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The article {{cite:53034cafa47ab405bf63cbb218450e77dfef0258}} contains a general discussion of redshift estimates,
which we use to prove our results in the context of the Reissner-Nordström-de Sitter spacetime.
Similar estimates are used in the article {{cite:c5faf6703fdb36a597fb69c70817f5be18d5f0b1}} to study the wave equation in the Schwarzschild-de Sitter spacetime, of which the Reissner-Nordström-de Sitter spacetime is a perturbation for large radius. Nevertheless, we do not appeal to these results, and instead of extracting what we need from these sources, we give a less technical, self-contained derivation for the convenience of the reader in §REF . Here we follow {{cite:b63a061dba36780f68af1c3b65fcc47d94eb8356}} (where a
similar derivation was given for the wave equation).
| r | 7a61fef64605d7717ba5368c5c4696ca |
{{cite:57ee3ea7e19b756a67b6b2c1908a1f42b0ee5943}} modeled the behavior of a jet propagating through the progenitor and the surrounding circumstellar material
and showed that the resulting light curves exhibited both short-term and long–term variability. They attribute the long-term
variability, at the scale of few seconds, to the interaction of the jet with the progenitor. The short-term scale, at the
level of milliseconds, they attribute to the variation in the activity of the central engine itself. Alternatively,
{{cite:8bc428923fb135a5d6855a158a59c4db1a597f6f}} consider a model in which the prompt emission is the result of a magnetically powered outflow which
is self-interacting and triggers rapid turbulent reconnections to power the observed GRBs. This model also predicts two
variability components but interestingly and in contrast to the findings of {{cite:57ee3ea7e19b756a67b6b2c1908a1f42b0ee5943}} , it is the slow component
that is associated with the activity of the central engine, and the fast component is linked to relativistic magnetic turbulence.
While we are not in a position to distinguish between these two models it is intriguing nonetheless to note (see Fig. REF )
that indeed there do appear to be two distinct time domains for the {{formula:d6a4b14e-d001-46bc-97e2-b0b6e6b674f2}} :
a plateau region dominated primarily by short bursts although
it includes some long bursts too, and a scaling region (i.e., a hint of a correlation between {{formula:9410613b-e5f4-4c76-b573-dd2181d3e945}} and {{formula:d1e5db3c-cb18-4656-9e7e-de8ae23577a3}} )
that is comprised solely of long bursts.
In addition, we observe that the time scale in the plateau region is the order of milliseconds whereas that for the scaling
region is approaching seconds.
| r | 03a68c67102d1216bfe6b3f803fec85b |
Generalization of minority classes.
Besides improving the mean accuracy (reported in Table REF ), finer exploration reveals that most of this overall improvement stems from a dramatic improvement in classification accuracy of minority classes, while preserving the accuracy of majority classes. Specifically, OPeN improves the accuracy of the 20 smallest classes of CIFAR100-LT (with IR=100, where minority classes have 5-12 samples) by 13.9% above baseline ERM training, from mean accuracy of 11.6% to 25.5%. OPeN also outperforms the baseline deferred oversampling {{cite:40e73128a09b6432bc2642adb13adef6c85d4eb8}} (without noise images) by 4.3% on the same subset of minor classes. On CIFAR10-LT, OPeN improves generalization of the two smallest classes by 6.3% compared to deferred oversampling, and by 15.6% above ERM training. These findings provide empirical evidence to our hypothesis that adding pure noise to minority classes (as opposed to only augmenting the existing training images) significantly diminishes the overfitting problem and increases the generalization capabilities. Please see sec:appendixclasssize for more detailed evaluations.
| r | 85e6575ac8805a82ac6ee51dbf9cbfb8 |
One limitation of the proposed technique is the potential difficulty in identifying causality in data with very high dimensionality (i.e., the number of observed signals) or very long temporal dependencies between latent sources. In either case, the covariance matrices required to identify the latent causal sources may be poorly estimated, potentially leading to erroneous estimates of latent Granger Causality. To mitigate this, it is required to assume some prior information about the structure of the observed signals. For example, a form of Tikhonov regularization {{cite:cfc4b426db4f3627a4747e76d3a9192f1976922c}} equivalent to adding uncorrelated noise to the measurements was employed here. More sophisticated approaches to covariance estimation in high dimensions will improve the performance of the proposed framework.
| d | 011039604f9e5cfa68959d98bb6cb4af |
Actor-critic experts are trained through a TD reinforcement learning algorithm {{cite:35a9d165337642d01a356cd2ed7fb91615af3ba6}}. The TD-error ({{formula:ea12ba41-88fe-4a5a-a51d-65a848fe8c6d}} ) is computed as:
{{formula:8b74c63f-008b-4cff-a6dc-efd4a305fa92}}
| d | 81dd99c031f1c24f6a608af07532e45a |
For other partial waves, no structures are observed directly
close to the real axis (c.f. Fig. REF ), while we do find several poles in those partial waves
located farther away from the real axis. All the poles obtained in this study
have isospin {{formula:7c1ab2e2-baac-42d6-9c43-c276d1a96d57}} , and no states with isospin {{formula:fc44bbdf-7717-4e69-86ad-75e959cffed3}} are found.
In Table REF , we present the pole positions and spin-parities for some of the observed states, which can be regarded as resonances in {{formula:446f3608-4906-47dc-9481-f7cf64262f08}} - or higher partial waves with relatively large widths.
The state at {{formula:900420e7-d027-419f-85df-d2bbd54211c7}} MeV having {{formula:2cd39096-203f-44a9-be43-024e689330b8}} is close to the mass of the newly observed
{{formula:192419a7-5b29-489c-971c-ce564f119f9a}} state. Although the width of this state here is larger than
that of the {{formula:e972896f-cb60-44f8-849a-15b335c69833}} state, which is about 29 MeV, the situation may change
after adjusting the cut-offs to the experimental data.
Similarly, the state at {{formula:e2e4f5b3-5d06-476d-923a-b0995468cfb4}} MeV with {{formula:84c68fee-80ed-4da0-ac32-fc4aaa74b3eb}} , which also
has a large width, could be related to the broad {{formula:916f936f-1c9a-4bc0-8e1b-a3bb711e0f10}} state proposed in 2015,
where the preferred spin is {{formula:cac0ee01-c284-403a-a56b-8450c5354064}} or {{formula:5aed5954-385c-4ed2-89de-006168597469}} {{cite:6b60cf177b943223c297eef9532e313cae7cb149}}.
In Ref. {{cite:a45d4d0c8c0d7c022cd5b3a90971029ba0fd3e5c}}, the existence of {{formula:bf34e439-8a6b-43b2-89fb-30979db2cf9f}} is weakened but not ruled out.
Furthermore, we see inconclusive indications for two poles with even larger
imaginary parts in the {{formula:446a5bff-b2a8-4135-81eb-9888ed5e3a04}} and {{formula:692dcfa0-a9c3-4fe1-b44b-7477364b278d}} partial waves, which are not listed
in Table REF .
{{table:a2caeb21-66ef-4f42-8016-cf5a72d3c357}} | r | 0bcd64876269617ac99532f1a7a55276 |
Overall Architecture Fig REF shows the overall architecture of our proposed method. As Fig REF (a) displays, we first train an IND intent classifier using CE or SCL+CE objectives in the training stage. Then in the test stage, we extract the intent feature of a test sample and employ the detection algorithms MSP {{cite:0cafe5578d02036a06f721c04854d471a3bc2078}}, LOF {{cite:e6568aab5e01ad9ec78ed92f3571c9c138edda5d}} or GDA {{cite:2ae774c036c0d6ab369764877531fcacc5383094}} to detect OOD. In this paper, we focus on the first training stage. Thus we dive into the details about the detection algorithms MSP, LOF and GDA in the appendix. Fig REF (b) demonstrates the effectiveness of our method capturing discriminative intent representations, where SCL+CE can maximize inter-class variance and minimize intra-class variance.
| m | e4629b876c16be012608452991e77f7b |
The {{formula:80ac1162-754c-4899-b66e-2d2a51ef5966}} mass distribution (normalised to unity) is shown in Fig. REF . The solid line is the result with no extra {{formula:39460b49-e561-4011-b2cd-2dc1b8f3592d}} breaking, mentioned earlier, i.e. {{formula:e675a702-ae06-470e-aa75-edf58bbd50ae}} .
For the small values of {{formula:0f354407-9272-41ee-8e15-3937858d310c}} , let's say around 30{{formula:a572ef59-e10b-4446-9fc2-a5f0b3152f7e}} , the {{formula:0e15df68-0fec-40e0-9760-64a7018cf805}} spectrum changes significantly for a variation of the mixing angle while when the mixing angle reaches around {{formula:d411cd8f-3721-45cd-a995-4da0a0774607}} , {{formula:8f10e492-1943-45a7-84c6-f67e0bce9c1f}} becomes totally dominant and it becomes difficult to distinguish the results with different {{formula:ed7a073b-58d9-4b5d-9b78-12e8ac9414ef}} . This pattern can be readily inferred from the dominant {{formula:00c1f4f2-271b-484b-9b72-38affd6b7b35}} -wave contributions in Eq. (REF ).
The coefficient for the {{formula:ad85bf91-6a14-4b93-95f9-2c2f87811f27}} contribution, {{formula:a119fd84-bca2-470b-b14c-7eb1707b09c6}} , is an increasing function in the region of {{formula:c08016d8-f574-4d38-9e3c-5cb9c41aa936}} we are considering. On the other hand, the coefficient for {{formula:8a4f5ca9-84fe-46fd-88c3-5130e1d55372}} , {{formula:3cbafd52-f151-40a0-b7ff-6a164afa0e46}} , rapidly decreases and hits zero at {{formula:8b178d03-2c4b-4191-b6b1-acfed5599f6f}} .
The coloured bound in Fig. REF is results including the extra {{formula:a7f088a4-8e5b-41ab-8bc6-5bd0137cd935}} breaking effect with amount of {{formula:088f1308-5fc0-4bd8-afae-9179a3ddb1fc}} . We can see that this effect has an impact only on the {{formula:a2bb7079-5fab-492b-8746-1d6bf3be2222}} and {{formula:d39310fa-3ecd-48db-8b84-98574cc432e6}} terms, and as a result, it is almost negligible for {{formula:de2eb315-b75b-4d73-b3b3-c7dca6163788}} >{{formula:ae481989-3ff5-4d23-a60b-b952a2ee8f2b}}{{formula:56f3e31b-e17b-412d-90f4-fb6db22006d1}} 40{{formula:086bf4f5-b682-4330-a332-c1203d37f5ff}} In order to clarity the achievable limit by the Belle (II) experiment, we perform a Monte Carlo study.
The {{formula:5bde2e8d-71d8-4daa-b14d-86f83980da4a}} process is simulated by using the KKMC package {{cite:3f5348f8f4aebc90ec1ebdd4e032587ec9b65687}}, {{cite:523107998bb981501e9b808324e4c11a4f4c36b6}} with the Belle beam energy, 8 GeV for electron and 3.5 GeV for positron.
We decay the tagging side of {{formula:a1c2cffa-c4bc-4f65-bb2c-4a9199f96052}} by using the TAUOLA package {{cite:432e3991a4d7f019ed156489abf4dc4f0e80a46c}}, {{cite:53dc8625a24eb435a7920904fdb51839139bf0e9}}, {{cite:9dce894285ff48ae262e8f438a98a856415d0f1d}}. We do not consider the spin correlation as we will use only the leptonic decay ({{formula:0d61d58f-f2b4-4e34-92bf-1a95e91306f9}} or {{formula:24d9d06f-7e66-4154-a0a4-53003cb5085a}} ) on the tagging side, which reduces significantly the {{formula:62f3e0c7-9256-43fe-8040-c4b2d2f418e8}} background. For the signal side, we use the differential decay rate formulae derived in this article to generate the {{formula:d9345374-0ea7-4604-ad5a-b35561752fc9}} decay distribution.
| r | 66c15ae465e13af50c37726074c1a721 |
There is a vast body of work on Generalized Linear Models {{cite:95da132c94a3cbdde62e4b2a2bf879bde1e8f552}}, {{cite:ba44da99627c0e6abde102683727cb3b8c0f54ec}}. Classically, the focus is on the setting where the function {{formula:10a0ef73-ab36-40ff-bdc4-d2583813db66}} defining the Bregman divergence and hence the link function {{formula:97cb8ce8-1b40-4714-860a-87f9bbc30170}} and its inverse {{formula:a8fde1cc-6f10-4f99-b77c-10da7543120f}} are known. The resulting program is convex and can be solved using the iteratively reweighted least squares algorithm {{cite:ba44da99627c0e6abde102683727cb3b8c0f54ec}}, {{cite:07af13d73e8abac785af0bf9da2d866732bbf695}}. The set of convex losses {{formula:497a8717-c566-4c05-9fcd-b56b0954622a}} derived from GLMs are also referred to as matching losses in the literature {{cite:4ea2bc0efcd5547b06bea636af4eb917a5261376}}.
| d | 6d627bf86bf23761403e059529b98a5e |
Let {{formula:781aabcd-d91e-4a92-a876-2d213db21950}} be a prime dividing {{formula:52baa940-1630-4fc3-8506-675b6d43cd04}} . Then {{formula:ac072f37-bae3-4125-bc6a-bc06af98beba}} . For {{formula:0c6f2128-b63e-4686-a18b-4849f355b507}} , {{formula:1a45b264-f009-400f-b455-d1dbb5ec44fe}} has a single side joining the points {{formula:a8010da1-dffd-4e1e-9aef-317231c2675f}}
and {{formula:dd3c7c87-09ec-4835-a7ac-bca0e99f2630}} . Then
{{formula:3b0697b8-1533-4f3d-b5ad-cb89e8a31917}} . Also by {{cite:5ecce86a1c976fe550d313b7a0c03e6f77224364}},
{{formula:52668250-d5e0-47df-908c-740db48729f4}} is a free {{formula:8639df25-d92d-4728-8025-8a630fbe6076}} -submodule of {{formula:4732fc18-78b9-4133-8101-f77fd1c82354}} .
Now, let {{formula:e40e146a-40cf-410d-994d-5cac0bc6a104}} gcd{{formula:6de1cd38-2782-437d-8360-f2638376a262}} . Then {{formula:209b5785-003c-4ac9-b474-73ac6318f25a}} , where {{formula:734c13d5-5bd4-45cd-a67d-6facdf30b89b}} . If 2 does not divide {{formula:7cf76ad5-f5f3-4cf2-9be9-9c1c4560de15}} , then {{formula:78f99f63-aa40-4165-8e71-d6f77527185b}} , {{formula:2c4a255e-0da0-4206-bdc5-cdfb4cd4dd3d}} is irreducible over {{formula:e6172246-a1e4-4516-a701-b4b381a4cbfd}} , and so by Theorem REF , {{formula:f48acbcf-8cbb-4cea-ac49-0d0c947b5646}} and {{formula:df9ebd61-261f-4710-b156-94c8239407cb}} is a {{formula:f1f0e860-4b94-4532-a968-2c3bc232cf46}} -integral basis of {{formula:4bf0c328-7ad6-4437-9255-5fe5e79ee723}} . If 2 divides {{formula:4b2c29aa-5a16-4a8a-8c62-58b2175c49b9}} , then {{formula:9e16ebe8-6c25-4097-81de-78b76e0340a4}} . In this case if {{formula:dd2d16ab-745a-4fdf-8f79-4058afc1faaf}} , then {{formula:9402db3a-261c-457f-8c58-89c5d2a0855d}} is square free over {{formula:f86c004f-7014-4102-9c60-9f1cc361bfc6}} (because {{formula:b01f1c2b-ad0a-4f51-a9ac-9c434ad07dd6}} , and so deg{{formula:036dce35-a35b-4d1c-9930-39f905f2ca6c}} ). Thus by Theorem REF , {{formula:61d0d926-bbc9-48ed-abe8-8f6729677d55}} and
{{formula:19def205-d812-4ce5-a436-20c05f4dcaa6}} is a {{formula:29a24cb8-9fa9-4f0b-935b-e092abdb5f82}} -integral basis of {{formula:52e4e80d-71cf-4e3a-890d-885ee17ae44f}} . It follows that if 2 divides {{formula:fd90d6ed-e879-4c95-a582-dbd0f36eb53e}} and {{formula:a9597dcb-4e8c-4da9-9883-bf8ebbad46d5}} is odd, then {{formula:da564c8e-5fef-4c44-b79c-10372e2ecd86}} is an integral basis of {{formula:99087923-43eb-4507-884e-6e87a175dc45}} .
If {{formula:5abe20f6-268a-4488-88e9-e48ed3ff8663}} and {{formula:7a45af1b-b8a6-4272-9049-c74bfa9ad04f}} , then {{formula:f3a69f90-7a92-4a60-b550-9ac3505b8535}} is not square free and we have to use second order Newton polygon techniques.
