text stringlengths 54 548k | label stringclasses 4
values | id_ stringlengths 32 32 |
|---|---|---|
Though the SOR method and the corresponding Jacobi method {{cite:cc83803044bb6a8f0f29683e53799d0e8655802a}} can be utilized to solve the series of linear systems produced by Newton's method, the SOR and Jacobi methods can also be extended to find a single solution to a SNE.
| m | a30a601a11879e98f27e0ac1dd4a97f8 |
The release of a native French Reading Comprehension dataset is motivated by the release of recent French monolingual models ({{cite:1a0ff1489e4941a257f41dc2a79309f83ceae818}}, {{cite:656d67a8629226977df43e3561418487e792d583}}) and by industrial opportunities.
In addition to that, we think that a French dataset opens up a wide range of possible experiments at the research level.
First, while it is generally accepted that monolingual models perform better than multilingual models we find that the gap is narrower than expected for the Reading Comprehension task.
Second, to fine-tune a model on a target language, translated datasets have been extensively used but the lack of native data to evaluate the approach, at least in French, makes it difficult to evaluate it.
Third, apart from Question Answering models for French applications, cross-lingual applications have found significant interest recently with {{cite:9a4298c795be704b82674740daa90a31ecee34e2}} and {{cite:67001240ceca8b39ca653d39a4e8ffc7d036b0cf}} where the need for quality annotated data on other languages than English are important to evaluate how models transfer across languages.
| d | 1807bdb38f5cf720d60891db7c2da677 |
To accomplish this MV classification task, we experimented with deep
feed forward neural networks, encouraged by success on a similar task reported in
{{cite:24259edd43a0514aec4505997347cbb8fe4002c9}}. Each hidden layer had 500 nodes, and we
tested 1-, 2-, 4-, and 6-hidden-layer models. To regularize we use
dropout and early stopping. Stochastic gradient descent with momentum
minimized the cross entropy loss. The inputs were vectors with 3300
elements: eleven words represented by their word2vec embeddings, which
come from the Google News pre-trained word2vec
(download).
Each word embedding vector is concatenated with the next to create the
network input vector. We used the free and open source Python package
gensim for loading the binary-formatted word2vec
{{cite:f56d71843fb4d1cb813b6ecd6d448fed8e7df324}}, {{cite:a682a81aaa8bcb271f3891c48d09554544a5616c}} word embeddings {{cite:04be0d55a5ad854bf5dac1b0fe8742f6260b3137}}.
Neural network construction, training, and testing was done primarily in
TensorFlow
{{cite:e6337ce723664d00bc9ba73384762cac9c7c6fa5}}, {{cite:44aa66efc5a4b8e0f0ad328626de6822f7d164fb}}. Performance
analysis was done using Scikit-Learn {{cite:aec445c27c4fc1b4057d558776ccf41cdf3f6e96}},
and data table reading, writing, and
subsetting was done with Pandas {{cite:0c9e9ef3f424cb2a9b1d0b7899d26b723e5ec2fb}}.
More details can be found by examining the
README and code for
this project on GitHub.
| m | b75179ffc2e49e4ed0707b7ad0f6e47f |
Our proposed method consists of two parts: (1) Self-Supervised pre-training of the encoder, and (2) Semi-Supervised fine-tuning of the network using consistency regularization. Taking reference from {{cite:b12d76c877a69c4b11aaf90eb38856d5753210f1}}, we propose a pairwise contrastive (dis)similarity learning, employing global and local feature exploration for pre-training the encoder. The pre-trained encoder is thereafter transferred for the downstream task of cross-supervision-based consistency regularization, which aims to fine-tune the network.
| m | 3e43d1b6a95d96e36314e306b253b05d |
Before analyzing asymptotic behaviors of optimization methods, we recall some fundamental notions which will be important in what follows. Consider a function {{formula:1f592de3-dede-436a-a59a-a39b2017aa2d}} twice continuously differentiable, a point {{formula:2ec51d9e-6f4a-487a-838d-8a962a9c2abc}} is a called local minimizer of {{formula:8f460bd8-3731-491d-b56c-95973127a5d6}} if there exists a neighborhood of {{formula:5ee31c2b-d363-4df3-916b-ead8fa7765d5}} such that {{formula:4c86070f-3c33-46ab-918c-31ada455bfe2}} is the smallest value achieved by {{formula:29219026-3b6a-47bd-9a44-c855ee104048}} on this neighborhood. It is a global minimizer if {{formula:5cef37f6-dd8a-4a88-a6ba-e303fde4edbe}} is the smallest value achieved by {{formula:bcfc203d-e96e-4819-bec7-598ec0628cd8}} on {{formula:052c0935-2891-4ef0-99d8-a7499be9a764}} . Local and global maximizers are defined similarly considering the largest values of {{formula:238dba71-5aee-4f44-a750-96a84f780cb3}} .
We now recall the following optimality conditions, see for example {{cite:7c274f190e60b3b57d2fcf1e5701c0d0d7f30ce7}}.
| d | e456cc26c8f07b56aeb8e166829283a3 |
According to Riloff et al.,{{cite:52669b20695d9ee526a42a92f22cb24fd6506766}} most sarcastic sentences carry
negative sentiment. We leverage this to improve both sentiment classification and sarcasm detection.
We use multi-task learning, where a single neural
network is used to perform more than one classification task (in our case,
sentiment classification and sarcasm detection). This network facilitates synergy
between the two tasks, resulting in improved performance on both
tasks in comparison with their standalone counterparts.
{{figure:c76c68ea-507a-4fe9-9a2c-9c1b28471529}} | m | bd9529660451079295b4c6fa4bf2e177 |
The above constructed descriptors
were thoroughly incorporated into
four linear Ridge (RD), {{cite:9c7872a180f5e0be194529b547f250be30c7e095}}
Bayesian Ridge (RD), {{cite:c2f143bff6bef2e96645beb7ea176423ca36ea62}}
LASSO (LS), {{cite:0db9fb4bf81513de271e3bc75e25e413fc128123}}, {{cite:9c7872a180f5e0be194529b547f250be30c7e095}}, {{cite:081793bc59f2681dcca2a955fedc7f7c0773245c}}, {{cite:3e72a176d0ba189e0933b05f96b29ab15511e661}}
and Elastic Net (EN) {{cite:9c7872a180f5e0be194529b547f250be30c7e095}}, {{cite:51c7bb45fb5bce9753e6180b17354b6ab322c00d}})
and three nonlinear Decision-Tree (DT) {{cite:9c7872a180f5e0be194529b547f250be30c7e095}},
Random Forest (RF) {{cite:9c7872a180f5e0be194529b547f250be30c7e095}}, {{cite:96dc45f9f03893b7019fd2a2d293f483641d5fe4}}, {{cite:23de3677913821bafdb18f6891cf71d8b2f976b8}},
and Extreme Gradient Boosting (XGBoost) {{cite:9c7872a180f5e0be194529b547f250be30c7e095}}, {{cite:7323e84df650ba6136683938d6e3a8fb8d76d551}})
regressors to predict {{formula:08705d44-5dba-4e1b-a7e6-1de2ab8b1612}} for the target compositions
(see Table REF );
the (maximum) depths of decision tree
for DT, RF, and XGBoost were set to be 21, 16, and 7, respectively.
To construct the regressiors,
533 data {{cite:8aac321b617efa22fe7fc636492c3bfdc7e4b5e6}}, {{cite:caad8e6eddaadd2269e272e181b2300399fe6380}}, {{cite:e4b3009a88398e2c4a0fbc14f7c6e16bbf5fa7e9}}, {{cite:2f1426da44379ab531096c4ac64911618f1b6ba1}}, {{cite:918aa078584aaf1394caf045ab63e0491f30ac06}}, {{cite:e4e307a7a3658bcada817875e770a4bc761fee6f}}, {{cite:0cb6f962505d2c71ecde8b815fbaa6f4432f5f77}}, {{cite:32c1e6810eae9a7fcba1314ba04622eb7983b2cb}}, {{cite:567fdd55627053aaae15e0661ed3eec83a832d14}}, {{cite:3d8692d19c69022d71a34e7a94ca11a918442b0b}}, {{cite:69f0612b22b7d0869e912ddb3439004b2ad3647b}}, {{cite:28ef3fd424232b43a6c1676e33dd96db33333820}}, {{cite:c83c6a243b358302649bd19f37f3b4a98d46fe26}}, {{cite:38d6396554b4fa2008980b06ab13ae54c3a7643a}}, {{cite:02bdd14d7c3871435c574dee242ed2429096dfb1}}, {{cite:474a607d0a1abe7d471ac1d3eeba65e01b6bfb9b}}, {{cite:5dc5b81211f134fc956075f92da484d566566c9f}}, {{cite:a4caba0a12780d1cc35bb49747d0454a185bef54}}, {{cite:2df84f51621d046999fb390fc6d8f9edc6087cd9}}, {{cite:7f233a7577debcabfe808e29c106997bc25dc55b}}, {{cite:6f14bde5dd951293e5da00e050e028627387f65b}}, {{cite:930b203f082d719bd7f91c82f48d569d8ef51e84}}, {{cite:e0a976840cb10949b5341b3fdb6ff8e6e91dd749}}, {{cite:409fd2bdf383fad43c7f94c618f89939e911cebd}}, {{cite:ce65e530569f61545502ca269b4ce11e05cedd83}}, {{cite:d14c6879a90cecb8afd1c788d0ec7aa2d52f366c}}, {{cite:0a66411b70b79f98e93f2f270b4afdbf8e811c31}}, {{cite:ec7158303baea23bed11c37afc219f8fff5ae1d9}}, {{cite:08c61aa8c249ba7a7ebcc7094f163446b8bc4f74}}, {{cite:6a4908e36bc6fc7d1638f67087ad14d66a3df0e7}}, {{cite:f0c0e2d6386c283d26ef625951c4e113242d4ea0}}, {{cite:e66953677dc706b59f8a9c77aefa5b81b283c989}}, {{cite:98959b438e8dd0d9b0b0052691e2f49b46831459}}, {{cite:af32407ed7bf37f4285f1f02c900d06bf78b00bd}}, {{cite:c845302b955e0d5b5c8a257f3cf5376929c8f067}}, {{cite:fcb7210af6d529ce938cdc9bc8e0235615d2b4c6}}, {{cite:ca03b03f1c50243342ea5d2af671584cdbe5a7c5}}, {{cite:3496ccf5f18e4215424542ebc8f8a4f4266a81da}}, {{cite:2d550c53d6f9c8f8e354eea2059f203c4c18ad75}}, {{cite:ca8a5a22e1b9ee9a03a1f8882f9629c36d9e7d63}}, {{cite:e6829fb7730455a2e8da1b8e11f983290c65d23a}}, {{cite:0bb7d517678f6332671eba3339ef32f1204aa688}}, {{cite:3e99e14e98267fdb750ccb8e6112da03bf2aeeb3}}, {{cite:c2601ea3e2fb973690136985c972b654d0a260b1}}, {{cite:dff5d91ea78bafce92e63b0825816bb0d750f386}}, {{cite:0e9d250b4cca6342fc050bc943444b6814ddb813}}, {{cite:8cad7b3c69a87fe43318f39cc1f87920e50ad63a}}, {{cite:ac85cc7dc8b6690ddef50b7e128eb0bfd5aa0a16}}, {{cite:8731bd680f8391750af257fff72d39244bcf49d1}}, {{cite:5afa7b406c6f1c83a8d10cdcbd184f014a1f36ae}}, {{cite:084ba887bf7973ad8180de7bb1c67b5e8d2da6ee}}, {{cite:53f3f8c819b0d21f2e411419bdb1f84a69083dac}}, {{cite:84c6e52da899536a8e3eef3ea10961d06d56fcad}}, {{cite:c344eaa7813c2eef0346001c067319e9beedb3ce}}, {{cite:cf3ea32f55a96d272f4d02205d11b41dbe850b15}}, {{cite:201c3bde259e558bd886de2aba08f0c3b05cc111}}, {{cite:c5987dfbec12d7b0a0459079c8bc795d3a68de35}}, {{cite:8b061d3c00d7f45dbb2ab0c0f8e3af8a04ef1632}}, {{cite:5f7da33cbe6065533e3748fe17a91f25e20d5daa}}, {{cite:12e92abc9f7033f96bec523b568bdd636da5a0be}}, {{cite:3dd4f4045d22f18bdf96a0dfbdfd4569e4dcab40}}, {{cite:a8975dae91cc8205b7788660d14f9c0e68f9319a}}, {{cite:a47ba3bc2e6c09e02fa113f4a546953f3cc550b5}}, {{cite:5c167f7ef245916c17db768ec69f8cb4f0e8aa5a}}, {{cite:75a234eda1067af149fd92389070c804892f7c1c}}, {{cite:2214f213da7536796181ab3aa1a42d01fd1f224e}}, {{cite:8670fe751b943886cc438d1c21e3cd2161f67a25}}, {{cite:47bcb3d35d1add3da6bae17bdd003a7c79555b8e}}, {{cite:84238a3d236da6651d7e1b92dfc686f5512f40d0}}, {{cite:768608d2253607f5fcfc63f248e9c4c4ad9c77c8}}, {{cite:64a3a4a1828d14ef675b13e8ad5dfacb50e77431}}, {{cite:c1cdbabcd46682907d16e5dfa7c57fa501cbad56}}, {{cite:dd98dda4f14dda55dfb2911136d15aa157fda8ab}}, {{cite:11976a0a9b9bb0c505366d1e92bf851b04702317}}, {{cite:63c46feb2e338d54317143e4a4042c3282f639cd}}, {{cite:f6e99e7174dc89354468caa6a7a82fbd45d5ce6d}}, {{cite:ea9c217a9c3cfdf54df615e00b168f65fd2788ca}}, {{cite:2313dbc16bbc86aad669edccadc2f2ec68c32029}}, {{cite:4fd372694fadcd73f7461d24c8d074f817d79bb8}}, {{cite:236dc4f6419d6b73e99484bf67d123f7e6a321da}}, {{cite:38c2c97380609c4beaa05c7db88cc7b96b5489e2}}, {{cite:1140dd431fdf2b6cf8c59ef47f77522314ed01ed}}, {{cite:d6742e9958885283044364878b48c94e17474a54}}, {{cite:6b7cbf24eb83a30cf72ea5ae901d17e5c7b4a60d}}, {{cite:182e40593222b26e172528675e797a153b6710a4}}, {{cite:06d7679b446f88f31aedf523135a6e3abf4c95cc}}, {{cite:f8631f8b278638b09b2a86b90f2b6d80628d3d40}}, {{cite:c9093084a269ab56d2944809dbf3a0a32740fd26}}, {{cite:685240026c077bc512b1d4b8e7d1d3bea5d85cfc}}, {{cite:6a52e0713ad714c029546661cd8cc3bdad25278d}}, {{cite:1de5d6e4ed626214ea22e32d28075560c37c3a5f}}, {{cite:900ecd6c5a44bddfa6ebb7ace28d0dc2b1479d98}}, {{cite:f5e7e4950c83940edf70825bcd8f5ee3948ce547}}, {{cite:20c8b548000aa9927225a87d773a25ff9d5e165a}}, {{cite:3351c3a6fa4d31b682feb4d8fcfb65798fa31fb4}}, {{cite:8c972f4bc5e7279f20cab4572ccf6b1ee27d85f2}}, {{cite:89cd505989620a73aa651ec91590156e451fa420}}, {{cite:80007b8e3af5530f9a07ee2a91cbfc52295b6590}}, {{cite:5d5b43ca642cb61ba42879bcf3afb81d9ad78929}}, {{cite:72405059f4ece290952e08da1d2001fcf624f446}}, {{cite:d1d180843bc47713a53a9f86f1d4ccd41fba7d49}}, {{cite:710b82b22ce5358c04d071e3c371498e2ad5b130}}, {{cite:332c82af9eb8fc3878a1bc108b5fafcf9fcbb806}}, {{cite:fb1d200a6cfaca405ccf7a5411c60a96ffe10898}}
are randomly divided into training and test data
with with the ratio of 80:20.
Hyperparameters in the models were chosen through
the Bayesian optimization technique implemented
in the HyperOpt software package {{cite:36af0a3f81c070d1d5b6aa832494f91872adb03f}}
to minimize the {{formula:409cfe6a-7835-4ee2-8bc8-317c887343a9}} 5-fold cross-validation score.
Model performance was
judged from {{formula:a243a69c-cf98-4068-8ccd-2470ab225581}} , MAE (Mean Absolute Error), and
RMSE (Root Mean Squared Error) as given in
Table REF .
Among the above regressors, we found the XGBoost exhibiting
the best performance for the test data, i.e.,
the lowest RMSE, {{formula:28721e0d-8c68-4273-84c6-a76a9cd498d7}} 20 K.
Thus, the XGBoost was chosen as our machine learning
model for {{formula:a295ec0a-506a-44af-b98b-25f8c7c65ebc}} -prediction used in the successive
high-throughput virtual screening of the ternary compositions.
{{table:da446f82-6c90-4293-87ff-b1f1fea7b552}} | m | 28328f23e56e35d6fbbd54b5e756633c |
Obviously the a.n.i. property implies (REF ), and we show the converse.
{{formula:06b30a5c-7e35-43f2-a42d-eb4c7bef6a8c}}
as {{formula:72641890-36d3-4e47-9896-f8c3d9df9e36}} . Moreover, since {{formula:6b265d32-f3a5-4d8b-9d08-1c8607ae7996}} is positive on {{formula:50053718-5c1f-496b-92aa-207144fece4f}} for some {{formula:5c1535d4-782e-49d4-940a-517fafcab692}} and {{formula:da957573-06b4-4084-ae61-805f9f85d23e}} as {{formula:a41ebf24-ba1f-42e6-a202-4a192251d626}} , there
exists {{formula:61fba494-2c98-4da1-8346-c04e5f9f7e81}} such that
{{formula:13f5fddb-7d61-48bd-8ece-3c95ff770e47}}
Letting {{formula:dc1659f7-e42c-49cf-983a-a72818513829}} and then {{formula:b826bc35-71d4-4ba6-839f-28c040d77caf}} , we obtain the result. Finally it suffices to notice that
{{formula:a989f052-2151-449c-87c9-81506bdace4c}} implies {{formula:6007d22f-e833-4754-9dc3-4ae102303bcb}} as {{formula:cc351ac5-cb6b-4e3d-ac40-7b15e20d031e}} (see {{cite:9e001d7123e7bfbae1044e96fa6a7145a7bb0339}}).
| r | 4c7ca3c416946fec986cdd53dae56857 |
One of the important aspects of graph theory is the notion of the coloring of graphs and the computation of a graph's chromatic number. It is well known that the coloring of graphs is an NP-Complete problem; see {{cite:92f7f23a85c27fa8d707702f898146391dbdf18f}}. However, for perfect graphs, coloring can be done in polynomial time. A perfect graph is a finite simple graph in which the chromatic number of every induced subgraph is equal to its clique number, that is, the order of the subgraph's largest clique. Efforts have been made to determine the classes of perfect graphs. For instance, it is known that the class of chordal graphs is perfect; see Dirac {{cite:7150f61a2299b85a56e1e3665a288de7ae0ba459}}. The notion of perfectness, weakly perfectness and chordalness of graphs associated with algebraic structures has been an active area of research; see {{cite:1dfd2e015af9e887b050488dfff1a54cebdfcc98}}, {{cite:8dea1617bf5821c422207e55b1021f4ea855cea3}}, {{cite:4b9a03dc8ab4cb391a613ceb83e110b8c82520f8}}, {{cite:ede2b2a28cdca5fe05817457cabd10cae407ff0c}}, {{cite:11ed1cede7ea4fa96b9e0acf56c783ded4445493}}, {{cite:3460d886f77f2e78389aa03a70602d533bccda30}}, {{cite:d2a1eaf2ef37c31c909f876bd5d3922c340241a0}}, {{cite:156c38c409ccf9e143728722679c747ca3cb8e59}}, etc.
| i | ec455ac08ff7cbea276e9b4db3713f6a |
In our study, we focused on a detailed investigation of the proposed query strategy and we didn't intend to achieve state-of-the-art results on the CT liver segmentation task.
