfd750daa8148c967ecc69}}, convolutional neural network (CNN) {{cite:57fc68c4dbb01ea8e3a9d2fe0dd8991c9ffdf6f3}}, etc., have been proposed.
| i | 8fcd8d226ab991073b5aa3dea3c694f7 |
As ultra-precise measurement schemes require the finest possible revolution technology in the detection, they are then convinced to be limited by the fundamental building block describing the physical nature at the microscope levels. More precisely, improving detection precision requires exploiting the resources of quantum mechanics, which deals with physical phenomena at the nanoscopic scale. In this context, the resources of quantum theory have succeeded in reaching a limit of accuracy that is impossible to deduce using its classical counterpart. In the terminology of quantum mechanics, the estimation theory is known as quantum estimation theory or quantum metrology {{cite:c1d6e0cff1d0b8577a6fab2a2ecb671964237ab3}}, {{cite:9b7b8bceec871f8b5811ad4c23be4cc4f739c500}}. It was formally adopted using the correspondence rule postulated by Niels Bohr in the so-called Copenhagen interpretation of quantum mechanics {{cite:00f433c95f50dde048575bc75a4adc00aacfc7f6}}, {{cite:a662e2f9463df53b3f1de333146a01c85eecf511}}, {{cite:1a66022252d92da6b9176c2bdc6cb7d6e6d05ed6}}. This rule also called the correspondence principle, stipulates that a new scientific theory should be able to explain the phenomenon under consideration as long as the earlier theory is valid. For example, Einstein's special relativity satisfies the correspondence principle ; because it is reduced to classical mechanics in the limit of velocities small compared to the speed of light. As well as, the theory of general relativity is reduced to Newtonian gravity in the limit of weak gravitational fields. Also, statistical mechanics reproduces thermodynamics when the number of particles is large. Therefore, according to this principle, quantum estimation theory must be reproduce its classical counterpart within certain limits. In estimation terminology, this limit is called the optimal limit, where there is a coincidence between the classical and quantum metrology {{cite:c1d6e0cff1d0b8577a6fab2a2ecb671964237ab3}}.
| i | 7b25d2ceb6e0e3a48320ebb9ffab9ea1 |
Segmentation of given point clouds: Segmentation of point cloud data is one of the popular 3D tasks. We carried out this experiment on the ShapeNet benchmark {{cite:b79553f69d3f90a9b3b6315530d936da12012b1e}} and followed the data split in {{cite:2476e5645d95641547991697d8479644bf08302f}}. ShapeNet contains 16881 models of 16 categories and they are labelled in 50 parts in total. Like {{cite:b79553f69d3f90a9b3b6315530d936da12012b1e}}, the Intersection-over-Union (IoU) of a shape is computed by averaging the IoUs of different parts in that shape, and the IoU of each category is obtained by averaging the IoUs of all the shapes belonging to that category. The results are summarized in Table REF . When the training set is small, the performance of our network is on par with the other methods. Our technique extracts common deep features between shapes so it needs a sufficiently large number of training samples. From the table, it can be seen that Pattern-Net outperforms the existing methods on relatively large categories like airplane, car, chair and lamp. A sample result of each category is illustrated in Fig. REF .
{{table:ed12b951-6f2f-48c2-8d1d-3b228e7a3c67}} | r | 0602a144e082c564a657bd0de1f15dd2 |
Assumption REF and REF are both standard, they have been used in {{cite:a7a943532ad7bcd7bbd6c1706fff70b3005c914b}} for theoretical analysis of reduced rank regression and in {{cite:ab0a1b61b8d0dcd5d42408c33c0cc7891bb51c46}} for trace regression and matrix completion.
| r | f320df3cd571b20f7475adbddc6186f6 |
The second category corresponds to a scenario where each agent knows its own local constraint {{formula:532fff0c-df2e-456e-8ebb-fcab55700d89}} . {{cite:98390e09ae0af151a124d8dcc3fb4db7f2718c32}} and {{cite:6fa66b07e95e06aed98fe3588f201a6d82b89213}} proposed projection onto local constraint sets in each iteration. They considered undirected communication graphs and proved a sub-linear rate of convergence for the optimality gap using suitable decaying step-sizes, only in two special cases: when the constraints are identical, or when the graph is fully connected {{cite:6fa66b07e95e06aed98fe3588f201a6d82b89213}}. No rate for the feasibility gap is established.
As the constraint at each node might be an intersection of several constraints, or in some applications, the nodes do not have access to all of their local constraints at each iteration, {{cite:91637bba27b38506d32bca7343d84f1386aa9f35}} has proposed a randomized projection scheme. This algorithm suffers the same limitations as {{cite:6fa66b07e95e06aed98fe3588f201a6d82b89213}}, that is, the proof is limited to fully connected networks or a setting with identical constraints at each node.
{{cite:41bd25a29ce758676acb717db4db41df40567412}} extends {{cite:98390e09ae0af151a124d8dcc3fb4db7f2718c32}} and {{cite:6fa66b07e95e06aed98fe3588f201a6d82b89213}} to the setup with noisy communication links and noisy (sub)gradients.
Finally, DDPS {{cite:5d2d384da41c424077bf44d3dbafafb1e8f6c2b5}} uses two row-stochastic and column-stochastic matrices, but it needs a diminishing step-size. In analysis, it is still subject to the restrictive assumption that the local constraints are identical. To the best of our knowledge, our proposed method is the first algorithm in the setup of constrained optimization with different local constraints considering directed graphs that can utilize a fixed step-size and has a generic guarantee of convergence.
| m | 5c0cfb33198f3f5c92973fb09ac4b7d8 |
In this paper, we review some theoretical results on least-squares methods, in particular, when they yield optimal estimates. We show how they can be applied to counting experiments without sacrificing optimality. The insights discussed here are known in the statistics community {{cite:f7be517a9d1b52d45a2a78e30fd1b4ec9d39d274}}, {{cite:e5ec2c2254dd7b7c26340cc9246847faec4f6ba1}}, but less so in the high-energy physics community. Standard text books on statistical methods and papers, see e.g. {{cite:87f886745436547ed3b52f4e1e965f9d363abfdd}}, {{cite:fba0dc768d0d53f8a4b2cccbd663f246018c533b}}, correctly warn about biased results when standard variants of the least-squares fit are applied to counting experiments with small numbers of events, but do not show that these can be overcome. The results presented here are of practical relevance for fits of linear models, where the iterated weighted least-squares method discussed in this paper converges faster than the standard maximum-likelihood method and does not require starting values near the optimum.
| i | 19261599cf3455ebd77b87af6884fc5f |
for {{formula:6b2a438b-7b0d-4ad6-8467-a5d18f3c6685}} and {{formula:26967062-0375-4df5-a9cc-56f489cfed3f}} .
This, together with the regularity estimates for solutions to elliptic partial differential equations
(see {{cite:29cda21a39f77137c21ee6564c586a99c7bc4056}}), implies that such estimates actually hold for partial derivatives of {{formula:51f0638d-8763-40c5-8bd8-b1b4bdc98e53}} of any order. Note that {{formula:f8232dfb-e18f-4372-b957-de271de5b595}} is related to {{formula:c5b13dd0-b134-45c3-bd33-626dd1e5121a}} and its
derivatives, thus the condition {{formula:de6a9eef-5a5e-4869-b165-37b53ad6a43c}} holds with {{formula:7c1e09df-dd4d-4dd8-a934-02a3d4891ce9}} and {{formula:cae16953-771d-419a-a249-efa6025c04b0}} only depends on {{formula:1105af29-f4e9-4260-bf4a-5791c6ad5c92}} .
The proof is thus complete.
| m | 98b2221d3c20dd051b6b0c6a1d6a3fae |
RFA{{cite:d0a85ee4c6867580bf862669e89b38e306df820e}}: RFA takes the weighted geometric median of collected local model updates using the smoothed Weiszfeld's algorithm as the aggregated global model. A particular round of the smoothed Weiszfeld's algorithm is computed as follows:
{{formula:b675f306-828c-4069-897e-edd68dfdd34d}}
{{formula:746838ac-853d-40d4-a921-9e9a046e5895}}
| m | 8fb4578c717ca1d18e80a8c64916a362 |
The full set is a concrete, learnable cousin of an abstraction called the manifold of data in the series of recent papers {{cite:49e9d99afa1e9819ce0a60b8f42ce0178587daeb}}, {{cite:bb8e88dd76f217ca91ccb731b11398a5344a697d}}, {{cite:e58588d44a881821544556789da79eea095c5cac}}.