If {{formula:b52aa70e-0a11-4d34-badf-175f1eb976fa}} , then for {{formula:0577ff8b-3a02-4bd1-8cb7-b564788e7679}} , we have {{formula:8e3dfa6b-9161-4d15-a65e-9d31c73e9446}} , {{formula:d4b71305-2282-4a48-8fc5-b20d3b14f6db}} has a single side of slope {{formula:736dcfe8-a45d-42a4-9176-36541c0f9f74}} , {{formula:9dc6bf62-fb7e-47fc-b3af-e1339820b00e}} , and {{formula:8202256e-3f94-4eb1-9a16-58e51b3c6cfe}} . According to the definitions and notations of {{cite:8422a01d8afe35696e0ff70726293853c9a87f93}}, {{cite:4a2d6d2587a59b1596cef6cd5b27eb03b2573646}}, let {{formula:8dcf502a-5dc9-45e0-86bb-63314acee729}} be the valuation of second order Newton polygon defined by {{formula:fc984478-f4cd-45a3-8fb9-a0f6d660c697}} for every {{formula:d5ab8380-f5ba-4e8c-8266-b3939208e3fa}} and {{formula:038fed0f-1497-4899-b81e-06f908debd2e}} , {{formula:ee298713-e8f6-486a-b0ab-a2c43f4a7971}} a key polynomial of {{formula:87453049-e832-4504-bfc0-39780c701795}} , and
{{formula:ca0b19ea-44e8-4cb6-8dc7-26e2d9bfbf7c}} the {{formula:f2b45675-1d2f-4fcf-a05f-da1694140914}} -expansion. As {{formula:a06469f3-b100-4518-9a91-02c08cd37cdd}} , {{formula:aa732dcb-968a-4e09-8b8a-267a161c410f}} , and {{formula:2b779be9-8f42-4f1c-ac57-8382828bc0cf}} . It follows that:
If {{formula:7207af33-41e8-4bff-9508-408f1f916d8b}} ; {{formula:637fb299-2a75-4535-8291-8ea78d70e16c}} , then there are 2 cases :
If {{formula:637d52a7-e373-4342-a575-83b61c873bc9}} ; {{formula:3846e627-b291-4313-bf54-cd0bcb7a7ad9}} , then for {{formula:b6610d86-681c-4456-9129-f3b6c2ba05e4}} , we have {{formula:a7965930-4e64-419d-9f0c-efd2261e4952}} is the {{formula:f8993a34-21a5-4e8a-8d99-fae0fee2175f}} -expansion of {{formula:60760df8-9150-494f-9bcf-4f34cb75659b}} . As {{formula:44c218ec-217b-4f7c-a973-93b437eebbbd}} , {{formula:2c43fcc0-e914-4f61-8281-0481d1884589}} , and {{formula:453d0007-6c9e-4a63-a81e-c675f0577736}} . It follows that if {{formula:ebc60b37-927a-4234-b0fc-a894c94e0354}} , then {{formula:09b0c730-07d0-42ed-b916-b2465494ca78}} has a single side and {{formula:9653c6b8-67fe-409a-88b1-225ab1fd6d50}} and
with {{formula:dbf7c7e1-7f29-42b6-8389-2e2b62db9870}} . If {{formula:60ca80c9-8648-4f3b-b0bc-b2c216468d1e}} , then {{formula:fb03214e-f8ac-4997-8739-ab6a9952a0d5}} has two sides of degree 1 each. In both cases {{formula:90dd3b92-a383-4b47-9113-5923f1d08845}} . Based on the polygon {{formula:56ddc08c-371f-4ac1-9bdb-26a8ba51694a}} , we conclude that {{formula:2eafcc0f-123d-43c0-8c3a-9a5a20ad894b}} . Similarly, based on the polygon {{formula:7ebdbe0c-1190-44d4-8bfa-729d6f24cbde}} , we conclude that
{{formula:d3fe3a11-3664-444d-9ee7-36bc6b23601e}} , and so {{formula:4ffa6eae-b19d-42e3-ad54-7e21f642e1f4}} is a 2-integral basis of {{formula:3cd3524a-0d4d-4474-ad2c-3f13a111d34b}} . Since the Montes algorithm is local; the algorithm {{formula:a2427759-7303-4c14-a9b4-dc1e56e9529b}} -integral elements, sometimes we have to replace {{formula:fd32e995-39e3-4977-8cbc-29bd1404c54c}} by an equivalent polynomial. For example, in our case, if {{formula:0829b99c-b7df-43d2-b188-51d3547d301f}} for some {{formula:fcaedeba-6b6c-45b7-8c9d-d9ad2bd98bfe}} and for some odd prime integer {{formula:8c571f8c-3bef-413f-bdb0-ae990c9cfd2c}} , then {{formula:d822b8ae-3d08-4c02-b26a-237e4d2a389f}} is not {{formula:63cc0bd9-de4e-48fb-a99a-63c647ef7366}} -integral ({{formula:6d957125-fd39-457c-a1b5-0e5a75a2cacc}} for some valuation {{formula:11e0800f-aed6-403e-96bb-b6973f6bf2e0}} of {{formula:4949a35a-6c94-4f14-bf36-c73a6eb34f81}} extending {{formula:1faed857-d111-4e42-98c8-9c54ff716476}} ). So, we have to replace {{formula:1df20bc7-710c-406f-939f-886712d2c472}} by {{formula:f6e130d8-44a9-4284-9aa0-b0dd94f679fc}} with {{formula:38fbe86c-9de4-4044-8ece-f0fc31f526a0}} an integer which satisfies {{formula:0085f214-7294-41d1-be42-0e63650abf64}} and show that {{formula:13413706-6f83-411b-a9b2-8fda5e9801f3}} is an integral basis of {{formula:eda378d9-f26b-474d-b64d-9926957e95c4}} . Since for every prime integer {{formula:8782f582-d7f8-42d4-ba15-c794f1c6f7a8}} , {{formula:b57b6cc9-3375-448e-83f6-7c6c81cc564a}} , we need only to show that every element of {{formula:6ba7150a-3f53-4742-9136-91543a558e31}} is integral over {{formula:e5d795dd-9d5a-487c-8b4e-6bcc413ffcfd}} . By the definition of {{formula:386db5ea-45fc-4062-9fce-080bc397e944}} and by the first point of this proof the {{formula:17f09390-2e7a-4159-94d2-d8df30bda0df}} -valuation of each element of {{formula:a0449643-7e20-43bf-a10a-5df6bdf3365f}} is greater or equal than 0 for every valuation {{formula:2141547e-c63c-4f56-aa62-8d7441f46558}} of {{formula:17da9bed-ff38-4db1-bb8b-40679aa69322}} extending {{formula:4e4460c8-9c96-444b-9ae6-1b0e322bdd38}} for every odd prime integer {{formula:5ad5c994-20cc-4f2d-8fb2-1b701c40307a}} . Let us show the same result for {{formula:3a9de4f7-3a27-4271-a48e-cbe68d9d6942}} . For this reason we need to gave a lower bound of {{formula:5e3d2f42-b7b9-479a-81fa-8265d815f145}} and {{formula:ef5924e4-b1da-4ae9-907c-5aeda1074c2c}} for every valuation {{formula:91d4afb5-d357-4c3d-bd74-1d573a96e194}} of {{formula:33ef2abb-7db2-4454-9956-7fb68d5db852}} extending {{formula:564167bd-5886-4c0a-ab2b-7d803330ae8b}} . Let {{formula:98047c7c-0d39-4540-a19f-b63aee6c70ac}} be a valuation of {{formula:68bc27b5-2090-4467-812d-55fef6345c7e}} extending {{formula:85bd3e66-5355-4a9f-916a-445bf005849d}} . Since {{formula:bf0c433e-00a7-4e6e-80b4-4baaf8885a0c}} , {{formula:20e68227-fe87-4d73-bc94-7ac9a6836791}} , {{formula:e990dc35-5581-4501-83f6-77df081c2ab1}} , and {{formula:2eb65a92-40f8-4236-9acb-6a639011b2e9}} , we conclude that {{formula:22da5c0d-caa4-43c1-aff3-6add3be66314}} . Thus {{formula:35c7b8dd-f00e-437b-966c-d8c656c50743}} , and so by a simple verification, the {{formula:59334114-5eda-4b90-928b-6a9552c65e60}} -valuation of each element of {{formula:5ba3c2e6-9a4c-4bdf-84e0-2a1d352fd93f}} is greater or equal than 0. Hence {{formula:08a78d72-75ba-4d2f-9f46-70e597f1680d}} is an integral basis of {{formula:94db65a4-1c61-4a1c-aee1-3afec267d7f8}} .
In the remainder of this proof, this technique will be repeated. So in every case, we give an adequate {{formula:287939b5-30ae-4f95-aeed-65e762f05130}} for which {{formula:e87092d7-c3e6-4e9c-a72d-dbda42a89fd0}} is regular with respect to {{formula:f7e9349d-e8cc-4ec2-bcef-91ad49a580d6}} , we give the {{formula:ded023bf-8f88-4dee-b9cc-fe7c603fcd40}} -expansion of {{formula:7f003fed-9502-475a-b37c-1d4ccb537467}} , and a lower bound of {{formula:471b83ea-1936-4fa8-83d3-6b71da7b81b4}} for every valuation {{formula:cb22fac4-fdb2-4df9-8967-a2da5d993e6e}} of {{formula:45ae788a-8c92-44f1-a0c5-eaf15c0372bf}} extending {{formula:852e3382-432f-41fe-8dc6-dc4a28876111}} .
If {{formula:76f35cdc-88d0-4267-8142-eac9425340d3}} ({{formula:0765cd8b-459c-45de-8186-bd8643eb5566}} ), then for {{formula:9bcebc84-122b-415e-9eae-156bf439f2d8}} , {{formula:a114482d-e45c-4aa9-b8cf-71b8fd7b3432}} is the {{formula:40338df3-436d-4361-a802-88283c1dbef0}} -expansion of {{formula:0bee29ac-6d7d-4b2d-b45d-d72547ba42ed}} .
As {{formula:2fc0a28d-0cd7-4342-ad6e-38ddc5e7aa23}} , {{formula:b6f73441-2834-4927-8c7f-ab3a1a1dd8ee}} , and
{{formula:514fa7ac-6fa0-49d9-9eb5-13e78d1dcc3a}} , we conclude that {{formula:b8bbd900-b156-4d81-b78e-ffe0123c45e5}} has a single side joining {{formula:b2c06b36-67be-4a34-bfab-e2521cb24baf}} and {{formula:2ba62b0c-5a8a-4ecf-9647-986717fc4912}} . Therefore {{formula:6082db38-9c9e-4e56-bb10-65e0dece5009}} , the side {{formula:5755aa4e-c2bb-4e10-90be-0f15c32abb97}} is of degree 1, and {{formula:f08e42d1-ffc0-4ccf-b9c5-038bb836227e}} , and so {{formula:256235cf-413e-4e1b-903d-92f5d0e7ea06}} is a 2-integral basis of {{formula:8b985b6d-a640-4f8c-ae22-4a19416645ff}} .
{{formula:af388a7c-7a04-414d-9cb6-4483c915154c}} , {{formula:c7d650f2-09cd-4299-9cef-0a7a9937c679}} , and
{{formula:fcb4d5ca-c054-47e8-b269-46a5c55b0c0d}} is a 2-integral basis of {{formula:4d92991f-13ed-41bd-a7fc-71c4fab2f9cb}} .
Now by replacing {{formula:2b503966-ae14-4a42-8d72-44db8ffa05b2}} by {{formula:270b47ef-5dba-433e-92e9-f7cd2ac8ea55}} with {{formula:413d568d-39a4-4ad2-a6eb-f8b13518e554}} an integer which satisfies {{formula:7cfd6982-64e4-421c-ae33-ffd70c922f30}} , we conclude that {{formula:a1dcb994-5eb4-425c-a714-ccc39666f179}} is an integral basis of {{formula:58a941d4-6038-474e-a88f-3267e7a171a1}} .
If {{formula:fbba7005-b1ab-4dd7-89e4-8db47b404c7e}} ; {{formula:e40248ac-87ca-46ab-9426-f65571d9a665}} , then {{formula:4519e2ea-11d5-4d40-8086-315df42c5c64}} and {{formula:453184e5-ded9-4e4c-80f4-b8d2e5ceaea8}} has a single side joining the points {{formula:cd1a4f70-2ea4-4453-a253-bbd2ba2ffada}} , {{formula:bf5e19a5-7287-4d61-a15a-ed3d93e72665}} , and {{formula:0342b0a1-434c-4ff3-97a5-b79958499ee3}} . Thus, {{formula:c605921f-46ae-4284-82f3-880576858d0f}} and {{formula:5b82d8cc-c629-4efc-80e4-703b7e56edfe}} is irreducible over {{formula:bafc1f3f-78c2-4866-b9c7-03527e2d6ee5}} (because deg{{formula:f37c6152-6aeb-4c70-85fb-ca69dabbcfb9}} deg{{formula:b0fd7f94-6920-44fe-b912-8d2ccd5b0720}} ). Hence by Theorem REF
{{formula:f5541533-690f-4c3c-8fb5-209b49eee131}} . Based on the polygon {{formula:69e5ddd4-8aa5-4042-aed1-f82b38f1da4b}} , we conclude that {{formula:64c1c8db-a310-4897-929a-c6f7624dbf05}} . Replacing {{formula:744a2416-5959-4fe4-89ca-a02fb809a50e}} by {{formula:544b2eaf-dd96-4af8-a3ea-0496f9b108e0}} with an integer {{formula:1a0628ef-ac32-4fde-a849-095dcbfb30c7}} satisfying {{formula:7e274e0e-ee8f-4447-b835-ab7d40e22e1a}} , we conclude that {{formula:c67c8c11-163a-4d52-8e6d-0aadc4b25e99}} is an integral basis of {{formula:90c0c857-5fc7-42f5-8307-7a919f536dd5}} .
If {{formula:f929f5e2-5247-43b7-9979-8de33247d0d8}} ; {{formula:d76ee9e9-ed2f-4378-ab44-99de17e0f424}} , then {{formula:4cfcdaeb-af72-499a-8916-3d56a1ef1bf0}} and {{formula:65a2c699-b9a3-410a-961e-d811ce24a068}} has two sides joining {{formula:83e35701-bb1f-4b1e-be56-8e586cef7ae6}} , {{formula:29c7ccbc-53b6-4bfb-8529-7696b6c8caf8}} , and {{formula:2a6ae6e8-b2ef-4215-a974-01a63ba04a57}} with {{formula:9c24159e-33d7-4c5d-929c-7b76227e1421}} . Thus each side is of degree 1, and so {{formula:068e60e9-ff74-442c-8c12-6f510ed244ee}} .
Based on {{formula:f56f647f-338a-4799-a07a-3a3eaa5f6d19}} , we have {{formula:90d674c6-8023-4039-8c0b-cb7d6c815cd7}} , and so by replacing {{formula:28a3d77e-b010-4183-b59c-347408db9410}} by {{formula:059e2bb2-cfa5-4dd5-bbd5-6fba128ccca7}} with an integer {{formula:0b96b3ce-e9ea-4300-8d41-c8242e016271}} satisfying {{formula:0bfac74f-f850-4646-b927-fe77268d0a65}} ,
we conclude that
{{formula:b4e96035-9bc1-4d23-bac1-b2f090c6fea3}} is an integral basis of {{formula:ce35f231-991e-4a7e-9421-ac65273e1682}} .
Note that the two cases {{formula:a13c13a0-0906-4967-b414-1b49388b2404}} and {{formula:f9eecbc9-6e1f-4819-8ebc-2cceef2d2b40}} could
combined into one case only, namely {{formula:8aa6b6cf-fc2d-4884-8618-2dd0830a298c}} .
If {{formula:56148a9a-3ab9-48d2-9b36-b360f789b772}} ; {{formula:784cc253-8442-40e6-8bac-74cba87a97fd}} , then for {{formula:5b874b4d-5a3b-441d-b02b-011fb3c92cd7}} , {{formula:ac57927b-901d-45ec-b74a-0daf72b3609e}} , {{formula:d323a0d0-e8c1-4817-9acf-5cd8a338522d}} has a single side of slope {{formula:587dd18b-0047-4e43-8615-b474da15356e}} , {{formula:b290d1eb-66f2-4839-a664-9f93e4c7c088}} . Let {{formula:523abe66-b170-42fc-b6ea-b27acee96fd1}} be the valuation of second order Newton polygon defined by {{formula:a0f18b41-bc8b-47d8-a07f-28995d091df8}} for every {{formula:439e4211-a196-4389-afb1-4c8f1647065b}} and {{formula:aaa7da5a-69e6-4dd7-bb3c-50af81b8079d}} . Let {{formula:102c03fb-3664-4e62-86e2-5cf151d50623}} and {{formula:4b090325-e585-4f62-a456-775eef5a4a92}} the {{formula:88e188c0-7578-42c8-8f66-a5740d7577b9}} -expansion of {{formula:08da5e56-9b0f-4443-9630-2a861a83125b}} . Since {{formula:ebcf8373-3e30-40ee-be09-de7ed5102848}} , then {{formula:30db4dcb-69c5-476e-832f-e1c32956c3e3}} . It follows that:
If {{formula:aefd8e3f-2164-4195-bec8-ef0f6adb8d6c}} ; {{formula:6502b6e3-c458-4921-adad-d246440d7293}} , then {{formula:fcc5e6eb-521c-448b-a5e9-41f475e9b415}} has a single side joining the points {{formula:502fea8d-d3c4-445b-8d28-7976bf04a04d}} and {{formula:131010ed-ece8-48f9-bd9b-abbaeee711b8}} with slope {{formula:7a04a014-13bf-4c69-8780-845d7a0ee483}} , {{formula:df20172e-a9fd-4976-b26c-51ff5bb49e6c}} , and attached residual polynomial {{formula:41284d89-5c49-4050-af2c-d5c9424bd27f}} . Let us use the third order Newton polygon associated to the data {{formula:2c667946-ee9f-47fa-865f-7888db4537b1}} , where {{formula:ef4283f7-cecc-488a-8e4d-ad77ea0ded39}} is a key polynomial of {{formula:9a1c90e4-ed6d-4718-80bb-0198f8ed829d}} and let {{formula:c432c637-5800-45bf-9552-6329a01adc3a}} be the valuation of third order Newton polygon; {{formula:8b64df54-5328-4f61-80d0-0d55d7bf4d34}}
for every {{formula:a3b566a3-8347-40ef-9106-5b6d6d012131}} , {{formula:4e647445-e6fd-4114-9c52-871615431c71}} , and {{formula:fb309fe3-1a90-41d5-9b15-db9acde105cc}} . Let
{{formula:2c20160c-a417-4e68-a8c0-39393579f32c}} be the {{formula:90bfc292-1d5f-4612-a2d4-e4580688c2f8}} -expansion of {{formula:64ff9df1-5c78-4ffa-af1a-86f29fa5ab48}} . Since {{formula:f348b71f-ab75-4a2d-9c85-602dc91292bd}} for some integer {{formula:522f66b2-c133-47d7-8ac4-81ca8770cecb}} , {{formula:6465ace0-3308-4366-a3fd-077ba98543b9}} , and so {{formula:470a6d85-00ae-414c-8ed4-07c18fae5eaa}} . Thus {{formula:e0481cd5-0d2e-4f88-a21b-719b18b5ddf2}} has a single side joining the points {{formula:b4bedaa5-da69-4384-b7d7-abe658364797}} and {{formula:dab3a0b0-5446-4182-8e73-66417b77d728}} . Thus its height is 1, and so {{formula:a147ee73-30e3-4c9a-9679-b4f222520af4}} . By Theorem REF {{formula:0b204d7b-7fab-4378-bc1b-7a3c5a6adf6b}} . Based on {{formula:241a1536-1f84-4d60-b1da-8e70f80d5c98}} , we have {{formula:6c5fb303-2c17-441d-83e0-af73be616ced}} and based on {{formula:0168bf3c-54f2-4286-8852-c4ae4c8c15b2}} , we get {{formula:e5c23c95-705c-4d67-b25e-3d324f67cd6f}} . Replacing {{formula:81825556-c76e-4e65-a958-cd07c666dec3}} by by {{formula:a3203fbf-5a4a-4f75-9dd8-88adb6024e90}} with {{formula:6892ff20-b29d-42a4-9501-77cf2f70c40c}} , we get {{formula:767a95bf-c0f3-4f5f-94da-e7952e0786cd}} is an integral basis of {{formula:93bfa2c2-cfee-46da-801c-c4e0c111eb95}} .
If {{formula:8bdbe52a-946c-43ec-a4de-8d9b2a0b0228}} ({{formula:7dfae96f-b061-4881-8175-3544698aba0e}} ), then {{formula:726bb904-0ada-44e5-89c3-57eec2226191}} has a single side joining the points {{formula:3729feda-0b2c-4630-a7f8-56a5991b0819}} and {{formula:38718ba0-19bf-4a20-8e79-7fdc1fe2f34e}} . Thus {{formula:8de76426-9f4a-4caf-96be-c2988d3936f7}} . As {{formula:220a64cc-7c2b-4653-aa7d-dc37ca231be5}} is of degree 4 and {{formula:3996cc7a-b3aa-41c2-8210-1630d786169c}} , we have to use third order Newton polygon techniques. Let {{formula:8c672249-05ab-4c50-b69d-5fcfed2e4ce1}} be the valuation of third order Newton polygon, {{formula:5d5d30c4-8458-461f-b5a0-a27415663c66}} and {{formula:be1abd02-e807-44df-b631-b0628f1a1e32}} . Since {{formula:79005f94-07d7-4376-9e91-cf87b4d80159}} , we conclude that {{formula:fdd59a77-5ff8-4f39-8a25-9419a1128ae1}} has a single side joining the points {{formula:38b16a9e-e7b3-40b1-8a8a-d448b18ec4e4}} and {{formula:d78db7c0-1b6a-4d75-80e5-796d6afd93d7}} , which is of degree 1. Thus {{formula:ffd64197-1783-4bf0-bc3a-a2c84e9419f6}} and {{formula:36cec52e-801d-4104-b8e9-4a98f13a6774}} .
Based on {{formula:cb2a7c14-d6b9-432b-9356-f98f499e9940}} and {{formula:8658a657-2c59-49e0-91dd-c9c5f8e834a9}} , we get {{formula:0b1027f2-5f3f-4b64-8f81-9d8efcf3c286}} and {{formula:aba3b770-a372-46c8-a2b4-26bde649e5ab}} .