We are aware that in addition to using more training data, increasing model capacity or changing the architecture could further boost the segmentation performance.
The influence of various neural network designs on the efficiency of our proposed query strategy would in our opinion make a compelling experiment.
Moreover, we think that investigation of active learning together with AutoML frameworks such as nnU-net{{cite:7c36be16697d9bf8e66aa0c0a01947df18ad743d}}, which make state-of-the-art segmentation accessible to people without ML expertise, would be an interesting extension of our work.
| d | ff55e788955102b1f979097839ecfc85 |
Space consumption.
We utilize EfficientNet-L2 {{cite:52ed1e3cff690231a696b67afed73721569fb58b}} as the machine annotator whose input resolution is {{formula:80b530e9-ed32-493d-82ce-4f3a7541ceee}} and the resulting label map dimension is {{formula:26cca708-239e-495b-b4fc-5bdd4337260e}} .
Saving the entire label maps for all classes will require more than 1 TB of storage: {{formula:0a6a1585-6009-4648-ad65-d7d41cdc255a}} .
Fortunately, for each image, pixel-wise predictions beyond a few top-{{formula:1b3df3d3-3f7b-47a3-9b07-dd36b7708574}} classes are essentially zero. Hence, we save the storage space by storing only the top-5 predictions per image, resulting in 10 GB of label map data. This corresponds to only 10% additional space on top of the original ImageNet data.
| d | 2bb8d341e3b2b39828c45e9e7787dcff |
The ideas explained in section relate concepts from different fields such as mathematics, statistics and image processing. Since ULoG uses scale-space representations to perform statistical inference, it can be viewed as an example of a statistical scale-space method {{cite:644942bf5db016f32176e5da8ef8475433e30be7}}. To our knowledge, the uncertainty-aware scale-space representation based on "blankets" (see section REF ) is new to the literature. Nevertheless, similar ideas have been used in variational imaging for a long time, although not in the context of uncertainty quantification, and are known as "taut string" or "tube methods" {{cite:701677f061d76287fea50b6ffcd13dd022ef5df1}}, {{cite:bb9741a5f3e79f161363f60f0e75743048bd899d}}, {{cite:f4870a848d794e66283d3759299c186e7fff3b0b}}, {{cite:4c02abd5bf78abd4f1fbbb5e03f72ab2036c8562}}. Clarifying all of these connections is a promising starting point for theoretical work, since the resulting insights could be used to address various inference problems in astronomical imaging.
| d | 3c1754f3f4a8ca6100110cdf1f9e4d1b |
Although we have shown quantum mean values for shallow QAOA circuits can be efficiently solved by classical computers, it remains an open question for other VQAs, e.g., VQE and QML. Besides, the sampling in the last stage of QAOA, which has been shown classically intractable, still requires NISQ processor. Our algorithm and software, however, can be used as a powerful classical-assisted tool to help finding and realizing the possible optimization problems that is suitable to demonstrate application-level quantum advantage in NISQ processor. It is also helpful of our algorithm for the verification and benchmarking of NISQ computers. Since QAOA deals with Ising Hamiltonian, our algorithm has the potential to assist realizing fast approximate ground state preparation of arbitrary long-range Ising-type Hamiltonian {{cite:14ec02d75590e32b0d340bc47d1897ebce25e1d1}}.
| d | 46de69eca0b314129285c0a6a817c6ec |
A major issue in perturbation theory for unbounded operators with varying domains is that their difference could be defined on a potentially very small subspace, e.g. on the zero subspace. This issue is not as severe when one talks about self-adjoint extensions {{formula:39ba62d7-84ce-4309-8149-3a0dbd8756fc}} of the same operator {{formula:3668fbb3-ae7b-473c-b13a-a3a060fa8478}} , since {{formula:2829d9ca-b0f8-48d4-8faf-76294d71a901}} but there is still a caveat: the difference {{formula:e6412480-286f-4e9b-a47d-fc6eccdec839}} could be the zero operator, hence, {{formula:aadc2163-13c1-48b6-ab4e-6587b6572e6d}} , {{formula:f8ce4165-c730-4a04-87a9-75c7d16241bf}} could be trivial additive perturbations of one another (again, think about the Dirichlet and Neumann realizations of the second derivative on a segmen). To deal with this issue, one considers instead of {{formula:04b0c71e-5f34-4167-b7ad-ae30bd9ff648}} the difference of the resolvents {{formula:8a2afb40-61bf-4e44-83b3-20b47a0cfaf2}} and, typically, expresses it in terms of the abstract Weyl {{formula:e626e343-b8d9-4473-a948-11c5fad34499}} -function, see Proposition REF and Appendix . Such an expression is called the Krein (or Krein-Naimark) resolvent formula. This foundational result in spectral theory has been studied and derived in various settings by many authors; we refer to the texts {{cite:b6eb2f8eca47ca238ace30e1bf8a49f9e95ae6c9}}, {{cite:a66b9d677f9728e5a7dc3454f7e464e3554e8f96}}, {{cite:aad7c5fd9e4c309305b9690984d84e56f2d4d9d7}} where one can find a detailed historical account and further bibliography. We mention here the work
by H. Abels, G. Grubb and I. Wood {{cite:38c48e4e6f9b6c4eddecdde03c723df107b425c5}}, W.O Amrein and D.B. Pearson {{cite:c12ae276bba8e6c602678d4742f4109d9e4319cb}}, S. Albeverio and K. Pankrashkin {{cite:f9f3a4fb7c2199b3ea28342382c1f6fb7312b577}}, J. Behrndt and M. Langer {{cite:8eac6756ff6f8fcb44805530f036832e31415380}}, S. Clark, F. Gesztesy, R. Nichols, and M. Zinchenko {{cite:bfa9874a918361f1f3ac32a63045faf2d7a8470a}}, V. Derkcach and M. Malamud {{cite:8fc8c645419b8faef79c47e71795a73406cfdba4}}, {{cite:ff0a7b59f88b3c95093941677031c555ca1cf919}}, F. Gesztesy and M. Mitrea {{cite:212d9b7bd39c6b737bcb37b69ce435d74e6af5d7}}, {{cite:31bfa65a75fcb1134366d08115a1b592afcc475b}}, {{cite:8cfce9de46466f2bfcfbb6bc51bb8fb018c60929}}, G. Grubb {{cite:4da36e430ee51e5775caeed350755f89416798ce}}, A. Posilicano {{cite:274d74e805ddc4320d29b553190abb30990ab217}}, A. Posilicano and L. Raimondi {{cite:520ed66c74491e6bbc0173fdf1e5a52570032cd6}}. Most closely related to our work is the Krein formula for two arbitrary self-adjoint extensions of the Lapalce operator expressing the resolvent difference in terms of an operator valued Herglotz function that has been obtained in {{cite:8cfce9de46466f2bfcfbb6bc51bb8fb018c60929}}, see also {{cite:183d7e376b22c41f0d3c42dce1ce4a582bf0c117}}, {{cite:212d9b7bd39c6b737bcb37b69ce435d74e6af5d7}}, {{cite:9f22502140c7a560b05ef9a2661fcdb424f4a6b7}}. However, all above-mentioned Krein-type formulas are not quite suited for the purposes of the current paper as they do not capture quantitatively the perturbations of operator-theoretic domains of the self-adjoint extensions as much as we need. One of the major points of this work is to fill the subtle gap in the vast literature on the Krein formulas. Specifically, we propose a new form of the Krein formula expressing the difference of the resolvents of two arbitrary self-adjoint extensions of a given symmetric operator in terms of the projections onto the Lagrangian planes determining the domains of the extensions. As far as we can see this simple but extremely handy version of the formula was overlooked in the literature in the generality that we offer.
| r | 5eff4b6f83091b351233341c1da90492 |
We compared the performance of ADAM {{cite:471d485254f007f1c07d33251c182d193a24e933}}, a contemporary stochastic gradient algorithm that scales
the direction based on accumulated history of apparent conditioning, sum of functions optimizer (SFO) {{cite:c77b14625a44397e9a52a8d660b67df0a1255d51}}, a second order
BFGS-type algorithm using batches, and the limited memory bundle method (LMBM) {{cite:17282e170578900465374e6274280dadf7058576}} on a model of
deep learning of security data from Cisco in Prague, in the Czech Republic. We studied their performance,
indicating the scalability, on a variety of sizes of batches, each composed of several hundred samples.
The LMBM was run in an entirely sequential and undistributed manner, i.e., treating the problem in its
entirety, while the other two methods are stochastic or single-batch based.
| r | 78e822d6ee4402f7c492f6ed53b99a91 |
Self-supervised features have been shown to outperform supervised representations in many papers {{cite:ff8bb8cc7f047cdd41f73712234c2b845f9ae5dd}}, {{cite:ba5f19bb19b86ed891455dd60f3a1f208c516d95}}, {{cite:2375ad86ee5c72ff629c42043570f7d650ccd84a}}, {{cite:1adda4507e8b3607dc94affe79053f3668e99d31}}.
However, as the self-supervised field makes important progress, supervised training recipes also improve greatly {{cite:ed9329bd2b366b0c08b15fd158e17bb087adfd7b}}, {{cite:546075e97a2a5ac6f416db948bac139e82bb60a7}}, {{cite:bbbc6d36cdf7a618a82372936fb338ba0bd04f66}}, {{cite:44c3e7fb7ff10e6f17cfe24c96d5fce11f0ffeb2}}, {{cite:a3dc4a7509d4ccbceee272100c9d2b23043890d7}}.
In this section, we try to keep the comparison up-to-date by considering state-of-the-art ImageNet supervised ViTs, namely AugReg {{cite:bbbc6d36cdf7a618a82372936fb338ba0bd04f66}} on ImageNet-21k and DeiT-III {{cite:ed9329bd2b366b0c08b15fd158e17bb087adfd7b}} for ImageNet-1k only.
We also compare to popular state-of-the-art SSL models for ViTs: DINO {{cite:1adda4507e8b3607dc94affe79053f3668e99d31}}, MoCo-v3 {{cite:61a655d1805dd8fc4752a414d6d4fce32f1e27a6}}, MAE {{cite:ba5f19bb19b86ed891455dd60f3a1f208c516d95}} and iBOT {{cite:9d428ef2a0ade76d63474cb9133938b638d1e447}}.
| r | b48e8bcf36cc31a4d7caa1a061fba7b2 |
It is well known that in any game and for any regret-minimizing dynamics the distribution of tuples of bids
approaches a “coarse correlated equilibrium” {{cite:1a14b6ce55a6e33f52f4f537f599d3cd912e2ae4}}, {{cite:e23b1705ded50b017e2f4b540686ff5f3354f612}}, {{cite:2e85c4c8966ac1879f17ed234cc2022e34ef0e43}} (CCE),
but as the space of CCE's
is quite wide, this often does not suffice for an analysis of parameters of interest like the revenue
or social welfare. For example, both for the first and second price auctions, there exist multiple
(full information) CCE's with different revenues and different social welfare {{cite:e3419d33bcac64c3fe097b7279098987dda4c5b1}}.
One of the contributions of this work, presented in Section
, is the identification of a refinement of the class of CCE's which we term co-undominated,
to which a large class of regret-minimizing algorithms
(“Mean-Based” ones, as defined in {{cite:6ef744d347d7de25cf8f04cade7aee5f2aeb21c9}}) may only converge. In some cases
this refinement suffices for an analysis, and for specific regret-minimization algorithms like “Multiplicative Weights”
we may get an even finer analysis.
| i | 531f5da6b7cb9308095532cdd6f58a60 |
Many distributed systems such as distributed sensor networks, systems for power flow control and large-scale architectures for machine learning use decentralized optimization as a basic mathematical tool. Several applications such as power systems control {{cite:5a4d402744ed2e7f38c53b6e3a999be2080f12db}}, {{cite:8ebef737ec0b66fd7c169d74bc3f07cc753cbebe}} lead to problems where the agents locally hold optimization objectives and aim to cooperatively minimize the sum of the objectives. Moreover, every node locally holds affine constraints for its decision variable.
| i | 0974f63af7e47370216c870a678395a3 |
where {{formula:2983d99f-97d4-4928-9601-4e3c65fcf390}} is the acceleration of a particle ({{formula:3566a632-0ebe-4dfd-a129-5c1970f31188}} ), {{formula:535e09a2-e214-43e2-9018-9bbf392adfeb}} is its {{formula:3880234c-e4a8-4d68-be75-5390783d280d}} -order time derivative, {{formula:46a6941b-903c-4894-b6eb-df2f00c58622}} is a smoothing parameter with the unit of acceleration. It avoids an unnecessarily small step when all the other terms are close to zero. {{formula:3ad0796e-1ff9-47e0-bd0f-ab0bd993ef53}} is the maximum time step.
In our simulations, {{formula:b63614c9-1b4f-409f-b1a8-276510aade3b}} , a choice used in previous works {{cite:ff6b14ae2f6b9e58f630937674071fe429ddb9f8}}, and {{formula:37a353aa-72d4-45ea-bdb4-83e85b93a516}} , where {{formula:728f063a-baa7-4ce4-a9c9-1ffc143de721}} is the local average stellar mass.
| m | e8655dcc9d19c7ed6c3562d6ea3651bd |
With recent successes in AI, there is a great interest in deploying autonomous agents into our day to day lives. In order to cohabit successfully with humans, it is highly important that the AI agent behaves in a way that is aligned with the human preferences. Ideally, we want a system that will enable every day users to specify their preferences over AI system behavior. In the reinforcement learning (RL) literature, the current go to approach for specifying behavioral preferences is through preference-based reinforcement learning techniques ({{cite:2daafdb9d4e7a301c28c5387c554df08b8f700f9}}, {{cite:3cfa18d0647a92e6ddc0253f2c1dfa8b400d654a}}) that try to learn the human's preference interactively through trajectory comparisons. These techniques are useful for tacit knowledge tasks. However, it would be highly inefficient to use these techniques in scenarios where the preference can simply be specified in symbolic terms. Another way for specifying behavioral preferences is through modifying rewards; but it can be fairly non-intuitive for a lay user to come up with a reward structure that leads to the preferred behavior {{cite:696b1c0616f90536bca38aaf0f21d6785469ca7a}}. In addition, specifying rewards becomes more challenging when the system is operating over an inscrutable high-dimensional state representation (like images). This makes using the recently proposed neuro-symbolic framework in {{cite:b5e8433987ddf76787a4a5cf7375427ca1e901e0}} more appropriate for tasks when the user's preference can be stated in terms of symbolic concepts. This framework consists of a symbolic interface that enables communication with the user while the agent uses some inscrutable internal representation for the task.
| i | b0018aebb559fa47629e3a3358714da7 |
Note that, both the expected empirical loss defined in Eq. REF and the entropy loss in Eq. REF can be used in Eq. REF as the loss function {{formula:3fd43091-3be9-4c83-a8de-7b7b91a01dee}}, since the derivation does not require a particular form of the non-negative {{formula:c20183de-09ba-40e3-83d9-c268700fbdd1}} . They also satisfy the requirements for the loss function employed in the influence function {{cite:8ba1ec4d5a547173a1ba68062c9d88be652b91a1}} and for deriving the reduction of average gradient norm (Appendix A.1). Furthermore, we provide quantitative evaluations to validate that more than 90% of the selected samples indeed have reduced gradient norm when the loss functions defined in Eq. REF and Eq. REF are used to compute gradient. This further demonstrates the reliability of the approximation in Eq. REF . We show the detailed evaluations in Appendix A.2.
| d | df648b7c7548dc91957a6f36453bc0d4 |
The phase transition of strongly interacting matter is an important topic in hadron physics. As the temperature and density increase, the strongly interacting matter will undergo a phase transition from hadronic phase to quark-gluon plasma (QGP), which is deconfined, approximate chiral symmetric state, superfluid and superconductivity, etc {{cite:dbeea110bfbd2aa4cbb659ee93a19288cf473721}}, {{cite:6d72c300b87cb906efba8f165a2fd9249ed88cbf}}, {{cite:7347cf29c936f63fc90157baa7f4bfc488ba735c}}. It is generally believed that quarks exist in a hadronic state within a few times the saturation density of nuclear matter. However, how many times is still an open question. This is due to our lack of limited density experimental data. From quark phase to hadron phase, the transition at high temperature and low density may occur as a crossover {{cite:a1dba938ccb2e122221b30de3e032a832f85b9d2}}, {{cite:db5cc0b3c2c33d9013eaac2dfc4eb56ca831ce8c}}, {{cite:50c718d9230575ef995c7f16b75b723e6fdd2761}}, {{cite:33ca01086b37e2ca56929ba7f825e2fe32c7c4bd}}. But whether there is a first-order phase transition at zero temperature and high density or not, along with the existence of the critical end point are still very unclear.
Many works indicate that a quarkyonic zone ( chiral symmetry is partly restored but quark is still confined) may exist in the phase diagram {{cite:06debb3b84463642f1124d75f25572c6a828e90a}}, {{cite:747b3dc68e28a6a7f131fc68701062fc966d9cd8}}, {{cite:dba16bbe78c7333ce369064fab613e4d2e39411b}}. If so, it will affect chemical equilibrium at the hadron-quark phase transition. Unfortunately, the lattice simulation at present is not successful in exploring high chemical potential regions. What's more serious is that experiments on Earth in the foreseeable future will have difficulty entering high density.
| i | 52015f366b890e8f13463abe91b676cb |
We note the very steep spectra for the diffuse emitting regions of the Spiderweb, such as in the eastern lobe, and the end of the western jet, where {{formula:5fbc1deb-626d-4b44-be6f-86ed2927859f}} (see Figure REF and Figure REF ). This may, in part, be due to increasing inverse Compton energy losses off the CMB for the relativistic electrons. Indeed, this phenomenon has been invoked to explain the correlation between redshift and ultra-steep spectrum radio galaxies (for a review, see {{cite:237976bf80d9071534351a09b59bb1f0c7195bd2}}). The VLA snapshot survey of {{cite:46794782ba31dce74cdf347ef46fbd3f28438882}} shows evidence that the majority of {{formula:0800ea65-bbf7-400a-8a82-b99ef23a88a2}} powerful radio galaxies have lobe regions with very steep spectra ({{formula:e3285c40-9869-4d65-9db0-77e79bae67f9}} between 5 GHz and 8 GHz), although the snap-shot sensitivity of the pre-upgraded VLA was inadequate to properly image these regions in detail.
| d | 718524e0789b3af50f008217a46c41c6 |
where {{formula:2666088d-5f4f-46df-b010-7d05c7c8e0af}} denotes the dry source signal of speaker {{formula:30bf7eed-44b6-42f7-b7ce-b83c1c23d98c}} (see our physical model in Eq. (REF )) and {{formula:e42bad7d-4172-49e3-9a00-2a1229d29858}} is a gain equalization (GEQ) factor {{cite:3e9a0a0d1fed01f697a5cda3a2ecc46777632d1b}}, {{cite:10887e5227224339300719fc0327c83fc0b8adee}} that allows estimated speech to have an energy level different from target speech.
| r | 28bb95905d5af878bf9decf421ca78e0 |
LanzcosNet {{cite:3d5f9dd38eec3aa11ce52f9d7918740b84e14c47}} appears to be able to successfully utilize multi-scale information from the graph Laplacian and avoid limited model capacity, outperforming both the MPNN and PAGTN. However, the inaccuracies from the low-rank approximation provided by the Lanczos algorithm likely limits what the network can learn from the representation.
| d | 302cc6ee3e31ea5112e568d2753b75ac |
Future work should leverage new advances in generative modeling.