The manifold of data, by definition, requires idealized “infinite data limit” when the training set grows indefinitely. This is in contrast with our approach suited for practically available datasets. We have seen in the case of MNIST digits, certain images from the train/test set fall outside of the full set defined via indicator function (REF ). We argued, this problem goes away as the size of the training set grows. In this case the distributions {{formula:737b4c22-34d9-4262-bc83-2cfec26afee8}} , {{formula:cb7a913b-de15-492f-9fa7-02b04580bf86}} , and {{formula:594e04b7-5554-400b-8b71-2b91bffa3843}} have smaller support and eventually, in the infinite data limit, collapse to a narrow vicinity of {{formula:fd587457-a558-4211-a719-8d33a9a9c134}} . This is the limit in which the full set, which would striclly include all images of a given digit, would become the manifold of data of refs. {{cite:49e9d99afa1e9819ce0a60b8f42ce0178587daeb}}, {{cite:bb8e88dd76f217ca91ccb731b11398a5344a697d}}, {{cite:e58588d44a881821544556789da79eea095c5cac}}.In our case the space of images {{formula:08874ed1-bc0b-41ee-bf1e-bcf57231595a}} is discrete, while the data discussed in {{cite:bb8e88dd76f217ca91ccb731b11398a5344a697d}} is parametrized by vectors in {{formula:feaf8a2c-4f8b-4789-9b29-bac040b9a992}} . Hence the full set in the infinite data limit will became a discrete version of the manifold of data. The rate with which the value of the loss function {{formula:c8f164c6-53ea-4e07-9538-a384bb9d0e28}} and {{formula:922ae2c9-4b91-4700-a87a-d51c98372207}} decreases with {{formula:0651968a-ea7c-4639-ab8e-58775eaa4f7b}} – the size of the training set, as well its dependence on bond dimension {{formula:b2f4806b-323a-4fb1-9e5e-8fed7392ed04}} , should presumably follow the universal scaling laws outlined in {{cite:49e9d99afa1e9819ce0a60b8f42ce0178587daeb}}, {{cite:bb8e88dd76f217ca91ccb731b11398a5344a697d}}, {{cite:e58588d44a881821544556789da79eea095c5cac}}. To verify that would be an interesting problem.
| d | 3768793d9da7e369f653bd87996de3c5 |
(ii) Set {{formula:42f91680-febe-45d2-822f-52d71381d74f}} . Clearly, by (REF ), {{formula:e91d76ee-d65b-4d06-a223-769b58744a0f}} . Let {{formula:02f80b73-b51e-486b-995b-b2f7bd8aa287}} be the largest invariant subset of {{formula:dcfa6097-1b5d-4c5e-bc5a-8e1ec52651f5}} . By Lemma REF , {{formula:9dcb0ebf-fe8d-4ba2-9736-7198689d92e9}} as {{formula:7b2cddd2-6113-4e9a-89dc-9749c0c7e3f2}} .
Take any {{formula:676011b9-1e22-4dee-90b4-44e3b36a50e1}} . Let {{formula:d8028349-2f60-4ab3-a948-128124c87ef4}} , and clearly {{formula:0ba7f400-b917-440b-ad95-fb873fcf19c2}} as well. Similar to (REF ), we take another Lyapunov function {{formula:f6dc5d4f-f7ef-4870-963e-246908203e33}} by replacing {{formula:b8c022fe-d802-4cad-961a-4dd4a7f5dc0b}} with {{formula:bbca9a29-e724-4fd2-8d99-e9c6db9bece1}} . Based on similar arguments, {{formula:15a7eb0b-fca9-4838-a8d4-678387573dac}} is Lyapunov stable, so is {{formula:b11506ac-99ff-4e80-942c-803d7306eb71}} . By Proposition 4.7 in {{cite:1d5b94bcd21fa565110ac601b73662261a8bb0d6}}, there exists {{formula:624c4312-b5d9-4213-b8aa-c4fa25560484}} such that {{formula:2c06428b-f685-423c-a938-5f514b824f1c}} as {{formula:bf3fcf5c-219c-44c1-99ea-29f2464e799b}} , which yields that {{formula:dbc384eb-8686-41bc-b3b3-babbfb47b394}} in Algorithm converges to an optimal solution to problem (REF ). {{formula:2ca57966-4752-46db-b0f1-f56a5ab4ef00}}
| r | 8ab92aa6561e8d6aa72fa9d08eeae071 |
The usual multihomogeneous start systems depend only on the degrees of {{formula:5c03469b-015b-40ed-bc08-4316599d3baf}} In contrast, the polyhedral homotopy introduced in {{cite:b15fcca59fc65975f70bbfbb95af5f6bf9116b7d}}, {{cite:181c69eea29744b504faf2cbc911625a14382382}} takes the Newton polytopes of {{formula:e655b152-83e8-4e4f-9baf-9975a3e09f7c}} into account.Here, it is more natural to let {{formula:5ed5516f-958e-4196-a0a2-a817c9a74e7a}} be Laurent polynomials, as we will do in later sections. In this setting, the polyhedral endgame {{cite:9547cb7bb7aab2b4d3f8bd6d877257019de2d601}} may be used to detect solutions at infinity by numerically extrapolating coefficients of power series solutions. The number of start solutions for the polyhedral homotopy is given by the BKK bound from the celebrated Bernstein-Khovanskii-Kushnirenko (BKK) theorem {{cite:6bf072a70b7c0f67899ec12d601ec03f87092e4e}}, {{cite:77fd0d201c307d8e77c901ea8a3c37cf71e633a2}}.
| i | f86f965cfb5bc4fad68277efdaf14f08 |
The small {{formula:3faca29a-16c4-418f-a198-830b2251cf66}} limit for {{formula:8cd672f9-097d-4a03-843c-cdbf34b46045}} ,
as Eq.(6) shows, is related to a Friedel-like {{cite:d0d83a9c1b218ec25dba6cc302226a8bd82d35e0}} sum of phase shifts since at the
forward limit ({{formula:7586c6bb-133c-4520-b945-8bdf8ae9348e}} ) one has {{formula:10b867fa-b9fc-475f-8a49-bc7b98a1ebfe}} and {{formula:0451845e-b5f2-457e-a340-ca6586775cb7}} for the Legendre functions. Such a sum determines, via the Fumi theorem {{cite:d0d83a9c1b218ec25dba6cc302226a8bd82d35e0}}, the kinetic-energy-change in the many-body system. At first-order in interparticle {{formula:76e6529e-bce8-47b0-8b8f-d8589488aead}} the variational consistency on the ground state requires
its minimization. And, in harmony with this energetic constraint, the Friedel sum must
be zero since we do not consider an excess charge in the charged host.
| r | 46081cc7c9a027e976d4ec8e8466a0a9 |
Related work:
Several existing algorithms such as sequential probability ratio test (SPRT), generalized likelihood ratio test (GLRT), CUSUM and its variants such as weighted CUSUM are based on the assumption that the density ratios can be readily computed for devising test-statistics for change detection {{cite:8bacbeb2d47d1e492efe5cdfc9508389d7c3f9f9}}.
To overcome this, one can estimate the distributions using Kernel density estimation (KDE) and histogram-based approach {{cite:45ae7a3b8e45d72fb0a99ffd81c1615873f86e34}}, {{cite:6adc0b028162f7f1d8972317bf824767f986307d}}.
Density estimation techniques for change detection has several shortcomings.
Firstly, density estimation based approaches are limited to applications with low-dimensional observations {{cite:9033fbc3976f54adeaf47dddac7cde650b83d985}}.
Secondly, the performance of change detection using density estimation techniques could deteriorate when division by the estimated density magnifies the estimation error of the log-likelihood ratio {{cite:66c26bee92e463967cc3ed99085cf431bbb2cb65}}.