Replacing {{formula:e6f3b932-17e9-475d-8831-dcb427943ba3}} by {{formula:945d381b-bb75-4de6-830e-9ee2ef16e8dd}} by {{formula:03c1a2fb-de42-46e3-9083-2a2f4d197f52}} , {{formula:4bd90b91-d1ee-4764-bcb5-adeaf9214810}} and {{formula:d1aa56b7-de3a-41f4-9832-4681e771bda8}} is an integral basis of {{formula:7fb21794-95b1-4735-84fd-fbc2b01670e8}} .
If {{formula:e8f685e8-95b8-453a-9928-a8c24e43b26f}} ; {{formula:74caa317-1df7-4f91-a72b-05ef18cef589}} , then {{formula:005008b1-d34a-4f58-bafa-a33beb35c252}} and {{formula:0cb81991-c536-46e0-8945-ce28e99bc533}} has 2 sides joining the points {{formula:412d3958-5eb2-4662-90d2-77ba87f75200}} , {{formula:37c2d1aa-e9ae-472a-be7e-9d40cf54c26b}} , {{formula:b6aaf1a2-4032-45ce-8b14-b3e0b7023b08}} , and {{formula:71bb21d0-d79c-4344-8d92-35667f1e9046}} . Thus {{formula:488ad45a-0ad5-47f1-ad30-fd8d3a6932dd}} . Since the attached residual polynomials of {{formula:52aa0412-2668-4a2a-8f4a-817ff56226f4}} are {{formula:9d665430-1801-4c70-8767-a9d7ab4731cb}} and {{formula:c9f60d6e-93fa-4246-997b-06a24740749f}} , in order to complete the calculation of the index {{formula:dc9980b8-85a6-41d3-92d1-22b37e7d2625}} , we have to use third order Newton polygon. Let {{formula:683f8cdc-7181-4702-b343-56f10e03f7f1}} be the key polynomial of {{formula:61fa8b6f-e447-4281-aca7-f2f9895e149e}} , {{formula:df40f98f-9c02-4144-b630-0457a8a37541}} the valuation of third order Newton polygon; {{formula:1fc4caa2-27bc-435b-8715-ac290b0b5789}}
for every {{formula:bf20757d-cc3b-4bea-a328-14123136d648}} , {{formula:603486a0-5d78-4946-913d-60c79d7db7fa}} , and {{formula:a3c446b1-b397-4e31-9cad-a1ab1fc40b52}} . Let
{{formula:6db3388e-c98e-4ce8-878e-cc89a755b1d5}} be the {{formula:64d486c9-a4a2-4ec2-8431-9f433a7f6442}} -expansion of {{formula:288f51ca-960a-4609-b61c-5935686b67a1}} .
As {{formula:4ad4eeca-f200-47b9-94f2-80e3548a89e2}} , {{formula:272833c1-2bf8-4946-b3b2-1678b24f0b8d}} , and {{formula:e5694493-67b2-40ce-aaac-a35b7b867099}} , {{formula:29d19601-03ba-4763-a392-4531e6696937}} has a single side joining the points {{formula:b8ca9815-9f69-4afd-91c9-dd9ed0edb827}} and {{formula:f3a5e13d-b0d2-4443-b4a6-90080dac19a2}} . Thus {{formula:6f51325f-9b29-44da-bae2-d7fd1d52af69}} is of height 1, and so {{formula:5c65ef94-e288-447a-b6f9-4d21a6ea29d1}} . Therefore {{formula:bf18a5eb-6ab8-48ee-a597-b7e3f9f426f4}} .
Based on {{formula:484374bb-32d7-43f9-b01c-6f22c7aee016}} , {{formula:4d9bb286-9c94-4077-b828-bd5f67669990}} , and {{formula:00d279b7-b4c0-42f9-9100-5279db8ce513}} , we get {{formula:6821e967-d532-4fac-b729-19a391556c86}} and {{formula:b67686e5-ed70-4db7-bc4c-f8688449c9e5}} .
Let {{formula:de7ea830-8c9e-4995-9e76-83eab3f5431c}} . We need to show that {{formula:575e8dbd-ebc9-473d-a1ed-6af85130e368}} . For this reason we have to show that {{formula:60207d29-a4af-4a0d-93f5-3a34cc142642}} for every valuation {{formula:119d98d8-6ed7-47db-b170-c78ed7701a70}} of {{formula:99114394-7b7e-43d7-ba79-a2ddc3d295a9}} extending {{formula:de4fe7d9-4553-4413-bd75-d164216b2bb8}} . Since {{formula:10f7d7d1-e468-43fa-9aaf-6b64e9ebce92}} has two sides of slopes {{formula:6c738dcc-2c08-4bc6-945e-113013f2ce49}} and {{formula:3725086d-cc44-43cf-8d7f-4948cf472e74}} , by Theorem REF , {{formula:810c0248-9239-42e7-b409-db05177c6506}} in {{formula:be24bd2c-2ab3-4986-b084-3e06de078858}} and there are two distinct valuations {{formula:ab503045-efa5-4703-b563-854f0c1dbaa7}} and {{formula:254dae5c-b3eb-462d-8591-fc15a4f1639a}} of {{formula:723f8481-d954-48d9-abf4-0406061254ec}} extending {{formula:801d832f-b1e4-4612-a9a5-c49bc8e5837a}} which satisfy {{formula:7a7d0360-ffb3-4d9c-9423-3553732dd1ec}} and {{formula:46c6a2b2-3eeb-4a48-8920-8fa01e8414ac}} . If {{formula:8a8d02bf-8552-404a-ac5e-55f6e48c03e9}} , then a simple verification shows that {{formula:d7a677db-6c1d-4e13-968b-8e946c22f7b7}} . If {{formula:147c511a-3114-41c2-863c-2ce0774d2ea6}} , as {{formula:bd540010-e380-44fb-8882-38d4d86b45f8}} , we have {{formula:3c58af38-e2af-474b-9934-c0187f37341d}} , and so {{formula:4ec53eec-e35a-486d-b21f-d69a93332cc2}} . Hence {{formula:8b390a5f-02cb-446c-9e68-6e1d5f0462b8}} and
{{formula:5822d6ba-adcc-4db2-85a4-51e68360e044}} is a 2-integral basis of {{formula:0083ff99-9d9c-47c0-8461-6d7233bd37d7}} .
By replacing {{formula:5347e624-d6b5-42d3-bbc9-561c9714f353}} by {{formula:81a39378-15cb-4e4c-a968-fd5086eb67ce}} with {{formula:1b401fb8-e40d-40b0-a33f-f1cf3ffd51fa}} , we get {{formula:b6299a70-5444-4cfc-b0fa-6068505d5b11}} is an integral basis of {{formula:bcc1d0f6-b932-4eea-8b03-0cce4a3badbe}} , where {{formula:b87b5804-a579-4e5f-9f6b-9134b7212427}} .
If {{formula:27886cec-51c4-46a9-9444-68c8753e772e}} , then {{formula:f650177e-2d80-411f-b535-f287e95ed427}} . Let {{formula:ca2ecf6d-7c90-4c67-9b16-298b095c323a}} , {{formula:ba44ae08-c08e-440d-9677-02347bdf5abf}} and {{formula:0e9fe912-3996-418a-ba3d-f09e9f4487a6}} be the {{formula:b1950aa3-d0a2-4cae-8729-c8c51863e4e9}} -expansion of {{formula:b7668e49-2aed-477e-a770-d0977223213f}} . If {{formula:5f40ae42-4a78-4ddb-a3c6-276cf9949ca0}} , then {{formula:dfe51ce8-61e7-4b82-816c-f895829db8b5}} has 3 sides joining the points {{formula:684cf4bc-b6bc-4692-b46a-59a56992045d}} , {{formula:1e0d1d48-0fb3-4afe-a488-e7d046392a7f}} , {{formula:0af668e4-977b-4824-9ac1-a2e521bff8f6}} , and {{formula:5f0ecfc9-68b0-422e-8a3b-133e63590912}} with {{formula:8faa4cf5-5556-4dd1-bc47-54fefbfcb3f9}} . If {{formula:ac0743c7-5e95-4664-90a1-43bb813d140b}} , then {{formula:147bd74c-f96a-4140-8471-fc1fc66f20f3}} has 2 sides joining the points {{formula:6232fb91-3688-4642-96ac-152048663830}} , {{formula:978c317e-62f8-458a-b32b-bc27ae0a336a}} , {{formula:5c766243-5289-45a2-8415-836a6129ddce}} , and {{formula:0e36e837-e6d9-4dd1-bcb3-d204a514010f}} . In both cases, {{formula:90aa21a5-f77a-46b0-8a7d-954e1105a804}} .
Since the attached residual polynomial of the last side is {{formula:39a02534-8c4b-4e4b-8f2d-51ec391c4394}} , we have to use third order Newton polygon techniques. Let {{formula:0b157845-d3f5-4455-ac4d-bcddb54e9171}} be the key polynomial of {{formula:39e120ff-b215-408e-8107-fac0096b707a}} , {{formula:927985bd-0233-4d3f-bd2b-5aacc193d16f}} the valuation of third order Newton polygon, and
{{formula:861fbdb6-f2c1-4016-b3da-e6b6be12abc2}} the {{formula:5a876fb6-3ae3-4eae-8575-81360f3c1782}} -expansion of {{formula:99486cad-8ad7-47f9-825b-b09ccf2ef749}} .
As {{formula:a446015d-bdf5-449f-93a6-4bb3d4d77717}} , {{formula:b25a6b56-de57-4eb6-ac3a-2838dccf3e23}} , and {{formula:b0fc110a-780b-4387-8013-b0fbc4dcd33e}} , {{formula:d5949aa8-8236-47f0-bc11-a556d2d296eb}} has a single side joining the points {{formula:0f97b51c-e916-4dcf-8d6c-86a37192ec50}} and {{formula:efb56588-3d67-4600-a797-62b8156c012c}} with height 1. Hence {{formula:7baa6f55-e910-425a-aaab-1a1c9f4b1af1}} , {{formula:507ca96d-d1ce-475f-92ad-0b5eacd34e32}} . Let {{formula:5362ce80-ae60-496d-a91e-0af9456cf587}} be a valuation of {{formula:90730493-75ea-43ac-a668-6da5c2ad86dc}} extending {{formula:03a7a402-f541-4305-abdc-3280aecda09e}} . Based on {{formula:cc6f35c9-d7b3-42e5-815e-960585dbd83b}} and {{formula:d790dcb5-54bc-4f74-beb8-f17da85ba30c}} , we get {{formula:b28dfec6-f8a5-478a-b769-c3799b83039d}} and {{formula:3d5a9129-1a16-4d34-923b-908876539f9d}} . If {{formula:46905f96-f817-495e-a1f9-7fd3a30c89ed}} , then {{formula:39352d63-00d5-4dd9-986f-90853470c3fc}} has two sides of slopes {{formula:f9cdfe40-df55-462b-a36b-bc2ff45eebdf}} and {{formula:82190f3b-9538-4af3-afa0-408b445361e6}} . So by Theorem REF , {{formula:e7c2395f-6e80-4964-8d2a-a7a77d3cf10b}} in {{formula:079523d3-3ab4-4ff5-a812-4e4810eda749}} and there are two distinct valuations {{formula:8c77bbf1-e114-4119-bc08-1da5481cd0c5}} and {{formula:84f99008-7ca2-47c3-8a45-71f64e34d8ca}} of {{formula:23a03fb8-9da6-4a8c-8232-2d3637fc93aa}} extending {{formula:0cdd72e9-be95-49a0-ad52-ffa56e6c770b}} which satisfy {{formula:22747284-e5b5-4338-b2e5-095e6b6b8fe3}} and {{formula:364996d1-0484-4338-a693-b450afcb0990}} . If {{formula:15cf48bd-0268-4769-b253-22a580e1f3a3}} , then {{formula:9ce89423-af54-40a1-98e9-e7c1cc437371}} has three sides of slopes {{formula:5f916bb8-e245-4194-a287-3edd44901185}} , {{formula:eabecd4a-2724-462a-87d3-e4822d455665}} and {{formula:f9426f30-cf72-4d2c-aaaa-9cdcc91d14e2}} . So by Theorem REF , {{formula:7ab01562-5b08-4705-b3ae-a86e7a054199}} in {{formula:39e47c37-447a-40c4-ab75-748e45fb99f6}} and there are three distinct valuations {{formula:0437d482-0bf0-44b2-88f5-644a3c34e50c}} , {{formula:614ede8e-f02b-4ae5-91c2-f4af1fd94fb6}} , and {{formula:e3947f09-dc8e-4350-983e-c5bfd054dfae}} of {{formula:0a19c8d4-348c-4c0f-9b97-99ec308d5fb2}} extending {{formula:d7689caa-7ba4-4a51-b3db-7d95d1d4bcc7}} which satisfy {{formula:92ea0042-eb60-4fd9-9882-146a05395394}} , {{formula:324b464f-4987-4a66-abd2-82c768174164}} , and {{formula:16acab22-8730-4cf5-b4af-fa3195122966}} .
If {{formula:2743c539-0c0d-4887-9a8c-bd665511fb1a}} , then {{formula:df206ed4-7822-4929-b63d-e4c9c406ccb9}} , and so
{{formula:fb2629cb-a9ee-48e5-bcce-545c5d744fb5}} , where {{formula:0b958c92-ff7f-46e9-8e7c-2bca6ca2fe45}} .
If {{formula:893d80a9-74f6-4563-b76a-8aa0f5f995d6}} , then {{formula:33ef9040-764e-4cab-9b16-90aa69afec3e}} . Thus {{formula:9e678f1d-9833-4b1b-ae03-27c447727b0a}} and {{formula:1db6539b-90c1-463f-99a8-b903cbdddee8}} for every valuation {{formula:8f3fa687-c034-4b13-bd34-276b413ddf6e}} of {{formula:02e08be1-2b92-4a38-ac66-8601039586e4}} extending {{formula:934b55ad-9600-4407-bb78-49187e297789}} . Thus
{{formula:0ff44fd4-320b-4dd8-9be3-0a0a51263517}} is a 2-integral basis of {{formula:b3e9a71d-fdba-4073-9766-fb7de6ce0b28}} .
Replace {{formula:6c2a3aa7-0312-44ef-a2ba-e052f6c4c98f}} by {{formula:cac4e9dc-8c2c-4d07-85ac-fe0a5af34a89}} with {{formula:ee0fad0f-43c3-424d-b371-c58a1a355686}} , we conclude that
{{formula:007942b2-1a3e-482f-ac72-783e9379bb22}} is an integral basis of {{formula:c2e71615-7907-46f7-b8c2-6aed169b4982}} , where {{formula:1a464b42-a882-4797-a525-807e2a2aa1d7}} .
If {{formula:2b7808bb-823c-4c07-b279-4b5eb4c7946d}} ; {{formula:463feb45-0966-43b0-b2e1-d02484de0d1a}} , then for {{formula:89b01a49-80cc-485d-b12f-f2551997373a}} , we have {{formula:28f89982-ba48-4d59-b713-14d580e08b94}} , {{formula:c52030aa-84f6-4571-97fb-b7472b91b356}} has a single side of slope {{formula:4fb1612f-5d71-4a42-8e0b-cc1938a6ce22}} , {{formula:9d6a6b43-98a3-497b-a9dd-2854288a03b0}} , and {{formula:fa50943d-7a80-49c3-859e-574ce806c9ae}} . Let {{formula:504f531b-c8ae-4975-9930-fdf25488e6a6}} be the valuation of second order Newton polygon defined by {{formula:5b1d728b-a967-4727-9929-a780656dc96c}} for every {{formula:99af024f-037a-4ea2-aee1-bffaf58f4eca}} and {{formula:a069f557-ff5a-44de-9d17-7d3fbd44cffd}} . It follows that:
If {{formula:d42f379a-242e-47ce-9dd4-891cde776c3d}} ({{formula:eed94e64-90f0-4c02-a440-0bdcd71deae6}} ), then there are two case:
If {{formula:88c2c62e-0396-4c70-a3b2-a3503f206ccd}} ({{formula:7c240852-3b31-40b6-adc6-fc0c7b03b6de}} ), then for {{formula:fe10d21c-9e86-4001-bd85-d2ab54686539}} ,
we have {{formula:4258d895-2fcf-4a9d-9fa5-c40a7745214a}} is the {{formula:d035dda0-7c48-4f77-bc4a-f28b2e5388b4}} -expansion of {{formula:77793479-70bd-4d3e-90a0-a6d014c900d8}} . As {{formula:0b3ca051-84ba-4641-8c0a-354982d288c3}} , {{formula:24e6ab9b-0483-4391-a390-cf406ba85023}} , and {{formula:826821ef-bacd-4add-94cd-916cc99868a4}} , we conclude that {{formula:14e92d22-444a-4bdf-acf9-e221e5c65489}} has a single side of degree 1. Thus, {{formula:cb3c8ee0-6c36-4a1b-8aad-d2a6207d3436}} and {{formula:110b3db5-9a80-4f66-a906-c4d6bf9f9772}} . Since {{formula:1da1d6d9-bbae-497c-9e80-d176ef22f043}} and {{formula:98612bb6-bec1-4a44-bfa0-615bf4a435b5}} . Replacing {{formula:7ff432d6-7c40-47cd-97b9-cbea1d770e91}} by {{formula:ec9caea4-d712-4afe-b12b-a37b72bc469f}} with {{formula:500ab778-b22b-4fed-8637-74c13be1178c}} , we get {{formula:e264a145-e472-450d-a102-cee2bdae3528}} is an integral basis of {{formula:bdc35511-1e97-4007-9d30-01e273425a0c}} .
If {{formula:06e28da7-4d66-4f35-a305-8a58690b29ba}} ({{formula:b26f247c-c297-4aa9-9fd4-5d43d6393ac4}} ), then for {{formula:74b6760b-2d6a-4326-b2c4-014f7cb7f14f}} , we have {{formula:08f13ba7-0e6c-40c9-a6d7-d01c819f3537}} is the {{formula:1bf9050f-395f-4228-895b-f4c3a7d59585}} -expansion of {{formula:d1ebce4e-23f8-4e44-8a11-5a47ddc060e8}} . As {{formula:21d34408-da07-4188-bdca-a163699d8546}} , {{formula:e0a97926-3fdc-4971-8199-22abc8ef8d52}} , and {{formula:7b8c9711-b91d-4296-970a-fcd65bd7cef8}} , then {{formula:bb5911e3-dbb3-4a74-a234-89900e715de5}} has a single side with {{formula:c7c771a6-27d7-4844-82ff-978cdfe9da38}} or 2 sides of degree 1 each. Thus, {{formula:c53de94a-b8ab-486e-a3f1-50ef86f4f1cf}} . Since {{formula:33ed7360-80fa-4548-8ada-ed2bd7416ad8}} and {{formula:ae44944f-c8be-4fe1-960d-59165013756d}} , if we replace {{formula:3af19bdf-c6a7-4d61-9999-fe5105fb5a90}} by {{formula:7939ca43-ba3b-4104-b5cd-3db8f45ee39f}} with {{formula:57f6de95-19c5-455f-ad13-06ab4689d23a}} , then {{formula:b2f07db2-d731-4588-be53-e26fec168f8a}} is an integral basis of {{formula:abe7c7b0-abe3-4e08-aa04-af10b0d7dd82}} .