One possibly useful technique could be to develop fooling features adversarially against a discriminator which is trained to recognize them from natural features.
We also believe that studying human responses to feature-level adversaries and the links between interpretable representations, robustness, and similarity to the primate visual system {{cite:55a68d831a17cbbe409c88258094c3103b01ceb5}} are promising directions for better understanding both networks and biological brains.
While more work remains to be done in grasping the inner representations of deep networks and ensuring that they are robust, we nonetheless believe that these findings make significant progress in understanding deep networks and the practical threats they face.
| d | 399c09e8266eb6eb2d34ef755fb2fa10 |
A more quantitative assessment can be achieved by comparing the reference input and the corresponding inversion solutions in terms of RMSE, Structural SIMilarity and Scoring values in the input domain {{cite:689160f109c2c6ce21a0122ea956ddc086d41e95}}, {{cite:cfabbbd2c6054062b5cb7f92f4f7fb71e8baa90c}}.
We consider the posterior mean from the posterior distribution, including elements from the null space, and compute the RMSE and Structural SSIMilarity for inversion based on PCE and straight-line-approximation trained on 900 sets with and without modelling error. To further assess both the statistical consistency between predictions and observations (calibration) and the sharpness of the prediction, we use the MCMC samples, transformed back in the pixel domain, to obtain a Gaussian approximation {{formula:e277333f-f546-471f-b29c-eb7733fb1137}} of the estimated posterior PDF and use it to compute the logarithmic score with respect to the true value {{formula:1346a592-207f-4cc6-b997-ad75655c3548}} at each point, that is, {{formula:0cc3c4a4-51ed-42e7-9ae0-9d8cc2a34961}} . Low values of the logarithmic score are associated with PDFs under which the true value has high probability {{cite:08540969b69f127fb82b4b23edd0c3c5a45c4bcc}}, {{cite:f0f17186596fccfcb33241f62f4d7d9c53ff0d2c}}. Scoring values for inversion results associated with PCE and straight-line-approximation solvers including and ignoring model error are shown in Fig. REF .
The results of the fitting performances of the inversion results in the input and output domains are summarized in Table REF .
{{table:1c22409d-01fe-4fae-8c11-6f33fcfb0924}} | r | 109319d3d9f67141ce6d9dfec4570b4c |
Multi-modal language-vision models demonstrated recently strong transfer capability to novel datasets in absense of per-sample labels {{cite:81c9e1c9af74055920e9b099fd281f10ef8aae22}}, {{cite:6d875ad25e8e856d9447ef630626d0e4a709dba1}}, {{cite:973fd240b76f052f25ab5d4afb125e88f8d833f3}}. This capability requires sufficiently large model and data scale during pre-training. Increasing data scale alone can often improve model performance {{cite:a7b1f496edd372ab8ec144a9f0d4fef0ea7d9559}}. When increasing model and compute budget scale in addition, scaling laws suggest further increase in generalization and transfer performance if not bottlenecked by the data scale {{cite:3e899476f04572edd044c9d8069c0dfbc1e6c6ae}}, {{cite:b9ae565c5e4cc2d4aa3d4dfd63b3b2aaa1fe7d8d}}, {{cite:e7e1fe877e98217e2aab62ef3da2a92394977aa7}}, {{cite:8e21daa7dd18450eafc0e05daee0782df43ae593}}. There is a plethora of recent works that have built massive datasets in order to optimally scale up various models {{cite:0a7faa4061be77079d981d0521534810a67d96d2}}, {{cite:81c9e1c9af74055920e9b099fd281f10ef8aae22}}, {{cite:6d875ad25e8e856d9447ef630626d0e4a709dba1}}, {{cite:973fd240b76f052f25ab5d4afb125e88f8d833f3}}. However, these massive datasets have rarely been released for various reasons. Gao et. al. recently released The Pile, an openly-available 800GB text dataset {{cite:614b5a836ae20a6d39229f197b59c590a6f23fe9}}, in an attempt to loosely mimic the dataset used for GPT-3. The largest publicly known image-text paired datasets range from 400 million to around a billion, but none of them has been released.
| i | 35a5561b31be8b9757487f7fd14579f7 |
Results (a), (b), (c) and (d) use an encoding scheme reminiscent of the concatenation idea from {{cite:060f9dff866cce8027e0b0647547a0d4784284e2}}, {{cite:8d3223195618003fe3b1586e792df8a795c32d69}}, {{cite:1d6b0467a871c7157dcc8d8350875a28ef9cffb7}} (and suggested to us by Ronald de Wolf). The underlying idea is to randomly break the initial string {{formula:5ca440ca-cd25-431e-b807-f69b85663c37}} into different `blocks' and encode them via a standard RAC/QRAC/EARAC. Result (a) breaks {{formula:ae03acd5-2ad3-482b-b96e-91359de7db3e}} into {{formula:b0058dff-4bf4-4fa8-b71c-bff1423dcb1a}} blocks and employs the {{formula:98e836e3-a49a-48d8-851b-91ffd0d59b43}} RAC from Theorem REF on every block, each with {{formula:59b16731-e908-428d-8089-d06a0200f120}} elements, while in results (b)/(c)/(d) we employ the {{formula:f4de2ea0-1c54-4302-88e3-43d1c77b6e45}} RAC/QRAC/EARAC from Theorems REF /REF /REF in order to encode {{formula:a2797590-d44b-4ed5-93f9-1c8fa7430004}} blocks, each with {{formula:35926704-5686-46cd-9f44-66525e17c053}} elements, into a single (qu)bit each, resulting in {{formula:6af82504-53d3-49ed-bcf2-86b924566a21}} encoded (qu)bits. With high probability all the bits from the needed string {{formula:bb1cbeae-81ca-4ecc-a7aa-04182170f251}} will be encoded into different blocks and therefore can be decoded and {{formula:a3841efe-b79d-47dd-b5e1-d46ee2d713aa}} evaluated. The decoded string {{formula:c033b111-27e5-458a-af10-5efb97542e57}} can be viewed as a `noisy' {{formula:bcbda421-f335-4997-8cc6-5d957ab0debe}} , to which the noise stability framework can be applied. The bias of the base RAC/QRAC/EARAC thus becomes the parameter {{formula:5c962aa7-8a89-4764-ac6e-4feed3c703ff}} in the noise stability of the corresponding {{formula:29b5cd5d-34e9-4e4b-ae66-1e1bc1e2a027}} -random access code. As a quick remark, since we opted to lower-bound the parameters {{formula:736b70bb-2f4b-48e3-b66f-959e6079a464}} in Theorem REF , in result (b) {{formula:445b71ba-dcc1-4b94-a014-1176c185ae85}} does not exactly equal the bias from Theorem REF . One could write, though, {{formula:a28c25bc-cf56-482f-bd8c-58923c57fe36}} .
| r | 3a2e27b9f2f682e9615aba6fdeb6a3a1 |
We decompose {{formula:1f63b056-ef72-48b8-8183-3815d84186ac}} into
{{formula:bbcc960a-4fde-4aaf-84dd-ddb9a99d633f}}
First we consider the compound Poisson {{formula:46c8fbe8-6002-4e7f-9de3-87b96fababca}} and let {{formula:b9811ae8-26e5-4a00-935e-06e1e5790535}} .
We write the proper absolutely continuous part as
{{formula:eae95cb1-33bf-4523-a0b0-05d4faf4a5e2}}
where {{formula:4abd493c-df15-4e14-a3b7-fb3d6a4d77b5}} . Since {{formula:197affd8-e7c4-4b94-8333-d752de1ac7b8}} is bounded, {{formula:b12cc92a-add4-49b6-96aa-17836de7042f}} is bounded as well.
Recall that for any {{formula:dd2859db-6f6f-4fec-899a-fdbfbed4819b}} ({{cite:c6ae162db131e56be73b17d86255140ad65580fe}}). So from e.g. {{cite:c6ae162db131e56be73b17d86255140ad65580fe}}
(cf. {{cite:6ca1cb84e0f1d6043c50da6dcbc40b936e2b7042}} and {{cite:7ca78f37f4972d7b7fe2dcc8d795fec2330878f8}}), we can define the exponential tilt {{formula:1b852302-1a18-4bee-b52d-e8eb87b8f682}} of {{formula:d8127816-7c27-4eaf-a4d8-34bed14ed841}} as
{{formula:39a211e7-81bc-4762-a9c1-d5fba0f69e37}}
Then {{formula:10793007-f1f5-4991-8426-e6e7e21dac45}} is again the compound Poisson with the proper absolutely continuous part
{{formula:a3951a3b-6ce9-43bd-be9d-0b0036cd0128}}
with {{formula:26e90dc8-cbc7-46d8-bf7f-f73f794d56a6}} and {{formula:67caa84b-68c4-4655-8725-571af73cd290}} .
For any {{formula:85ce36b3-7256-4d71-aa3e-f93a353bef58}} , the right-hand side is well defined.
Since the support of {{formula:14e53f60-9cbe-4ef1-b9fb-dd564666d6e2}} is included in the interval {{formula:c0195e24-56de-4771-9cb1-68bd382c6c0e}} , we have
{{formula:2559d07b-228e-4e4f-bc7c-a135e08f8d20}}
Now since {{formula:62674193-cd07-4f00-bd7c-c7744ebb1d1e}} is a compound Poisson with non-negative support,
it suffices to check that for the absolutely continuous part {{formula:d1b0f031-a00b-447c-807c-cfba7d16e4e7}} of {{formula:fabbbd84-68d5-4f6d-9dc0-66317bbba66c}} ,
{{formula:c8cd11a8-d434-44e0-8433-97fa4fbb0208}}
Thus we may take some {{formula:ad7e3e3d-5805-4eac-9238-8606f262b3a2}} such that {{formula:18d8c8dc-9066-4d43-8475-7e5332e4147c}} .
| r | 261162facf1493c0e838d005b9398e1c |
The details of the code that is used for the simulations is going
to be explained in detail elsewhere, here we point out only the key
features. Both the field stars and the test stars feel the potential
of the SMBH, including the general relativistic (GR) correction that
leads to the prograde precession of the orbitsWe use the
treatment of {{cite:63c7414a08aa1ed32d965fee1d07e6de350b56ad}}. The test
stars also feel the individual potential of the field stars, which
leads to retrograde precession of their orbits and changes in angular
momentum and energy.
The field stars do not feel the individual
potential of each other, but instead see the potential of a smooth
cusp that is consistent with their distribution. This approximation
decreases the time required for force computation significantly and
was already employed by {{cite:f923506c0e29b0b3eac904f845efe718e63f47b0}} in their {{formula:23cee644-a817-4bae-8c56-3dc7599fb57d}} -body
simulations. For the interactions between the test stars and field
stars we use a softening kernel ({{formula:800cfe1a-526a-435a-b0e0-17515ce15c85}} ) of {{cite:a5c265d2cb172500329cadec2966da6529b373e1}},
with a softening length {{formula:e7490947-c9cc-42a7-a8e8-32cea59ffadc}} pc. The units we adopted are
{{formula:849d71b8-e216-4016-b413-1f8901b38987}} .
| m | 23050bc77db5e9eded943a6f6be985e6 |
We emphasize that, while two-local sparsely-connected codes can be desirable in hardware (e.g. to reduce crosstalk {{cite:f373b3c479f9ef7d719c2e5ae25e83d0eae5c4eb}}), two-locality often greatly diminishes the quality of error-correction {{cite:86cfb73e6ffcc1f782daf737ee0160078c631880}}, {{cite:bcf480d95d75e36c2f84d6cd00d64bd0fde3b6a7}}. By comparison, our results show that the honeycomb memory remains surprisingly robust, and further, embeds in a lattice of average degree {{formula:e810ef2b-9bdf-4a42-93e7-c58a4e9796aa}} . We study its “teraquop regime” - informally, the ratio of physical qubits to logical qubits required to implement trillions of logical operations successfully (see [sec:figuresofmerit]Section sec:figuresofmerit). Without considering its potential hardware advantages, the honeycomb memory requires between a {{formula:f3234222-94cd-4edb-864d-b7692177867b}}{{formula:564864e4-077e-496e-8a1e-0f1777619cb4}}{{formula:a053e3e6-dd1f-4d45-a84c-779899f799c0}} qubit overhead to reach the teraquop regime compared to the surface code at {{formula:f39a528f-ef10-42a9-9a5d-931df533ced5}} error rates. However, this gap widens in a superconducting-inspired model in which the measurement channel is the dominant error, as each parity check is assembled as the product of twelve measurements (compared with two in the surface code).
{{figure:e7151fc3-683b-4766-bc37-79c081319983}} | r | 10feeea9d4b82d54df3990b23e46f7d6 |
A recent review {{cite:1d41cf19ce31f01ad4cbf15f17fb10e0b00436e7}} discusses the
basic problem of the large expected decay widths into two mesons,
which contradicts experimental observations. Around the mass of the
{{formula:cbb3e1cb-57bb-4464-b1da-f4d0dc282c33}} , there are two conventional {{formula:2c3f8c53-c01e-4558-99fe-ef1a652f3ccf}} {{formula:7d53b489-9e65-495f-a108-ea9f82f76c2a}} states in the
quark model, {{formula:1e094d44-d989-424b-8d99-6bc3d467ff9e}} and {{formula:772f35de-6874-4f8a-9493-834aaba436fb}} . According to Ref. {{cite:a297dd0a5e3e13c070d13b6d8b4045b5e51e2c53}},
the width of the {{formula:48026c59-1e8d-4453-a771-0a832cd9b4fa}} {{formula:4bbf72b8-5e14-4629-9883-a5e6965e273b}} state is expected to be about 380 MeV. The total
width of the {{formula:0b2589cd-28fb-495c-8593-10f92acd06d6}} state from both {{formula:22f6978a-c627-4e23-9f66-f012a143caa2}} and flux tube model is
expected to be around {{formula:1a9053b9-636e-4cf3-bbc1-1fd9f9090932}} MeV {{cite:bf8b19a319907b5dbcaedfa8d90491dcb953c638}}. However, the predictions from
these strong decay models sometimes deviate from the experimentally found
width by a factor of two or three. For comparison, the widths of the
{{formula:2b4ba672-806a-4668-a364-63b567a682bc}} and {{formula:f6ab2c12-9c5c-49df-b155-5b4bfea8399b}} charmonium are less than 110 MeV
{{cite:abf244315249fd60937aea915d5c1ebed5322f23}}. Fortunately, the characteristic decay modes of Y(2175) as
either a hybrid or {{formula:7acde815-b080-4ef0-a101-b0381cfed759}} state are quite different, which may be
used to distinguish the hybrid and {{formula:d031e9cb-ad4e-4453-ad37-b7409a4f5c6e}} schemes. The possibility
of {{formula:6d9926ec-de7a-40c7-aec5-f35032085259}} arising from {{formula:b7a654ff-5b74-4f68-89ce-46380bd36582}} -wave threshold effects is not excluded. As
of now, none of these interpretations have been either established or
ruled out by experiment. The confirmation and study of the {{formula:60da3a23-5197-4a46-92f7-9d4037e831ed}}
in {{formula:68cdcf4d-47ff-43aa-a33a-225413ff1174}} with a large data sample is
necessary for clarifying its nature.
| i | 883bfd4bb23719670c3b8b464633e022 |
as {{formula:b85e7e4f-7178-42f4-84ba-964926e4d6ee}} is finite for every {{formula:f13d0d79-a55d-4a27-9226-eda24806d527}} with {{formula:34666664-1080-4abe-bcb7-233e7b8b8c1b}} , see Theorem (26) of {{cite:0bb1da6a31d9dffcd306f152edbb3b4e89e4f201}}. Next, by the submultiplicativity of the spectral norm, Lemma REF and proposition 4.1 of {{cite:8e8f9726fe18432e0d44b8c2aad8d69efc9d6d26}} we obtain
{{formula:f710a2f4-dfe7-41b5-9938-6753cd9559be}}
| r | 3609cc6a6103894cd8e45c9c26851d24 |
This localised perturbation is injected in the DNS with different initial energies. Its time evolution for the minimal initial energy able to induce turbulent bands, i.e., {{formula:896668ad-f4c5-4bdf-a27f-1a1f74f6e05a}} , is reported in figure REF . At first, the oblique streaks increase their amplitude ({{formula:e8b42c50-e2b5-4b17-a3b1-405c86094210}} ) and start to saturate nonlinearly, until secondary instability arises ({{formula:f90e78b5-3a39-45b6-ab08-603205434b2f}} ) and triggers turbulence in a localised zone plunged in the laminar flow ({{formula:2017ad4c-8fcc-4cab-805f-a3c818a608c5}} ). At {{formula:db61a7be-be4e-4ef6-b93e-b5e393ebc5f8}} , the flow presents the same configuration shown in figure REF for a turbulent band generated by decreasing the Reynolds number starting from a fully turbulent velocity field. Notably, inflection points similar to those observed in figure REF , are observed at small time in the velocity profiles (see the dashed line on figure REF ). Thus, it appears that for triggering a turbulent band in the tilted domain, starting from a rather weak perturbation, two main elements are needed: small-scale oblique streaks aligned with the baseflow, that saturate creating inflection points, and a large-scale vortical flow ensuring spatial localisation in the {{formula:fb88b25d-1010-42ff-804b-fbcd9324cd6a}} direction. The transition at the small-scale is due to the classical lift-up mechanism, followed by secondary instability of the saturated streaks, which triggers the self-sustained cycle supporting turbulence {{cite:9cf9095940014df2a1697f2600bc033ccd17d051}}, {{cite:1fa71598584d74903f667a55c2870a461ae121d2}}. However, in the absence of a large-scale flow ensuring localisation and allowing to maintain the band, these mechanisms are not sufficient to generate localised turbulence. Of course the initial phase of growth due to the lift-up mechanism can be skipped by directly feeding the flow with inflection points, as done by {{cite:86b4d0ebf779c8dbf40fd62b3c3b05e2f3bce4be}}, but at the cost of a larger amplitude disturbance, which can be more difficult and expensive to obtain in an experimental setup.
| r | 11dbe27dd66fed6b153a7abdafc6b144 |
Various phenomenological and experimental investigations on top
quark hadro-production with top mass renormalized in the {{formula:e3afc283-224e-4fc6-a9c4-4bb762ba33c6}} scheme
already exist in the literature (see e.g. {{cite:b68bace6749f65689cc7751aedff07acf56c6855}}, {{cite:45affdc93d3d1344bc5c393bd0ecbd13f8932bc7}}, {{cite:dcdedcfd690bfb146b3ff9ecdd9fc9380cfc1127}}, {{cite:6daa82cc7dd3c2d5534b09056426bb3ac937897d}}, {{cite:ac5dbe674640dde32712317fa1cefda4733dc326}}, {{cite:f1ae780d6db76f97efa550eb4e581d11517e8ea6}}, {{cite:5b284cb667bc1592efff1cf2adc4689188130b8f}}). On the other hand, the MSR mass is
discussed in various theory papers, mainly focusing on its definition and
properties (see e.g. {{cite:bceb58519fb012e8fcac608eec698e57ecd437ac}}, {{cite:c878a358ee32396911a48d4c49b03a495484a73f}}, {{cite:229be9a34329bd916529cf0632150a2cccf5eb47}}). As for the top quark case, the main novelties of our work
are the phenomenological predictions for NLO differential
cross-sections in {{formula:42397729-cad5-4fd3-a411-0225860dd4a6}} collisions using the MSR mass, which we compare to
those with the {{formula:afa0b8ae-9abc-4908-b0d6-d01d9872e606}} and pole masses in a consistent framework, the
implementation of a dynamical mass renormalization scale in the computation
of transverse momentum distributions of the heavy-quarks, as an alternative
to the static {{formula:492d6d12-2fd3-4028-8fd7-0377b5c420cf}} case, and the extraction of a top MSR mass value from the
analysis of state-of-the-art LHC triple-differential cross-section data,
previously used for extracting {{formula:c90cdcb4-7719-4870-852d-a7d40820ec17}} {{cite:c1ced3987b987bb0b6899bb8454f36de957babb9}}. The
extraction is done preserving correlations with the strong coupling constant {{formula:68bc4cc1-03cf-4284-aa6e-87b02f58f581}}
and the PDFs, fitted simultaneously to the heavy-quark mass.