Lastly, the samples from pre- and post-change distributions must be labelled.
| i | 97cd575cc0d7ab1271732405e825eb28 |
Tunneling is a purely quantum mechanical phenomenon which takes place in classically-forbidden region, originally intended to account for {{formula:b8d1e7a1-1609-4f13-80c8-5c395e14bd8c}} -decay, fusion, and fission in nuclear physics {{cite:e76177447525acdc6a6dac426c80c9b890d79ac4}}, {{cite:15476a90793a176af00df4b0fe5e6d22beb8fa6f}}. Apart from nuclear physics, tunneling occurs naturally in photoassociation and photodissociation processes, and in solid-state structures {{cite:77b917c48d1a6c2a4e6d3fbf5cfae77c0cdb1cdc}}, {{cite:444c1c5c5c56163a16fb03130e0b3efc294723ee}}, {{cite:66a247a3e61a88961c3a318be82bd409969329a7}}, {{cite:125e90e9a0ff43d8677a1ef2523dd981837e2fac}}, {{cite:4c468f9ae385022f908ae630d5d7f758e5dd3024}}. Ultracold quantum gasses have been the subject of research to simulate solid-state systems {{cite:8e8b4785d3f32b68d9ea5e0668e9cb4242b0e660}}, {{cite:a0d140c13663df914335b3dab6f2451918219c20}}, {{cite:6ad5277885ad221b65fd59c0d8b3e5245ae0dc54}}, {{cite:3be8bdabc14da9e14ae6f8b9d46a5b5763062839}}, {{cite:8d96f299abff1f46c5c2c7030a6f80b0c38d0b39}}, {{cite:93c90f5711009ea04a1db6892052dcb568ee13b3}}. In the context of the study of tunneling dynamics of ultracold atoms, a double-well potential with static barrier is a standard example. Most of the tunneling phenomena were investigated with ultracold atoms in one dimension, either in a double-well potential or in periodic optical lattices, and focused on the atomic motion in the lowest band, i.e., particularly with the ground state {{cite:24938574e0ff2194633070fe0b2d88a45163510b}}, {{cite:bc4e35f3db6a0b6e1aae28939d140ceec2398766}}, {{cite:0c76f330167d976a283b621f09f11b329e3a2b9f}}, {{cite:52ed904951e13acbb271a5c1caf0180dbd6657bd}}, {{cite:b7ca96e3157bfc64c48a21a4b7efb930f308fa76}}, {{cite:139dedeba199782fac355e9f84039f01502102db}}. Moreover, it was shown in a double-well potential that the inclusion of higher single-particle levels is fundamentally important for correlations {{cite:b8bf6f355b69d0bc5fe08c78b45bb88f8c152e58}}, {{cite:3a7c5ffc07864a9d8dee0808ddb21f56384856e5}}. Josephson-like dynamics of a Bose-Einstein condensate of rubidium atoms was investigated in the second Bloch band of an optical square lattice {{cite:355e017766b00120946c74d0bac1c70de3b4c042}}. Unconventional orbital superfluidity in the {{formula:9a762b7b-93a7-4aed-81bb-5b0dce23cf7c}} - and {{formula:ac422ac2-65e6-4210-9024-8bf47d155ab9}} -bands of a bipartite optical square lattice was achieved in {{cite:cb30f47f1f1ff8cf201ef076cb53d0e4674b32cc}}, {{cite:426f9ca2609328641b09f42a00ce9aa2254b9cb2}}. Recently, we explored the tunneling dynamics of ultracold bosons in a symmetric double-well potential where the atomic motion lies in the ground as well as excited bands {{cite:828b97db1507ea6a6b9f25a198753a95f5565425}}.
| i | 4289b9dc023a1ab4ec2eed61557dda8b |
These discrepancies can primarily be attributed to three factors. First, it is known that solitary wave-defect interactions lead to `leaking' of energy into the infinite dimensional subspace of linear waves (`phonons'), even in the continuum setting. Our reduced-order model can potentially be made more accurate by including this radiation damping {{cite:881f17777ea2eec200061f23f811aec2ee856760}}. It is a challenging task to derive an accurate analytical description of the damping terms to be appended to the Hamiltonian equations, since it involves a careful study of resonances between modes corresponding to the discrete and continuous spectra {{cite:b48ec028096db0ab1d93d28a4356d4b3d0124a26}}. Recent advances in data-driven sparse learning of governing equations {{cite:051b8490b67f0bd3e64b6cedaa20b93104e9f414}} may provide an alternative way to obtain the dominant damping terms. Once a dynamical model is available, the current framework can potentially be extended to understand the damped dynamics, since lobe dynamics and other related phase space transport methods have been used to study non-conservative systems {{cite:a72dd42bdd944c7fd05f9b3419ba01f4ee661211}}, {{cite:bba332158f23c519cd38021198fc8c1119817df8}}.
| d | b5182f588800d78087dfa94fb469f758 |
Using the 3D SPH models of {{cite:aa8dff2fc1267422962efba2a5887790f7040988}} and simple geometric models, we determined that the high-ionization emission originates from a distorted paraboloidal structure lying in the skirt of the Homunculus. Based upon the blue-shifted velocities and near symmetry for PAs ranging from {{formula:f4e820b9-46d0-4078-82e4-cfea1d502ec2}} 22 to {{formula:4c4829a6-141a-40ce-96b8-91d34eadd6e7}} 38, the paraboloid points in our general direction with axis of rotation projecting onto the sky at PA{{formula:7c4da507-13ee-42c0-94b1-3b1074b337d5}} 25.
| d | e6ccb32e5447ebe8e1e92f0098350888 |
Task-Content
In terms of 6-class classification for image content, although all modalities outperform the baseline, the task is shown to be very challenging. It is surprising that the performance with I-M is lower than T-M. The reason might be that visual argumentative tasks demand more specific image encoders that learn sufficient knowledge on persuasiveness and social science; however, the used image encoder is pretrained on a general object detection task on the ImageNet {{cite:c71b0fb5537bf27308d03de565dbc48f64755e87}}, thus our model is unable to learn well for this argumentative task with very limited training data.
| r | 130b498bedbdda32cfd53b443df2ff01 |
Pre-trained language models (e.g., BERT {{cite:7ad643be419fd45a1f76c495702517294fe70e73}}, GPT {{cite:dc30439986aa9547c1322060b574c074554642af}}, XLNet {{cite:2cb426fefc88e2b44641831bcb0b855c3c467105}}, MASS {{cite:e22be7bacb113593f0e58c937136294b6f6271a2}} and etc) have achieved significant progress in natural language processing. They usually employ specific self-supervised tasks and pre-train on large-scale unlabeled data corpus to improve the understanding and generation capability. MASS {{cite:e22be7bacb113593f0e58c937136294b6f6271a2}} is the first and one of most successful pre-training methods for sequence to sequence learning tasks, and several pre-training methods such as BART {{cite:24f36b54115c1f0d5413762a39e81531939ebd88}} and T5 {{cite:159408f0d771ebf980bc5f175be3d66ea5ee2b98}} are also proposed to handle this kind of task. In this paper, we build our pre-training method upon MASS considering its popularity for sequence to sequence learning tasks and suitability for different modalities. Given a sequence from the unpaired sentence corpus, MASS randomly replaces a segment of tokens with mask tokens and takes the masked sequence as the encoder input and predicts the masked segment in the decoder. We leverage the basic idea of MASS and extend it with several improvements to address the distinctive challenges in the pre-training of L2M and M2L.
| m | 0a257c1489f598efda7026243b74dfa4 |
We aim to leverage state-of-the-art out-of-distribution detection methods {{cite:db671a341cf08542ea69ac79dbb240b1bf07b307}}, {{cite:87ab20903d2f36d129af8afb8a2d19802dc90f31}}, {{cite:3f6f30c7f17d5716aeddd2c00c9f59b842b84ab4}} in the health domain for users to safely use health deep learning models.
We selected three out-of-distribution methods that show high accuracy on different out-of-distribution datasets, do not require re-training and prior knowledge of out-of-distribution datasets, and work on pre-trained discrimitive classifiers.
These characteristics are important to help developers or other stakeholders (e.g., regulators, auditors, platforms) easily adopt out-of-distribution detectors to any pre-trained models.