If {{formula:ad916bf2-a19c-49bb-8466-4d527babcf08}} ( {{formula:dc95f993-ca26-4b81-8a03-1ef2f07bde8c}} ), then for {{formula:364134ba-e8c8-4a98-bc46-44bc4170ed63}} , we have {{formula:5a4590b3-f1c6-423a-acfa-352e2516fbee}} is the {{formula:10272c86-cf9d-4c51-82d9-01c5616e7e29}} -expansion of {{formula:8479d73d-8353-4079-9ccd-479eac4b9dc0}} . Since {{formula:20012883-8d42-49db-9504-3077bb42bf38}} , {{formula:a4ec63fb-276e-4d2e-a21b-cca38b88af81}} , and {{formula:411b34fa-438f-4341-94b3-8753e881b6e8}} , it follows that if {{formula:01d985cf-efdf-44ce-97c6-f0a12af9afcc}} , then {{formula:2c4f2d68-2355-4e5b-934a-ceba31865e2a}} has a single side with {{formula:971bb1c5-359c-425a-a3bd-1491db0af675}} . So {{formula:dc046905-c9b5-472d-b141-034dcd773e9d}} . If {{formula:bb43806a-1ec5-4ba0-8f63-8e8b2e887bbc}} , then
{{formula:ac477b60-ab5b-4b07-a556-3c632f5f7ef0}} has two side with degree 1 each. Thus, {{formula:8674f134-0a91-4158-911e-e3a7474cfcc4}} . In both cases we have {{formula:d9da0c05-4197-474d-9c6d-22384ecd2a0b}} and {{formula:f32d13a4-e205-4bb7-8450-8eeac7b3d7fe}} . Replacing {{formula:3c463a78-3d48-4697-8d25-928689b6a5e0}} by {{formula:a10af6e0-185e-43ba-9514-a48a1ac8b166}} with {{formula:a3a092b9-d499-476c-8248-d3c8f44e8599}} , we get {{formula:82f4ab36-6c6b-467e-a462-4d00ab460fa0}} an integral basis of {{formula:de3640a6-5fcd-4a25-84a1-41144dab27d0}} .
If {{formula:d88ace56-90b6-4442-bb45-aa4e92d27ef5}} , then {{formula:77331923-b22d-4a02-9a44-eb56d806bf86}} . Let {{formula:7b607ddb-b0b6-4364-ab31-9c1cec923411}} , {{formula:6fbb34ae-aa14-4526-acec-0c9b56ba0d95}} .
It follows that:
If {{formula:45f4ab0b-b93c-4b01-8b2d-e354135da867}} ; {{formula:576760bf-937c-45e8-8fab-0eeb8c884d09}} , then {{formula:98b7d24e-552a-4769-b04a-f59b82579203}} has a single side joining {{formula:b75c21df-dd73-4838-bf62-6f9b576c49b8}} and {{formula:fa42f7a6-2f79-4d33-a432-25e985e0f36e}} . Thus {{formula:17608522-a0fd-4a5b-a6c1-d891af01a20a}} . It follows
that {{formula:016145ea-c994-42c2-b86b-3dc87327ebe4}} is an integral basis of {{formula:c9b0c8d7-bc92-4d65-ace3-8ce99b4aaa3d}} .
If {{formula:f5cf9073-1107-423e-b3d8-d7c444f1acc9}} ; {{formula:ba9941da-5d3d-46e8-99ee-dfec31776559}} , then {{formula:658860f9-9adb-4f76-b296-5840ec46ac11}} has a single side joining {{formula:0f902c3b-ee2f-4e56-b7a4-820da6a94607}} , {{formula:18b59fed-72de-4f06-9549-030cac94f950}} and {{formula:1cf8dd9f-5962-40a2-a7cb-ad5f64d3838e}} with residual polynomial {{formula:cb702293-d0fb-4dc9-95d3-1126e782423f}} , which is irreducible over {{formula:89df8807-9eb1-4c91-8def-96c7b2d01477}} . Thus {{formula:349f8bf4-2fc7-4d4c-8171-d8ef29b438ea}} and
{{formula:8b4b12ba-cd33-4fe6-b076-978930150db0}} is an integral basis of {{formula:5ee013bb-5cd8-4b9b-9409-4b6b4e1ab4d8}} .
If {{formula:44f0d2aa-7bda-4494-9f47-6ad5e2c1e53e}} ; {{formula:e251e534-861c-494e-8fcd-253e5b3bd16f}} , then {{formula:27029628-fd11-463b-9518-aedd800c3b4d}} has 2 sides joining {{formula:8c889926-d301-46fc-9ee6-b3303110dbd3}} , {{formula:8fcdefe8-bf58-4800-9555-159b7626364d}} , {{formula:90c26f0a-a730-446a-9d80-7398544fee9e}} , and {{formula:d62ecf7a-e626-46d2-a2f5-836e28587f77}} . Thus
{{formula:92b7a761-218b-482c-903c-10989187529a}} and {{formula:3486f3c0-1a76-4e3f-bb0e-7ecbd6af7ed6}} . It follows by Theorem REF that {{formula:2125c362-f489-4e2e-b88c-81f21857c85f}} and
{{formula:6fd9f160-6290-498c-abb9-7f6d14db0591}}
{{formula:b4be89fe-7f2d-4132-9500-2d18a4c39443}} is an integral basis of {{formula:91867ac0-b839-4fda-b4a5-534ef02adb65}} .
If {{formula:59473bac-1c63-461f-a872-5107648a4ae7}} ; {{formula:d4505df4-0687-4e67-b0bd-14ebb5820920}} , then {{formula:47346380-eff9-4d6b-8ad5-a7a80faeca5a}} has 3 sides joining {{formula:5352af1c-31c2-403f-9739-66994e6cf62a}} , {{formula:d08db37c-9531-412d-8bce-a4f15d5c6356}} , {{formula:e9940363-2877-43c6-848b-9907872e4e62}} , {{formula:252fd2ac-7937-4bb5-86f0-8ffb655fbbb4}} , and {{formula:83d82b44-88e4-4bff-958e-fee6be4b8e3c}} . Thus {{formula:8a9a1ef8-eebb-4080-be3a-51a4c3acd87c}} and {{formula:dd1d9e07-b2e8-4831-92e9-f3e52f688627}} for every {{formula:ae8e315c-30a2-4cec-8aaf-71d305cb903e}} . It follows by Theorem REF that {{formula:02ec2420-64e4-4076-8baf-86c361fec637}}
and
{{formula:d699c208-474e-4765-ae9a-2d76e7f5f33b}} is an integral basis of {{formula:2a986bf4-f80a-4f02-ba47-6ef72a8a3792}} .
If {{formula:802d7472-8cad-407c-8b58-ba47ca386555}} ; {{formula:ca5dbec6-8020-421e-920c-aeca4407efbb}} , then {{formula:ab8bbfbb-fde4-47c3-97dd-9904429afdff}} has 4 sides joining {{formula:06c0b9af-d8ba-4c19-9fd6-4a7fafcc7657}} , {{formula:cd8889a9-0f04-4c9b-a814-43e06c684bac}} , {{formula:6af8a93a-3c54-4b2d-ac03-68d42af332c1}} , {{formula:22ed917f-3d10-4a98-9276-d566b00e06b8}} , and {{formula:8b943d4a-2c42-4c47-925e-96d19311084c}} with {{formula:ce9183da-ca94-4a66-ab5d-8014b8ff0eac}} . Thus {{formula:898727e6-233e-426b-ae56-916fcc4c1c48}} for every {{formula:c84ac93e-f31f-4737-aedd-642e293bd701}} . It follows by Theorem REF that {{formula:96ae7e8c-ec4f-4331-845c-64047750b62f}}
and
{{formula:f4f67977-9344-4721-9e7f-cc4ad52e5205}} is an integral basis of {{formula:7441cf6f-1472-4a8f-946e-5f3eb32f1197}} .
| r | 32e1662b6e2c374b16ad0272fc194962 |
The integro-differential system Eq. (REF ) is usually solved by the conventional iteration scheme. Given the value of {{formula:ac7c28e2-a544-4637-9fd8-14163b77ee28}} at the {{formula:ca83970c-2676-4d2e-a20f-af80e5e0f317}} -th iteration step, the velocity distribution function at the next iteration step is calculated by solving the following equation {{cite:fc2934915020bef23b9c348785326d26d44f91eb}}, {{cite:2424beae88c927def4faa37136f458df69d86561}}, {{cite:62f7e134d2859d6f545c6a7b8ef7aaabce39905b}}:
{{formula:702b33a8-2587-443d-8c61-b8941dbfa3d7}}
| m | b6cec42c0d5d60baec34f38071d6adb0 |
The base-field interaction Hamiltonian is given by a dipolar coupling, in the rotating-wave approximation {{cite:96a8f06f90d73c32665581190b6247d5e0163050}}, {{cite:91d65ef3bf2fdb54d81cba0e837a09f810e16a57}}, {{cite:172221091d592f3c2d6c5be20392d5dde9a017a3}},
{{formula:a928934b-13a2-4768-9613-c50b54d49f18}}
| r | ddfb29a8fd5d1e05b463983c0af91265 |
In our study, we adopt a Transformer-based model architecture which has been shown to produce state-of-the-art results for AAC {{cite:fce85d2c47d2d91710105a379debd8f6f3a8ce48}}, {{cite:8b8f20ffba88e53c86fb12e99bd5abd865b86611}}, {{cite:748681db1dc9d124e1be81a765f21375ab9e2f53}}.
An overview of our method is presented in Figure REF .
It consists of an audio encoder, {{formula:9b8d4987-472a-4026-8dde-85bd83c02071}} , an embeddings' adapter, {{formula:650fa79a-8d7a-4093-8e6d-38cdc61f8e9c}} , and a decoder {{formula:7dc9a72d-aee8-408c-822f-432184b5dd7a}} .
As {{formula:990e4998-d543-45b2-a382-80887513d831}} , we employ different pre-trained models for general audio processing.
For {{formula:de49050f-f7db-462b-be1c-9ddf46950ddd}} , we compare the use of no adapter, a MLP, and a MHA component.
The output of {{formula:c1bc38c9-de9e-4362-9fab-f661b344a512}} is used together with word embeddings of the previously predicted words as an input to {{formula:5855c7ac-20f4-422c-9936-4c9f6acfa991}} , a Transformer-based decoderFor a complete description of the Transformer decoder, refer to {{cite:48bd3d0b9f073deb60140635d891df95327a94e5}}..
| m | 69f5076bca49d82b362dea05a9ab0bbd |
Proposition 8.1 (Lemma 1 in {{cite:4bf0cd54eb6b3cfe82c6bfcc2289df86d5da9c56}})
Let {{formula:cc59fef6-a97f-490d-a192-5cdcc5614b2a}} be the importance weight for two distributions {{formula:68898709-a071-490a-980d-b7621d4c56f5}} and {{formula:de84e50a-e88c-4333-84d4-3d58baf64776}} . The following identities hold for the expectation, second moment, and variance of {{formula:437b9824-c4e2-40a7-9b7a-32bc2a54eb54}} :
{{formula:8a02b793-a462-4d52-8c53-736dfb48ebcb}}
| r | c73a1f0ee513dcb0ae6b04227c1b2eae |
Over a relatively short period of time a plethora of explanation methods and strategies have come into existence, driven by the need of expert users to analyze and debug their DNNs. However, apart from a non-exhaustive overview of existing methods {{cite:d703e92d5a4466cf045d356a08feb873c2f0c0bb}} and classification schemes for purely visual methods {{cite:d773c885c3c0416923b3143b8295c2c7b6d45492}}, {{cite:272c50f0d7d99f589d3f5f2c036a207e2474b933}}, {{cite:3e65fd0c1ae24d61784cdbf910ec643f053cc78f}}, {{cite:41e67237dc3fd14a75025d75ed843a24bb95a0fe}}, little is known about efforts to rigorously map the landscape of explanation methods and isolate the underlying patterns that guide explanation methods. In this section a taxonomy for explanation methods is proposed. Three main classes of explanation methods are identified and their features described. The taxonomy was derived by analyzing the historical and contemporary trends surrounding the topic of interpretation of DNNs and explainable AI. We realize that we cannot foresee the future developments of DNNs and their explainability methods. As such it is possible that in the future the taxonomy needs to be modified. We propose the following taxonomy:
| m | cce01503baca1b1e7ecf1cd428fddd0d |
For each tracer, we calculated the temporal variation of the total unsigned magnetic flux by summing the absolute values of the magnetic flux density in pixels multiplied by a pixel area. Before calculating the magnetic flux, the maps of the magnetic field were preprocessed by applying a {{formula:eeb578e7-f2cd-44b7-97cb-1ad69d915c9f}} -correction to each pixel as described in {{cite:d615a957199b3599c4ddd472f4d04f15f3839cd6}}. The summing was performed over the pixels with the absolute magnetic flux density exceeding 18 Mx cm-2 that is a threefold noise level in SDO/HMI LOS 720-s magnetograms {{cite:d5e2d57c10c68b1e2dbe1c18142d0ef40c9aa110}}.
| m | 736dc5a2685e24f17b5478d9fa5be37d |
Main results. This paper makes two main contributions. The first is to introduce type-theoretic awfs's and show that they give rise to models of Martin-Löf's type theory with {{formula:5c35c642-6166-486b-99b4-6904e6b3a0e7}} -types, {{formula:6e7c8cbb-d33f-460c-b12b-4c36faad31c3}} -types and
{{formula:a8ed3027-17bb-4007-884e-9f04f2ed4ca0}} -types. The second is to introduce a general method to obtain examples of type-theoretic awfs's and to give a homogeneous account of several models in which dependent types are interpreted as uniform fibrations (in the sense of {{cite:1807d16fdde2ed80c8e71b8bc3ce9f08f32541f9}}, {{cite:baf93549d0e1ed26a52d720b754ff132128b4574}}), including the groupoid model {{cite:aaf4ecf00263c8aa077718a6ab65818851b897cd}}, in which dependent types are interpreted as split fibrations, and models based on simplicial and cubical sets {{cite:1807d16fdde2ed80c8e71b8bc3ce9f08f32541f9}}, {{cite:baf93549d0e1ed26a52d720b754ff132128b4574}}, in which dependent types are interpreted as uniform Kan fibrations.
| i | 588499366372928b2eff335d2d70fc27 |
CSSL's simple training pipeline enables the algorithm to be analyzed theoretically.
To do this, we extend analysis of the neural tangent random feature (NTRF) {{cite:2b626d0fbc6f9e7d2caf128b29864c14075fc7d4}} to encompass multi-layer networks trained via streaming to perform binary classification using a replay mechanism and data augmentation.
The analytical setup is similar to Algorithm with a few minor differences.
We begin by providing relevant notation and definitions, then present the main theoretical result.
| r | f8dbb934e132aef4f0b4b1c79df020fa |
Video Frame Interpolation (VFI) aims to synthesize intermediate frames from a low frame rate input video. It plays an important role in many applications, such as slow-motion effect simulation {{cite:c21f49570d137e9e80b56dbab04218d9a86523b3}}, {{cite:13e81d8358b33349c558fa8bc8cd2ae84b992fab}}, {{cite:0b97d5692ce5c709bc8d5782d45218d41929cbf9}}, {{cite:631c30b79c08bd055f29aaa707d585b2da1a36e8}}, {{cite:bd84d93324f822b1866c10b182bcaeb6de3a9089}}, {{cite:0e90b40b1cbe385e657ce7a18bb1bc5a765dfbb7}} and low-frame-rate video restoration {{cite:6ec82ff039b0bda2799e30233c35c77178572329}}, {{cite:75959b726a7de5ace0920efddd7bc4f8b9d4d5f6}}, {{cite:cc7d5ca8e424053457652ab6f936dc6bb989a77b}}, {{cite:cdb5ea0632ecfe2986925e7df40e64655f8dd0a8}}, {{cite:5d54d53ce072e0082495c487a653e3d2d84328c7}}. VFI is a challenging task especially for objects exhibiting large motions, not only because it is an under-constrained problem, but also because the complex deformation and occlusion can significantly hamper the performance of many existing methods that rely on accurate correspondence estimation between frames.
| i | 894c68e47217fb8d92dad8d84f4f6203 |
RIS-empowered wireless transmission has recently drawn substantial attention from both academia and industry {{cite:a0e4e2c7ca1353c1d457b3a34cd8a43a1cc09304}}, {{cite:7bc928b85ab2a4560fec8ba35acaa9d6446aaa44}}, {{cite:23cdc860f3eac1f981fa1136f2377064ab129f90}}.
There are many research efforts examining the differences between RIS and relaying technologies. Although RISs and relaying are similar technologies used to alleviate the blockage effect and enhance the system performance, the received signal is actively processed at the relay by regenerating and retransmitting with an amplification, while the RIS only reflects the incident signal without any active transmit module {{cite:6b41078a14a77670a6892aee2b33b99aacdf7da7}}. In {{cite:438bed6deb3cc8e7d6b60ebc37754ecfe9af2229}}, half-duplex decode-and-forward (DF) relaying and RIS-assisted transmission are compared in terms of energy efficiency, and it has been shown that the performance of a single antenna relay is achievable when hundreds of reflecting elements are used at the RIS. Moreover, a full-duplex relay-assisted transmission scheme comprising two horn antennas and two RISs very close to the relay has been proposed in {{cite:f23327ee96b490461629e46674973ec00d599f3f}}, and considerable improvements in achievable rate are achieved even with a low number of reflective elements. However, the consideration of two horn antennas for the full-duplex relay will cause high hardware cost, rendering end-to-end channel estimation difficult in the case of large numbers of transmission nodes and terminals. Recently in {{cite:489e3da08263fd5347fbca9c49fee57147340b60}}, the authors proposed a hybrid transmission scenario combining a DF relay with an RIS and showed that using a single relay for low and moderate signal-to-noise ratio (SNR) values outperforms an RIS with massive number of reflecting elements, while for high SNRs, RIS-assisted transmissions are preferable.
| i | 0b4f92bee6438c5eda6975d607fc97cf |
According to Cori et al. {{cite:4e24760371b0fc0b31961d42e747b26329f470ea}}, the size of the time window will impact the estimations of the instantaneous reproduction number. Small sizes lead to faster detection of transmission changes and higher statistical noise, whereas large sizes lead to more smoothing and reductions in statistical noise. In accordance with Cori et al. {{cite:4e24760371b0fc0b31961d42e747b26329f470ea}}, who suggest an appropriate way of choosing the time window size, we have selected a weekly time window to analyse the real data.
| d | edf9dc41b4f5c6d38f2f0dc22587583f |
Comparative Performance Analysis : To best of our knowledge, this is the first ever proposed multi-modal biometrics deep learning segmentation network. Hence, we have not compared our results with any other method. Although, one can compare it with the existing techniques, such as {{cite:75f0876d50047ab7d90efd8650dc7e7e01ab51ee}}, {{cite:fb890d10ad0f26527af9580bf75beb645e0cc11e}}, {{cite:2464ac9e7f56b1e19df61fd5f191489039e85543}}, {{cite:d8dc56285f38414aefc827922cf23425dfa7cc75}}, {{cite:16378466e0f72ddf28800533c378c1b90bb524a7}}, but such comparison may not be justified due to two reasons : (i) They have been tested only over single trait (we have performed multi-class classification) and (ii) None of them have used deep learning. Still we have observed that the proposed network performs better that previous individual trait techniques.