| i | 1357c94d6e503ed75269a60e48ffaf34 |
To maximize spectral efficiency up to tens of bps/Hz and conserve energy, the researchers in {{cite:d016e652a131348a0854a320fc699dcff5898e49}}, {{cite:927636feedfec1ca7cb142d4e4c8172b75528fcd}}, {{cite:a953d776b28840089529e9d8592ad2cf5a3fd660}}, {{cite:b137b4472f300680f6505db2f3c904105bd864bd}}, {{cite:2c5c4e4f55e839ca2bc981cecedd54791f28edab}} have proposed massive MIMO with tens of antennas as a core technology of 5G. They considered using simple linear precoders and filters to mitigate the interferences in massive MIMO systems. One key challenge in commercializing massive MIMO systems is the estimation of the high-dimensional MIMO channel matrix. This paper focuses on the channel estimation based on practical channel characteristics {{cite:927636feedfec1ca7cb142d4e4c8172b75528fcd}}, {{cite:a953d776b28840089529e9d8592ad2cf5a3fd660}}, {{cite:b137b4472f300680f6505db2f3c904105bd864bd}}. Specifically, the authors in {{cite:927636feedfec1ca7cb142d4e4c8172b75528fcd}}, {{cite:a953d776b28840089529e9d8592ad2cf5a3fd660}} studied the downlink performance of the maximum ratio transmission (MRT) and zero-forcing (ZF) precoders while assuming either perfect or imperfect channel estimation at the base station (BS). The authors in {{cite:b137b4472f300680f6505db2f3c904105bd864bd}} investigated the uplink performance of the maximum ratio combining (MRC), ZF, and minimum mean square error (MMSE) filters with perfect or imperfect channel estimation.
| i | 5e1c150c394317594ea3dbfeee74c443 |
We benchmark PLACL on six keypoint localization datasets, including LSPET {{cite:b27fa1474193041074b7c18f8e3426433136402c}}, MPII {{cite:c3555bf26fbdfbfd611b74c4e59dd10949f978c6}}, CUB-200-2011 {{cite:f29ac8c80d927963c421493a52e86a69d31021d6}}, ATRW {{cite:f80a7f2c0c4ad62b0cbbc95ec95bd720278ed434}}, MS-COCO {{cite:6944280cd4c851d3ec7c135211ece8409907c806}}, and AnimalPose {{cite:adeddc0ea90f1570908d4820fd1c855a7385c9b5}}. We empirically show that PLACL is general and can be applied to various keypoint localization tasks (human and animal pose estimation) and different keypoint localization networks. With a simple yet effective search paradigm, our method significantly boosts the keypoint estimation performance and achieves superior performance to other SSL methods.
We hope our method will inspire the community to rethink the potential of PL-based methods for semi-supervised keypoint localization.
| i | 40ec3337ff996de4d309a91135d8cae9 |
Let us make a brief comment on the generalization to other topologically ordered phases. We also study the {{formula:56c179cc-9043-4945-b593-c152e2c6295c}} modified surface code on the book-page lattice {{cite:f0d6433073f36bb9d6675552a873c277df94369f}}. One distinction from the toric code is that one can design the model such that both of {{formula:34f19ca6-e33e-4f97-9dd5-b671d8c9c376}} - and {{formula:ae9eb5aa-5950-412a-a5ad-32b7acf5a310}} -anyons are subject to unusual fusion rules. Such a feature can clearly be seen in the form of the non-local entanglement entropy in the presence of the boundary.
We relegate the details of these arguments to Appendix. .
Also, by introducing a topological defect where some of the pages of the book-page lattice are removed, a single isolated Abelian anyon is bound at the dislocation. More thorough discussion on this defect and other types of defects such as twist defect will be discussed in a future project.
| d | 6c5028fd572800f5b19e4c3cd986e9a5 |
The literature on characterizations of strategyproof mechanisms {{cite:f4c8755472b52d3cd47d1a47859c015729565907}}, {{cite:c81ff3a924f0018434192d0d82c428ea51852126}}, {{cite:da04a5fca62881cc7ccc44835228ab93feee15b3}} for resource allocation problems belong to the line of research initiated by the famous Gibbard-Satterthwaite Theorem {{cite:7e2a2726a7a592bf67c37eb476fbba4fd04b0df0}}, {{cite:2d6dfec2239aab96b7feb06aacae53046d23713a}} which showed that dictatorships are the only strategyproof voting rules which satisfy non-imposition, which means that every alternative is selected under some preference profile. Several following works have focused on circumventing these negative results by identifying reasonable and natural restrictions on the domain of preferences. For voting, {{cite:ffeea4fcb14a48a34d9b8bd69e806365d911a03a}} provide non-dictatorial rules satisfying strategyproofness and non-imposition under single-peaked {{cite:09e3f0af51ed366e458460ba20e8a982a98c8b77}} preferences. Our work follows in this vein and is closely related to the works by {{cite:47dc9356492c4e00e614f3aa45a71c53bb2048dd}}, who assume that agents' preferences are separable, and more recently, {{cite:7d838ddacd35fcbced3bfaf33a44746513079f53}} who consider the multi-issue voting problem under the restriction of {{formula:dc17b471-fe8b-4729-be19-704db5bb808b}} -legal lexicographic preferences, allowing for conditional preferences given by CP-nets similar to our work. {{cite:68043b76f5d0e9c4ffc7205f04869532d53327b8}} consider a weaker and more expressive domain of lexicographic preferences allowing for conditional preferences. Here, agents have a common importance order on the issues, and the agents preferences over any issue is conditioned only on the outcome of more important issues. They characterize the class of voting rules satisfying strategyproofness and non-imposition as being exactly the class of all CR-nets. CR-nets define a hierarchy of voting rules, where the voting rule for the most important issue is fixed, and the voting rule for every subsequent issue depends only on the outcome of the previous issues. Similar results were shown earlier by {{cite:9e48d4d0f496d1b22c93e4c23234d0f2dc2fda45}}, {{cite:fdebd1bc08bd5cbb45a4fff0566902dff20a7a50}}, {{cite:fd04d1939c9fcbafc55f00364738db823f39cb4d}}.
| d | 86ee48e2a4ff5b2c3a9a2756db765e42 |
In what follows we will work on the space {{formula:1a04567b-f0ae-474e-a3fc-edb20de76a8a}} of real functions defined on an open set {{formula:1af886b6-1188-4843-8b4d-b8b3ddc4a5c8}} of {{formula:d0b59c1c-c306-402a-abfd-f4a651c86c30}} that we can assume to be the open ball {{formula:34d874d1-2007-4870-862d-9287ffc1e901}} . This space will be endowed with its structure of Fréchet metric space {{cite:43c0364c8201c13179a01330c44558277d00eef1}}.
| r | a00868f8bcbe0bb400b042defee4a3a8 |
We used the function defined by Eq. REF as a loss function. For solving the ODE system, we used RK4 scheme with step size {{formula:f4d3d23c-548f-4276-aca9-708301eda26c}} equivalent to a one-month interval. For optimization, we used ADAM optimizer with default parameters for all 3 variants of the proposed method. For NeuralODE part, we used the code provided by Chen et al.https://github.com/rtqichen/torchdiffeq
During training the proposed method takes a constant amount of GPU memory, independent of the time-interval over which the ODE is evolved by using the adjoint method {{cite:db54970b5f3af05ab64effa86a02654afb567a38}} for backpropagation. This allowed our method to be trained over large time intervals with limited GPU memory.
| m | db5315f1cec6571922161d7e30cd3cfc |
Another feature of using a cost function for NN training, like in {{cite:d83f074a0b5fa1e494819e8c21a8c431bc8014d4}}, we can fit the boundary condition or even the data as part of the objective, and thus, include two or more terms in the cost function.
For the data fitting case, this amounts to something like the wavefield reconstruction method {{cite:202dc3b1336a6faf116980d32b86e957f0f94218}}, which is also
solved in the frequency domain and faces similar challenges with regard to data and model sizes {{cite:bf5291cf1e21c3667b9e37e4c93f9f68e5db2b72}}. Thus, an important feature of such neural network wavefield solutions is the fixed memory requirements, mainly controlled by the architecture of the network. It is, thus, independent of the size of the gridded velocity model. As we saw, the errors associated with reducing the size of the network are not of the dispersion kind, like for
conventional numerical solvers considering the velocity model discretization, but they manifest themselves in smoothing the wavefield.
| d | 5c005fdbca36547a8ccb6ba89d7f17d1 |
We propose a Multi-Task Learning (MTL) method (Figure REF ) for this offensive language detection task. It takes good advantage of the nature of the OLID {{cite:7099710b8c5210ca1300acd176540d4be50ed711}}, and achieves an excellent result comparable to state-of-the-art performance only with the OLID {{cite:7099710b8c5210ca1300acd176540d4be50ed711}} and no external data resources. A thorough analysis is provided in Section REF to explain the reasons of not using the new SOLID dataset created in OffensEval-2020 {{cite:19b45dcf9559247b6ffa7c4e42001abd88a5a88b}}.
| m | a0f063c2eb038ef7af1f6d00f9d8f4d2 |
The formulation of gravity as a `double copy' of gauge theory has been remarkably fruitful over the past decade or so; see {{cite:f12c62deb3aa7c5bb8a6c95d9b86c9d4b3556dbb}} for a review. It originated in the realisation of gravity and gauge theory as low-energy limits of closed and open strings, due to the double copy relation between the respective scattering amplitudes {{cite:db6cbefd0ff8bbdda88b89e2c9582af244ce7c0a}}. Particularly after the framework of {{cite:f927a5fbeda47bd44a70ff39c4f52927390f5abb}}, {{cite:48f0ef08d268cf6df66fde3889c3e65ecf43280f}}, this general idea has been exploited to great effect to study a range of perturbative problems, from the ultraviolet divergences of supergravity theories to the classical dynamics of black hole binaries.
| i | 9705e25c16b34132106104d1bf9486f7 |
{{figure:9f52f4c0-3c10-49c0-adc6-4e51e2dbd28b}} ESPER consists of three components: 1) CLIP's non-generative image/text encoders {{cite:4e4837b9eab7c60739869b9ee509d98b181aea6f}};While we describe image modeling here, we also experiment with audio/text encoders, specifically Wav2CLIP {{cite:4baed9e2b56c8a6cbf4dda24cee2c723bb20d931}}, in § REF that extend ESPER to audio inputs.
2) GPT-2 {{cite:8708d822d0cd7fa34708047e0426cf0bed8009ca}}, a left-to-right language generator; and 3) an encoder that
projects multimodal inputs into the word embedding space of GPT-2.In principle, any models with the same APIs could be used, e.g., ALIGN {{cite:05e2af17e65127aada0da2c9d2f18a7052b88a71}} could be substituted for CLIP, or T5 {{cite:a030d612c34f15a908e7d81853e260ad95699b03}} could be substituted for GPT-2 During training, CLIP and GPT-2's parameters are frozen; gradients are back-propagated through the frozen language model to train the encoder parameters.
We employ reinforcement learning (specifically, PPO {{cite:2a7b078903812874fa2887b6b994eef9d8b026fa}}) to derive these gradients: the reward function is the similarity of the sampled generations to the input image, as estimated by CLIP.
After RL training, we evaluate ESPER in various zero-shot scenarios.
| m | 49a608142f1aa52095ad242d67096a57 |
Several mechanisms determine the morphology of the supernova remnants
of massive progenitors. Clumpiness affecting the shock-wave propagation
can arise from wind-wind interaction as observed in the supernova remnant
Cas A {{cite:f55e0e26a82655637189c2ac074f71c8a14aeac8}}.
In addition to instabilities directly developing in the supernova explosion
itself {{cite:cb58c2028694f33010bdd1e1750df38b973d0e7a}}, asymmetries in supernova remnants
may be a direct consequence of interactions between the expanding shock wave and
an anisotropic circumstellar medium. Of prime importance for the shaping of
supernova remnants is the peculiar motion of very
high-mass progenitors moving through the ISM {{cite:62bae2903301c80d27bc5d166b91cf11a8783cd3}}.
As an example, RWC 86 {{cite:8bd10fabc5eafe7b82eff077d8a60fe37ec1b1d7}}, {{cite:44f239382ec683f477b2f98310c6a6e9a9283c6c}} or the
Cygnus Loop {{cite:da91a1ecff794539661f7890d6cfb83365226561}}, {{cite:67fbb01db17108aae98c23b9729d8ce2ac293a3f}} reveal features
consistent with the typical characteristics of off-center explosions in
massive stellar wind bubbles, suggesting that they might have been produced
by a fast-moving progenitor, see also {{cite:7d36c560dadec6cf971cddd23147448d9ee56867}}.
All the numerous mechanisms, that induce deviations from sphericity in supernova
shock waves, can operate in parallel, providing a huge parameter space governing
the evolution of core-collapse supernova remnants. Explanations of
their observed morphologies are subject to degeneracies and alternative scenarios.
Runaway Wolf-Rayet stars constitute therefore the ideal candidates for the production of
isolated, asymmetric core-collapse supernova remnants {{cite:b624c359afb2332236f5d8a55dca7b98f0055471}}.
| i | 7bc5dce859db39c8714cf7268c0c81f7 |
An alternative paradigm for parameter setting are methods that modify the parameter objective function itself. Indeed, one can find closed form expressions for expected cost as a function of parameters in some cases, for example MaxCut at {{formula:07f53d5e-cdf4-412d-b1ab-11c5f71b0dd9}} {{cite:46487f2f7641fe2d697144311678ead3dfb3cb92}}, or {{formula:5234074f-0d8a-4011-aa03-267d64e042b8}} for high-girth regular graphs {{cite:1bce16f9ad82871d954825321584c1a10241dcd8}}. Moreover, when applicable one can take advantage of problem locality considerations (such as graphs of bounded vertex degree for MaxCut) to compute the necessary expectation values without requiring the full quantum state vector {{cite:6ffb5e19383a51e464005e090f98cb6c7720d020}}, {{cite:46487f2f7641fe2d697144311678ead3dfb3cb92}}. In these cases, then, one could optimize parameters with respect to these expressions rather than by evaluating the entire dynamics. Other examples of parameter objective function modification include using conditional value at risk {{cite:cb3698ead8cc16ed068b0887139ff7319bc042dd}} and Gibbs-like functions {{cite:097a0eda8af40a441436c9d0feb6a0bd44190f4b}}, which are closely related to the usual parameter objective function. Similar in spirit to our approach, recent work {{cite:14533a9d18d2035d0fabf52bed833f75cee3421d}}, {{cite:81026bdfef0985d64bd8d0daca1fe225b32c8165}}, {{cite:fd94e49f8231464c6163ba38dd05a008f78f13c5}} has proposed the use of surrogate models, which use quantum circuit measurement outcomes to construct an approximate parameter objective function. In contrast, our approach is a entirely classical, and the parameters it outputs may be used directly, or possibly improved further, given access to a quantum device. Additionally, a related perspective was recently proposed in {{cite:e0666ac1581c0eba10e1082994962a80e9364b43}}, wherein the authors study the connection between single-layer QAOA states and pseudo-Boltzmann states where computational basis amplitudes are also expressed as functions of the corresponding costs, i.e., perfectly homogeneous in our terminology. While {{cite:e0666ac1581c0eba10e1082994962a80e9364b43}} provides additional motivation for our approach, the authors there do not consider cases beyond {{formula:23aee24f-b180-4076-bcb8-3ba775a83447}} and so their results do not immediately apply to parameter setting in the same way.
| i | 7fd9aeaa261a4897065b1c1aab6b4c96 |
And we take the background chemical potential perturbation as zero for simplicity.
{{formula:089c9e39-06a1-475a-b813-baced5d598bf}} is the collision term, we will discuss it in detail in next section.
The collision term and the EOM of the background field are model-dependent.
Here we use the Higgs sextic effective model {{cite:36622bb79193f6f8f6d988267e786f26ed714d05}}, {{cite:d968a0305715bba580b8871719fd89035e938489}} as a representative model to give a concrete model-dependent analysis.
With the leading-order thermal corrections, the effective potential for this model can be expressed as
{{formula:e443afcc-d120-4c40-83f2-96cf04f233cf}}
| m | 9bfe8319d4abd09690fc511a02fe7317 |
Removing Cross-Entropy against the hard label from the loss function as done in AIT
could be a penalty, because some methods {{cite:d51149b66931daaf7dfb567c47ad0f189a8d7ff9}} rely on the sample labels.
However, as we demonstrated in sec:exp, AIT applied to Qimera was able to obtain significantly better performance despite the exclusion of the mixed labels.
In addition, our method does not depend on per-image hard label, so it can be widely used for segmentation {{cite:e7c26fe41d508ce1377f911eba29c6a9fef23e61}}, {{cite:05cb807ab1def1a4edc092f1d93b3b0a88f10f6e}} or object detection {{cite:585d8c9b99339d8028a8c9848a1749c877195e60}}, {{cite:14a49f45abdfcb537e5b2f71d28c292c2f447e00}}.
| d | bc90037a3e12a9c0dc8b9922d18c98c1 |
ALRC can also be extended to limit losses more than a number of standard deviations below their mean. This had no effect in our experiments. However, preemptively reducing loss spikes by clipping rewards between user-provided upper and lower bounds can improve reinforcement learning{{cite:a1913d77168e87b8d8201c9b665a10ad5e23afdf}}. Subsequently, we suggest that clipping losses below their means did not improve learning because losses mainly spiked above their means; not below. Some partial-STEM losses did spike below; however, they were mainly for blank or otherwise trivial completions.
| d | 326b59f56e4a6530119dd82b6a3b3eb2 |
where {{formula:c9ed466b-70e6-4084-a60e-441666f9e8f8}} is the restored image at the {{formula:080c6691-dd6c-4fa1-b285-f51c0aa58793}} th iteration.
In all examples, the {{formula:7db87b13-b414-4bb1-a977-b3f81347be02}} equal to {{formula:d50f57ff-f2b6-4e94-be5e-887739460c56}} is selected.