In this section, we provide background on each out-of-distribution detection methods.
| m | 1bf27c943c9385e4eb2e32122bf2d7c9 |
Code availability. The polymer simulations are performed using LAMMPS Molecular Dynamics Simulation software {{cite:e47657730a163fb88b848f7e039766a172dfa38f}}, which is an open source code available at http://lammps.sandia.gov. The codes used to analyze data in the present study are deposited to Github repository https://github.com/anyuzx/chromosome-heterogeneity-analysis.
| m | 7a427fe73269bf7cce88229a38df5738 |
We introduce an additional loss called Diverse Loss {{formula:b17365af-cd70-4d08-bbf5-5e7105c87b44}} given in (REF ) that further encourages the complementary information across time-series and spectrogram views. Due to contrastive loss on concatenated features, the time-series and spectrogram representations can tend to maximize the mutual information between them. Such a process can ignore the complementary information inherent to the views. Different from the contrastive loss used above, here the contrastive loss is applied on features obtained from only time-series and spectrogram projection heads {{formula:39ca6989-b4e2-4890-af38-79cdb6d87b5b}} on a single sample {{formula:1dadf818-ed0d-4d81-852f-5333d4b5ce37}} instead on entire batch {{formula:56da70ec-9ed4-41c1-8847-83c1392646b5}} . The contrastive loss here tries to pull time-series features closer while pushing away spectrogram features from time-series features for a single sample. Similarly, spectrogram features are pushed closer while pushing away time-series features for a sample. This allows the representations learned by both time-series and spectrogram views to have diverse information from each other for a single sample. The total loss given in (REF ), is a combination of contrastve loss on time-series, spectrogram, and concatenated features that in turn combined with
diverse loss. Our method can be extended to use along with recent SSL strategies, using moving average encoder {{cite:abc92447b86c87f365fa2ec0283a7879a7d31b11}}, {{cite:fe89812accb607dc1998dcedf2b6c046fb5c2842}}, negative sampling strategies {{cite:cc975c6d45457b54163bdd84655d2f4dbfe1b134}}, etc.
{{formula:01878192-7644-442e-804e-08137dcd6e3d}}
{{formula:0c24a42a-34fa-476a-9934-428f423cde42}}
{{formula:d34aef81-bccc-4e24-b759-dfb25251f1b0}}
| m | bb386304ab743bd3c6327bbbd05b10a0 |
Ideas and computations of the proposal of gravity with Hayward term of {{cite:1cb6df839b499a5250a94ef9aeebdb213c72bf68}} were tested for JT gravity.
Supplementary suppositions of {{cite:1cb6df839b499a5250a94ef9aeebdb213c72bf68}} in the JT lab on the holographic correspondence between subsystems were investigated. In particular, the von Neumann decomposition of the bulk Hilbert space in superselection (SS) sectors, claimed to be labeled by the entangling surfaces (a point in 2d) {{formula:ea859a95-29a6-441c-bb86-1bbeaf667b51}} . These sectors are characterized by observables as the areas {{formula:c2b9cd0f-b937-4059-8141-9aecb29c90be}} and we compare this point of view with the fixed area states {{cite:0d7750e2377e88c53856583c9c196888d27b39ef}}.
In this sense, a relation between these SS sectors and representations as in ordinary gauge theories are found as well as several remarks on the symmetry group and its representations; and in particular on edge modes. We recover the result of {{cite:58c211cdf9d0208cfd44a41d93a8fc451efb29ce}} using different arguments and propose a
generalization of her formula in presence of a conical defect, which indirectly implies that the symmetry/representations are deformed in this case.
The partition function for this theory of gravity with corner terms is evaluated, at classical and quantum level.
The density of states of an hypothetical dual random matrix model, {{formula:7cd9495c-1dc4-4424-aa1f-eda1de8649a9}} is computed.
A novel formula for the Euclidean JT action is found as the conical geometry is recovered by closing the Pacman manifold {{formula:5b43d631-0979-45f3-9c7a-806da6968cf1}} . We argue that this is crucial to compute Rényi entropies correctly.
Well-established recipes {{cite:2fc9552a0b3678f6ecd836ea79763e8a55bb2775}}, {{cite:e506d81e5e41cc57cbed14d49bb739dccb8a6896}} to compute Rényi entropies are reproduced.
The defect operator introduced in {{cite:68984c6be3c5c657492a4370f570a68ebaf42d1a}} is also reproduced.
The modular Hamiltonian in JT gravity (+ corner terms) is computed and the JLMS proposal is reproduced.
| r | 78ca44686ce1940c6ff248fc35bd4375 |
In Section REF , we introduce the planet-disc interaction
model adopted from {{cite:b725fa3b9ab9eccaed856898c63b1e94a33e4426}},and we show how planet migration as
well as eccentricity and inclination damping of protoplanetary orbits
are modelled in our code. We also updated the type II migration
prescription by following {{cite:06aaf67beaa2b6c28dc69a7f6e8e9f170958df44}}. In Section REF ,
we introduce planet formation and disc evolution models. We adopted
the {{formula:5ce80d04-0083-4705-bfa6-eec23c85327c}} disc model {{cite:01c21e12a8ee7a6e8cf0402271b2e37b1e6d0fc0}},
but we modified it to take
account of a recent development in the field. Finally, in Section
REF , we present the initial conditions
of our simulations, and show a simple example of planet formation
based on the prescriptions introduced in this section.
| m | 48dacec4fdb1ba6f99ecac4f8f335547 |
Tab. REF shows that our pretrained model generalizes well to novel scenes and consistently outperforms LLFF {{cite:4aceb01fb0af5677a1b4b9ab30076ce13c90cc99}} on all test scenes. After finetuning, our model's performance is competitive with state-of-the-art neural rendering methods like NeRF {{cite:784ad94b893a20b528bb13c8635472d006c1fe66}}: We outperform NeRF on both Diffuse Synthetic {{formula:ac030710-1caf-4558-9166-dac5ba4c6220}} and Real Forward-Facing {{cite:4aceb01fb0af5677a1b4b9ab30076ce13c90cc99}} and only have lower PSNR and SSIM on Realistic Synthetic {{formula:c4de0de3-15cc-4c3e-9bd9-4d632c567975}}.
One reason that we underperform NeRF on Realistic Synthetic {{formula:d3b93846-51d7-4935-9dc2-7367edc0a2db}} is that this data has very sparse training views for scenes with very complex geometry. Therefore, the information contained in the limited set of local source views may be insufficient for synthesizing a novel view, in which case methods that optimize a global radiance field using all views like NeRF may be better suited.
| r | 5538ed78b4acc658ea838e1a7b951b83 |
Then, RCG (Q) updates {{formula:23f44e92-0786-4890-98e0-1d31dd77a1d0}} along the conjugate direction, followed by retraction.
Regarding the step size, the optimal choice of {{formula:2fd6750d-ca7e-46e8-a70d-bdcac138022f}} would be the minimizer of the objective function: {{formula:b0db6fc3-fe62-4590-af4a-8c9d336d90d8}} .
However, for the retraction (REF ), the exact {{formula:8ffff3dc-a034-4c23-926e-fcf06810b33a}} is expensive to calculate, since the minimization problem is a degree {{formula:ca774261-9fe5-496a-a3a7-4a9276687da0}} polynomial in {{formula:92e66933-d7a7-4ca9-aece-873f22147bd3}} . Inspired by {{cite:9f8961524c9d1e38795c5695aa6df12776b27f61}}, we instead consider a degree 2 polynomial approximation of the minimization problem,
{{formula:aef8eef2-86c7-4336-a6ca-6ac1e57e688d}}
| m | 38be708769563c82588e214890a9ebb0 |
However, as the first work to address the multi-degraded LF image SR problem, we adopt the non-blind SR settings as in {{cite:ade05958ec695a6cb2b11e55a7691ae05957c782}}, and take both degraded LF images and their degradations (blur kernel width and noise level) as inputs of our LF-DAnet. Reasons are in three folds.
First, performing non-blind SR helps us to better investigate the impact of input degradations to the SR performance, which has not been studied in LF image SR. Since the kernel width and noise level are independently fed to our LF-DAnet, performing non-blind SR can help us decouple different degradation elements and investigate their influence respectively, as demonstrated in Section REF .
Second, performing non-blind SR helps us to explore the upper bound of blind SR. As the first work to handle multi-degraded LF image SR, one of the major contributions of this paper is to break the limitation of single fixed degradation and show the great potential and practical values of multi-degraded LF image SR. To this end, non-blind SR is purer and more suitable than blind SR.
Third, since the proposed degradation model has only two under-determined coefficients, we can easily find a proper input degradation by observing the super-resolved images to correct the input degradations, or adopting a grid search strategy {{cite:ade05958ec695a6cb2b11e55a7691ae05957c782}} to traverse kernel widths and noise levels in a reasonable range, as described in Section REF .