{{figure:7a588bd4-5dac-47c1-a36e-8de50f64a96a}} | r | 74da7b35b30d5edb29376f1a8870c793 |
The grand-canonical TB evolutionary search is performed using the USPEX code {{cite:b02d489a6bea3472b6296d509e10753ca7c36061}}, {{cite:346ced512dbe796f1f140795f3bc5f9d58dcdfda}}. The details of this method are described in the work by Zhu et al. {{cite:332678c55caca10be2dd937be7ef157d16cfb33e}}. In this approach, various mutation operations including the displacement of atoms, insertion and removal of atoms from the TB and sampling of larger-area TB reconstructions are performed to predict the low-energy configurations. The setup for USPEX is made in a way that we start with the supercell with the TB and apply relative displacements of the two crystals on either side of the interface. In addition, we perform addition and removal of atoms to a sub-region of the structure near the interface, allowing atoms in this region to be relaxed while the rest of the atoms in the bulk regions away from the interface remain constrained. The morphology and the thickness of the interface is found to be insensitive to these constraints. The robustness of these results is validated by two analyses: (i) the obtained structures from the USPEX search have been further relaxed by adding {{formula:39e17c07-8bd2-47df-b0ab-7e5111ee5ba4}} of vacuum layer on the free surfaces and removing all constrains allowing all the atom positions to relax. No changes in the TB excess energies and interfacial width have been identified in this process; (ii) the same USPEX calculations were also performed around a wider sampling range of {{formula:d6ba8eba-cf23-4496-aec0-9f6ea7cfcdd5}} subregion around the interface (compared to the {{formula:10c96ce9-66f7-416f-bab5-47e780700dc2}} region used in the original search) which is allowed to relax during the search process while keeping all other simulation parameters and inputs the same. Both of these analyses validated the robustness of the results in identifying the identical minimum-energy structures with the same interfacial thickness and TB energy. The USPEX analysis is performed with classical potential calculations at {{formula:3933e764-960e-4c0d-85bc-3cb0068a3bd7}} K temperature using the LAMMPS {{cite:e79388495378c346afb7d4db496a7dab19b73908}} software. The modified embedded atom method (MEAM) potential of Hennig et al. {{cite:ca5b25ef483c09a9941a864cac66d5d827d7cb8e}} was used for evolutionary search calculations. This potential is able to capture the TB excess energy of the ground-state and metastable structures of {{formula:6d760f36-1957-48a7-889d-4de0e13f2c5d}} within {{formula:0eff9aa7-d4f3-4ab0-9b7f-0923ccf190c1}} accuracy. Relaxation was terminated when the norm of the forces on all atoms is less than {{formula:6d760690-e6fb-4e04-892c-d1fc44fb45fb}} .
| m | a4df7e622dd07b3d72cd6368c78ce52c |
The privacy risks of DNNs have already been pointed out, where a DNN is prone to memorizing sensitive information of the training dataset {{cite:615e4f8e5cf534237c0e71fabfffe72883152267}}, {{cite:dc717e91ad3ea671fe7e8cd5bd2bf548b86af385}}, {{cite:4212dd5c67ccab54451184a6b0ab52ba8ddeeb1a}}, {{cite:6cc931377e6fdc5c911dcfe9db93bc475c1ac2af}}. Taking the membership inference attack (MIA) as an example, an adversary can infer whether a given data sample was used to train a DNN, seriously threatening the individual privacy. For instance, an adversary can infer an individual was a confirmed case, if it is known that the individual's record was used to train an infectious disease model. The MIA was first proposed against black-box models in {{cite:749695df1ed59513163c87e31d94669e3f90ebf8}}, where the adversary only has access to the data sample and predictions of the target model. Later on, more attention has been attracted against various DNN models, such as generative models {{cite:dc717e91ad3ea671fe7e8cd5bd2bf548b86af385}}, {{cite:4212dd5c67ccab54451184a6b0ab52ba8ddeeb1a}}, graph models {{cite:efbf484c970c895b31ddc7eb72cb3780a342df86}}, machine translation {{cite:d15da7cedd4dc9a9f73a51335f37ba69d7d0cb9b}}, text generation {{cite:346294f3eb39b852c3f72466a1926f950a4c8476}}, genomic analysis {{cite:84ce1235a325a59fc2d814be67b5bc0a4978cdbb}}, and transfer learning {{cite:4581b116619b822d972def111995d4e8319089a8}}. Although extensive analysis has been conducted, none of the existing efforts have been put into analyzing MIAs against pruned neural networks.
| i | 1f4a168e890c41228079ec4eda3bbf27 |
e) The Hamiltonian describing the odd system (REF ) involves a term {{formula:c8f33ab7-39c9-4fe9-b4c0-5facbdd53488}} which describes in a realistic fashion the neighboring even-even system. Indeed, this has been used in Ref.{{cite:61cbe98051a6b47777e820869b83eb776c85a4fd}} to describe simultaneously eight rotational bands, four of positive and four of negative parity. By contrast, in Ref.{{cite:e662682e45ba00181fb60b93579a6bad94b469a1}} the terms associated to the core are not appropriate for describing the complex structure of the even-even sub-system.
| r | 061f15b183051b122c6d33fa1911af47 |
It is possible to define the eigenscheme of a tensor which is not partially symmetric, as in {{cite:c58286be2f267608432002181ca35fd8c9541a64}} or in {{cite:0451cd3618591e46bc35035434031d7569977a11}}. However, with the choice of a basis described in Remark REF , it is apparent from the definition that for every tensor {{formula:d8a04317-1ed3-42be-b509-c09dc9fc11dc}} there exists a partially symmetric tensor {{formula:42c5ef4b-9bfb-4630-bb44-204f1a4d1a53}} such that {{formula:c3aa0571-bd70-4750-bca7-e01eb4b0c884}} . For this reason, it is not restrictive to consider partially symmetric tensors.
| r | cd66bc32a31b322c7418ff3f5583d69e |
To answer these questions, we first extrapolate the gas production rate in our KB from the most recent extrasolar models. To do so, we compute the dust mass loss rate in the KB due to collisions using a state-of-the-art model of dust in our Solar System {{cite:1f8f8b478def452a4fe7262577d4aa17a64ed9bf}}, {{cite:b00ad50e656c05d707e9a153b5d9432c562b7c04}}. Indeed, according to extrasolar models that fit most observations to date {{cite:66f4655a6f09bd962dea1ee90a4c97828890d8d7}}, the gas production rate is proportional to the mass loss rate of the belt's collisional cascade, and we find (see Appendix ) that {{formula:5fc5df7d-7cac-4255-8d25-c0abbffa902e}} M{{formula:b4a2877a-5c48-436a-8bb5-82aaaa6477c6}} /Myr of CO gas should be released in the current KB. The model's idea (which fits extrasolar observations) is that large planetesimals are composed of {{formula:89b501f8-5df3-41c5-af20-04f6c305fa22}} 10% of CO {{cite:66f4655a6f09bd962dea1ee90a4c97828890d8d7}} that is released along with collisions that produce the observed dust (but the detailed physical mechanism is not constrained), either at the top (large km bodies) or further down the collisional cascade, but before solid bodies are ground down to dust and expelled by radiation pressure. We also use a more direct approach relying on the counting rate of the New Horizons dust counter to determine the dust production rate (rather than a numerical model) and arrive at the same value for the gas production rate. We also test a different more physically motivated model for releasing the CO and assume it comes from the slow heating provided by the Sun over long timescales, which warms up large bodies at greater depths as time goes by, and releases the CO in these increasingly deeper layers. We find that after 4.6 Gyr of evolution, only bodies larger than about 4 km can still contain CO (smaller bodies would have lost it already), and all together they release CO at a rate of {{formula:dd00edc1-f5b6-44db-b89e-5ef9b4fdb03b}} M{{formula:1b9a9992-958b-42ab-a380-6518c3e5a5f6}} /Myr. In this model, a single 30 km radius planetesimal would release around {{formula:14bcc80a-b17f-4ea7-b7af-b8a3372fbc5a}} M{{formula:c317f3c8-e751-4a0b-8d75-42892ee4c0f4}} /Myr, i.e., it is much lower than what can be detected with missions targeting specific KBOs {{cite:823d25ed522429c630d8159c3e08f091a9d35452}}. Fig. REF shows the temporal evolution of the release rate, which goes down with time as only larger and larger bodies can participate as time goes by (see Appendix ). We note that this means that sampling the material in the KB now would not lead to the primordial volatile composition of planetesimals. We also test this slow stellar-driven heating model on more massive belts (similar to those observed around extrasolar systems) and show that it provides the right order of magnitude to explain CO observed around younger exo-systems, which may provide the first physical explanation for their ubiquitous CO presence.
{{figure:ed3c6125-450b-46fe-ba9f-2612c9082cda}} | r | 576a96acfef8121d6cc68a77e8df1498 |
Although this work focuses on the MPO algorithm for policy optimization,
our results also suggest that the benefits discussed in this report generalize to
other approaches that make use of a critic (e.g. DDPG). Recall that DDPG
with a C51 distributional critic is the very competitive agent known as D4PG {{cite:9ce1da245791d03894bca7bc916a100bb2d8c346}}.
{{figure:71555fef-e466-4ca1-8b57-dee8e24b4769}} | m | 1f6876d731500d9f952e679e8daa169d |
We then study the entanglement properties of states from these ensembles, focusing on the bipartite case (two fermions and two bosons). We analyze the spectrum of the partial transposition {{cite:35a046778a830786fe08145635152808340178a5}}, {{cite:8a6967c3b32ee3b065bf3bc9c2612b4d99544886}} of these random density matrices in the large {{formula:066e1330-dd91-4aa2-aeaa-9b284b668a12}} limit. For the bipartite fermionic ensemble, we find (see Corollary REF ) that a typical fermionic mixed state is entangled. This is due to the presence of a large negative eigenvalue in the spectrum of the partial transposition of these states.
In the bosonic case, the situation is more complicated, since the symmetry of the state is responsible for a large positive eigenvalue of the partial transposition. This outlier eigenvalue makes the study of the spectrum of the partial transposition more delicate. The asymptotic spectrum of the partial transposition of a random bosonic density matrix is computed in Theorem REF , which we state informally here:
| i | d3c7389054228c5c3b847ed0262b2b54 |
We consider a multi-label image classification problem with a training set {{formula:68c460eb-17df-4f4b-9814-7f0adaca1b65}} , where {{formula:9fc62614-c81b-4c78-8d6e-a3c600562c4b}} denotes the {{formula:150c41dc-c267-4582-8347-7f8aa93e4cc1}} training image labeled by a multi hot vector {{formula:c9675bac-86c4-4420-91e0-55b8d51ccbd7}} representing the corresponding labels over {{formula:98160565-77fa-4c0e-85ee-b79b7852f1bd}} classes, where {{formula:4c954f7a-d7d1-4327-ac67-1187940609c6}} , if {{formula:c3b822ba-a512-4f8d-8663-987af3c88079}} , and {{formula:f195b6ca-012c-42d3-9a87-70756a7dbf7f}} , if {{formula:114d81c5-3690-4b5e-823d-7ad3f3bd1fc9}} . We use two identical CNNs that are represented as {{formula:cbc88197-346b-4260-8787-928a70658aad}} and {{formula:cc1fd2ae-979d-4652-9534-31fdf18b3a3d}} with parameters {{formula:f7cf17e3-7d06-473a-ab4b-f3c117018536}} and {{formula:c91ceaae-7677-4bca-9204-48356c92aa75}} , respectively. For the classification loss function we employ the Binary Cross Entropy (BCE) as suggested in {{cite:bf7f959035143fe6d295d9781956513c5c2375c3}} for each network.
| m | ec590e8508731411820c575cd823b15c |
In this work, we introduce a regularization method for contrastive language-image pre-trained models which encourages shrinkage of the image-patch and text-token similarities. We demonstrate how our regularization method can benefit zero-shot performance of these models by training a model that achieves SOTA zero-shot classification performance on a broad set of CXR findings. The improvements were robust across a wide range of tasks relative to many strong benchmarks, though in some instances the improvements were modest. Though our work was confined to a medical context, we believe it should be broadly applicable to many other areas where CLIP-style models are used, though these applications were beyond the scope of the present work. We believe our work contributes to a growing literature {{cite:9f6f641beb5f3eac8a24cd5188daf3f4d5911890}}, {{cite:ed9092bd30c38fb99be4e2dddac9db7f9fda9050}}, {{cite:c5c294f757e590e8d71968c18c8c122cb52e04e7}} seeking to augment and improve CLIP-style models with inductive biases and domain-specific observations.
| d | 857c479104e5e91e9869bf24f14c2ede |
It would be interesting to extend our analysis to other types of inner boundaries. For instance, one can imagine cutting a disk from the cigar at some {{formula:45239b2d-e128-41e7-b3f8-7090ee2ebf58}} with {{formula:d71948dd-9f39-43f9-aa45-1bce9008bbd8}} and compute the inner boundary contribution to the entropy of strings and branes as a function of {{formula:a0a6926f-454e-4cda-990c-f6091561a8fe}} . A different boundary which would be interesting to study is a tip with a conical singularity, which was recently discussed in {{cite:c9273f92a9c56a12ee3afab0cec0c980445378b8}}. Another example to consider would be the Euclidean version of de-Sitter spacetime.
An interesting question is what fraction of the entropy does each string and brane condensate carry? We expect that for solutions without fluxes, the winding modes of winding number {{formula:2ef73df6-9f70-4021-906d-68704f0bde46}} carry most of the entropy because they are lighter than the other modes in a larger region of the manifold. For such solutions with a small string coupling throughout the manifold, branes are expected to carry a tiny fraction of the entropy because they are heavy.
Another interesting question is whether a near-puncture region can be embedded in string theory. This could be answered by attempting to construct an appropriate 2D worldsheet superconformal field theory.
Finally, our results could be complemented by mapping our Euclidean, target-space calculations to Lorentzian, CFT calculations as in {{cite:365a4a77473c94fdf202392637168b695144e6bf}}. We expect that the entropy is equal to the logarithm of the number of Lorentzian microstates with the same macroscopic energy and charges. We also expect the total length of a string to be related in a simple way to its entropy in a weakly-coupled string theory.
| d | 44824e16e641f2daa0408196e1e706ac |
Our proposed TokenMix consists of two parts, i.e., token-level mixing and label refinement. We decouple the two parts and then compare them with the previous methods by fixing one part. In Table REF , we compare TokenMix to ReLabel {{cite:7f595cac7597d9f34ad4e37fb7a6497dede5b0f2}} and TokenLabeling {{cite:f5a3876d915a2670c4ad2342e8cef4ef1ba9faef}} with the same data augmentation method. The two methods utilize pixel-level supervision, but our TokenMix summarizes neural activations to create image-level target scores and is, therefore, more robust to individual pixel-level errors. Note that we use the same teacher network, i.e., NFNet-F6, to generate the offline targets.
As shown in Table REF , TokenMix outperforms both ReLabel (+0.5%) and TokenLabeling (+0.3%) with the same training cost.
We further compare TokenMix to previous mixing-based augmentation methods in Table REF . For a more fair comparison, we only use the labels from ImageNet.
As shown in Table REF , TokenMix have performance advantages compared to other approaches. We see that the methods that introduce more foreground regions fail to improve CutMix on Vision Transformer. In contrast, our proposed TokenMix improves CutMix for +0.5% accuracy.
{{table:05d7b649-b2b8-4175-a800-7c4c3c95043d}}{{table:beccd507-3b7b-47e2-977c-b5c68dff5399}} | r | 0c9c51e9cdc4b08f8f39f403a9338042 |
Effect of Backbone Network:
In this experiment, we evaluated how our model behaves with respect to different encoder backbones. For this purpose, we employed MobileNet {{cite:e9b95f88a1b1ef608b170489af79eeaf20fec810}}, VGG-16 {{cite:06a12389ff19f84a1c67618a1420272352863528}}, ResNet-50 {{cite:f4d9ee1b16aa16fd3f9cba8c932d6e2cbf672b5d}}, and the proposed Dilated Residual Network (DRN), and measured the performance of the proposed framework (employing these backbones) for extracting the Gleason tissue patterns, in terms of mean DC scores. The results, reported in Table REF , reveals the DRN as the optimal encoder option.
{{table:57a6ac12-db63-4f01-adbd-9ec4f7aaa4a9}} | r | 8340ab7771d7bfeaf489631bf5f48ef9 |
Supervised learning has achieved remarkable progress in many fields with the help of a large number of labeled training samples {{cite:7b8c102199bdc20f6f2da942eaa3730fc7df73c1}}. However, when there are few and even no labeled samples, it is difficult to, if not impossible, induce a supervised classifier. Rather, there is a need for versatile algorithms that reduce the need for large labeled datasets across multiple domains. Unsupervised domain adaptation address this need by transferring knowledge from a different but related domain (source domain) with labeled samples to a target domain with unlabeled samples to improve the performance of the target domain {{cite:133bb3157a229f1323a0a33215dcf4dd20cbb951}}. For example, an object classification model trained on manually annotated images may not generalize well to new images obtained under substantial variations in pose, occlusion, or light. Domain adaptation aims to enable knowledge transfer from the labeled source domain to the unlabeled target domain by exploring domain-invariant features that bridge different domains {{cite:9993968432a8c42b3c9214214357024fd609047b}}.
{{figure:22275b03-0cbb-43c1-9968-ecb91535f1c1}} | i | baca8a431fa0b17c9e3a2848962a5e44 |
To tackle this issue, an intuitive solution in conventional SAR ATR algorithms is to collect the distributions of strong scattering points of the target in full ({{formula:d758a913-42e5-400e-bce9-391f274f335a}} ) aspect angles uniformly {{cite:1c0a4c7d9c6d900f0910792b13f3de6b7b61b38c}}, {{cite:66cae3efcaee5e468644f1a6e43b7d25419f5f2c}}, which will be subsequently constructed as a feature template in the hope to record all the scattering signatures in different poses. Then the identity of a query test target can be determined in a pairwise class-template matching manner. However, this approach is not robust to many disturbances such as speckle noise and motion ambiguity, which heavily influence its practical recognition performance. To improve the robustness, several hand-crafted image feature extractors such as scale-invariant feature transform (SIFT) focus on some pose invariant features to describe some intrinsic visual signatures of the target. These visual features will be normally more robust and achieve a better generalization performance by choosing a suitable discriminative classifier such as support vector machine (SVM) {{cite:5f7a4a675e75f2b3f40bf35f888283ffd8dd37c4}}. To further improve the discrimination and adaptivity of the features, many machine learning-based algorithms are gradually devoted to SAR ATR {{cite:c09bfe75f9de4596c1156ee81ce5368be6249972}}, {{cite:76f6a499012ce33a19917076a2c529c2b78ca5f0}}, {{cite:e714d4825e596b6f7acd548abe22593cb4df5cab}}, {{cite:09549d8bd8ab430dd04edb8bc4151e00035a8c82}}, {{cite:737d1f9d5a702a738a73f0de5ebc37314c2a5313}}, {{cite:5e21a130f9a723c01d2028b63e56647710907fb8}}, {{cite:647f390c4e1b06c65e45fb1f5ef44a70027e1a08}}, {{cite:569bb8f26de1265518170a6a961d17900c04b848}}, {{cite:29b7e46c9ebc11d9a6b8e867d26671075915ac7b}}, {{cite:1f1e9f4bb4baacafb73c5209c46e89b1988e5392}}, {{cite:40d74d937119256bcc6dcaab398f1958c5627628}}, among which the most notable model will be the convolutional neural networks (CNN). Distinct from the above feature engineering algorithms, the core idea of CNN-based algorithms to address the pose sensitivity issue is to fit a set of rotating target images as well as their class-labels with a deep neural network through which every intra-class rotating targets can be mapped to the same class-label. In this way, some label-invariant features are expected to be obtained in a discriminative learning way without concerning their variances in aspect angle, and the recognition performance can be remarkably improved in terms of both accuracy and efficiency.
| i | d0085831e8d44eaed591c19f06cf3716 |
Inverse source problems are of importance in several scientific areas including biomedical engineering, antenna synthesis, geology, and medical imaging {{cite:665c0f41c78f60658e6b65afdc425649ba7c65dc}}, {{cite:a19ce347dee387fc1004ddf17a72c8bc95ec9f5a}}, {{cite:cacc73a0c4f295712245f3f0a18e3ea47de96561}}, {{cite:5059210211ae0ae5bcd76a78dcf3e47833375f44}}, {{cite:4d276f8f589d220a32baba7eb0d47017da112010}}, {{cite:6417bc192eb984faa053334bc62181e76a004ac4}}, {{cite:e5cdf670fb9d7081716d87ff60017ee4ecec4c70}}, {{cite:61ecc0a9993df582fdf900e6a797f92e89b3ced3}}, {{cite:75fe9e2033e709f810fb3050f2a09f6ac3f440a3}}. In this paper we consider the inverse source problem for the wave equation. Precisely, we study the problem of determining the trajectory of a moving source in a bounded domain from a single boundary measurement. Identification of sources with time-varying locations has many significant applications such as the recovery of mobile pollution sources, or small debris in low-earth orbit, and underwater sonar systems.
| i | 4e60359953bb62fa62621e98ead9abce |
From Definition 2 any genuinely multipartite entanglement in the biseparable model {{cite:59b439d9a622d82a7a4d6db83aadac6cdd8e93f2}} is 1-CGE. Moreover, the present {{formula:1beb4804-fb79-47ce-b31b-ffe13c12d52b}} -CGE is stronger than robust entanglement with the robustness-depth {{formula:6dafde24-f48d-4c30-bff7-ba8e05e4dfee}} since the particle-losing channel {{cite:d5441e3002b2a875311c66dcfc1ef76eb61678e3}} is local CPTP channel. From Result 3 it generally requires to evaluate Schmidt numbers of almost all the reduced density matrices. This yields to a NP hard problem for general entanglement because of exponential number of reduced states. Instead, it is easy for some special states.
| r | 4de74a696b3eb74113adfe293a8aa344 |
We introduced the quantum theory of measurement to the process of HHG, which establishes the connection between the two mainly unrelated fields of quantum information science and intense laser matter interaction.