In the analysis of the proposed algorithm various tests including
peak signal to noise ratio (PSNR), signal-to-noise
ratio (SNR), structural similarity (SSIM), Feature Similarity (FSIM)
and Relative Error (ReErr) are studied. More information on these
criteria value can be found in {{cite:58fef8578b45c718d8303cf13d78dd7079419939}}, {{cite:891317128b1ed0f7e8d4580609af684927923f59}}, {{cite:9fde7b2764c88f062b8ea8a1fcd7be924776c3e3}}. Also ReErr is calculated as
{{formula:29f5ac89-0088-4aeb-b455-6bf34823df44}}
| r | e3e5fc37b41a33b324edc7a3a3e808e0 |
In terms of generalizing both the methods and scope of our approach, we first re-emphasize that parameter optimization for parameterized quantum circuits consists of two primary components: a parameter update scheme outer loop, and a parameter objective function evaluation subroutine. The inner subroutine is typically evaluated using the quantum computer. The key idea of our approach is to replace the inner subroutine with an efficiently computable classical strategy based on the assumption of Perfect Homogeneity. Hence a natural extension is to consider other efficiently computable proxies for the inner loop. For example, in cases where the problem instance comes with a high degrees of classical symmetries, the dimension of the effective Hilbert space can be drastically reduced, and so the evaluation and optimization of the typical parameter objective can be sped up significantly {{cite:c6d20010125f0621f15526ce205bd287002648cf}}. Similarly, different proxies may follow from related ideas and results in the literature such as the small-parameter analysis of {{cite:35ad86153124d0fed4b6cb428941d6e9ce39c3c9}}, the pseudo-Boltzmann approximation of {{cite:e0666ac1581c0eba10e1082994962a80e9364b43}}, and classical or quantum surrogate models {{cite:14533a9d18d2035d0fabf52bed833f75cee3421d}}, {{cite:81026bdfef0985d64bd8d0daca1fe225b32c8165}}. We remark that a promising direction that appears relatively straightforward in light of our results is to extend the analysis of {{cite:e0666ac1581c0eba10e1082994962a80e9364b43}} to QAOA levels beyond {{formula:ed941de3-bd04-4987-91eb-abd2f59f488a}} . Finally, an important direction is to explicitly generalize our approach to algorithms beyond QAOA and, more generally, problems beyond combinatorial optimization, such as the parameter setting problem for Variational Quantum Eigensolvers. Generally, it is important to better understand and characterize regimes where such classical proxies are most advantages, such as when the noisy computation and measurements of real-world quantum devices is taken into account, as well as to what degree undesirable effects such as barren plateaus may apply when such proxies are utilized for parameter setting.
| d | eb460b879c706ff79315630a3fcb4b23 |
Column Subset Selection and CUR Decomposition: In the column subset selection problem, one seeks a
small subset {{formula:bda6f623-3b7d-4f9e-8db2-a79f524498a0}} of columns of {{formula:cf018d3d-ccd4-450a-9118-ac585219e432}} for which there is a matrix {{formula:eb5871fe-baee-4c40-a705-5a063af399ad}} for which {{formula:f1cc5e4a-96c2-44b3-af67-fcb77f4a305b}} is small, under some
norm. The matrix {{formula:6070a336-b75b-4b29-9d80-06f8e4332226}} provides a low rank approximation to {{formula:7ee60f3c-86dd-46ca-b462-98c6c129aa4a}} which is often more interpretable, since it
stores actual columns of {{formula:8405b200-7c5b-48cd-921b-5f1a15f7fcac}} , preserves sparsity, etc. These have been extensively studied when
the norm is the Frobenius or operator norm (see, e.g., {{cite:de30e1e8dbaa1a71ef1297e3a8b562b0be526153}}, {{cite:d4f75395f3ca10209983ed25b9fb58ee760f811f}}, {{cite:47147bbc0661f2dc4b637a52c288473d053d5aa2}} and the references therein).
We initiate the study of this problem with respect to
the {{formula:c94a1450-a60c-4d18-a9a7-89b0689a3f51}} -norm. We first prove an existence result, namely, that there exist matrices {{formula:b297e32a-5fdb-4344-b9ca-53aa64af625b}} for which any
subset {{formula:103a4582-a8eb-4a28-8a09-79958c34f1a9}} of {{formula:fb973635-6fba-4925-ac0c-565624cc21c3}} columns satisfies
{{formula:8cbe1f0e-123d-49aa-a3b1-474c3d9b8d48}} , where {{formula:4555496b-42da-454d-a82e-940a0b4baca9}} is an arbitrarily small constant.
This result
is in stark contrast to the Frobenius norm for which for every matrix there exist {{formula:b5427253-8e0c-4b17-adfe-e1de167ba96c}} columns
for which the approximation factor is {{formula:f70ea397-7d7b-4ab5-a4a2-0742e38dbfe3}} .
We also show that our bound is nearly optimal in this regime,
by showing for every matrix there exists a subset of {{formula:749b5ebb-4854-4d2c-b857-53feb01de29f}}
columns providing an {{formula:3f4a3a4f-4556-4c2f-9e56-8c63f828bc72}} -approximation.
One can find such columns in {{formula:650d1d8c-0e11-4908-86c9-a4ee4bed1398}} time by enumerating
and evaluating the cost of each subset. Although this is exponential in {{formula:f810932f-e09f-41d3-8b26-fdfb492fed6f}} ,
we show it is possible to find {{formula:bcde5e6a-8251-412b-9e21-3e26e8de9989}} columns providing an
{{formula:04d0b29c-fa3d-4a9e-b6d6-5b284fcf45c8}} -approximation in polynomial time for every {{formula:d332c2e8-ed4c-4e95-b74f-741e85a9358e}} .
| r | fe0854a9222fbc668797c400b56eab16 |
Most of the works on Lnn has focused on relatively simpler particle-based systems such as springs and pendulums {{cite:f61d535d38f9ecde0e05be950e1b449e04f20467}}, {{cite:5f66d0071a97008bbc008f5b15eba7cb3c0e6d73}}, {{cite:a27747f1154b3ecd9de430a9d9e13bc252e72265}}, {{cite:895106eec2005cbd559faa1be4af105a7df415b4}}, {{cite:b8008a95a39c4b8efb97a2c24746a6b4c98110a4}}. This approach models a rigid body, for instance a ball, as a particle and predicts the dynamics. This approach thus ignores the additional rotational degrees of freedom of the body due to its finite volume. Specifically, while a particle in 3D has three degrees of freedom (translational), a rigid body in 3D has six degrees of freedom (translational and rotational). Thus, the dynamics and energetics associated with these degrees of motions are lost by modeling a rigid body as a particle. To the best of authors' knowledge, thus far, only one work has attempted to learn rigid body dynamics using Lnns and Hnns, where it was demonstrated the dynamics of simple rigid bodies such as a gyroscope or rotating rotor can be learned {{cite:5f66d0071a97008bbc008f5b15eba7cb3c0e6d73}}. However, the Lnns used in this work, owing to their fully connected MLP architecture, are transductive in nature. An Lnn trained on a double-pendulum system or 3-spring system can be used only for the same system and does not generalize to a different system size such as 3-pendulum or 5-spring, respectively. In realistic situations the number of particles in a system can vary arbitrarily, and accordingly, a large number of trained models might be required to model these systems.
| i | 741d914b7bc947b46b771ee8e7244201 |
In order to prove that {{formula:c9a3421d-56a3-441b-b6bd-3b270e477523}} is the trace of a Radon measure we refer to Lemma REF , and define the increasing set function {{formula:886fccb8-f62e-4867-8338-0ba77077f681}} as
{{formula:9c0a20a7-6060-4579-9988-b01281d711a7}}
By defintion of {{formula:955bf961-0a36-4159-b178-c262516ffd04}} , we know that there exists a sequence {{formula:c00edfac-b8c3-499d-9734-55101a25ecc7}} such that {{formula:775c5ac7-2ee2-4213-bbff-f1405a95b784}} in {{formula:15c8b76a-553a-4325-93a0-1b3898efa2ea}} and {{formula:ecd39380-82dd-4450-8ea9-f78326eb162f}} in {{formula:f7941c7e-b791-41e8-b46b-3eee2478198c}} such that
{{formula:d129e1ec-6daa-4f22-8659-d07204d015cb}}
Next, denoting by {{formula:c992c630-ff70-4520-86cd-8d3e8a926848}} the measures {{formula:e2e0021e-eca0-452d-8f37-ccd56da7015f}} , it converges weakly * in the sense of measures (duality with elements in {{formula:9461f5fc-b858-4ab3-b6a3-43a8bfca97a8}} ), up to a subsequence (due to the bounds) to a measure {{formula:ec9c8cc4-3a4b-4eae-8a43-f46484e76670}} .
Now, due to the lower semicontinuity with respect to the weak* convergence, we have
{{formula:db3fde52-1bce-4c1f-a92b-f4eae6083207}}
Then, by the definition of {{formula:c25d4cd1-1249-49a7-bf32-fc591feff619}} , we have, for every {{formula:67725ebc-df41-41cc-8931-ac47bc305948}}
{{formula:ef6d6724-0b85-4459-ae09-d44242ad7bde}}
Now by the previous lemma we would have that {{formula:5f8dfe1a-bb80-4b5e-b875-b8432dcb2aae}} if we prove inner regularity and subadditivity for {{formula:29c8df05-97cb-4bb5-9141-402df7729be3}} .
For what concerns inner regularity (i.e., {{formula:ac5f06f4-7fe7-4e18-bfa9-8147dcfe60fd}} in Lemma REF ), it follows by Lemma REF and {{formula:21834dd6-3ac4-4f57-91cd-aaecb0e412b8}} . Indeed the growth condition from above and an argument similar to {{cite:4a9ae71a1b0ac9739053d842eacf4585ca741418}} guarantee that
{{formula:c9eb9f10-de0c-461f-8dd8-963a7b2aac2a}} . Thus the inner regularity of the upper bound measures provides inner regularity for {{formula:3214208b-1f8a-4f16-bf69-ccd1fbdbc18c}} .
Indeed one can extend {{formula:28092edc-3c91-4bcf-af23-553d839e2bc0}} and {{formula:7eca9ac4-3951-4092-81b1-f5542ac2ceca}} by zero outside {{formula:797a5ada-8daa-4ee0-8f9e-03027667a6f2}} , thus obtaining elements in {{formula:3d4f0476-ecc1-4c88-8b83-a9bd93b842ec}} and {{formula:c4591bf4-715b-4006-a05e-b191e8e755b9}} , respectively.
If one first considers an open set {{formula:0d0d7cf3-0daa-479f-ba84-5391d782b1fd}} with Lipschitz boundary such that {{formula:795964f9-602b-4004-aab5-ff757530f251}} , then one can take a sequence of standard mollifiers {{formula:ef8040c9-8d91-4a91-be27-a3c647a3ae87}} such that {{formula:305cfa80-3cc2-404f-9402-39c25a7df5da}} in {{formula:d43d930c-05d5-4ff8-aaea-da96b2c8657d}} . Moreover since {{formula:2c10d292-f3d9-4620-9531-133c07adc82b}} , we have {{formula:aa0e53ca-f4b4-4dd9-9f97-0f644f31ff6a}} , thus, taking {{formula:2e93bc1f-7664-4ea4-9333-be9327d7c15d}} as test function for {{formula:0ea68314-cb00-4195-87a5-00da4610d838}} , and using Lemma REF , we have
{{formula:9134120b-1720-4865-a771-a5129bf5e421}}
If we take an element {{formula:0c65e86e-5ea6-4065-99f4-b7447a30e766}} which is open in {{formula:9ea52a38-1c8f-45db-8c85-b8e757559ebf}} , then, for any {{formula:aea829bb-a765-4799-958d-60c4c03195f6}} , arguing as in {{cite:9cb6c96dd094ea987133e43cd79e80648a647bcb}}, we can find another open set {{formula:1ec51b87-30bd-43a9-ba36-4e3e680b1d4b}} with smooth boundary, such that {{formula:3f9ea6fa-5f5f-4e6d-950c-ba3b0a0a09d8}}
and
{{formula:77c4d61d-f8a2-41ea-9e2f-4df0170fe278}}
Moreover the set {{formula:e020071b-a273-45bc-8d83-e900cfaabf72}} itself can be chosen as a subset of {{formula:5bff50a3-a524-4259-a4d9-4964d5611023}} , in this case the proof develops in full analogy with the one of {{cite:4a9ae71a1b0ac9739053d842eacf4585ca741418}}, and the estimate (REF ) holds.
On the other hand, if {{formula:5cdab60f-4dca-4e84-8402-754a67fc4518}} is only open in the relative topology of {{formula:cf0e7893-c74c-43c6-a7cb-ef3b65e1ce0d}} , i.e. it has {{formula:03a0bd8d-07ba-469e-ad4d-5e838d078124}} , then the same arguments in {{cite:9cb6c96dd094ea987133e43cd79e80648a647bcb}} allows to construct a set {{formula:4905afaf-1ea8-4bcf-ac26-bb216351a9b1}} with regular boundary, with {{formula:2f3d9a04-baab-476c-b435-f21cb5b215ce}} open (as a subset of {{formula:f4f89513-6e24-4f22-801c-c1aa38fc3def}} ), {{formula:e86615e3-40c6-48e1-adec-3f2b814e7a7b}} , and such that (REF ) holds. One can construct a family {{formula:60301e7b-f4d0-4efb-86cc-2bcf84e9016f}} , of sets, invading {{formula:2713c43f-acff-400a-be4f-bfd40aed6180}} as {{formula:046ed591-94fa-4594-ae6a-dcb58702cc79}} , open in the relative topology such that {{formula:bdf4ac3e-3a49-48f7-a4e8-d1481333ee46}}
with {{formula:5d7383fa-70b7-4824-a893-7d914505303c}} . Moreover one can find a {{formula:c3e513dd-e0ba-435d-a4b6-9758683c9956}} such that {{formula:49a0581e-def7-421f-8344-35f88ea59cea}} .
Then, exploiting that {{formula:61cbe0b1-c5e0-4160-817a-113b8c362f66}} is an increasing set function, we obtain the estimate
{{formula:5b7cf1cd-31fb-462f-afd5-153290ded8f1}}
The arbitrariness of {{formula:c77c58cd-cca8-4295-9c5f-6af783d3da72}} gives the inner regularity.
It remains to prove that {{formula:3b25f266-51e5-4df2-aed2-cf59b9fef29c}} is subadditive in the sense of {{formula:1abb6cb5-7a7d-4bb0-9e8f-b1377eac39bd}} in Lemma REF , i.e. it suffices to prove that
{{formula:632debab-0efd-4a1d-b628-78976caf2c90}}
for all {{formula:69a37104-cd76-4f18-993f-bc8953bf16fc}} with {{formula:f51ad182-be47-4ead-839a-c62fe99bdba0}} , {{formula:f9a09786-c41f-439a-9b08-14eb2c9cc4e0}} and {{formula:7108384e-f072-40f8-99f9-485097a9f413}} , (see e.g. {{cite:65cc2e58d001263e070131621a767e374c26999b}}).
Without loss of generality, in view of Proposition REF , we can assume {{formula:e07f9449-350f-4ab5-b84d-d394e1759e93}} convex and {{formula:34853a7b-ca15-471d-87af-fcde434b7935}} quasiconvex.
Fix {{formula:67c16c0f-4b96-4354-a3ff-07c8b71e1711}} and find {{formula:c10154eb-f9c7-4eca-9d10-fe5c4c431857}} such that {{formula:9f5a69af-d187-44fb-835c-69573cff5719}} in {{formula:4890b3cf-86a1-413d-a1d0-72104ecd3978}} in {{formula:ef307206-b59d-42fb-aad3-cd6f9d1f295a}} and
{{formula:7b931526-ee60-4197-8f60-79eb09300a05}}
Extract a subsequence still denoted by n such that the above upper limit is a
limit.
Let {{formula:a186d81a-a07f-45ed-a85a-e40c001e37ed}} be a relatively open subset of {{formula:9ce3b675-9692-4214-b9b9-1a01e5f65d10}} with Lipschitz boundary such that {{formula:5c969400-2aea-4314-a1bf-a521e841edaf}} . Then there exist {{formula:a990e66c-9a51-4fea-bf57-ed94c7a26dfe}} and {{formula:117540cc-416c-478b-85e0-18b823dabe05}}
such that {{formula:9e81f49d-250e-4925-9eaa-4833cbe1797c}} in {{formula:b43b602d-0a55-4b81-bf8c-d3977ef81cb1}} , {{formula:f48ba3b9-724f-48de-9bed-c84b1afe4b83}} in {{formula:0cdbe746-740e-4a18-b650-eac7b67bc9f9}} and
{{formula:a351b4e8-9f6d-4d69-959b-f594a6745c8d}}
Consider, for every {{formula:3be932d6-347c-4672-b499-da3c51d6e6bd}} the set function
{{formula:a461ae29-1893-4671-85bf-2814bf2df375}} .
Due to {{formula:cab3ec87-64af-4592-8a57-df69aa41b6ac}} , we
may extract a bounded subsequence, that we will not relabel, from the sequences of measures {{formula:94623e2e-655c-47f0-a651-d25a1f0af5fd}} restricted to {{formula:3707d985-2c2f-4d2e-8711-6227a2722bc0}} , converging in the sense of distributions to some Radon measure
{{formula:49c0c53c-55c5-4b76-bc14-a6346c54f252}} defined on {{formula:dfa04e84-e45b-46af-9c6b-7330f2776103}} .
For every {{formula:d60c8b60-0369-4ca6-9dfb-efdb4b4205f8}} let {{formula:28e10ed8-39fe-47c5-b140-47572f7679c6}} . Define, for {{formula:43a301c9-3226-4ad0-95df-4e5b9e79b15d}} , the subsets {{formula:e9220b31-d43e-43eb-beee-ce0e048f2b46}} . Consider a smooth cut-off function {{formula:aff26a79-1ce3-4f70-95a6-349b13fbceb1}} such that {{formula:beda2aff-07c2-425c-b679-bfa82ef1d568}} on {{formula:58d7c47b-2d8e-4ca4-8fd5-bd8d5d98142c}} .
As the thickness of the strip {{formula:0494b033-17c3-43a9-911f-ea0baffeefe8}} is of order {{formula:f7371418-51ff-42ce-bee2-66f8e33058f8}} , we have an upper bound of the form {{formula:6876b68f-33ee-4ff8-b77b-1a4d46fd5896}} .
Define
{{formula:db1935be-5ee3-4426-bf1d-77f548274f63}}
Clearly the sequences {{formula:dca4fa17-86a2-4428-8eb9-b6b86b4ec291}} and {{formula:68d0c3f6-030b-4ecb-a4a5-241a36716f7d}} weakly* converge to {{formula:71dd5903-62e4-4bde-81c0-f8f36e6f191f}} in {{formula:c0e1f99f-4ce4-4425-9442-d292d2a6ae6c}} and to {{formula:92db266a-8b89-4172-bc89-844c033c3129}} in {{formula:5b70293a-9386-4fc0-9dc4-9439656e953c}} as {{formula:892af0ac-909d-42aa-b444-bc35d5bd2ec2}} , respectively, and
{{formula:ef542dc2-cf8d-421f-93e3-9e817195ad6f}}
By the growth conditions {{formula:1c74f3cc-4f44-477f-881d-61d977cd9e41}} , we have the estimate
{{formula:cfb092a3-9c20-42f2-bda2-1cca9997835b}}
Thus, passing to the limit as {{formula:eb3df9b4-d3ac-4d9b-8215-eb5ed98dc87a}} and making use of the lower semicontinuity of {{formula:1f6d08c0-6436-4ca6-a374-e3742e1273c8}} (which is a consequence of its definition (REF )), (REF ) and (REF ), we obtain
{{formula:86b0983d-d462-4891-827f-1100c4eb9885}}
Now passing to the limit as {{formula:1c7ca07d-801f-4af5-a4c7-6943ef3acc7a}} we get
{{formula:7207601f-fd3d-49fa-9463-8011c31c6546}}
It suffices to choose a subsequence {{formula:1728798a-c19d-48e7-ac39-0137aaa2736a}} such that {{formula:48b90567-0144-4e16-a5bf-2b0f2d078d89}} and {{formula:213cca42-2666-4913-be7b-ab54ead81009}} , to conclude the proof of (REF ).
| r | ba0697025854397987e91a90a2470333 |
Note that in general {{formula:52c5ee2c-5d78-4add-b71a-05a35ca8b5e0}} .