{{figure:ddedc779-c074-40e5-889d-01fa3f2fa737}} | d | f8be0f78ebe637b4eae3a5d6754b9774 |
Multi-modal fusion can be grouped into early, late, and intermediate fusion approaches. In the context of early fusion, the multi-modal features are fused at the input level before the learning algorithm {{cite:3be03ee320c30b4e32ab6a2bf393b1496f5cf15d}}. Besides, in the late fusion, the features from the multi-modal are fused at the decision level. However, studies from neuroscience suggest that intermediate fusion could provide the necessary assistance in learning the feature representation from multi-modalities {{cite:d6df800a993255a2a2912cb4d3a058e646c92d77}} {{cite:865aad9362bc8fcbd4a63e8d0525c43d6c21f19e}}. In order to evaluate the efficacy of the proposed method and analysis, early and late fusion approaches are designed using frame-based RGB and event cameras as modalities. Fig.REF (a) and Fig.REF (b) illustrate the early and late fusion architectures, respectively. The frame-based RGB and event data are fused in the early fusion network by stacking both modalities. In the early fusion, the encoder follows the same architecture as utilized by the proposed network. We have employed the RMSE and MAE as evaluation metrics for the steering angle prediction for the quantitative evaluation of the early fusion with the proposed method. Fig.REF , Fig.REF and Fig.REF illustrate the quantitative results of early fusion on our collected, DDD and EventScape datasets, respectively.
{{figure:ea1bd2ac-f062-4c2a-8248-ce5b6d27d577}}{{figure:1987c6b2-db26-4a39-809d-41b88431ce71}} | m | 59474064c13930e5b949dcd0453dfc24 |
The advances in methods of evaluation of multi-leg virtual
amplitudes {{cite:75d0abe8e89a5a12640067daad56b4c6d9c58ef5}}, {{cite:1043bcb6dc0ee785eae0a9b906e0873266ec58cd}}, {{cite:8d07e3b704718612d4bfb2d6ae0758b84e99ee05}}, {{cite:6a6f0f4aed1c5291c7067336ae55f8ab5747cb40}}, {{cite:bc688421573ed7bf01217e4cfffd016d066da3b8}}, {{cite:54bc2f87efe0b02cc2196899eed947740eea9c75}}, {{cite:ce44373a6636449e1a75ad789a77076f1f10a8c6}}, {{cite:fafd4f6bc7bd0175f9666181b3df1c9188145c17}}, {{cite:46da4110c3f900b99887768d82cf9ffbb9d2ea37}}, {{cite:b21bee45b70e0a7308a8eae6fb58d65876fb1b68}}, {{cite:b00fd072c97237eb3ffeb11dc2263a29065e5fb7}}, {{cite:721fa7b10c9a03ece32c5d85c356ba32023d845d}}, {{cite:84bfc384b9096c415739168ff4e17bf0259ac07e}}, {{cite:0623a1762e74bea324f78c957e9bb1d539944943}}, {{cite:fbd9e218eda56c5c6ddf94984a1f93b714d18e53}}
have inspired many efforts to automate NLO computations {{cite:7161ff68fb374212fee0ac64cdbd3960224c3dff}}, {{cite:bfe2fa2252719523b73dea542bd580d5c75a8e82}}, {{cite:2e4c14836e2bae8b45f2a0bb62e7662f5f4a98cd}}, {{cite:9db083f56f7d7b554ab52f0be68fd128a9b39f7d}}, {{cite:c39a84fafae0ec34ec2aa762d47d503dcb66f729}}, {{cite:a803b1750fd56b2c77400caab33b5214951191ef}}.
Processes with four final states, previously out of reach, can now be
routinely used for phenomenological
predictions {{cite:f20f3b2df6ec859050e82be1ac6e2ec65fbd3666}}, {{cite:1f4fccb29911b0886a3f7b44581db67176bbab1e}}, {{cite:0e0ae10b7d83ae5a57e608e1a6d034850654fd69}}, {{cite:52e63226ed2dd85ca766fef8bcce2caa2b13c953}}, {{cite:ae70f7549fde993900f1ea4c9c3c71b52e4ab544}}, {{cite:11efe165c61a5501967823168175b562dfa482ba}}, {{cite:74c5051f2454f4879da389d54f613f3ba86a732a}}.
We refer the reader to other contributions to these proceedings for further details on the current
state-of-the art {{cite:a90fbee681e6cc772c157b03c691a2f8d8dcd322}}, {{cite:8b7be364bdf56f6f1e143545343d4d155db1c6aa}}, {{cite:dd2ef1f24d99ed58acc8f9ec316f3f96a41c662c}}.
| i | 0bc50b08eba461c4eca840935537fce0 |
Beyond elucidating the behavior of vanilla self-attention architectures, our work theoretically motivates architectural changes that can provide the next leap in self-attention network expressiveness.
By indicating the network width as the limiting factor for depth-efficiency, our analysis encourages the development of methods for increasing network width with low expenses.
For example, we point at the concept of ShuffleNet {{cite:338e8f567657297286697fc7a839dc36a33a533f}}, which has proven to be efficient for convolutional networks. They increase the representation dimension while using only a fraction of it for computation in each layer. This way, the computational costs are contained, but the width related theoretical limitations, posed by our work, are relaxed.
Recently, {{cite:5e34d7f61765f509a72a388da226b2f5f14d03e8}} trained a 1-Trillion parameter model via a related approach which learns to choose the subset of parameters to apply in each layer.
Indeed, we view our work as part of an effort to provide timely interpretations as feedback for the tremendous empirical pull in our field.
| d | cc5c9a37157f35f89bc4474c1d22f573 |
Our aim in this work is to study the physics that emerges when two
slabs of WSM are twisted with respect to each other and
tunnel-coupled. From the analogy to graphene bilayers
{{cite:9ff974a2bc6846e06bb1c2ca1f6cf0edd33a4855}}, {{cite:766bc67c9b781ec3d5cc3bc5a2023f1c120bc748}}, {{cite:70b3f3b9c6eb5b3c2a95b8c91be7cb36b82d2b5e}}, {{cite:b7c1b95c0ab23f68dbd2c58026ec0ac8bb072030}} which show
interesting effects, including the emergence of highly correlated
states when the two layers have a small “magic angle” twist with
respect to each other, {{cite:28dbf1e99b9aaa8fe7c9cc924e0461b8f95d8aee}}, {{cite:484c95f90aea93d1692bc0a234d93b003d727a35}} we might
expect new physics, both in the bulk of the WSMs and in the interface
FA states.
| i | 980b868fd1baa3c8ee0e16fa11d6d9a5 |
Cache-Hit-Ratio: This metric illustrates the number of requests served by caching nodes versus the total number of requests made across the network. The high value of cache-hit-ratio shows the superiority of the framework. Since we assume that ground users can download one segment in each contact, we evaluate the cache-hit-ratio in terms of the number of fragmented contents served by caching nodes. Fig. REF compares the cache-hit-ratio of the UUF ({{formula:483ec228-ee45-4da7-93e7-933138912b51}} ), the proposed CCUF ({{formula:0a270a40-af8b-42c6-975a-ee499637cb29}} ), and conventional CCUF ({{formula:e2ee6542-c7b4-43d6-9c27-ff09f2bac5dd}} ) frameworks versus the value of {{formula:3be4308e-bb05-4de7-af79-c9f03fb37d32}} . As previously mentioned, parameter {{formula:cf6417ac-4968-49fb-99ab-540e26fdfb0b}} shows the skewness of the content popularity, where {{formula:3cb027fa-2f1e-4c68-bc2b-c2d071c11f96}} . Note that the large value of {{formula:7cf0bba6-1930-49fe-8656-6bb262eef59a}} indicates that a small number of contents has a high popularity, where a small value of {{formula:c5709c94-35d3-4f24-b857-33c9fbe906e9}} illustrates an almost uniform popularity distribution for the majority of contents. As it can be seen from Fig. REF , depending on the popularity distribution of contents, {{formula:f4240fb9-2db1-444a-b261-3281865b814b}} , the conventional CCUF framework results in a higher cache-hit-ratio. The most important reason is that given a constant cache capacity, the coded content placement of the conventional CCUF strategy leads to a remarkable surge in the content diversity. In contrast, for a high value of {{formula:28be6256-b70a-4fba-a911-beb45d5b517a}} , where a small number of contents is widely requested, the UUF and the proposed CCUF frameworks have better results compared to the conventional CCUF. By considering the fact that the common value of {{formula:58a44443-99b0-49ed-8f19-c6c60d247ac3}} is about {{formula:087c222b-c5e3-4d26-85c3-8082035732f6}} (e.g., see {{cite:a0383f6dcee3d6dc02ff40a46231fe46ab173ba1}}, {{cite:8f878730030e132f63e73bfb36cc960959ad5b71}}), we define {{formula:3ad329f9-b7ba-4ca3-aefc-39b5999c0d46}} as the threshold cache-hit-ratio, which is the average of cache-hit-ratio of different values of {{formula:ae487b0e-9925-47f6-95ea-399d3b6c040c}} for a specific {{formula:4d0935f3-84c4-459f-b677-36b55e41db7a}} . As it can be seen from Fig. REF , the proposed CCUF framework with {{formula:463f47b4-cce4-44e9-8739-6cbda13b47f4}} and the UUF scheme outperform other schemes from the aspect of cache-hit-ratio.
| r | 5cebbbe69da2ebf0a611760e3e9917de |
We implemented the three enumeration methods (Methods REF , REF and REF ) described in Subsection REF on Magma V2.26-10 {{cite:801bc247bc6cc19158cd55b6d3cd7a4bdf5bab4f}} in a PC with macOS Monterey 12.0.1, at 2.6 GHz CPU 6 Core (Intel Core i7) and 16GB memory.