Using the general quantum operation in terms of coherent states allows to conceive new light engineering protocols for the generation of high dimensional, and controllable, optical entangled states.
Using attosecond physics as a novel platform for quantum information processing brings the advantage of the intrinsic ultrafast time-scale, together with the high degree of coherent control of the HHG mechanism by complex polarization states or spatial modes of the driving field {{cite:b80fc8df2e1320c1d88f678663f783a179cc5dd2}}, {{cite:9081f191ca21dbb996ff69dc4b92e9286f358f7d}}, {{cite:056e1897ec33e0e2a490266e70dfc6472fff208c}}, {{cite:0828720b7667c9c1b160addef57fc8dd5cd54774}}. This allows to tailor the continuous-variable non-classical field states in the desired way for quantum information processing protocols {{cite:586810d1e88996ccae6b530d64307b74df8e7dbe}}, {{cite:db8360b04a77f0f06c2fe7da3a3dfd0d0abfe8ba}}, {{cite:104f887145cfa2924d26cb09a9b20ee36d18dee3}}, {{cite:ce98ed9ffa2ed4784ba669f44081593c93d4ede1}}, {{cite:b144daaf03546460d152303ece63b43632e37b49}}, {{cite:bedcb2322e279646be3c15ce407dd62bd4c8ea64}}, quantum computation {{cite:cbf22bdadf1c2b74196d99edbee64bd37f7fe1ec}} or quantum key distribution {{cite:be0513ede99449947319a5a2bd3bb5b7454e23e0}}.
Furthermore, the entangled coherent state can be used for quantum metrology {{cite:aea97b8c10fb7b55e279a7dac136968fc2cd9528}}, or in correlation experiments towards the use for fundamental tests of quantum theory by violating Bell-type inequalities {{cite:582bb919b574de609ea2a0743788f46da70dc2e6}}, {{cite:85cf6d5fe6748bfb114894f9c03def143edc1526}}, {{cite:cbe256f195684ca65de2924f25fb62ce62af9ca4}}, {{cite:f84ee7c85663b3b35d3be5779a5c01c2c3c9477e}}, whereas the optical cat states allow for spectroscopy with non-classical states of light {{cite:dc29770b658f4e54554132f9310fd4524c461923}}, {{cite:189b53861667acc0a01241826cd0166edf5d25a7}}, {{cite:643cdede77b87aaf7c9bf4622c08c9ee3a8878b6}}.
Considering that HHG from more complex materials such as solids or plasma {{cite:ae654d55ff9becea5f1307d85e4c309fb4691efd}}, {{cite:2521d4d632ab21cc6f2ef533dcb2ff1b26478ac3}}, {{cite:62cf29b19996169cb23f02278fe06f0d4eca90fc}}, {{cite:e870c2fc6a46b42a0f25b31775d609ec9fdc8f1c}}, {{cite:6d0c44a142022dfae8ceb1b278e096312c07ff3b}}, strongly correlated {{cite:d651c174f48f43daa4b622c1ca1846734f1b3e2e}}, or topological systems {{cite:0de0532f4b4397cf42d342bb52c3387c1a4e8c15}}, {{cite:e45b530c356d181aab5d3e0d66145a0dd25ba7ea}}, {{cite:9e59b86fa1b194c39bb23aac0b914446b83e39b3}}, {{cite:fd068f2691bcdd87854216d515e77864170e93d2}}, {{cite:e7dbe43b0e0205304f4dc11fb93b36ea3c36bbf2}} follows very similar mechanism anticipates for further investigation of the non-classical properties from the interaction with such materials.
In particular, entanglement in strong field driven processes, for instance, between the ion and ionized electron {{cite:cb6843335bee35b713a86af8d3050101360f355b}}, or in two-electron ionization {{cite:e6ecdb8ea1a5d890b1a4668a8cd2ff97cf7c869c}} are of current interest.
The connection to quantum information science will
ultimately help to answer the question of the quantum mechanical properties in intense laser matter interaction from atoms to complex materials, and how new quantum states of light with the use for modern quantum technologies can be generated.
| d | 32951c56661bb58c2dc3a889a537c3d0 |
It should be mentioned that as for the unconstrained tensor decompositions in {{cite:0f7026177f523b7df506f4f6a40835c0d11a4bed}} and {{cite:aabcebba9d88b3b87f73b0b1c8ace00e5e5e3276}}, there is no guarantee that the proposed constrained Tucker2 decomposition is unique or that it will converge to a global minimum. In fact, through extensive simulations, we have been able to verify that the non-uniqueness is, in general, up to a permutation and/or a phase rotation in the columns of {{formula:75018bc4-e81c-40dc-8bfe-dcb261909452}} and {{formula:3bcd1564-7dcd-4431-b25d-5dd4d888214c}} .
Simulations under different scenarios have also shown that each inner iteration in Alg. REF provides increasingly better value for the objective function in (REF ). Thus, the convergence is determined once the objective function ceases to increase. From our simulations, the algorithm require on average 4.36 iterations to find each analog precoder and combiner vector pair, and has converged with less than 10 iterations in nearly 95% of the trials.
| r | b77b0d081f0591270b2db6136b417d1d |
We conducted small experiments on only models described in {{cite:d1a65c6c744156342350e8bc7d96da1d501eeccd}}, {{cite:92f9fdeef234f0eb56d30c909b9dad4a28b18d8f}}, {{cite:f2688cda9b4f3de7d651dc628035821d42731a3b}} using the same experimental setup described in sec:experiments. The CIFAR-10 dataset was used, and the results are presented in appendix:table:otherformularesult. appendix:table:otherformularesult shows that the ASR of the formulas whose enumerator is {{formula:929080c6-1b5d-453a-b1df-d2416a28094b}} (PR, HS, LS) were higher than those of the formulas whose numerator is {{formula:2066750d-29b6-424f-83ff-9f4fb4e8f177}} (FR, DY), and that the ASR of the HS formula was the highest.
| r | 64d27b19efd8daf051365824f2ff8b0b |
The TAP equations have many important consequences in the study of mean-field spin glass models and related applications. First of all, based on his iteration, Bolthausen {{cite:2e7cbc69fdd8c37bc6d6e7c8e66da1f628489404}} performed a conditional second moment method to derive the replica symmetry formula for the limiting free energy in the SK model at very high temperature. In a follow-up work, Brennecke-Yau {{cite:b29262330d1215cda55d106ac52d483b88c79604}} provided a simplified argument for Bolthausen's approach and extended the replica symmetry formula to a larger regime. In addition, the TAP equations have played a key role in some optimization problems in spin glasses and statistical inference problems. Most importantly, they naturally give rise to the so-called Approximate Message Passing (AMP) algorithms based on Bolthausen's iteration scheme {{cite:dbb33fb77de856e322d2173aabbf51348e366156}}; several generalizations of the AMP algorithms can be found in Bayati-Montanari {{cite:0c97caad95c77e81fefa90dddba07cac02723677}} and Javanmard-Montanari {{cite:3d15d494c7bb3c7e9719f5077049667ce3d03a32}}. By using the AMP algorithms, Montanari {{cite:157c4a42f4ffb4964c5c839decb2d8a6ecb212f0}} constructed a polynomial-time random algorithms to produce a near ground state for the SK Hamiltonian under the assumption that the Parisi measure is full replica symmetry breaking. The same construction was also carried out in the mixed {{formula:b5e9f6b1-fe79-4c6c-b97c-b996ba1b7b81}} -spin model by El Alaoui-Montanari-Sellke {{cite:73b806a419130221c651aeb03a4c5b42c65feca4}}. In the context of Bayesian inferences, various AMPs driven by the TAP equations have also been popularly used, see, e.g., {{cite:254b114e541fcdb3750eaa05ffa225ce5d80405a}}, {{cite:7c6d27e9d4c4338a1d14e008591b6696b875c4e7}}, {{cite:b029036f2888373fdb4c28f15616be8c9ab4d851}}, {{cite:20a9129333b5b9f0cc9867ff851744fe92698f57}}.
| r | c0767253c259d5a4dec47c7ca2bca148 |
The Standard Model (SM) predicts a neutral Higgs boson particle whose couplings
to other particles are proportional to the particle masses, and that couples to
photons and gluons via one-loop-generated effective couplings. While the Higgs
boson mass is not predicted, the relation between the Higgs boson mass and
its width is fixed from the predicted couplings. Virtual Higgs boson
contributions to electroweak precision observables have been computed,
and precision data favor {{formula:2f728098-c25b-4074-90e9-e986fd244a18}} at 95% confidence level
{{cite:c17639718d0d62a8ea1771e53a05347b631f489a}}. Searches at the CERN Large Hadron Collider have
produced 95% confidence level exclusion of a SM Higgs boson for a
broad mass range above 145 GeV {{cite:4deb03326cffba6a06b51b667cd1d0bc5b51af07}}, {{cite:f25314c8b8e86bc2f01ec67da58b74cf19291f75}}.
| i | dfd9be75c6a6ab5668b1162b118bdb4b |
We evaluate our late fusion multimodal classifiers following the cross-subject protocol from {{cite:e07d9d332854c28a5f800eec4b9229c749179b48}} for Toyota, the inter-dataset protocol from {{cite:d7b0a7f5c182e3387c04b717a0525333856fc702}} for ETRI, and the official test split for Sims4Action from {{cite:895c362968aef64964bcb0545dc1688a14242863}}. We follow the original Sims4Action{{formula:4f85a6f7-bf62-4c8d-8276-706cc591f1c2}} Toyota evaluation protocol of {{cite:895c362968aef64964bcb0545dc1688a14242863}} and utilize the mean-per-class accuracy (mPCA) as the number of samples per class are imbalanced in the Real test sets. The mPCA metric avoids bias towards overrepresented classes and is often used in unbalanced activity recognition datasets {{cite:e07d9d332854c28a5f800eec4b9229c749179b48}}, {{cite:e424450c203535eb7c220d7c8dc5c259e0394fc3}}, {{cite:f8268f9cbb58f32460f453764d6a74b0fdd78afa}}, {{cite:895c362968aef64964bcb0545dc1688a14242863}}.
| r | 7d198847249fb740b132f41824cb3cc7 |
In TABLE REF we provide the reconstruction results, training datasets, and model parameters of these models (lightweight models and large models are separated by the bold black line). According to the results, we can find that: (1) using a large dataset (e.g., DIV2K+Flickr2K) can make the model achieve better results; (2) it is not entirely correct that the more model parameters, the better the model performance. This means that unreasonably increasing the model size is not the best solution; (3) Transformer-based models show strong advantages, whether in lightweight models (e.g., ESRT {{cite:6059142f334df43f8349b9188d1f828065e6808c}}) or large models (e.g., SwinIR {{cite:36d2925ff898a5abef95b1ba4c1ee285803f46ab}}); (4) research on the tiny model (parameters less than 1000K) is still lacking. In the future, it is still important to explore more discriminative evaluation indicators and develop more effective
SISR models.
| r | b0c527f48ee29ec0e402dd652246cae3 |
More recently, in view of its impressive performance in domains such as computer vision {{cite:e209c330dbcec6d0461037d8f847ae7227325321}}, speech processing {{cite:6532c68cc7b638c0d3e25314adb845f211863c7f}} and natural language processing {{cite:5a81ce5e4bef64de15c16234ef54ddd41d57bb51}}, researchers have also been using deep learning (DL) approaches to support source or channel coding. For example, in the source coding domain, Google research has demonstrated that DL can lead to outstanding image compression results {{cite:6fd189a8f58e4bc7fb4c310a46cb4937204183de}}, {{cite:909099168394185098ec10448e12cff67092e4c0}}, {{cite:7933a52670a56f5c5a11783ae9e8c380d52ec7a9}}, {{cite:b5a369b38f00f240e8612d452ff692b65dea8092}}. Toderici et al. {{cite:6fd189a8f58e4bc7fb4c310a46cb4937204183de}} and Ballé et al. {{cite:909099168394185098ec10448e12cff67092e4c0}} demonstrated the DL based autoencoder {{cite:0273943d2ae001665674715e6b315ddbaeb007a5}} can achieve better compression performance than JPEG and JPEG2000, respectively. Minnen et al. further improved the method of {{cite:909099168394185098ec10448e12cff67092e4c0}} that completely surpasses the hand-engineered image codec BPG in {{cite:7933a52670a56f5c5a11783ae9e8c380d52ec7a9}} and {{cite:b5a369b38f00f240e8612d452ff692b65dea8092}}. There are also some other works. To improve the quality of image compression, Jiang et al. {{cite:4076ad5b30cccca2258a55eb3ef7937650403702}}, Mishra et al. {{cite:f0239348c10d3c1e1d4984e60cfd881a4b55ba1a}} and Zhao et al. {{cite:f16db263460a9fcd1d50674ae8486503b18e3006}} proposed to combine existing codecs (e.g., JPEG, JPEG2000 and BPG), wavelet transform and multiple description coding with autoencoders, respectively.
| i | 3cb5b5b3f86677ea705d8ce991384e79 |
Case 1. Since the DP equation (REF ) also admit the peakon solution {{cite:698e9855e8e47becdd57d9cdf8dd45641732932e}} {{formula:384691a2-1000-400a-b279-7ad10a8cee7d}} , thus we consider
the initial value condition (REF ) and periodic boundary condition {{formula:9c38b843-e880-469e-aaff-3b4ad1a88495}} . The considered PINN {{formula:0eb62e8e-ccd2-4e42-8fbb-160c5602e8c7}} is chosen as
{{formula:97c75d50-dec5-4fa6-b965-b0893d6bb6f2}}
| d | 9be1f7a8bfdbbd8729f732a3a0bc6867 |
More precisely, the process {{formula:024dd82c-ca7e-448a-8955-3a384c2a62c0}} considered here is
non-evanescent due to the periodic boundary conditions of {{formula:92847d08-732d-402b-8aa0-bd6d9dc867c8}} . It
is Harris recurrent if it is in addition a {{formula:cff6e1be-cb77-4c61-b38d-cdb909a42253}} -irreducible
T-process ({{cite:3da9475100e66be504488329399a8457931bc7b2}}, Theorem 3.2) and the positivity comes
from the existence of an invariant probability distribution
({{cite:c1a3b8b0bd893f7e66a81f0c315bdf1593d86fee}}, {{cite:237f806c42def36c51b5a3015f1761eedad20ed4}}). Finally, a positive Harris recurrent
process with an invariant probability distribution is ergodic if some
skeleton chain is irreducible ({{cite:3da9475100e66be504488329399a8457931bc7b2}}, Theorem 6.1). This
leads to
| r | fbb27b872aaae659dfdd094c56b410a1 |
Approach 1 - Stratified batch sampling: This strategy aims to modify the training sampling strategy to remove the discrimination before training. For each training batch, the data are stratified by the protected attribute(s) and samples are selected to ensure that each protected group is equally represented.
This approach has previously been used to train fair classifiers {{cite:7ba2a9458b70ee2c946228d4b8107df632165b72}}.
| m | c22e20c2335b24dfe96d3fad16e60c25 |
JPEG {{cite:725bab6993a0291bbe4d9d8998a90fda15ba5f60}} provides a lossless operation mode which uses a pixel based predictive coding scheme for compression. The current pixel is predicted from the immediate neighbor pixels to the left, up, upper-left and upper-right. There are eight predefined prediction modes which are generated as different linear combination of neighbor pixels using only addition subtraction and bit-shift operations.
| m | 44056e75e38f46dd1b9991fb02c7d197 |
The screening effect from rare-earth atoms {{cite:aa9c545c66674b7fc76e8e63ebb76ee8cbddce56}}, {{cite:11797884b5776a8f238c21eca3f40bd9f68c114c}} could be
responsible for the competition of magnetic orders. At small {{formula:33559b3d-c50a-405c-98dd-e874a60308e6}}
where the screening effect from rare-earth is strong, the electrons tend
to form on-site triplets with energy {{formula:6052b964-ca86-428a-af41-bc39f375aa87}}
{{cite:0a17be2a20137674d4b45845d8af50e5c7c9c536}}, coexisting with singly occupied {{formula:8a1c084a-1d7d-43a1-bec3-1ae8e0b9e155}} orbitals. Then
increasing {{formula:0a4352f6-3685-4e8c-8cf9-5d2b2063c1ff}} enhances the interactions on {{formula:b0af3374-7d24-431a-8add-3ec852067f48}} orbitals and the
on-site triplet energy surpasses the bandwidth of {{formula:05ea8ba5-cec2-461c-af90-1429ba4f5e41}} orbital, i.e.,
{{formula:6e4f24ac-11e0-4318-846e-04a4735609de}} ({{formula:57c850cd-f35c-4da7-8af4-fd53252aac73}} ). The largest hopping elements
are the in-plane hoppings along {{formula:f9f6e02d-af22-4c08-bc7c-cd45a542e1b3}} and {{formula:60bd766c-1e20-4c07-a59c-369424278dea}} direction of {{formula:41025c87-e532-4545-b2a2-1eccd06db219}}
orbital. Another transition then occurs when the on-site triplet energy
overcome the bandwidth of {{formula:3d4641a8-a370-41f1-a660-ec28c422ff48}} orbital, becoming a Mott insulator.
| r | 86f07f8348ba01ff7ed9b7117525dca1 |
This work features a low-complexity version of the framework to assist with network comparison and reducing computation time.
For comparison purposes, the number of deep learning techniques applied to any NN architecture was kept to a minimum: only dropout, which itself was inspired by the stochastic Poisson-like firing of neurons {{cite:9eb3fd519464beb52c0cee7e7a6d10db545d004a}}, {{cite:c530e8510bb8d1ea8abaf36654c6f49f233de335}}, was employed.
For computational purposes, the maximal simplicial dimension was capped at two.