A way around this problem is to choose a space approximation such that {{formula:5be7f89c-c997-4033-91e6-c954e77fc4c0}} , such as the Scott-Vogelius mixed elements
(see {{cite:2b6f76ea4a71042365586a8ed224ded94c8900d7}} and {{cite:77c6e81a91bcc7e6943476e3dde03c6d423e19ee}}).
This particular case yields a better approximation. Indeed, on one hand the pressure will not appear in the upper estimate, and on the
other hand a different localization will provide a polynomial error in the case of an additive noise.
| m | 4153906f6bc6f33f3b83e325d4200447 |
In this work, we have presented a rich generalization of the hardwall model in ten dimensions, by introducing a full DBI action in the 10D-2B supergravity action to model the quark degrees of freedom. Working in ten dimensions allows us the possibilities of changing the compact part of the 10D-spacetime from {{formula:12761748-3920-4b61-a42c-ad10ef868c5c}} to other scenarios {{cite:076d719058d7f44665c06b14d9c22ba1cb467a16}} which are closer to QCD. This potentially enables a systematic exploration of universality classes and features in the phase diagrams. Using the full DBI action has the consequence that the quark degrees of freedom see a different effective geometry given by the open-string metric {{formula:62e2a704-68f8-4496-a661-572fbf533982}} which depends on the shape of the embedding {{formula:2b76ee84-1fec-45fe-92dc-83277cae5fe9}} . This shape degree of freedom allows us to describe the phases geometrically and can motivate searches for other natural brane embeddings including polarized branes as arising from the Dielectric effect {{cite:8596dbf642cce4b3edb320b486ce60c8c450aae6}} which are likely to be important at finite densities {{cite:3d38d655f8594b8f67099209944e9d802224ccee}}. Finally, our model is significantly different from all previous work in the introduction of two distinct cutoffs for the DBI and the bulk gravity parts of the action, the sole exception being the recent work {{cite:a86670f4fd51777204b044f5e0ada1038d6da211}}. This is likely to be a key advantage since complex back reaction and Non-Abelian configurations deep in the interior of the bulk can be hidden behind the IR cutoff. Nevertheless, the effects of this interior geometry can be incorporated by suitable IR boundary conditions which can be fixed by using experiments as illustrated in this work.
| d | 014bc1d37bb98211ab461daa1e591b04 |
ADMM requires every node to transmit at each iteration,
so for ADMM the total number of transmissions scales directly with the number of iterations needed to achieve the desired accuracy.
[rgb]0.00,0.00,0.00Note that when ADMM is applied to linear regression,
it is possible to optimize the stepsize for different network densities
{{cite:ffc8b60f76ac2225293dd780905b079daab22152}}. Here we continue to use the stepsize from Fig. REF which was suggested in {{cite:d7d802d49ccc43cc80c3184cb7dfae07e7ffdaeb}}.
Fig. REF shows that, for this range of densities, OADMM is less sensitive to the changing network density and generally saves more than half the total number of transmissions.
{{figure:f1682e56-d826-4040-b7cc-45db14624136}} | r | 9e4e03d728a41df3d705d4a886db5061 |
Note that a Markov chain is uniformly ergodic if it is irreducible (i.e., possibly gets to any state from any state) and aperiodic {{cite:6da3eb1da2771ae23b71f09ba8dbedcf67187c4e}}. As for any {{formula:7c754816-bf36-418e-a003-2f988655191f}} , {{formula:382b7406-e439-491c-aee8-0e3ca5ae1d78}} is the optimal policy for the entropy-regularized MDP with the reward {{formula:390d00e4-5707-43c4-bb4a-407c240f60cd}} , and is therefore a softmax policy {{cite:c42f89cadd90ebfca675b101c66a7e395de007d8}}, which takes any action with non-zero probability. Therefore, Assumption REF can be easily satisfied in practice.
| r | 28f6721f939c1887904146f94d020cde |
As already noted, one can casually state that three dimensional gravity is all about the choice of boundary conditions. More precisely, the specification of boundary conditions is pivotal in comprehending how a theory that (locally) admits only a single solution. This analysis was first carried out by Brown and Henneaux {{cite:979f274b5d69134cbbe7da680d646222719af645}} in their famous paper. Their study has also been encouraging to propose new sets of boundary conditions by sparking a vigorous research area which has gained in breadth over the years modifying {{cite:a45b1bf6e679bf2254851a8ab41394e8978c068e}}, {{cite:729e4f84a2aea6c37408c83e8010b96636e44a05}}, {{cite:6bb73ba085c081d35af94695827f4021ddada3b1}}, {{cite:1629f9d6467a2e0906ef487aca0a13fb62f9d870}}, {{cite:67f3973d300efd1b875dcf64503dde3105cc043c}}, {{cite:842312fb8b9261f17bfb2bd7c10409fff8a4fc16}}, {{cite:2d9d284191c15002a45a1a6bdd83f29002def633}}, {{cite:eb6f965a44d25be6635b7ecabc1464927cc95697}} and generalizing {{cite:73411160c53580cf7437cfbacde5306cb581e39a}}, {{cite:2b008ce48a6d2268b0efe673fe9c330cd8092654}}, {{cite:3a973a74d95e4531fa1ca585df8093b0b5d01125}}, {{cite:cb4a5ca55a7be9faf8e27e61f35ab76116087ab6}}, {{cite:22ed656dca601e234d383461f7c0ccd4400f3bf2}}, {{cite:5b560e4c30f52d26a194486ab5904e8470e5e0a7}}, {{cite:fd210d139c731c69ab763f08e8262e0199f29eae}}, {{cite:affd4fdcd4049f9d91b19623bcb36b9666b51393}} these bc{{formula:bf3b29fe-60d7-41ed-91d7-f3559986cd12}} s. In {{cite:a45b1bf6e679bf2254851a8ab41394e8978c068e}}, Grumiller and Riegler have considered the most general {{formula:56662eb2-dcc7-4cd9-a059-8b0a59fb96a9}} boundary conditions, as a consequence, they have derived the asymptotic symmetry algebra consists of two {{formula:c7d9f47e-bbbe-4b3b-8f9d-a3faf317b673}} current algebras. Furthermore, they have recovered all other previously found boundary conditions, imposing some certain restrictions to their most general boundary conditions. It is pertinent to address that there have been several papers recently inspired by them, i.e.,flat space {{cite:375b9aae3a622989a5805f79747a09fc0e8d1020}} and chiral higher spin gravity {{cite:63c1c77bd00c96afa305e4b50958e6bfb0640bbf}}, which is shown a new class of boundary conditions for higher spin theories in {{formula:530f653c-eccb-4c25-9774-f99172b0a566}} . The simplest extension of Grumiller and Riegler's procedure for the most general {{formula:10fc582a-4308-40fe-b11a-5a28b52e3508}} , and {{formula:dbc7f419-b192-4213-8901-07001409c8b6}} extended higher spin supergravity is introduced by Valcarcel {{cite:a40f571a466e16256ede3400d65d3ede470e1bc5}} where the asymptotic symmetry algebra for the loosest set of boundary conditions for (extended) supergravity has been obtained. The most general {{formula:999c62e0-3683-4275-a460-b499f0f1cf3d}} extended {{formula:92ea3e3a-fab2-49f4-a4c6-78eff8e120cc}} higher spin supergravity theory has been similarly presented, including further {{cite:615651fa7baf5070a01c6b7f206bfe3a4f850cab}}.
| i | 05369d86929bbb98ed8702f3aad9c17e |
Source separation of acoustic signals is a long-standing problem where the conventional approach for decades has been to perform beamforming using multiple microphones. Signal processing-based beamformers that are computationally lightweight can encode the spatial information but do not effectively capture acoustic cues {{cite:a388ab75e0b26d2c263fe20de22b479b5e2b715f}}, {{cite:7d982e7b3a8a57f243081bbbd6d605cd5b8b8dcb}}, {{cite:2dfec7d1717c8a4db56d02468a1c15504e1713f6}}. Recent work has shown that deep neural networks can encode both spatial and acoustic information and hence can achieve superior source separation with gains of up to 9 dB over signal processing baselines {{cite:e2c7f9fc4701cf83c1c0d2a764f0d060591ae3cf}}, {{cite:9988c88189423bd6e5df6eeec3b7b57c41bd3dcc}}. However, these neural networks are computationally expensive. None of the existing binaural (i.e., using two microphones) neural networks can meet the end-to-end latency required for telephony applications or have been evaluated with real earbud data. Commercial end-to-end systems, like Krisp {{cite:6d476706cb4a78bc64c5145fc53cb95f53319c65}}, use neural networks on a cloud server for single-channel speech enhancement, with implications to cost and privacy.
| i | 37e78a5f29fb78366d65369585266d9e |
The GQME formalism provides a general framework for deriving the exact EoM for any quantity of interest.
The derivation begins with the Nakajima-Zwanzig equation {{cite:d3608f34b832ad9c20ceb79378b80f0c2b739328}}, {{cite:0397e29996037b84102cc98a87549fe500c64aec}},
which describes the dynamics of a projected state {{formula:ee2963bb-1f9e-4f49-b9ec-75b92d6037dd}} , where {{formula:4ccc51cf-1481-4e5e-a68f-a7fb26098c60}} is a projection superoperator and {{formula:dfb2a7a6-ff26-4f7a-93df-569bbb6ec31b}} is the density operator of the overall system:
{{formula:2130df8b-6493-4078-99fd-2fb0284c1c2e}}
| m | 1728444dba48ecb6501b2b2588222373 |
As a demonstration of our analysis, we look at the generation of a small 4-qubit tree cluster made of finite-energy approximate GKP qubits, tracing the first few steps of the protocol followed in Ref. {{cite:e34a47d7c9082e9cc512cec10f3117fa6604617e}}.
The protocol is described step by step in Fig. REF .
While the analysis in Ref. {{cite:e34a47d7c9082e9cc512cec10f3117fa6604617e}} tracked the individual quadrature noise variances of mixed state GKP qubits, our analysis with truly finite energy GKP qubits tracks the full covariance matrix of the Gaussian error wavefunction of the graph state along with the mean displacement vector. This work thus provides a more accurate analysis of the errors that are introduced during the graph creation from approximate GKP qubit pure states due to (a) the finite-energy approximation, and (b)
homodyne measurements that are part of the graph state generation protocol. Since the 4-qubit tree cluster generation as per the protocol involves 1 steane error correction and 1 fusion operation, there are 3 homodyne measurements. This results in a total of 8 terms in superposition at the ouptut, which correspond to finite-energy GKP qubit graph states whose error wavefunctions {{formula:44cf6d63-ef2e-4c85-a482-52ef775006ee}} are given by square roots of Gaussian distribution functions with identical covariance matrices of the form in () given in Table REF , but with different mean displacement vectors, as tabulated in Table REF indexed by {{formula:1dfd1847-7903-4120-818d-e338c3ddf92c}} . The total error probability, i.e., the norm of the weights associated with all but the term corresponding to {{formula:71e327d6-3ba8-46e7-9717-2a847e617369}} in the superposition, averaged over the outcomes homodyne measurement outcomes in the Steane error correction and the fusion, are plotted for the 3 types of fusion in Fig. REF as function of initial GKP-qubit squeezing variance {{formula:d297c3a3-f73a-45e3-9f8a-2b7130077518}} .
We observe that the error probabilities with all three Fusions converge in the ideal limit of small variance, while at larger variances Fusion C results in marginally lesser average error compared to Fusions A and B.
The error probabilities can be further reduced by considering post-selected homodyne measurements as part of both the Steane error correction and fusion, as discussed earlier in Sec. A.
| d | 6c848702c5ed277961f3e5c3e007512c |
The dashed orange and solid green lines in Figure REF explore two different scenarios matching the Th and Eu trends simultaneously. The dashed orange line still assumes one prompt r-process source and a constant yield for Eu, but assumes metallicity-dependent Th yields where Th is boosted by a factor of 4.5 at low metallicity relative to high metallicity, with a continuous decrease between {{formula:fe311908-2472-4de0-bc90-ab01e044d480}} and 0.02. The solid green line, on the other hand, combines two r-process sources — neutron star mergers with long delay times, and exotic SNe or collapsars with short delays (see also e.g., {{cite:d9db697ac1cee77681fb84a7fb95ad1980752300}}, {{cite:38d5d037fccfc1aef9fff4694cde554fe9a735f4}}, {{cite:b066911afbf84baa37fa910cedfac0e8b231adfd}}, {{cite:c4b1e12626d78f7fd286bb88b47e95b3b53727c2}}, {{cite:8d5cb82b4724436d2d7945ee10ce3c87dbcb42ac}}). In this case, Th and Eu yields are kept constant as a function of metallicity for both sources. However, the frequency of the short-delay source is assumed to be metallicity dependent, such that its rate is three times higher than the long-delay source at {{formula:c7e6f242-4b5d-4c5f-9837-73b3536d06be}} , and becomes negligible {{formula:bc7f7e1a-1127-4be4-baed-ecd3427c7d2b}} . Such a computational experiment would boost the Th production at low metallicity as we may expect. A type of exotic SNe that would fit these assumptions are magneto-rotational (MHD) supernovae. MHD supernovae were originally proposed as a source of a strong r-process {{cite:87921247b70fdc85c49bf28eb69b28a3298952f4}}. However, it was later shown by {{cite:a9997fa656aa3c6e55ec7dc7a03402e6284a1b38}} that a strong r-process can only be obtained with (unlikely) very extreme pre-collapse magnetic fields, which are required to eject neutron-rich matter stemming from the electron capture during the collapse to high densities. If sufficient rotation exists also weaker pre-collape magnetic fields can be enhanced by the magneto-rotational instability (MRI), lead to a successful explosion and a highly magnetized neutron star (magnetar), but during the delay encountered before the MRI had its impact, neutrino absorptions enhance the electron fraction and limit the reach of the r-process. On the other hand, black-hole accretion disk outflows can lead to highly r-process enriched matter with {{formula:fcd33b54-c702-4271-b289-48769eb1fe02}} -values in the ejecta just in the range leading to an actinide boost, as observed in many r-II stars {{cite:8d5cb82b4724436d2d7945ee10ce3c87dbcb42ac}}. As the collapsar behavior leading to black holes requires the core-collapse of quite massive progenitors, their frequency is expected to be much higher at low metallicities. The reason is that low-metallicity progenitors have lower opacities, experience - as a consequence - less mass loss during their stellar evolution and possess at the point of core collapse significantly higher masses, favoring the collapse to a black hole.
| r | 9da3ad96ae0336e653ab783fcab11f85 |
However, our framework avoids several of the limitations of the linear control framework {{cite:6e3411d842c99ad9de781783bede2bfeb0d1eca5}}, {{cite:912a1947d1d89a6a2e06b76755b72b68c332b8f8}}. First, it was possible to identify nonlinear equivalences between algorithms. Second, by considering just the Koopman eigenvalues, it was possible to identify (semi-)conjugacy, unifying the several different definitions of equivalence introduced by Zhao et al. (2021). Third, it was possible to identify equivalence without the underlying equations. As long as a sequence of outputs from the algorithms are available, the Koopman framework can be used, making it especially useful in the case of proprietary software. Fourth, it can be used to distinguish between conjuagcies with different properties (such as local and global conjugacy), an important distinction when comparing algorithms. Finally, this was all possible solely by viewing algorithms as discrete-time dynamical systems. No additional considerations, such as control, were required.
| d | a0da32fcef511ea012bc96a4f4bfedf9 |
In addition to be applicable to multicellular aggregates, one can wonder if similar instabilities could arise in vivo. During development, transition from solid-like to fluid-like tissue properties, tissue surface tension, and flow patterns have been shown to play a crucial role (see, e.g., {{cite:6076ff9b92daf90a4aa53f07bc67a2339a1a357a}}). Recently, three-dimensional aggregates of mouse embryonic stem cells have been shown to undergo a first morphological transformation from a spherical into an oblong shape during gastrulation, associated with a reduced level of E-cadherin expression at the developing tip {{cite:6601e5563c2dd3ace40401b9cf7206705f484777}}. Such shapes resemble a superposition of instability modes such as {{formula:5a7a7733-e3c6-429f-893c-c99fcceb4770}} and 3, and potentially higher, as illustrated in figure REF . Interestingly with respect to our current study, the polarisation of E-cadherin expression precedes the onset of tip formation, and when the level of E-cadherin expression is maintained high, the aggregate remains generally devoid of any pole {{cite:6601e5563c2dd3ace40401b9cf7206705f484777}}. These observations suggest a role for a reduced surface tension in the development of the protrusion, similar to what we are proposing here. However, in these examples, and to our knowledge more generally during development, it seems that an original inhomogeneity in the tissue rheological parameters—such as surface tension and viscosity—is at the origin of the shape formation. Such inhomogeneities are however absent in our proposed mechanism, which relies solely on the presence of a permanent flow of duplicating cells.
| d | 2f5ee5c170d7f634c687d1aedb3cdd39 |
Although the DEIM index selection procedure is basis-dependent, if the interpolation indices are determined, the DEIM interpolatory projector is independent of the choice of basis spanning the space Range{{formula:4298838e-e755-4ea6-940c-275a5cfa312e}} .
({{cite:405f2715eae181b1813d020ca96a844241f8a4ed}} ).
Let {{formula:b07891c8-1b6a-488c-8116-f1b670110c1d}} be an orthonormal basis of Range{{formula:18d887ac-f02d-4b6d-86ba-2495e4810dd4}} where {{formula:fd575923-c73a-4b61-b778-df53f27f6978}} for {{formula:ad7c8c0c-7538-4982-9e69-19a26c9bb0ec}} , then
{{formula:8e7c51fe-543b-4cc5-8b71-794e2af0c759}}
| m | 2b1b8121e4bddcf89d2a11f4a8a462c7 |
An intriguing finding of this research is that we provide an empirical realization of a new central-limit theorem (CLT).
In the usual CLT, the addition of a large but fixed number of independent identically distributed random variables (with finite variance)
leads to a normal distribution, whereas in the generalized CLT the limiting distributions are Lévy
distributions if the added independent variables have infinite variance {{cite:8d1f61e60a0e3cc01794f5ae6186022e0851a67b}}, {{cite:0704f5d3bd92569214fcd1969ed7d20fffc7c7df}}.
Here we have an empirical distribution (fitted reasonably well by the gamma distribution) that is invariant
under addition with rescaling, not being neither normal nor Lévy.
So, neither the usual nor the generalized CLT is fulfilled.
The reason of this discrepancy, is, of course, the existence of strong dependence between the added variables.
To be more concrete, if we double the width of the cells
(and this {{formula:910401e7-b249-48b4-8234-cdc85b7b1f78}} transforms to {{formula:6c5d5490-ef56-4e6c-9612-64c15df4eed6}} ),
the resulting number of inhabitants is the sum of 4 realizations of {{formula:a71c97b5-2ae4-49a3-9d6d-1f29c5ec7fc7}} at the small scale ({{formula:3d9690ea-b017-444b-a6a5-a203abda272e}} ).