We also implemented decision-versions of the three methods in the same environment; a decision-version terminates once a single s.sp. curve is found, and outputs “true” together with the s.sp. curve (otherwise outputs “false”).
The source codes are available at the following web page:
| r | ee5119740fcae319d1e0f6fd4704f249 |
Exploration methods in RL improve the agent's policy by motivating the agent to explore the environment. As the agent explores an environment, the agent improves its policy. The researchers proposed methods to motivate the agent to explore less visited states {{cite:183cf0afb4daba8d0e276e1cb5baeaf9d7aa2b19}} {{cite:605ed70cebc1fc1ec2eb7bde6cf97b5089014405}} {{cite:78ace72ef937279660755f34f25a89519042465f}}. Exploration methods vastly improved the agent's score in Montezuma's Revenge {{cite:183cf0afb4daba8d0e276e1cb5baeaf9d7aa2b19}}. Therefore, we propose our APF approach based on exploration methods. We penalize the agent when it visits states similar to the ones in the previous playtests. We reward the agent when the agent visits a novel state. We show how we augment an RL agent using the APF framework to generate new and unique playtests.
| i | 4ae484bd79f8b580666893d2509d34f6 |
Inspired by the feedforward multilayer perceptron
(FF-MLP) {{cite:fdb861ffcf8bb431bfb11ddc8cc1bb1fba97b330}}, decision tree (DT) {{cite:26a1a18380e19f8cc605805a43bfc9db1b2eeb62}} and extreme learning machine
(ELM) {{cite:4bbfb92499ed7c0f0c894606ae762a3d8ce4c5dd}}, a new machine learning model named SLM was proposed by
Fu et al. in {{cite:e04bcd6aa6c8a4208a1f4848c66d4e6f9335f3fb}} recently. Its main idea is
subspace partitioning, where an input feature space is partitioned into
multiple discriminant sets in a hierarchical manner. The whole input
feature space is treated as a parent node and it is partitioned by a
hyperplane into two subsets, where each subset has a lower entropy
value. Each subset is denoted by a child node. This partitioning
process is conducted recursively until samples in leaf nodes are pure
enough or the sample number is small enough to avoid overfitting.
Majority vote is adopted at each leaf node where all test samples in the
node are predicted as the majority class. Different from traditional DT
methods, SLM allows multiple splitting of a parent node at one level,
which makes the SLM tree wider and shallower to prevent overfitting.
| m | b267bcd41b15a2f8d074e95de49d691a |
We numerically studied the mechanical and geometrical properties of wet granular materials with {{formula:b493fade-6271-4613-b258-769d2ef3e34e}} .
For {{formula:ac63e4c3-a235-492e-8fbf-99a2dac96bf7}} , the shear modulus {{formula:5c647012-1144-4af6-81ed-e1197c140e1c}} has two inflection points, and the bulk modulus {{formula:3842a22b-5447-4e66-849c-4f8d1ff9b1fc}} exhibits a non-monotonic behavior.
These mechanical properties are qualitatively different from those for dry particles with {{formula:42677519-454e-4391-833e-0965ac447c8a}} , where {{formula:92962da3-2ccc-49cf-bc7a-dbf6abe08003}} and {{formula:de88b494-6e7a-41cc-89e2-aa67f8a3cefd}} obey simple power law scalings near {{formula:b854b52a-2ec5-47d1-8b14-efcc42b9be75}}
{{cite:bae775d70ae839823d1ae932eb43946eac13d6b1}}, {{cite:157b5a106e09d5643059b2b8d70206e50c785e41}}.
The excess coordination number {{formula:45fd45ca-7355-47fc-acc5-c4cbaef5f8ba}} also has two inflection points.
The peak position in the pair correlation function {{formula:d1416f05-3ee0-47f2-88f6-f0b630461c72}} becomes lower than the diameter {{formula:88d213e3-dd34-4bd6-bc21-0881a42ef461}} due to the attractive capillary force.
The probability density function for the volume of the Voronoi cell broadens as the packing fraction approaches {{formula:f1c16986-9779-4413-ad65-7e4ab22008b7}} .
These results indicate that the geometrical properties change with the mechanical properties due to the capillary force.
| d | 8fce16a2b33b7cc687fa34c88840a352 |
Our result suggests that so far there is no evidence of FRBs associated with catastrophic events such as GRBs. This is consistent with the consensus in the community that the majority of FRBs, if not all, are related to non-catastrophic, repeating sources {{cite:1c549fd327a951ee673c5c8be552d7219ea7ef0c}}, {{cite:921bb21d3412f4d79427154538c3522fb893808b}}, {{cite:e81e58a5988e82c913317cf0c5d387903b5c0a19}}. The existence of catastrophic events remains possible, but the fraction should be quite small {{cite:170de03198f2026b60f1417749e19c9e56d14018}}. Continued searches of FRBs in association with catastrophic events (GRBs and compact binary coalescence gravitational wave signals) will progressively tighten the upper limit of the fraction of catastrophic FRBs.
| d | 8161cb3bb4a08c858f1f384599e8d1ec |
The convergence test of the projection scheme is presented in Appendix REF , where the computation of the end-of-step velocity is found to be indispensible to the numerical stability, which is contrary to some conventional understanding as in {{cite:9d5df5205cd7a7c0f7d6037b67a2bd96bfe8ba66}}.
| m | 95ca6a58661ada718242e1c0d4b2dc86 |
The dependence of the predicted values on the quantities {{formula:dd9f4ae8-b33a-41b2-8d52-4eb44d6af271}} , and {{formula:bdd0c981-2dfc-479c-8eb4-40d3227bf06c}}
is described in detail in the Appendix. The {{formula:3b60ee7b-f2ad-4560-9d4b-bebe5015e281}} are measured inputs to these predicted values, including the Wolfenstein parameters {{cite:7a38c165c8baf20a69d7ace7cd7a937091e477d6}} {{formula:cdc40be5-d3ce-4406-980f-ba5287fd8200}} and {{formula:6de6c710-021b-4dfd-bb06-50bd990deba8}} and the quark masses and {{formula:d776394d-d020-4ec4-98c4-14ef8ae38fa0}} meson masses. We add terms in the {{formula:3be62e26-269f-4fab-bbb9-14e1eae55362}} , denoted generically by {{formula:2795ea3b-7ba0-469b-887c-9da126d3cd09}} , accounting for the contributions from
the uncertainties in the {{formula:82be5dbb-a3ab-4cbb-940c-5d0dff7c1352}} . Note that the dependence on these terms introduces
correlations in the {{formula:be6cb179-0b3f-4112-b178-66cf913fe584}} expression.
The {{formula:d83c55ca-1d54-4808-9426-c36b19f4a2ac}} represent parameters having a theoretical uncertainty, e.g. the QCD parameters as well
as {{formula:a10a27e8-05cb-4472-9251-58413356577a}} and {{formula:dfc6d4cd-fc74-4399-82e2-7bac9c226b64}} .
| m | d761d84e9c2fa359427ad7d3686c4866 |
It is easy to see that our operator satisfies the assumptions in {{cite:695ed9ce09bcd6055bbe4a4219ef48e5b8bcf5bb}}.
Define the following two functions,
{{formula:d887ce72-e526-4cad-ab28-cea77f0b12e2}}
where {{formula:f3001393-7624-4bb4-921c-ce6fde90a43a}} is a small constant to be chosen depending on {{formula:c443d90d-af48-4eda-9c45-46f6797d5691}} and {{formula:1c0e1431-0dde-4fd9-83f8-9461964eb44e}} is a large constant to be chosen.
Apply the maximum principle to the following test function:
{{formula:b9eb7585-d8bf-4e27-97c9-9cb32faab690}}
where {{formula:0db3037a-f099-4ccf-ab07-c984a12329aa}} is the largest eigenvalue of the
Hermitian endomorphism {{formula:dd328c5b-7342-4068-94e2-fe3f1b650465}} .