Future work could involve higher complexity, for example, a biologically relevant functional simplicial complex of higher dimensions where simplices imply a connection that is experimentally supported.
In both the low-complexity and biologically inspired cases, it would be worthwhile to analyze the learned filter parameters and better understand the dynamics of the simplicial convolutional layers.
Similar analysis to existing NN architectures, such as CNNs, has shown an understanding of the learned parameter space can be exploited to improve network performance
{{cite:de70c6aabb5223788f50e470bb0b080e72a512cb}}.
| d | a2fe9160a4cd32b959ec49b773526308 |
Generalizing our work to the learning of other minor subspace analysis based tasks, such as slow feature analysis {{cite:0bd202d7f63f4d565d1719e02b7cd44b722fee5f}}, will open a path towards principled biologically plausible for invariance learning {{cite:e078bcebe35788a9360632ea6d1536f09ceada53}}, complementing the work on transformation learning from {{cite:31299bb02f5afbf17217c23040b165c9eefca8f7}}.
| d | 7a1a7b1d67db1b44c635efe0405e786d |
The practical scenario considered for simulation is illustrated in figure REF .
The AP is located in {{formula:f5745e82-e419-40ed-a50b-cf0fc56e6330}} .
The multi-antenna user is located in {{formula:55bb0b72-8cca-435d-a909-5a59e3e76336}} .
The distance between the AP and the IRS is {{formula:702b1ff1-c919-4b1b-89cc-bfe385ce6070}} and hence the location of the IRS is {{formula:88c787a4-43ba-4b4b-8f02-61609a815912}} .
The unit of the distance is meter.
The path loss of the direct link is calculated by 32.6 + 36.7{{formula:8c0ce1da-d705-4e82-a704-9af873aa5046}} dB and that for the reflected link is 35.6 + 22.0{{formula:81091ded-f4e4-4a92-ba18-e53b9297490e}} dB {{cite:80c0a734d28d4a3de8e841790f78bd63dcde9d12}}.
The noise power spectral density is set to -170 dBm/Hz and transmission bandwidth is set to 180 kHz {{cite:80c0a734d28d4a3de8e841790f78bd63dcde9d12}}.
| r | d093ab8b6858d14b301983ae523361be |
Various GNNs have been proposed to achieve higher performance in low-homophily settings. For instance, Geom-GCN {{cite:25d0fdf82b83ee0b5dd6803a46892da5900cc48f}} introduces a geometric aggregation scheme, MixHop {{cite:6fda67ceb8d69ea3603b8c64d2350808624f8ddc}} uses a graph convolutional layer that mixes powers of the adjacency matrix, GPR-GNN {{cite:a5bda46dbf86d8a1517f053c1db621197d99406e}} uses learnable weights that can be positive and negative in feature propagation, and H2GCN {{cite:0968006db138223535749a229b513de57d368717}} shows that separation of ego and neighbor embeddings, aggregation in higher-order neighborhoods, and the combination of intermediate representations improves GNN performance in low-homophily. Also, various methods that only depend on graph topology have been proposed for non-homophilous settings, which are based on label propagation or supervised learning models {{cite:a3db7ac872750436481362e0a19e009da78e77f7}}, {{cite:058821bbabf63cdaf2ca8adbcfdbd021ccd93588}}, {{cite:a7617b166d68f95782f2904dcd1cd32ebc49128f}}, {{cite:9f1c4e2af12ae533c0ac808b374d04139ec84ea8}}. There are several recurring design decisions across these methods that appear to strengthen performance in non-homophilous settings: using higher-order neighborhoods, decoupling neighbor information from ego information, and combining graph information at different scales.
| m | f7c7808aabce4afea426819407d36568 |
The Hubble constant, measured by the SH0ES collaboration to be {{formula:4dbed65c-6df2-4c6a-961c-679173afe998}} {{formula:451fc64e-6c47-4bf0-bf45-d23564b1e11d}} {{formula:afa19582-b3de-4817-9b1b-6d4cf3da6af2}} km/s/Mpc {{cite:4f3038a857e9687a08a83288159a9e312f88affd}},
is in conflict with its inferred value from the Planck 2018 measurements of the Cosmic Microwave Background (CMB) power spectrum, {{formula:cd84e61b-8d89-4c70-b61d-daec42b96c3c}} km/s/Mpc {{cite:2fa1f1b865861c22b404f6c2df415968ada817c7}}. This difference constitutes a {{formula:1f3a8b34-de21-47c2-938d-56bd2861b1b2}} tension. There is also tension in measurements of the amount of large-scale structure in the universe. The tension is most commonly characterized through the quantity {{formula:2b2c2e67-0a97-4c12-8a5e-778f95088ff6}} , which is defined as root mean square of fluctuations in the matter density contrast at the scale {{formula:9feb08d4-fbd0-42d0-8058-895d3a661a39}} Mpc {{cite:2504882ac2302aca4437603ee59844ef6d6b5a06}}. Often, the value {{formula:bb2f4a94-d82b-497a-8366-a69632a3d2ef}} , where {{formula:adf73ff3-b7d2-4fc1-9b11-483daf81e2ea}} is the total matter abundance, is used instead. The value predicted in the {{formula:596a2203-7952-4d87-ab5e-c354f083b615}} model from Planck measurements is {{formula:9c98bed6-535d-4269-a9f1-121191ce3dd9}} higher than the value measured in various galaxy clustering and cosmic shear surveys {{cite:0163d54d2977b4c0e87bdf3efe3876437c6a62df}}, {{cite:ec697cb9bef41df598a062fba4558d3a99b68aec}}, {{cite:2504882ac2302aca4437603ee59844ef6d6b5a06}}, {{cite:00c635653bf0d2deffa7baa4ab9b98c94304aa95}}, {{cite:7844c47102aaaa6420dc34199ae6188d62d535bc}}, {{cite:3d4e7bde08a9fbe8a7d8ee52af88f9af69834dfc}}, {{cite:a4839514a253356989818c991f2ee2c9ad475200}}, {{cite:bca95875208074e3cb1819fcbef703316eb89365}}, {{cite:5aa6562f407b6b7a5f42aac639fa7314907a1268}}, {{cite:0426b42cfbff186a602b9883414e065ef848c3bd}}. The statistical significances of these tensions vary, but as time passes without a resolution attributable to misunderstood systematics or errors in the local measurements, solutions to these anomalies based on physics in the dark matter sector have garnered increased attention (see e.g. {{cite:2153cb47f74c146b7d2bb7f75efeeadb939f23cf}}, {{cite:2bd47933c1627618dfdeac7d708415172fc93706}} for a general overview).
| i | 5cab9fedb1b47ca66e3d8315ed48afbe |
The angular averaged sensitivity is one of the basic measures to characterize gravitational wave detectors {{cite:3ba3fc8086fd69b6ae10788e79ac8b6a8f0317b9}}, {{cite:bc0a172c7f5444cd7cec5805bfb7ae38665dcd46}}. If the noises of detectors are statistically independent and have an identical spectrum, the angular averaged sensitivity of their network should follow a simple scaling relation with respect to the number of detectors. But, in reality, gravitational wave backgrounds can induce correlated noises between separated detectors {{cite:10b1eaafbfccae6f442231c539340b04dee3bd85}}, {{cite:abcaa39cbd14b37fc9f57a3612b24712c063209e}}, {{cite:da202ee432a2202b86495868e715e2322ccc3bec}}, {{cite:24fed0cb9b76986ce51292dad4699c509b1e71b1}}. Resultantly, the background noises break the simple scaling relation for the angular averaged sensitivity.
The situation should depend on the geometry of the detector network and the strength of the background noises relative to the instrumental noises.
| i | 09e74813635e4dce3f4984588b426750 |
To the best of our knowledge, we are first to propose a GAN-based framework that is able to learn an abstract representation of the market that can also react to the observed market state.
The proposed framework leverages a Conditional Generative Adversarial Network (CGAN) {{cite:dbe38ee530e9ffb565175fe7894b6fb97a146b47}}, {{cite:bfb0c83f6c5e35a874428f7e8ee379b1dce803b7}} trained on real historical data, to capture the market’s behavior as a whole arising from the activity of different participants. The CGAN is trained to generate limit orders conditioned by the currently observed market situation.
A world agent impersonated by a pre-trained CGAN that is placed in a simulation environment, produces orders to be processed by the exchange. This agent represents the whole ensemble of trading agents of the particular symbol on which it was trained. Such simulation test-bed allows to evaluate any experimental agent, while guaranteeing realism of the produced market trend and market responsiveness to the experimental agent's activity. We show that the market traces generated by the proposed CGAN-based agent preserve the statistical properties of historical data, and at the same time expose a reactive behavior against experimental agents.
| i | b28d47561becff539048de8637918133 |
Comparison between the present formalism and that of Ref. {{cite:e662682e45ba00181fb60b93579a6bad94b469a1}} reveals the following features:
| r | 59d42d30312a79d5186ae9cb6e8adf46 |
Most studies consider long-ranged topologically ordered systems in two and three dimensions.
The models predominantly are located on lattices that discretize a two- or three-dimensional differentiable manifold.
In this paper we construct exactly solvable models for quantum phases on connected graphs which do not fall into the usual setups for physical systems, since graphs include broader objects than discretized manifolds.
However a graph is still a topological space and can be conveniently thought of as a one-dimensional CW complex {{cite:2aa947bb33cde4b9a8255fcc26115f08dfa460a0}}. In fact physics on graphs or networks, as it is sometimes called in the literature, can be rather non-trivial, with early works studying the issue of particle statistics on such spaces {{cite:7a844ab90cb30fe41f3a4af2af39f59c16c71c49}}.Graph structures also appear in the physics and math literature under the name of quantum graphs especially in the area of mesoscopic physics {{cite:2d6e3acb7bb6d996bb1c8c9365185790f596e77b}}, {{cite:f42ec1a6f7ea17231b965b3f87425c9ff830e9eb}}, {{cite:d3dd5af667ed43f9b23d3dc39202df8e8c6d7569}}.
More importantly, there have been studies exploring the possibilities of anyons on graphs, both abelian and non-abelian ones {{cite:975c87c42a024afcdfbd158a1a69eb58fe2a365e}}, {{cite:f15e2b83d1e5cd288fdca04533e61bf743e5bbac}}, {{cite:9dbb7e377b324e58fb74c023d7dafc82d15fa04f}}, {{cite:cf60a448dbebcc91045b26e4913f001ebf4bbeb8}}.
Analogous to braid groups being the fundamental groups of the configuration space of {{formula:f23dae4a-3f68-4113-b405-b98b2d874acd}} identical particles in {{formula:f2ad7893-d9d0-4545-83cf-23145563ca03}} {{cite:e82c94d50e04118effab2e377bff335418adc82e}}, graph braid groups play a similar role on
different types of graphs {{cite:88e2c6feb203d71b9b98f5b782a1f63a960691da}}, {{cite:bf83c1b90375a6c5deac2852e820fd26468eb427}}, {{cite:3285e451308c2c3024028e32e99534b36fef96ee}}.
However, these have a fundamental difference from the conventional braid groups, as the generators do not obey a Yang-Baxter type relation.
| i | 6297778e856548a815d4fbcc6c7e818f |
Subgraphs are studied to understand underlying mechanisms of graphs like gene regulatory networks, food webs, and the vulnerability of networks to attack, and sometimes used prognostically. A popular example investigates motifs, subgraphs that appear more frequently than under chance {{cite:28d66f7a091809791ebd4320724e609d146ee776}}, {{cite:248e482855eb64b14d130368a50d34086a1f1e0f}}, {{cite:9899a257c8e915c99b06bd2068d0e3b0c7606e8d}}, {{cite:04be222cfc481425139d8c186c753f49ef00d622}}, {{cite:680b3b4dd15ea2ad4babe1e6789121448700484c}}, {{cite:fcadcb707632ecec316280b055a50e2a7c4a7a21}}, {{cite:23d54509ca5577fb0589c8725f728c6895e09ef7}}, {{cite:78796c1ca789e0eba1607cdca9d222f685caa1ba}}, {{cite:912d975a6ae5891e7a4b556c120992d0b1feca01}}, {{cite:108ce6703a66278fadf9005779c575d3d4342aa3}}, {{cite:aa429ae4413a3d89b7a07eb7589f8efbd8cb5463}}, {{cite:51eeb128106a5eb61b5e5fbcecdb2df6efdc9d9b}}. Although the study of motifs is along a different direction and often focus on one-graph datasets, our framework learns rich latent representations of subgraphs.
Another line of work uses subgraph counts as graph similarity measures, an example being matching real-world graphs to their most similar random graph generation models {{cite:8d66007417eb3bd3f81215aae13b8f84f3faef6d}}.
| m | e91b28fae685454750e7156c96b7b522 |
Human Judgements. For more comprehensive comparisons,
50 inpainted images from GC {{cite:358be4d3b510bcb2e32a9af3167f1b871efbb99a}}, EC {{cite:4ccd3f33e38d996f9a20cd964c819be9f5096f58}},
and ours are chosen from ShanghaiTech and P2M randomly. And these
samples are compared by 3 uncorrelated volunteers. Particularly, volunteers need to choose the
best one from the mixed pool of the inpainted images with different
methods, and give one score to the respective approach. If all methods
work roughly the same for a certain sample, it will be ignored. The
average scores are shown in Tab. REF . Ours method
is significantly better than other competitors.
| r | 11631004b0ab4302d7b6ea910d0f4c9d |
Representation learning of patient Electronic Health Records (EHRs) is the foundation for data-driven personalized healthcare and clinical decision support {{cite:de55622024d2e286cd042f35d4d6f8b7af2ae07c}}. Many approaches, in particular deep learning models, were proposed to learn EHR representation {{cite:0a194b2e5d9f3398f16ec8c2f6ebeb44c33bf8cb}}, {{cite:b1778afb07f4c5d9f1e4ab8c5f1e5e3eb2332f4b}}, {{cite:292ec5afc02374bab1789b090ffcd16861f02433}}, {{cite:63e80d37f0d792567aeb0717b720d145f60792b7}}, {{cite:44008929bd9a7e4decf7859b41128d5249b677a1}}. However, all of them rely on task-specific label supervision. Annotation on large-scale EHR is challenging, thus, not ideal for an unknown clinical problem with unlabeled medical records, e.g., patient similarity search {{cite:fbfa1ec1b1d7f35713ceffe8a6c8c69e6cd2b613}}. Autoencoders {{cite:b035cdf815eee14713555535a133590ab19d251f}}, {{cite:d75920f2b7b3fb4347a035b5507c1f930a2eacf8}} provide the option for unsupervised learning. But, sparse medical coding and lengthy temporal sequences often lead to poor reconstruction loss optimization. Though the BERT-based language model {{cite:c7fcc6eb3384b235afe1c10bc00caf3180a9dfe2}} shows the remarkable clinical document pre-training, it still requires downstream clinical task fine-tuning to obtain promising performance. Yet, a universal representation is still lacking.
| i | f557e7ca1008db385901471bc3e25bf3 |
Neurons in the brain must operate under highly non-stationary conditions. In fact, most behaviorally relevant sensory stimuli as well as internal signals are rarely constant in time but may change rapidly. In the presence of noise, such dynamic stimuli can be reliably encoded in the time-dependent population activity of a large population of spiking neurons {{cite:3b2c7013c92d878965d4b10041c1dccd811955f0}}. The time-dependent population activity also provides a concise, coarse-grained description of the collective dynamics of interacting spiking neurons. Therefore, theories that predict the population activity in response to a time-dependent signal have been of fundamental interest in theoretical neuroscience {{cite:418e44fd2e1e255945434452b7be0058a0e896c3}}, {{cite:9721f2884ad1cd86802bee63ad4af6d3a18a6221}}, {{cite:8e13f5d43455c22a0accd4a948f716e693d357b5}}, {{cite:9f67377237b688073200bb82c12a972cd8b3f9c6}}.
| i | 760de8d1652ac603fc702fee4092fc15 |
In this paper, we have calculated the Rényi entropies (with a spherical entangling surface) and entanglement spectrum from a class of hyperbolic black holes with scalar hair in terms of the conformal mapping approach {{cite:88670ea665a47140abb33fa7eea92fd08d09d269}}, {{cite:083f0ecdf7e814b9bee1db22bc71472df7925771}}. The main conclusions are as follows:
| d | 007081ff65b09ad8139276aebdc4a586 |
For our future plans, we intend to integrate the proposed method to a SLAM framework.
Moreover, an increase in the classification accuracy will lead to an increase of recall in the whole system, therefore using more powerful networks, such as ResNeXt {{cite:fb210c3842964539a424d7d21705b05031ff71e2}} and ResNeSt {{cite:fc3cdc6f72945fd2c71b2b36ad119447e48643ba}}, will naturally improve the performance of our system.
| d | db61d4e24b652491987770cd9fa52412 |
Neural representations have also been used to learn deformation priors that encode the variation of object shapes across semantic categories using direct 3D supervision {{cite:5c28fa5a77867a32b8598b9ab851c79ec1ebbded}}, {{cite:6e7ec6ad0ccfaa37ef456752dde03986c09e744c}}, {{cite:076af639acfefdfc6713e581255743f0e192b089}}, {{cite:7826deef414ab8dbb15b9d4b387d1ff993110c07}}. DeepSDF {{cite:076af639acfefdfc6713e581255743f0e192b089}} is an auto-decoder architecture that jointly learns a latent embedding and the weights of a fully connected network that maps 3D coordinates to signed distance values. This representation uses test time optimization to estimate the shape code associated with a new unseen object. While DeepSDF {{cite:076af639acfefdfc6713e581255743f0e192b089}} has been an extremely popular representation, successfully used as a shape prior to drive 3D reconstruction of object categories from multiple images {{cite:ddef60cad8eaf15c79d232845d0f65ed3c1d0f04}}, {{cite:7a82170b0f2e99d027b5e206674779da71d7d56b}}, its training requires 3D supervision and cannot be learnt from 2D images only.
{{figure:06641d9f-e727-49d8-91a9-af406749763e}} | i | 0ae78d159286014e8c9b50dd57abb62c |
A simple shape of primordial power spectrum, obtained through deconvolution (hereafter referred as Reconstruction) solves the lensing amplitude anomaly.
The Reconstruction also solves the closed Universe anomaly and brings back cosmic concordance.
Importantly, we find that a solution to the anomalies within the Planck CMB data automatically resolves or greatly reduces the tension between different datasets.
Our analytical power spectrum model, New Spectrum, that is designed to match the Reconstruction, prefers lower matter density and lower {{formula:f5c4866c-00cf-4ef5-b4d8-417c8b15cc0e}} and higher {{formula:b6c3f40e-21dd-4675-b2d5-9ebf376d1018}} . When the New Spectrum and Restricted Spectrum (a simpler version of the former) are compared with Planck temperature data with priors on Hubble constant, we get moderate to very strong evidence for the models compared to the Standard Model.
The proposed form of the spectrum stays consistent with small scale CMB measurements from Atacama Cosmology Telescope observation {{cite:0332ff50b43b1714cb75c557cec591fba17e65c0}}, large scale structure measurements from Dark Energy Survey {{cite:2a1b529543a47cb20aa6a83d50edb4ef831b9392}} and recently estimated age of the Universe from globular clusters {{cite:cff2cf07bed2cd19f4ced2278edd30afa40b1749}}, {{cite:2992e0037e1a145384a24612ba9d7cb0d6a5ab04}}.
| r | 1cfd738a98b017c0c95f8aac01cbcd2f |
To bridge the gap between pixel-level classification and image-level annotation, it is essential to localize object classes in the image from image-level labels.
Most WSSS methods rely on the Class Activation Map (CAM) {{cite:6511a0201ac130fa9f0bee03ceb7fc65e397b85a}} as initial seeds from the image-level label to learn pixel-level labeling.