The new {{formula:ed5c68dc-87ae-4c69-af0c-4a01772def55}} has to be rescaled as {{formula:4d75a411-e795-4f4a-8ac0-9722b07547f2}} to yield a “stable” distribution, which is a highly nontrivial result.
| d | 3c9ccd4ce41b29dc93a011961a4edda4 |
We propose our framework for fair inference on outcomes which are measured only through error-prone proxies. To clarify the framework and make it more comparable to earlier work, we use the running example of health risk score prediction from {{cite:8a9826df53201c65d9f0bef3e14431d995d5abb8}}. Their healthcare data set contains several clinical features {{formula:1075f37e-e798-48e2-ab2d-e74cefd5231f}} at time point {{formula:43f93bd7-95d6-4b59-9e88-1995bef445aa}} (e.g., age, gender, care utilisation, biomarker values and comorbidities) which are used to predict healthcare cost {{formula:e786ea2d-fd11-4869-949a-b4581d1d254a}} at time {{formula:2cfcca29-b4b1-40e8-8729-19a1412cf12c}} . In addition, the patient's race is the sensitive feature {{formula:5b928de9-0bb5-4e19-a788-289d0222d02d}} , coded as {{formula:dbda9a63-8930-4693-8d2d-c7b3f0315775}} for black patients and {{formula:59b74bd6-0e0c-4a7e-9b90-a44e2dfd1a7b}} for white patients. The relations between these features are shown in panel A of Figure REF .
| m | bf95b2a403bc4e09f403269055d87850 |
We follow the simulation setup used in {{cite:86eb47107d4c32730a119174055f25af166f2c8a}}. Specifically, we consider {{formula:4460c4bd-69be-4b4e-8b08-5730f86a20a3}} single-antenna APs, randomly deployed in a {{formula:42aaf99b-b840-49e1-bae4-24feb66d5dd0}} km area, serving {{formula:edeb87fa-cee0-4e78-b1e5-411693374f0b}} randomly located UEs, in an urban environment complying with 3GPP Urband Microcell model {{cite:13e33693994a14d9153663a750e40a66564c153d}}. The large scale fading coefficient is given as
{{formula:39d8d9aa-de70-4c0e-b472-9a067597d801}}
| r | b4f7453a0b0c220b01cc17e3dbe3a50f |
Measuring the bounds of the PISN mass gap will provide insights into stellar evolution and fundamental physics {{cite:756c3b2a39d63d1ad410f24f373c858bcbea94cd}}, {{cite:7bcf3efe394b52ec90ecaf124a36bda2c423e4e6}}, {{cite:369c14131f2a035b34fc09c6aa92c9449f7a5cfe}}, {{cite:64e3eb2af607b0b8e09884b8e8dcd8b16314cf56}}.
However, one needs to account for the dynamical processes that can lead to black holes in this mass range.
In dense stellar environments, such as globular clusters and nuclear star clusters, gravitational encounters of black holes in the cluster core harden the orbits of binary black hole systems, facilitating mergers within the cluster {{cite:b0a7dba739ca02dfbd876da724099aeb38e38559}}, {{cite:9e0f799195ebfe5e8ba22e901607a0f5807dad93}}, {{cite:0d4d7a4dec244cb0e5f77396851581206e2d08a5}}.
| i | 040cd13e815ae9fe0459be7fd056ba6d |
Till the last decade, the field of signal processing was dominated by conventional model-based algorithms, which rely on mathematical and physical models of the real world.
Inherently, they are interpretable and often incorporate domain knowledge such as statistical assumptions, smoothness, structure of the model space, or origin of the noise. However, this approach becomes mathematically intractable in case of complex problems. Machine learning (ML) provides an alternative to solve this challenge by building up data-driven mathematical models. Especially, neural networks (NNs) and supervised learning provide a proper framework for various signal processing problems {{cite:4b407f3379b222ca9eb76e1f07713af37de47ead}}. In the following, we briefly review a few recent trends that serve as motivations for the proposed variable projection network (VPNet).
| i | 764e15f36f7fdf910b3e776b32e5e0e2 |
These results have multiple implications for using PAH emission as a proxy for other quantities. While PAH emission cannot be used on sub-kpc scales to measure accurate star formation rates, groups such as {{cite:b34974dd907eb0bb2a824b616e8c90a99a72cec9}} and {{cite:a131b85ac8b72c332e3bcf74cf05001e7878ed8a}} have suggested using globally-integrated PAH emission to estimate extinction corrections for optical star formation tracers such as H{{formula:062c7160-6ac7-4af5-9d61-c7242e89476c}} emission, thus producing extinction corrected global star formation metrics. When PAHs are excited by star forming regions, globally-integrated PAH emission should more accurately represent the light attenuated by dust in star forming regions and should provide fairly accurate star formation rates. When PAHs are excited by the diffuse ISRF, however, the connection between star formation and PAH emission is less clear, and star formation rates calculated using PAH emission could be less reliable.
| d | d0f00634589cacf7fb0de77a9209497e |
We could, if we wanted, also consider “dressing away” the sub-leading modes {{cite:794d229e31e4e26cd3d0d857127a0e157fc23ded}}. In our semiclassical model we could try adding sub-leading dressing in the same way as we dressed away the leading modes, by setting {{formula:c5b53e5c-0122-4266-83ae-09b16c69b4e2}} to zero everywhere. However, although we can do this, it isn't clear why we would need to; infrared divergences appear to mandate that we dress away {{formula:660d50f3-c351-41e7-addf-95aa6b3e73a8}} , but the contribution of {{formula:a552e077-4c26-4d7e-b024-c0233b32e988}} is perfectly well-behaved. Furthermore the soft currents {{formula:57221654-a944-4fbd-9f3a-1e08471a7cf2}} and {{formula:4443e973-54a4-40b7-8b78-2b90925f437a}} have been shown {{cite:105608f3f0b289868b14e1fe5face92e002a5f03}} to encode the leading and sub-leading soft photon theorems at tree level. While the leading soft photon theorem is exact at tree level, the sub-leading soft photon theorem in general receives loop corrections {{cite:8a5233cc2c8519fa23a4f9e28184762b9dbbbd48}}, {{cite:8fc509a78d7de4f70789ca9205ac25e73c69d894}}, {{cite:a9bba6cdae3518326dbf289fdc2e9fc654f1be90}}, {{cite:544fc368dc6007e38b26561a4f5e6770430b43f0}}. It then seems prudent to explore quantum corrections to our simple semiclassical model, if we hope to fully understand whether any sub-leading dressing is required, and what form it might take.
| d | 75e87494964cbfc62c31341db9ebface |
Although there are intrinsic differences between the human visual system and artificial neural networks (e.g., the global error signals required for learning via back-propagation {{cite:4c5e2a65bf8d8a363b274bbcc044a05c8e842a43}}), we argue that the current findings highlight three key similarities with biological vision. First, both systems may engage similar global processing of illusory contours. In the visual system, Pan et al. reported that illusory contours activate equivalent representations in V4 compared to real contours {{cite:179afd7a89660a2075a6d94fec01a4fa1ef1700b}}, whereas V1 and V2 differently encode their respective local features. That is, in addition to local processing in early visual regions, there exists a global processing mode whereby illusory inducers form integral contour representations. In a similar way, when presented with illusory contours the current network assigned much higher probability of the “square” class than for either Random or All-out control images, though they shared the same local features as the All-in illusory contour images. This indicates that the network also possesses a capability of global processing. Moreover, this global processing primarily results from the feedback connections, since none of the tested feedforward networks could perceive illusory contours (Table REF ). Second, the “behavioural” performance (i.e. decision probability) of the network is also consistent with physiological research on illusory contours. Lee et al compared EEG activity for illusory contours and other patterns, and found that the activity for illusory contours is significantly higher than control random stimuli, but still lower than real contours {{cite:f8efd95357c33a70e572d9569ab1ac4f2a0b209a}}. In the current study, the “Square” class probabilities assigned by the network after the Softmax layer indicate a similar pattern (see Figure REF ). Lastly, at the “perceptual” level, we directly checked the internal representation at the first layer of the network (through its generative “image reconstruction” pathway). The FG metric suggested that the network perceives a brighter (or darker) illusory shape, consistently with the “illusory brightness” reported when humans perceive illusory contours {{cite:b6c5f3fd8bc9184dea06e67c9e0619f0626559d9}}, {{cite:04bbe66d087906ed8df5a9d2373da126f553ecd9}}, {{cite:c96a9bf2f6ccba68c373c188626a19f7c471d503}}.
| d | 499a8142cf7d4b489faa51be888ddf70 |
Using a fully-connected ResNet block as the equilibrium model cell of width 512, we trained a number of equilibrium models where we varied 1) the forward pass (fixed point iterations vs. solver) 2) the backwards pass (backprop gradients or implicit gradients) 3) learning rate ({{formula:5b8157c8-3e46-4dcf-82fa-999f36867a07}} , {{formula:ab65a3fd-010d-43ee-a66c-9c4bdee5ed9c}} and {{formula:55b1c29d-afa2-408f-81de-dc40ed9aa714}} ), 4) learning rate schedule (step decays of magnitude {{formula:404fb6e4-174f-43a4-b7ff-fcceb01ff5c0}} at different points during training) and 5) whether layer normalization {{cite:dc22cf4c99ff02a5bdd680d0533f8132743a8a9f}} was used or not. The results can be seen in Figure REF . We see a similar pattern that we saw on earlier tasks: lack of path independence correlates with poor generalization. Note that our best model matches the performance of the energy based model approach proposed by {{cite:09dc02186470f4d735fdd511132cf0e8ad91e08b}} in the matrix inversion task and significantly beats their baselines.
{{figure:3d8f4c2a-075f-4cf9-81ad-36006482a595}} | r | 0e6e73244413cc7e2a09c4d35e82fff4 |
Furthermore, there are approaches to use the closure principle to control other error rates than FWER, such as false discovery proportion tail probabilities {{cite:6c7b4a4172a6d9a155dbe61f30abb8db35becf22}}. There also exist connections between FDR and closed testing. In {{cite:b85732ea909fe379be354c1b7e2c4f0904e98b5b}}, they introduced an approach to use graphical procedures for FDR control and, in {{cite:56cea2ed80cf409b6abab2dde52a62542b27a601}}, a connection between Simes-based closed testing and the Benjamini-Hochberg procedure {{cite:bddfd1dc0fefeccedbd5380f55ad9295dbb2c863}} was shown. In addition, every FDR controlling procedure provides weak FWER control and thereby defines an {{formula:aa6ecd9c-2c58-4987-ae74-8220fc3ea5fa}} -level intersection test. Hence, all procedures that were constructed for FDR control can be used to derive new closed testing procedures with FWER control. It would be interesting to examine the extension of these results in the online multiple testing setting.
| d | a0bb153cd0f711a3688ba01131f3a73e |
Measuring generalization in the outer loop objective of meta-learning algorithms is a common training strategy {{cite:ab57203d754856c764d815d72cfeb9b193d54e16}}, {{cite:5e7ab440be5abda89440d97693431abd0bd38212}}, and can be applied here as well. For example, we could consider adapting the episode-level latent variables using only a strict subset of the observations in the episode {{formula:023bbe56-75bc-4796-8de6-82757b242725}} . We could then compute the evidence lower bound for the entire episode {{formula:2eae2480-beb8-4989-b08e-f5c5ccc46428}} by applying the recognition model to select variational parameters for {{formula:e6771941-cc06-4706-8497-c23dbd76b388}} and applying mean-field variational Bayes to the distribution {{formula:4a095e07-cde6-46ff-8bfb-735d81d1fff0}} . This would measure a certain type of generalization of the episode-level latent variables' variational distribution {{formula:3bb92cb7-8f23-46f4-918c-51df7e0a9bd5}} , since these would have only been tuned on a strict subset of the episode.
| d | 64dd40c576e68ba11b5f06de1e5b3f7a |
To improve the accuracy of finite temperature perturbation theory, dimensional reduction at next to next to leading order appears to provide a recipe, reducing theoretical uncertainties to the percent level {{cite:5606ef84807b867f537d58ac7ea676aba346dec4}}. Dimensional reduction relies on the observation that in imaginary time, the quantum field theory is identical to a three dimensional theory with a compactified time dimension whose size is determined by the temperature {{cite:683f91494552dd2118d9369ea892f8dce10f779a}}. One can then integrate out the heavy Kaluza-Klein like modes, known as Matsubara modes, leaving an effective field theory in three dimensions. If a scale hierarchy persists between the remaining states, typically a soft and ultrasoft scale of order {{formula:486dd218-a04e-459a-8171-6fd93a238236}} and {{formula:b83ec8fb-e162-43ad-8106-00c1eec6f07f}} respectively, the soft states can be integrated out leaving behind a simpler effective field theory again.
| m | ec985b58b221597a6b170e627519e025 |
For positive weights, {{formula:0ec330eb-5f22-4744-b4fa-651d8ec04042}} maximizes the weighted log-likelihood of {{formula:bf20aa60-17ab-4aad-bcf7-b4270a79bfa3}} .
The argument under the {{formula:a088271f-9ee2-43dc-b5db-337d47156062}} in the RHS of (REF ) is the negative cross-entropy
between {{formula:3ee4e7c8-2bb7-4fef-872b-45aa6a6e793c}} and the distribution of censored (elitist) samples {{formula:8238b52a-29e4-4d64-bd6c-f306cc6a44ad}} or of {{formula:6190a02d-ba0a-40c0-b046-02361753338a}} realizations of such samples.
The distribution {{formula:37bebc0a-5c42-42d2-a607-b9c3dd773910}} has therefore minimal cross-entropy and
minimal KL-divergence to the distribution of the {{formula:a2efbb79-9658-4510-9fb0-489ec976e5b2}} best
samples.Let {{formula:4d9e3ec7-26f4-4272-ab66-946abe8d90f8}} denote the distribution of the weighted
samples: {{formula:ee2453d7-d11c-4add-a308-b4e74229b856}} and {{formula:c344f161-f878-4034-8ef5-b4075aca412c}} . Then the
cross-entropy between {{formula:45a74966-5eee-4301-8ade-22ea06d5aa73}} and {{formula:1db32a21-7316-46ab-8cf5-919349d1d59c}} reads {{formula:68d3a09c-fe56-4353-9933-c1220511f864}}
and the KL-divergence reads {{formula:60659f06-6e35-49ca-82e9-ecefefcf4864}} . Minimization of both terms in {{formula:a95f5003-63fe-40da-b6cf-dfde382e0655}} result in {{formula:a882b53e-296c-46cf-839c-6b8e69e5bafb}} .
As said above, (REF ) recovers the cross-entropy method (CEM) {{cite:57c3888f5eb8868f51574135e1662e48747e7ce6}}, {{cite:18b22fe4d8f2a29f2ddc5b25c88be79df76e3945}}.
| m | 1ddd357089c70d85c3913344ae361e52 |
Previously, {{formula:88e7fe1b-2989-4ffe-9194-9f4a1a659dd7}} was used (first in {{cite:09672cf6f4c79f4a15406a2c98aa7bf96652eb33}} for one-dimensional case, and later it was extended and further developed by {{cite:71bd005d26e2d998ecab2a73e8a60aea079c0471}} for bi-variate multidimensional random vectors) for construction of statistical independence tests and measures. Distance covariance and distance correlation proposed by {{cite:71bd005d26e2d998ecab2a73e8a60aea079c0471}} relies on the weighted {{formula:a0875bfe-f259-40b1-862c-8903fc65a0b9}} -norm of (REF ).Recent result of {{cite:0c52d56dd101febe9360305646a2f0623a647883}} generalizes {{cite:71bd005d26e2d998ecab2a73e8a60aea079c0471}} to multivariable case. {{cite:960c20c4881e29f04db8781c10b5e0c43e6a58dc}} proposed computationally efficient algorithm for estimation of distance correlation measure, reducing the computational complexity from {{formula:1b8c6a2d-0524-4cba-aaba-6aa46fd86bf0}} to {{formula:a06fb5f9-5ade-4757-a482-c216bedafd4b}} , where {{formula:fb0e43f8-2cc8-4fc5-a7d0-0358ca9faa14}} is sample size.
| m | c3b5e9449b7a5a39c6497e2fc8502d8b |
In Section REF , the structure equations for causal geometries with vanishing Wsf curvature are examined. It is shown that if the Lie derivative of the Fubini cubic form along the vector fields tangent to the characteristic curves is proportional to itself, then the Wsf curvature has to vanish, unless the causal geometry is a pseudo-conformal structure. Such spaces are the causal analogues of Landsberg spaces in Finsler geometrySee {{cite:b8fb449dc131241c0739e20e3027c686982779cd}} for an account..
Moreover, having defined the scalar shadow flag curvature (referred to as the ssf curvature), and the notion of completeness of characteristic curves for a causal structure, the following theorem is proved in Section REF .
| r | f95bf81f2d2d4d89cc2e106d88f519ba |
Finally, our study also sheds light on the so-called strength of weak ties phenomenon. This concept was introduced by Mark Granovetter who showed that the most common way of finding a new job is through personal contacts with distant acquaintances, and not via close friends, as one would instead have expected {{cite:61ed2807e33d1511e7e3a6bd662bb7de6444cca0}}, {{cite:c04c376532a68a74722824d2ab39de41b04bb465}}. Distant acquaintances represent links connecting different groups of people, and therefore provide each individual with a unique way to receive useful information about distant groups.
| d | 2f977945b5f3ae2e37957ca275611d4a |
Fine tuning of the pre-trained ST-GCN model was done using several methods as detailed in TL literature {{cite:27d8e42570c7248fb317150e406124463ffa6139}}, {{cite:916f85a7aaac1f4d34ebaf6b07a746171628892f}}.
| m | ba5c4fa4f4b9bdcac2727541dcc17f0f |
Based on the previous works {{cite:64fbbdef638686bd86c6d8b892970b14344f6d34}}, {{cite:f6ac05bb6e596bc4c2c9d45d426ee5955ceb145f}}, {{cite:467f6800cd32a906564d5b4635b5be0fda5a0ecb}}, {{cite:8046f74c3637de205af347f62b68f7de2b1d0599}}, in {{cite:14eddd592416d9efba5b4d560fcad57e5bad6155}} the identity
{{formula:75cc09bc-f045-4290-b299-a5ebf06419f2}}
| r | 78319175b3158c4dde52808251cfc989 |
In this work the RLBM model reproduces a two-dimensional quasi-particle flow in a {{formula:eada5f47-b794-4605-816c-e7867da86b72}} by {{formula:cea14fa1-775c-4760-a83c-9b8b80cfa1c7}} sample of graphene with one or two rigid impurities obstructing the flow. The sample is simulated with a {{formula:88e0d6b4-4f42-4c49-a901-221b290b09c4}} node lattice with a spacing of {{formula:47bf8593-23c9-4d9e-b597-3213650b15bb}} . Initial tests incorporate a single circular impurity with a diameter {{formula:d8e15f23-332c-4844-8621-6e7e8e14dbe5}} of {{formula:64ae7796-3bd7-464d-8dc2-643744f26372}} placed within the sample in a region near the inflow boundary, referred to as the “obstruction region”. Subsequent tests are conducted with a second impurity placed at controlled distances from the first within the same region. At normal temperatures the impurities within a graphene sample are believed to be charged, creating charge puddles in the surrounding region that affect the electric flow. The impurities are largely sourced from the substrate {{cite:b10e8dea1410a615f771198b64deeca67c3cff84}} {{cite:cd3d64a7d8858c79dc0d608ed64580caab27ddcf}}, but can also be embedded within the sample itself. The size of the impurities can vary greatly depending on the foreign material, but they typically stay below approximately {{formula:ef707c8b-0c35-4ba7-b6f8-367ebf306ae0}} {{cite:8a082cba32042d03e35f290c01bcf7dcf1ede6ef}}. The size and placement of the impurities are difficult to control in an experimental setting, but the model seeks to simulate the effects of one or two quasi-isolated impurities on the current density in ideal but realistic conditions in order to determine if the detection of a turbulent signal is possible. Therefore the diameter of the obstacle is chosen to maximize its turbulence producing potential while maintaining a realistic size. The velocity of the charged flow in the Dirac liquid can be relatively high owing to a large effective electric coupling constant. Flow speeds on the order of {{formula:e757661a-82cd-46cf-ae6e-0bf6bb8b12f1}} {{formula:db967d2f-1c54-474a-8836-2625c9b02a6e}} are common {{cite:112472d62efa25dfabd1c610ad2ba5f5f57fef25}} {{cite:cd7f5b045429a7e2b181d3ae09519daefdf08967}}, but the flow can approach velocities as large as 10% of the Fermi velocity, {{formula:20dc3afe-3f67-4af3-af17-ffcc8abcee3c}} {{cite:8a082cba32042d03e35f290c01bcf7dcf1ede6ef}}. In order to maximize the possibility of a turbulent signal, the model introduces the largest realizable fluid velocity of {{formula:88c8c606-7b0d-4755-ab0b-6357c7a576a2}} {{formula:f1288fbb-7eae-45c7-ab14-f12e75a5e18c}} ({{formula:783931dc-eb80-4472-b0f7-a636f4084d97}} {{formula:66f5aec9-62d2-4211-bd7e-083dde82a163}} ) into the sample at the same magnitude along the inflow border. The borders that are perpendicular to the inflow border use periodic boundary conditions, effectively simulating an infinitely wide sample with multiple, regularly placed obstacles, but at a distance where the wakes created by the obstacles cannot affect each other. Each lattice node in a region occupied by an impurity implements bounce-back boundary conditions.