By the argument in {{cite:1dc9ec9ee361977d16dd05528d270c1e188d8f46}} and {{cite:695ed9ce09bcd6055bbe4a4219ef48e5b8bcf5bb}}, we can
conclude the estimate (REF ).
| r | 5662edf06128f20b0bb5a6b693a55092 |
ImageNet.
We perform experiments on ImageNet to validate the existence and effectiveness of feature transformation on large scale classification dataset.
Furthermore, we also adopt different architectures of teacher and student to validate them.
A ResNet50 is chosen to be the teacher while a ResNet18 and a MobileNetV2-0.5{{formula:4e902119-f236-4648-a0b8-56f5db884fd4}} are used to be students separately.
We compare the top-1 accuracy with other distillation method and show the results in Table REF .
The results show that knowledge discrepancy also exists in large scale classification, and equipped with our method can also further improve the performances of state-of-the-art methods {{cite:7dcb7f5c27df24f8b223477cd89693072046f1f9}}{{cite:8ec427915187743bc842dffc17c3c9935d457e39}}{{cite:c98f99c0150f6ba1c1ebda0317c39d7041953102}}.
{{table:d8055a72-feb7-4585-8543-3dcab3131aee}} | m | 268377a97100573906cb2a90e3cf1111 |
where {{formula:ef228c73-1f3f-431d-ba1a-c5cadbc9bae3}} is a constant depending on the carrier frequency, the
user and AP heights, given in {{cite:24dcdb3146bbf8f232bfc96e4fc11143a3b13886}}. We further use the correlated shadowing model for {{formula:4a157f59-972e-4525-af2d-b9ae847738e4}} as described in {{cite:24dcdb3146bbf8f232bfc96e4fc11143a3b13886}}. Here, we choose {{formula:6aff7395-3c2f-446e-8cfd-9efd0076bfa8}} dB, {{formula:85568565-a079-498e-8ac7-7d7ae9a67653}} km, {{formula:963e1359-d850-4178-9f9d-76e6df64a070}} m, and {{formula:8e46c346-0e94-4f97-b2b1-06df091a47ef}} m. We further set the noise figure {{formula:db3baa0a-5b04-44c4-8129-fafcc3149714}} dB, and thus the noise power {{formula:0dec2450-2b64-4fa2-855a-47d366fdc20b}} dBm ({{formula:875a2606-c994-4cea-afbc-a3e723c24970}} W, where {{formula:34cd6047-3bd3-45bd-8876-663f1af96f03}} Joules{{formula:e2049972-4de5-4cbf-9b13-20326b70552b}} K is the Boltzmann constant, while {{formula:80fea93d-875d-4629-87e7-fa9c3adc9591}} K is the noise temperature). Let {{formula:1328d80c-4c46-4466-89f8-01b06cf677c1}} W, {{formula:6cf07367-add2-498d-91f5-ca71a376588b}} W and {{formula:72d43bbd-3e7b-44e6-929a-5915aa36ddc2}} W be the maximum transmit power of the APs, users and uplink training pilots, respectively. The normalized maximum transmit power {{formula:efe18830-a743-4d6d-8730-9f4ef28e8511}} , {{formula:9c651edb-6c61-4590-869a-04bac3db85f9}} , and {{formula:e71718f3-6c2c-4fa8-b70a-469e24446f76}} are calculated by dividing these powers by the noise power {{formula:beb6654c-57eb-4954-adfe-6190fefc30b4}} . We assume that all APs transmit with full power, and at
the {{formula:03abdf9e-dc04-4616-9696-6f67ef78c738}} th AP, the power control coefficients {{formula:653eb714-3d3b-4038-9ec9-a7ba75ad64f7}} , {{formula:ff2fc799-260b-4f3c-aff8-547364c15aaa}} , are the same, i.e.,
{{formula:097f8003-5fd8-49d0-8572-972ae290ae0f}} , {{formula:ce661bac-5f92-42d7-ba3b-e7399417f9d9}} .
{{figure:719e7b2a-e2bf-4c60-a347-9307c7f8b7f7}} | r | 50580fb6f032c60ef13ea945ae2dbff4 |
On the other hand, the units of biological networks are in general not rational agents, and it is not straightforward to argue that benefits in terms of betweenness centrality shaped, for instance, the structure of metabolic, genetic or brain networks along their million year long evolutionary path {{cite:1585ea5b083711616609d3092664e8cfc7eefd4d}}, {{cite:06f9959384fccc49310cc900b1965233080be060}}, {{cite:07c6bc3ba21d81d2f39e07732d52da4209ff64f5}}. However, one cannot rule out that other compensation mechanisms could have played a pivotal role in this case too, with different benefit functions (e.g. resilience to random perturbations or failures {{cite:c0ee43d69e4e48714b79c2574468b07439d2126d}}, {{cite:18e426a77d33991a5adfd0b2fb0d34175b9586f5}}, or local or global efficiency {{cite:14b6daa318cef4215f85a63f6d93e3744535712f}}) recouping for the cost to form or maintain a specific adjacency structure. In neural structures, for instance, it is well known that the functional gains associated with link formation must offset the associated structural costs {{cite:fa1af50af43a00fcd5c843151801c7842aa3f1c8}}, {{cite:e530238b5b156b3c37ea30ac1ee23d921eeae4e7}}, {{cite:291a9e5faa6c3c5415ce143bd52196c8a17d5c83}}. Note that, for neural structures, while this principle holds in general at evolutionary and developmental time scales, it may also take place at much shorter scales, comparable to those of social network dynamics.
| d | 44d026dd823b3e3301b2190cda8a5916 |
In this section, we first revisit ImageMAE {{cite:9537d968a32218a97bc63bdd4cb14ab013abf75e}}. Then we analyze the characteristics of video data. Finally, we show how we explore MAE in the video data by presenting our VideoMAE.
| m | 3dc2f5808e88ad4070078556684e960d |
Our results are different from existing work on image classification.
Using logits with Mahalanobis distance as proposed by
{{cite:d17a372d028329259a9f9cc749d639433f26a335}} is out-performed by the backbone features by a
large margin in our experiments. Similarly, our OC-SVM model with early layer
features could not achieve good separation between ID and OOD objects as observed by
{{cite:7c0d96b20660c8e039b28d8765e3daedc9d8d837}} in image classification.
| r | 17f5bbf50ec5bf1cd77e595a5bb9429a |
We studied in this work the kinetic EOS (both with and without the HMT) in some details in the general dimension {{formula:489f98b8-6953-45a5-914c-0cfa87f0c9af}} , the next important step is to effectively/reasonably incorporate the nucleon-nucleon interactions/potentials in a self-consistent way, either at the phenomenological or at the microscopic levels. For example, one needs to consider how to determine the model parameters in {{formula:2df81671-793a-4a0c-b1ec-e0960f00f255}} D, and the basic principles and/or symmetries to be considered, etc.
Before detailed schemes (fitting schemes and/or the principles) are available, the {{formula:b43a1f77-c808-4733-bd66-49a06db30dee}} -expansion provides a practical starting point, e.g., one can use (REF ) to investigate how the 3D knowledge on the symmetry energy could induce relevant information in dimensions {{formula:7830a205-fcf0-4f32-9134-53d64e200479}} .
Considering the HMT issue, how can one obtain the EOS of ANM based on the HVH theorem in general {{formula:2eba54d7-f33c-42c7-8843-44d1d430de2a}} D, i.e., the close relation between the partial derivative of the energy density with respect to the density and the single energy at {{formula:0c27f800-762c-4446-8289-13acd779ee9a}} , since when the momentum distribution has depletion as well as the HMT, one does not have {{formula:eee856b7-4956-428f-8e18-b5af51b36783}} , where {{formula:38bad8e8-7247-4be5-8abe-e79c63b93f9b}} is the single-nucleon energy as the sum of the kinetic part and the potential part, and {{formula:370108bd-48a5-4e30-8a9a-21f268c0a98f}} is the energy density of the system, i.e., {{formula:0d158733-7926-447a-975a-c20c893a7011}} is generally not the chemical potential of the nucleons (which however holds for the FFG model). This is in fact a fundamental problem in (nuclear) many-body theories {{cite:9258236d4dc39faebbcef9c1e7149307b74bc5a3}}.
As discussed in the last section, considering that the many-nucleon system in low dimensions is close to its FFG counterpart, can one rely on it (e.g., via the higher-order {{formula:2026970b-9c52-46a8-8519-e9bb297b0a92}} -expansions) to extract useful information for the corresponding EOS in 3D?