| m | 14a57e745448349bcfd2bf574ec27c68 |
Remark 6 In the setting of Theorem REF above, Theorem 5.2 of {{cite:32a363557e43d9fd919ea0b6624f9f8a3df1cdd3}} yields
{{formula:a0d37a98-0c1f-414c-8211-32e29b576527}}
| r | 8bdcca44d5f8aa38499e01fa0d0b1996 |
Quantum computing recently emerged with machine learning (ML) to introduce a new field, called, quantum machine learning (QML) {{cite:aa6a3b12474187be3c817fa59fc4ec2549286300}}. Quantum computing is applied to enhance classical ML. QML is introduced in many concepts, including QML, quantum-hybrid ML, and quantum-inspired ML {{cite:432cbe9f966476adda2aa830b6c49af10adb15d8}}.Various ML algorithms have been proposed in quantum versions, such as quantum k-means clustering {{cite:44633ec3f30601b041f22d10eb6e5761e059d378}}, quantum nearest-neighbor {{cite:51e50ab26d5dde5ed1c124aaccb1b68e11c5fc5d}}, and decision tree classifier {{cite:fc8f74905eaa8bb205820dc2aea2095d82262a2a}}. The QSVM is introduced in many versions {{cite:1a8e77dbe97acaa216e4e518fb979da9d1b6ecf4}}, {{cite:41e77375f97e94b586a92a02555c3b1ab3d92436}}, {{cite:55565b5cd70fe3ddda5791a11030895730597534}}. In this work, we focus on a quantum kernel-enhanced SVM. Kernel functions for ML are commonly used in pattern recognition and classification tasks. Kernel estimation has become expensive and difficult for classical devices with the data size increase. Quantum devices can easily estimate the kernel function with large-dimensional vectors; however, the current quantum hardware is limited by the available number of qubits.
| i | e951a3b0785f46926123f44c3f13dc0a |
For the velocity measurements, we employ constant temperature anemometry (CTA) using a hot film sensor (Dantec 55R11, 70 diameter with a 2 nickel coating, 1.3 long and up to 30 frequency response) placed in the middle of the tunnel. We note that since a CTA measurement requires negligible temperature variation of the flow, the velocity is measured when the heaters are switched off. The velocity statistics are not influenced by the temperature because the fluctuations in the flow are completely dominated by the turbulence generated by the active grid and upward mean flow rather than by buoyancy caused by density differences due to the temperature differences. To substantiate this statement, we must compare the relative importance of the buoyancy force (parallel to the streamwise direction) to the inertial force due to the advection of a passive scalar. The ratio of these forces equals the ratio of the Grashof number {{formula:4f7cb4bb-ff1c-4469-84f0-30198596a8ea}} and the square of the Reynolds number {{formula:26683a85-69ee-4ad8-b4f2-608c8c7c9fd9}} ({{cite:4cdedd8e10d23e5a2e63c786037de467cabc3adf}}). Here we base these numbers on the vertical distance between {{formula:d7aa81da-ee51-431b-95b6-1a8bcd6b5a08}} from the middle of the measurement section, the temperature difference across such height {{formula:688e608d-3943-4245-a4ef-0ba5b3c215d2}} and the mean liquid velocity {{formula:e7eaa202-8ea9-40bf-ad5c-ccb3eecc8126}} . This gives {{formula:61cb3e94-522b-4879-ba91-ea1fd841c43c}} , where {{formula:5542d7d3-01f3-4528-bb79-291d6d9f1d31}} and {{formula:c201fb50-327f-41c3-ab01-a2e68d0cd2bc}} are the gravitational constant and volumetric expansion coefficient of water, respectively. The small value of this ratio implies that the temperature can be seen as passive scalar under our flow conditions.
{{figure:0d66dffd-3012-4a6b-84f5-ba33bc80ea20}} | m | c42fe06afc1fd2b9b116acd582e02250 |
Our results can also be discussed in comparison to previous observations made for non-Brownian elastic fibers in 2D. For non-Brownian fibers, shape fluctuations as well as rotational diffusion are absent. {{cite:12e1ee7432ac6aaa72af5525cf9b1f78efff21c6}} and {{cite:ad62d920ff8ec782d68b6505115b690dbff951a0}} predicted the onset of normal stress differences and shear thinning above the buckling threshold from 2D simulations. In contrast to the case of Brownian rods, normal stress differences are zero and the shear viscosity is constant blackin the absence of buckling. No scaling laws for {{formula:3e865798-1e53-4bdc-b3e4-d08d4f1f4d7d}} blackand {{formula:6960dc53-dd70-4446-b834-63432a9c801a}} blackexist for non-Brownian fibers in the dilute limit.
| d | 07d874d9d89106c767656580a4dd8648 |
In {{cite:f33d618437a878ca33f8b72ca03d8579138a716e}}, it was proved that if {{formula:5fdcdd2a-4079-4975-845d-4027b239c0cd}} and {{formula:b6739b78-4e33-4759-80f4-a18238a75db3}} be conjugations on {{formula:97b5e402-31c8-4ec4-bbbb-096f2ce15ac7}} . Then {{formula:375e9c94-5111-4e1b-8d6b-029035c4d3a5}} is a conjugation on {{formula:3c06786c-4775-4510-bbfb-82be613c7800}} .
| r | 3981e96cc0e94e7f80dc211e8e8cb3a3 |
Over the past three decades, there has been an intense amount of interest in the properties and applications of light beams carrying orbital angular momentum {{cite:7cc5e8dd845f371f5a950e698258afe6575282b3}}, {{cite:19bef73070870b99f0a31be75cc9e2845d84d522}}. These beams have been considered for optical communications {{cite:1a60ec9878b2c5c44525ad615fe3a4a41da05788}}, {{cite:5c9f0f05ded9b2a725b545dc5b85c90e761d75f3}}, for the trapping and rotation of small particles {{cite:6a00a0dd13fa52e5979db8195af0056e775672c8}}, {{cite:028ee77f9f9f59197d450686bb5c8cb13168e9c1}}, and for image processing {{cite:91f8d84b8b372212b940b804977cfdd1e62d57e4}}, {{cite:5efcd2a77e3bd6577ffcc43ae4578970b4dca905}}, among other applications. The study of beams carrying orbital angular momentum (OAM) is a subset of the field of singular optics, which is concerned with the topological singularities in various properties of light fields {{cite:601bc3c06b0d6a3beac438269304f154d7114df2}}. Laguerre-Gauss beams are commonly used pure states of OAM; they possess a line of zero intensity on the propagation axis with a helical phase around it, usually referred to as an optical vortex, and the OAM per photon is directly proportional to the axial phase twist. For non-pure states, the relationship between the phase structure and the OAM is much more complicated {{cite:a44e5085c3eabf3baa83f148c0e2e85bbd496231}}.
| i | d5f45d5555a42a6a1489ab544cc7ad99 |
Black hole is one of the most fascinating objects predicted by general relativity and has attracted great interests in both theoretical and observational aspects. The recent observations of gravitational waves by advanced LIGO {{cite:8ac29feea7f0f42a36d7958f7876f23c7b6eae18}} and the photos of the shadow of a black hole {{cite:8a91b5b5081d7044e4c7943d5e399216d91b4f25}}, {{cite:3abf0a9d966a71127a57539ff5343dfdc4a72a27}}, {{cite:30cb374ee563bf36d6e5d8baed22e876df73d6e4}} give us the definite evidence of the existence of black holes as well as offer us new and powerful venues to study black holes. While the exterior of black holes has been widely investigated and many important properties were established (see e.g. Refs. {{cite:9570766401a95e3faf36153f406a48bb301414c0}}, {{cite:490ce19b5634d4ddae93a2c4935d1e74de5589bf}} for reviews), the structure behind the event horizon is lack of enough study and still mysterious even in theory. Definitely, the inner structure of black hole is an interesting problem in its own right and is important for black hole physics, gravitation and quantum physics. This has been strengthened by recent developments. For example, the interior of black hole is crucial in holographic computational complexity {{cite:e3d658e3b8f66aa9e160f31222ec3841cea5b5bd}}, {{cite:7bae5b33c69b596c943f60f34409dde04e959881}}, {{cite:f1d8f6651b7ea6b2de28ab668f583333a3f036ff}} and recent proposals toward the resolution of information loss paradox {{cite:183e5f3902944f5cc8523c1d9431a88f9451ad47}}, {{cite:874b843c2d3c048f85320ed0d300d8ccc164d4c8}}, {{cite:a7f44e02b8ebc393f961666148a4aa565333b193}}, {{cite:3f1f3f6fb2d4d570b171aea3878f49b4b296e84f}}, {{cite:b1ed943e30a8bc087d40edaf60a7a183808d0134}}.
| i | 749c8daac6e4d11afbe5f3d673301da1 |
We use a similar expression at {{formula:f6a63036-37c0-4178-90d9-a6e8cdffc3a2}} . This results in a set of first-order ordinary differential equations for both the field {{formula:a74402b2-9915-4525-b834-511c89bf68b7}} and its time derivative {{formula:fb8fbed1-9e7a-4efb-aef3-e7916467cb9b}} . The equations are integrated using a fifth-order Runge-Kutta algorithm with adaptive step size and error control {{cite:81f07d1e2d5d677bd8bfa52edc8f1f10f584f27e}}. The algorithm implemented in the solve_ivp method of the SciPy library in Python. For the {{formula:00bb9426-71d1-4ea5-b178-dade484359bd}} model and the toy model with {{formula:f0cdb562-557b-46db-a356-98e672a067a6}} , we ignore the slow decay of the shape modeThe amplitude of the shape mode is not constant because it slowly emits radiation {{cite:6443377e5ead3867bc48ddff02f49e65ae5cd154}}. and we write the scalar field as {{formula:526bbfcd-8b0f-46a7-8e28-3f99e8b3e15e}} . When considering quasinormal modes, we must numerically integrate the linearized equation for the perturbation, eq. (REF ). This is done using the method of lines in a similar manner. The partial derivatives with respect to {{formula:ce09c7b2-3dc4-4c45-a40e-fde79cfad9ae}} are computed using a five-point stencil approximation, and the resulting set of ordinary differential equations are integreted using the same Runge-Kutta method. At the boundaries, we also set {{formula:64bc14e0-3ab6-4892-ac02-98e6350a30ab}} .
| m | 11aa0b40a3e05544efc736082c013fa4 |
A complete introduction to power-law distributions along with a statistical framework for discerning and quantifying power-law behavior in empirical data can be found in {{cite:586f4acb335a0b12aa236289e9d1fb887aff93ed}}, whereas extensive discussions can be found in {{cite:d98f9ff0e7cee2f1a6c36491c3dc9e59555601b9}}, {{cite:6e2f565afb482b40f8fb9576c05e03fc73a294da}}, {{cite:e1e2db00640d82a1daa4dd361073b25ded7ded18}}, and references therein.
| i | 2150c4ae1fee6435bdec06a9ea8d7df6 |
A listening test {{cite:a9908456a48f34c1b5d5e0a8128366aa83c7e704}} with 10 native Brazilian volunteers (5 male and 5 female) was conducted adopting a closed scenario of phonetic balanced words[2].
Their ages ranged from 20 to 24 years with an average of 22.
A simulated room with {{formula:4b1b93c7-7bd3-4207-8965-0afda9059cf5}} x {{formula:7ac53a60-7f06-42b8-85be-ffc1985850c6}} x {{formula:7d20c7f2-d0d3-4cb5-acd4-c56c388010d1}} m{{formula:b95a0082-bf7e-46ee-afdd-f4d5025cd17c}} and {{formula:bbb8fb8b-a882-429d-a27b-bd8ec7c26652}} s was generated by the image source method (ISM) {{cite:b4feb9e2cd405cd1a946f5bb831e5c6051789d46}}.
The SSN acoustic noise was adopted with SNRs of {{formula:3e3609b6-97b8-4306-a0b9-b3c95c660752}} dB, 0 dB and 3 dB.
10 words were considered for each of test conditions, i.e., 3 SNR levels for 5 methods plus the unprocessed case.
Participants were introduced to the task in a training session with 4 words.
The material was diotically presented using a pair of Sennheiser HD200 headphones. Listeners heard each word once in an arbitrary presentation order and selected one among five words in order to compute the Word Recognition Rate (WRR).
| d | 47d8d256c06c406ae7e9e53d21954f87 |
Utility under DP. The baseline model over the STL-10 dataset without differential privacy (DP) achieves accuracy of {{formula:850d8420-ddec-4864-bd1e-f776d7765705}} .
Such accuracy level also appeared in prior works {{cite:89f2ea46ec9047f8c53710b6109cc8b3156ab33c}}, {{cite:8d3e133e18731f845f20662e90163a5e53cf5f63}}, and is orthogonal to our study in this paper.
In Fig. REF , we show the accuracy results of the DP method (Fig. REF (a)) as well as the normalized accuracy loss (Fig. REF (b)) against the baseline accuracy, under varying values of the privacy budget {{formula:64c74ebf-d855-4a71-9187-9c3b276582e1}} .
As depicted in the figure, the DNN model under the DP method has essentially no utility for {{formula:d0ffb6c3-9cbd-4f19-aaa9-459444a5edf9}} .
For {{formula:52a598a3-b431-4a3a-bdc4-1ebcf63f8ae9}} , the accuracy achieved by the DP method is getting close to the baseline accuracy.
For instance, the accuracy is {{formula:c61d1890-6329-4d92-8c21-b9d2fe321ee4}} for {{formula:11acfe5e-3528-4477-b875-077589e46e61}} (normalized accuracy loss of {{formula:d976fcba-ac24-41d2-a992-84c93480780d}} ), {{formula:308e7325-70c9-47d2-bf68-2e61fd67069a}} for {{formula:10f08020-cd17-465f-a1ea-79cced60e211}} (normalized accuracy loss of {{formula:138eaa5a-5461-471e-91cf-d1a815f5b856}} ), and {{formula:b2a3a124-9f80-4159-a81d-909432b3618a}} for {{formula:ae59dcaa-0f5c-4337-8506-a53d307e1508}} (normalized accuracy loss of {{formula:3759fb58-ae69-49ef-a99c-f7e5f708b2b9}} ).
These results show that on the STL-10 dataset, the DP method can achieve accuracy comparable to the baseline under suitable {{formula:54fe4db9-ba09-4029-9432-c711aa286f36}} values.
{{figure:69bbe5ff-bb5a-4901-aedb-7592afae3141}}{{figure:8e6fb37c-d922-418f-80eb-a1802f746f30}}{{figure:5375de51-833f-409a-a29e-d8c16b6e28a5}}{{figure:8cad7603-8486-40db-b587-dbb24a94f6ca}}{{figure:469ab1c1-a14c-499c-bce3-5193aaa76b2c}}{{figure:6a9d529d-20b3-44d8-b28b-fa26fa3c2f6a}} | r | 4ba594674db9c85b77a1737aca69c41e |
Although young star clusters are well represented by single stellar populations {{cite:d59429fa0e21545ddb7d839207b4c5fa7c684d48}}, we note that some of our 8 {{formula:110c8348-79e1-4ee4-afbc-75d0586a4e58}} m luminosity estimates exceed the predictions of the instantaneous burst models for ages{{formula:2fdfd0d0-053a-4be5-ada1-6cc2b6505c22}} 10{{formula:0ad9e459-2ae7-4f45-b6de-f2cefd7d9656}} yr and at high dust absorption fractions (blue solid line in Figure REF ).
There are 5 clusters (8% of total, magenta circles in Figure REF ) whose mass-normalized 8 {{formula:36ff5f75-f68c-4a07-983c-9339b6433944}} m luminosity exceeds the topmost model prediction for instantaneous burst population by at least 2 {{formula:46032ef5-f8dc-40a7-9d03-dc0ad393bbe9}} and are better explained by constant star formation (cyan solid line in Figure REF ). {{cite:27f8944c0d948fe7330ceed808f1b17dd424a393}} find a similar discrepancy between the strongest dust emitting clusters and instantaneous models in their sample. However, because of the distance of their targets (3.5–5 Mpc), {{cite:27f8944c0d948fe7330ceed808f1b17dd424a393}} cannot exclude that part of the observed excess may be due to blends of star clusters with different ages or contamination from the background population, which could artificially increase the observed 8 {{formula:4e5700e1-8c03-4a63-8111-b60839aed0c6}} m luminosity relative to the assigned cluster age. This type of contamination is not applicable to our homogeneous sample from a single very nearby galaxy where blends of clusters can be easily recognized and removed. Furthermore, the emission from our star clusters is measured at {{formula:4ade7657-879d-4434-b551-4db51dfe0d63}} 20 pc resolution, which removes much of the potential contamination from the background populations. If the four outliers were the result of constant star formation within the photometric aperture, the SFR of each region would be {{formula:5b3de5e3-b682-4637-8bae-fa052cecaac5}} 10{{formula:3a368d97-2ae7-49a2-9e00-90b3828ed279}} M{{formula:d78a00e1-deb3-432b-98bf-aff667ec97d1}} yr{{formula:0ca1ba72-ef0c-4107-bb0d-f18d45b434bf}} , sufficiently low that star formation would be sporadic {{cite:cdab7b90cb494001812742c3e06a8ba76fb169fa}}. We can therefore exclude constant star formation as an explanation for the five outliers.
| d | e1ed914ae9558ebf2f52b29934e641e8 |
We quantitatively evaluate our model in terms of 1-nearest neighbor accuracy (1-NNA), as proposed by Yang {{cite:b0244ac31cf10b54f8d8817fe0949d133ab0969e}} and report the Earth Mover's Distance (EMD) and Chamfer Distance (CD), as in {{cite:212a5234566b53609719b2ee88ad5cd55df2be06}}. 1-NNA measures the distributional discrepancy between two sets of point clouds, , it quantifies both the quality (distance to the nearest point clouds) and diversity (membership of closest point cloud). We use point clouds from {{cite:b0244ac31cf10b54f8d8817fe0949d133ab0969e}} as ground truth and resample our predicted meshes into point clouds. A value close to 50{{formula:055a9a02-1208-4ff3-8eec-00cc35d1e321}} for 1-NNA is considered optimal, lower values close to zero indicate overfitting.
| r | 191e64c6fb1a67edf8df34d272b1dc10 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.