A related issue is on the correlation between the symmetry energy and its slope parameter. It is known that the latter (at {{formula:8a102d02-aa0b-4fb4-ad66-f9836a6cebbf}} ) in 3D is constrained to be about {{formula:06a5e7c0-1433-402b-948f-8f5e4a717bf6}} with {{formula:dfb2062d-8d47-41de-b9ab-b238f8969fa3}} being about 2-3 {{cite:f3d39c534f2746ccc99e61b047917f8d9366d173}} and {{formula:86c30425-de03-435a-885d-c6b5db030241}} , which is in fact quite close to its FFG prediction {{formula:c0a45bb4-5fd4-4729-9f64-3821d99a718a}} .
If the low-dimensional system is close to the free model, can one establish the corresponding correlation (even with the effective potential included) to be near {{formula:fdfed041-610f-4dc3-b827-f076cb0009ff}} in 2D or {{formula:e395e70b-0606-4d8e-b5e9-b72f550526e0}} in 1D, or more generally {{formula:e90be372-566e-4a21-9f05-f6014cc78f4c}} ?
In this work, we study the EOS of ANM in a space of general dimension {{formula:4efd8a07-e9ac-4e0e-8816-156958b87e91}} totally adopting the non-relativistic calculations. Since the relativistic kinematics, the nucleon-nucleon interactions, and/or the dimensionality together may effectively affect the EOS of ANM {{cite:5f11b88e1e457f9a9682ace26c00ed58429ff1c7}}, it would be extremely interesting to combine the relativistic kinematics and the fruitful nucleon-nucleon interactions (we have already found that the momentum dependence of the single-nucleon potential could effectively influence certain problems) in the general dimension {{formula:20551504-2779-4494-a050-a44397e3b340}} and to explore how they influence each other coherently.
See the following overall scheme (see (REF ) for the definition of {{formula:6aaae26d-5e00-493c-8456-9d99b40be2e5}} and {{formula:842f9665-1498-48e2-9757-89bfc5cb692e}} is the general relativistic single-nucleon energy {{cite:4024518afa8fa6c567e902c4328d9b3c5f25067a}}) on its inner relations.
{{formula:fbaeb994-6d88-4dd1-8b45-4af4a6d14211}}
The role played by the momentum-dependences of the single-nucleon potentials especially that of the symmetry potential {{formula:cefa90d9-e7aa-4c46-adf8-319066115fc1}} on the symmetry energy is revealed. Currently, we can not determine whether an enhancement or a reduction may be induced to the {{formula:3d620f35-94d5-4720-b755-1acd34ed8812}} if {{formula:5c544ab1-0a74-402c-8b8e-f296acc5f51a}} is perturbed, see the formula () and Tab. REF , the discussions after Eq. (REF ) and those after Eq. (REF ).
To be deterministic, more detailed information about the momentum dependence of the symmetry potential {{formula:a5718756-8e97-442b-a6c5-d3af14577c0f}} and more accurate calculations (e.g., to higher orders of {{formula:c0b9d8d9-7c48-4c9f-bf70-c8a469a11b05}} ) are needed.
The last but not least, it is really important to find applications where the low-dimensional EOS of ANM could be used. As we have speculated in the Introduction, the crust of a neutron star may be treated as a quasi-2D system while its non-rotating core may be consider as a 1D system, and certain sub-systems of particles in heavy-ion reactions may be also treated as a low-dimensional manifold. Finding novel signatures of these problems adopting the general {{formula:764ca459-6e36-40e3-a1e6-13607d9fc0d8}} D EOS of ANM is a big challenge and also an exciting task. For example, the radial equation relating the crust EOS of neutron star matter with observables should also be derived starting from a suitable 2D setting {{cite:7e62fb7728b052fd2020b14428dc607896495461}}, {{cite:515a22078eb333a3c4b77201831339b952196b9b}} (e.g., via the 2D Christoffel coefficients). Thus, the conventional Tolman-Oppenheimer-Volkoff equation {{cite:06792c7134ebec5d370c555f008e7837be694360}} and its input EOS may both need to be modified to account for the changes from 3D to {{formula:a4bf0ec3-96ba-4fd9-913b-3389d8290a8f}} D spaces.
| d | f5d630d9924d05047edfef3850a10214 |
Observe that, in finding {{formula:ac139279-64c2-478f-a0b4-b41dcf0fbb7a}} , the operator {{formula:f891aaef-e9ba-4ded-9b0c-eaf3816e6d58}} is evaluated (possibly)
many times, but no extra projections onto the set {{formula:e795f0ff-e0b2-4117-9531-b1c8c351bcf4}} are needed. This
is in contrast to a couple of related algorithms for the solution of
monotone variational inequalities where the calculation of a suitable
step-size requires (possibly) many projections onto {{formula:bb88c625-51e1-4ac6-94cb-a349eb901d76}} , see, e.g.,
{{cite:936557ece3b54be7e3116f98bf21d19fe1f62bef}}, {{cite:40b162be6fd265bafcf852e295e72caa562c5e4d}}, {{cite:cea141b1e3033400c8ecc33770cdc835037ec945}}.
| m | 83a45a31e4bf680a6d3b40f371302b11 |
One challenge for the future is to extend this work beyond purely
geometric situations, e.g. to images with multiple digits as in
{{cite:361a9e4996b4dc65e51380e2eef77a3bb3bca6b9}}. The theory for this is presented in
supp. material .
The other notable challenge is around generalizing RANSAC-style
inference. For the geometric testbed, this is remarkably
effective, and it leads to the question if similar techniques could
work in a more general setting.
| d | 7db46f55360a5736f7c2bb9414c272a1 |
Inspired by the single perfect fluid exact solutions in Einstein's gravity {{cite:2296ab31901253e9245882c301cefe53696547eb}}, we consider the ansatz
{{formula:657a563a-e253-46f9-a1c3-118aced9f681}}
| r | 71c704959924f0215d9919acf4df2498 |
Among other similar works, in {{cite:d9714919819184357557e4c61579f6e7017a5bee}}, the authors study in the framework of Bethe-Salpeter equation, the production ratio of neutral to charged kaon pair in {{formula:68b3f127-7e86-4224-a66e-f6a643d03e46}} annihilation below the {{formula:936151ec-7517-4ef1-807f-ef290c1513f6}} mass by employing the two leading Dirac structures in hadronic wave functions as per the power counting rule {{cite:cdce0faeee58091f78265f5a9aeb7f1c7db78ac3}}, {{cite:2122e581ca33fb7c16b008c3da99c352148beb25}} we had proposed some time ago. We wish to extend this study to calculation of cross section for each of these processes with the involvement of all the possible Dirac structures.
| d | 1f3bd516c8398a748a1e452ba46a7430 |
Finally, the notation we employ is standard and follows
{{cite:868ac067eb1282dc40ac45cb13fe76f43d649e39}} and {{cite:4162ab3030554d4dbf08195ffeac45e597e9404f}}.
| i | d38cc464442fd503d10b2f1a773ed135 |
Assumption REF allows the policy to explore, but in the limit ({{formula:fa99e5d9-8524-42b5-8ca5-34d1b7e1e439}} ) this assumption requires the policy to choose greedy actions. Assumption REF is strong, however, {{cite:a0798d6924eb23f58242e3c98ef1075c5aaaaf35}} show that similar assumptions are required to prove convergence in theory but not necessary to observe convergence in practice, which is consistent with our observations as well. Thus, even if such assumptions are violated in practice, convergence is still observed. Further, it is to be noted that Assumption REF is a
weaker condition than the assumption in {{cite:a0798d6924eb23f58242e3c98ef1075c5aaaaf35}}, since it does not require calculating the Nash equilibrium at each stage game and using the same to update the {{formula:a56c7cb7-c946-40f9-b729-98f6ca3d761b}} -values.
| r | c0e1bd87ceb4c79e4a80cf8ed7ec2c76 |
The main contribution of this work is that we create a connection between exploration methods and model-based reinforcement learning. We present a method of maximum-entropy exploration for model-based reinforcement learning agents and build a MaxEnt Dreamer that improves the performance to model-based Dreamer {{cite:bf8d73ce141e2dae954f1b652d14726a4d9bc662}}. We also introduce some additional modifications to improve the stability and perform an ablations study to show their effectiveness. Experimental results show that our exploration method and our modifications significantly improve the performance of Dreamer. We also perform an ablation study to show that it is indeed exploration techniques that contribute the majority of the improvement.
| i | f57a5ea92714795451dd48f54b9f118f |
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