Typical multi-stage image-level WSSS methods usually adopt progressive steps {{cite:867bcddcdc6937da22655f121de8fabf0868b943}}, {{cite:69593b534c5fb1e9bf78a78875d63a5e600366c9}}, {{cite:1167324878f564dc7af265efa4632ee77b3bcf51}}, {{cite:e3ccccfff77797b8996e72e3cf9de4e6e31fc83e}}, {{cite:f84f2eb3afe454d9849e6dbeebcdb2f7227a1e8c}}, {{cite:c12f36554794ac034219fec1cbbd5cb37195f347}}, {{cite:88d8185ad0cff1372b34e0d9ec8753906f4e225a}}:
1) training a CNN classifier
to obtain object activation maps {{cite:6511a0201ac130fa9f0bee03ceb7fc65e397b85a}}, {{cite:867bcddcdc6937da22655f121de8fabf0868b943}}, {{cite:69593b534c5fb1e9bf78a78875d63a5e600366c9}}, {{cite:f84f2eb3afe454d9849e6dbeebcdb2f7227a1e8c}}, {{cite:88d8185ad0cff1372b34e0d9ec8753906f4e225a}}, {{cite:793027c723f101bf79e39480be0426f51a7a896c}};
2) refining the maps with non-learning {{cite:46523fe82be09bd7676ee73c174a84ba9fb51cd7}} or learning based methods {{cite:dacae39d95067f5b4da9dfeb109059ecb366a233}}, {{cite:e2d46cd6ee67df3a0d79a4cdebbddb53fb601a58}}
to obtain pseudo labels; and
3) using these pseudo labels for fully-supervised training of an off-the-shelf semantic segmentation network, such as Deeplab {{cite:2bcd8a44c9991ea7c96273d928a42c25f7075d9a}}.
Alternatively, recently end-to-end WSSS methods have become more prevalent {{cite:e3ccccfff77797b8996e72e3cf9de4e6e31fc83e}}, {{cite:c92f40a188fe690cdabd6d5230bb62b6d78f43e9}}.
In both cases, the quality of the initial response map plays a key role in WSSS. However, it is recognized by many approaches {{cite:867bcddcdc6937da22655f121de8fabf0868b943}}, {{cite:69593b534c5fb1e9bf78a78875d63a5e600366c9}}, {{cite:1167324878f564dc7af265efa4632ee77b3bcf51}}, {{cite:e3ccccfff77797b8996e72e3cf9de4e6e31fc83e}}, {{cite:f84f2eb3afe454d9849e6dbeebcdb2f7227a1e8c}}, {{cite:c12f36554794ac034219fec1cbbd5cb37195f347}}, {{cite:88d8185ad0cff1372b34e0d9ec8753906f4e225a}}, {{cite:46523fe82be09bd7676ee73c174a84ba9fb51cd7}}, {{cite:a01738c7f609f3bdb38a78207d6aa4ffd6ca3db0}}, {{cite:dbd9a85a28e16914ba4b9de4470c353c1b23e775}} that CAMs suffer from two issues: 1) CAMs tend to only activate the discriminative regions of objects; 2) the rough object activation of CAMs loses accurate object shapes.
The main causes of above issues are limited receptive fields and the progressively down-sampled CNN feature maps.
| i | 197862b77c5b75b249c1f5d3dab86356 |
From Fig. REF ,
one notices that most of the BPs are excluded by these experimental bounds.
From the 4.47 k viable BPS used previously, 3k are excluded by the experimental bounds {{cite:3c5dbe17c98b727bc103b15fced9d58bdc18e9f9}}, {{cite:b8be1362ed6c9a3cd1e6d94b622b0d02fca26643}}, {{cite:1498e7605c4f8d98d6870ef7c4b7846fd0a7f96a}}, {{cite:ee1a81689bf27f866f364ef25b0d49788ad08855}}, {{cite:aa1915d28b7f96fd5dd01293f0fd6b09f4e9b031}}, {{cite:32484e0712dec3165fb8ece777bc981ebd88b066}}, {{cite:65a824bbf63da161290123d10178e4891dd78e79}}. One has to mention that the resonant {{formula:b6ee78b8-442c-4f96-b1f5-07fff8c4b1a7}} experimental bounds are very efficient in constraining the parameter space.
| d | c295522c6064d7b4f8924cef2ab2d140 |
The results for MoNuSeg Test-1 and Test-2 are shown in Tables
REF and REF ,
respectively. All benchmarking methods except CBM are DL-based. As
shown in Table REF , one can see that HUNIS
outperforms all DL unsupervised approaches by large margins in Test-1.
It also outperforms CBM by 0.0245 in terms of the AJI score.
Furthermore, HUNIS achieves a competitive standing among
state-of-the-art supervised DL methods in Test-1. Its performance is
close to that of the 2nd best in the table, namely, UNet-Atten.
{{cite:d7c09378ccff506723e143e6ac698c4311eed7e5}}.
| r | 38691527a820984f92104857c80ba253 |
Tab. REF reports the conventional PQ scores between our method and Mask2Former {{cite:2122a3db2ff660d25734d85d12551f2b704dd6c3}}. As mentioned in the main paper, this does not take into account the instance consistency across the scene, since matching between ground-truth and predicted instances is done on a per-frame basis. We further report SQ{{formula:faa9447a-03ad-4428-af6e-d8d5d1e0e78e}} and RQ{{formula:7130fa8b-1de3-4267-8b7e-2247c9c92d59}} in Tab. REF .
| r | e51122b6bb59871e0f03850f5909a3a3 |
It is known that the prograde 1:{{formula:d5d4b655-2722-40cb-9b86-a10f303b8a6e}} resonances hold asymmetric libration centres with the usual critical argument {{formula:1dd29caf-4c3f-4a03-bec9-d2133b850004}} different from zero or {{formula:9e2c82be-a92d-42c6-81f6-bfa1b757338d}} {{cite:d7a1951193cde79ecf3868236b9358e23fe81153}}, {{cite:8b7fb68d0932da45af3c636ce7e3cb81ffe25c13}}. The appearance of the asymmetric libration centres is because the second-order harmonics dominates the resonant Hamiltonian {{cite:8b7fb68d0932da45af3c636ce7e3cb81ffe25c13}}. However, there is no asymmetric libration centres in the phase portraits of the retrograde 1:2 resonance. The difference about the symmetric properties of libration centres between the prograde and retrograde 1:{{formula:e2264b73-8534-482c-af46-dba4df35a76d}} resonances has been noticed by {{cite:bcc09ce9d127ec88f0e5a67182f086d20c57ef89}}.
| r | 5c68759212d47cb778b3a5e468d021c0 |
In policy transfer a previously learned policy is used to learn the new policy. One way to achieve this is by policy distillation {{cite:92ab275ef696eece38ceac9bc1b8a4fbcf30a8b0}}, which means that the agent will select an action by minimizing the divergence of action distributions between the `teacher'(source) policies and the `student'(target) policy. Another approach is probabilistic policy reuse {{cite:f9a02ba0610eb02ce8bf410dcf0b8ca68cb77e5e}}, where the agent can select an action based on the pre-learned policy instead of his own policy. For example, {{cite:2f422adaf61911fbf2e5089bb82bf6f50be39484}} use this to teach a humanoid robot how to walk fast by exploiting a policy that allows the robot to walk in a normal speed.
| i | 8e6529f610cab79be42c28b72171ba86 |
for any smooth parametric submodel {{formula:7c60e4d2-7c47-4d11-99ac-14cf8a30cdb5}} {{cite:8cfa98dcb0b347927f9a8b5753e89b22e7b5585b}}. Thus, the candidate influence function satisfies the above pathwise differentiability condition and hence, is an efficient influence function. Moreover, since the model is non-parametric, {{formula:7f22170e-bde9-408f-a008-976f7fa67324}} is the only efficient influence function {{cite:1a9afb07b14bb1ae19200f57dd1e63ffce679a9e}}, {{cite:a258d51233881a8e4fc40e1c9815505c3431a423}}, {{cite:7d91dbb939bef60ee19de223e633408bec77a2ce}}.
| r | 89ed906bfa0600ee2cb00258d4e57da1 |
As could have been expected, in particular settings SAM is dominated by algorithms specifically designed for this setting, such as
CAM {{cite:981429df2a7825c2571fec1cb683ed895c580125}} in the case of additive noise model and Gaussian process mechanisms, and GENIE3 when facing causal graphs with feedback loops. Nevertheless, SAM most often ranks first and always avoids catastrophic failures.
The main limitation of SAM is its computational cost, higher by an order of magnitude than other approaches on 20-variable problems. On 100-variable problems however, SAM catches up with the other approaches as it avoids the combinatorial exploration of the graph space.
| d | 8ccb80b3678f5bfb81f8076b76e99c75 |
As shown in Fig. REF (a), previous SimSiam {{cite:a3d7592e439cd5506e8400e32b7fa2e2abfbc34d}} adopts a siamese network directly predicting the output of one view from another view, where one branch adopts a stop gradient to prevent from collapsing. As shown in Fig. REF (b), our framework contains two kinds of positive pairs with three branches for similarity optimization. Comparing to the previous siamese structure, we further adopt a branch with mixed images, which is forced to predict invariant discriminative representations for these hard samples.
In the following, we first revisit SimSiam {{cite:a3d7592e439cd5506e8400e32b7fa2e2abfbc34d}} as one of the leading methods in this domain. Next, we introduce our approach in detail.
| m | c8232371568d9015c3635dd7cdb34b26 |
[h(x*;)] + (1f”(1) + f”(1) (f*)”(0) C(f, ¶*)2)Var[h(x*;)],
where the first inequality above is based on the weak duality condition, i.e. Theorem 1 in {{cite:0e00abf15a8450644af305df7bdbb9a54b098c07}}Although strong duality holds generally in this problem, we only need weak duality in our proof., and the second inequality above is given by {{formula:35beaedb-afd9-40eb-a64c-4d43729270c6}} as the feasible dual solution, and the third inequality plugging in the value of {{formula:c2f50cac-a24a-49de-8fe8-937dbeec348c}} and {{formula:aee98398-674f-42af-ac8a-02856721fc7a}} , then we take the Taylor expansion up to the second order for {{formula:0a072a31-e5f9-4e59-87e6-3c27ea1778c8}} with a proxy of Maclaurin remainder {{formula:4ce33015-b3f0-45bd-bf82-b60e24473f46}} when {{formula:285eb03b-98f8-442f-993f-2cfe10c9c0dd}} :
[f*(h(x*;) - )] [f*(0) + (f*)'(0)(h(x*;) - ) + (f*)”(0) C(f, ¶*)2(h(x*;) - )2],
| r | afa2ad64a927a5b976d3d7cf9f15b5fa |
Since its introduction by {{cite:54f6e1a7482ee32c9461e6d4550660a0ad486456}}, the BIC Bayes factor has been a popular method for estimating evidential value from empirical data. One of the attractive features of the BIC Bayes factor is that it can be computed with a simple calculator. This makes it easy to implement not only for the researcher, but also in the context of a beginning statistics course. However, it is a large-sample approximation, and the discussion above calls into question its computational stability for smaller examples, especially those which might be used in a traditional statistics course.
| m | e02d382e1fc69dedfaeb0f620b6af8e3 |
We use the CosmoMC package {{cite:e6cbbaa36f982c690e536b2548f7af0145a7fd44}} to infer the posterior probability distributions of the sterile neutrino parameters and other cosmological parameters.
| m | 7f1ab36d6762b91728b2a827afec55fd |
Margin has played an important role on the design of learning algorithms from the pioneer work {{cite:f75449a3135555484b3374a8391ee4b074cf90d8}}, which proposed the famous Support Vector Machines (SVMs) by maximizing the minimum margin, i.e. the smallest distance from the instances to the classification boundary. {{cite:c57a9f19a65121ded1abf809534f0dd0ece7a9ce}} Boser:Guyon:Vapnik1992 introduced the kernel technique for SVMs to relax the linear separation. Large margin has been one of the most important principles on the design of learning algorithms in the history of machine learning {{cite:12db03ea817ff27784bf3390fa5c563dd8af7880}}, {{cite:935dcb7ff8860a04ef32eb9e5840148560699b73}}, {{cite:23bacf0c47e2f93ae8cc1db3860ba8fe4b55cb9c}}, {{cite:f69de0f3d03dbf4d3676b5ff8bb352d3d0061ff7}}, {{cite:5becfe7ce303eb1995b290af65bbffa63d88d917}}, even for recent deep learning {{cite:cb0d103e1c4e1a4ee16d2cb8865dd5fd7472bb9a}}, {{cite:ddd61d5dc09768ed5c466a9b5ce05bc09719da6d}}.
| i | d45d1156ceb3535f1136b6b7cdc2e355 |
where {{formula:fa005d8b-f955-4468-be4c-f9c6605d8870}} is the Dirac delta function, {{formula:4c6f7567-96a2-41f2-b37f-bc0dc1b3cc45}} are the weights of the particles and {{formula:c295dc8d-4bb6-44c0-8848-7b5d5d73593e}} are their corresponding positions {{cite:842da3ecc6aad91ace214f03dc358f54045c44e3}}.
One can make inferences about the signal process using Bayes' theorem, the time-evolution induced by the model, and observations {{cite:0b34244356ee82571055fb9d45d089c9df23e835}}, {{cite:842da3ecc6aad91ace214f03dc358f54045c44e3}}. Observations are modelled as noisy measurements of the truth, using the observation operator:
{{formula:0fd1ecb6-c1a7-4a67-afff-ee1e7a6aa14e}}
{{formula:859e2e35-2aad-4edd-871f-9b0ab49f09ed}}
| i | 826de13e4c03db1b13f13a4685b2b823 |
Local UniBlock vs. ST-Adapter {{cite:b33586ddd02e13ebf8eca48ca32072b03d087213}}.
Our Local UniBlock is motivated by the style of UniForme r{{cite:c95d8931cb36d5f728d2681dd3041ca4f63e8867}},
i.e., we treat temporal depth-wise convolution as local temporal relation aggregator.
Hence,
like UniFormer,
we introduce extra BatchNorm {{cite:cdfc2ce85e73a8ece3d46e3deea0b78d6a21ac55}} before the first linear projection {{formula:4acbdc5b-e02c-4d9c-ba42-7c42691ab2c9}} .
Alternatively,
ST-adapter does not have this design,
since it simply treats temporal depth-wise convolution as adaptation.
With such motivation,
it further introduces extra activation function for enhancing such adaptation,
while our local UniBlock does not need it.
In fact,
we have also made comparisons in Table REF .
It shows that our local MHRA beats ST-Adapter (69.1% vs. 68.0%).
| d | 265af2faf16fd3788e548534f091b74b |
The remainder of this section is dedicated to proving Theorems
REF and REF . As stated in our
proofs, several of our
arguments involve computations performed via GAP {{cite:e68b7efa1a83da0799db4d0aa7083078673d2804}} and Magma
{{cite:c10c6f0e64a2af60ba685b0f63b473234de345bd}}. Our proofs also contain details about specific
elements {{formula:411eae24-bc37-496e-b2c8-3ae6eca9a92d}} that may be chosen.
| r | 061d933aee443d56d5e7ecc0112f8472 |
Proof [sketch]: The assumption of this lemma implies that {{formula:a2dcd218-9da0-4930-893e-24081566f07c}}
has a subalgebra (induced by {{formula:f332978f-747c-409a-979f-45e0b210f19c}} and {{formula:fc7718e0-dff0-427b-942f-4c747888c603}} , respectively) such
that all operations of the subalgebra preserve the relation {{formula:2317b5b2-f8aa-4cd5-b007-886d221bb873}} . It
is well-known (see, e.g., {{cite:ce678daa86488196971ff670803780dcc2c651f6}}) that all operations
preserving the disequality relation on {{formula:a86b3673-7b66-4bb8-bc83-0cb1bc89c3ac}} are essentially unary,
while it is easy to check that the order relation on a 2-element set
cannot admit operations satisfying
identities (REF )–(), so one can use
Lemma REF .
{{formula:14bcbffc-5435-44a3-a30b-f201265b40b7}}
The following lemma connects the characterisation of bi-arc graphs
given in {{cite:c662ad6717766c69457ce5c5c7f9e06533cb6fbc}} with a type-omitting condition.
Let {{formula:086de988-edc3-41af-ac0a-6230094b99b3}} be a graph. Then the following conditions are equivalent:
the variety {{formula:293f6a22-1ba1-4dd0-bb28-4014bf40a26a}} omits type 1;
the graph {{formula:b642e94a-9af1-48e2-9c21-f79e6077abd5}} admits a conservative majority operation;
the graph {{formula:f7fc78c1-5766-4328-82a6-a7f2b96ebdd6}} is a bi-arc graph.
The results summarised in the following theorem are known (or easily follow from
known results, with a little help from Lemma REF ).
Let {{formula:1f95cbe9-03f1-48c9-a66b-f7529cba30ee}} be a graph.
If {{formula:fa558e95-7a21-4820-bc3e-33f28c8325b8}} admits type 1, then {{formula:2070c672-be71-4255-845b-40a466351d95}} is not expressible in Datalog and {{formula:6b1ebc09-a7d3-4cdf-ac64-21ccf150209d}} is
{{formula:cc1d4ed3-5df9-4f05-b5a6-4c9f8588c756}} -complete (under first-order reductions);
if
{{formula:0dd15380-b3a6-4518-85c2-9543891f3413}} omits type 1 but admits type 4 then
{{formula:3c0a282c-31e5-4028-9fd7-630c000a2b23}} is not expressible in symmetric Datalog but is
expressible in linear Datalog, and {{formula:3ca57161-63ca-4074-ab93-93b93a65db47}} is
{{formula:f66b9a71-7dc9-4b2d-8077-56b4f11e8bf9}} -complete (under first-order reductions.)
The first statement is shown in {{cite:3201799257e81db9cc6b3f5837c3a6387ed02770}}. If the variety
omits type 1, then {{formula:d9e00fb3-ae0b-41a7-94b1-72dc0ebfced5}} admits a majority operation by Lemma REF and
then {{formula:6c30329e-1a61-4446-9c07-2c3fdff92196}} is expressible in linear Datalog
by {{cite:286d719d6eec659fa78defa4905435d69b154306}}; in particular the problem is in NL. If, furthermore,
the variety admits type 4, then {{formula:5648c74f-6254-45b2-b7c1-0fb9299254ef}} is not expressible in symmetric
Datalog and is NL-hard by results in {{cite:3201799257e81db9cc6b3f5837c3a6387ed02770}}. {{formula:2fc2c1d6-ae68-49d0-80a9-693e85962c54}}
By Lemma REF , the presence of a majority operation in {{formula:4c3f502c-7868-4e9a-b478-a12b81626988}} implies
that {{formula:06a7f469-e24a-4b41-83c0-629196da8980}} can contain only types 3 and 4. Type 4 is dealt with
in Theorem REF ,
so it remains to investigate graphs
H with {{formula:203fa0aa-4d49-4620-bc36-5b7071c2998f}} .
The next theorem is the main result of this paper.
Let {{formula:9dc3e3ae-b98a-4a5f-9e29-df45ede269bd}} be a graph. Then the following
conditions are equivalent:
{{formula:901b1c47-f852-4ef7-a073-0dfe5f6daddf}} admits conservative operations
satisfying (REF )–() for {{formula:0f246a9d-770b-4082-bbb7-2bb065f9b6c1}} ;
{{formula:70bb27c9-1b40-405d-aa54-770a8ac9d12f}} admits conservative operations
satisfying (REF )–() for some {{formula:33e9ee4b-cba6-4950-85cb-00fc10362895}} ;
{{formula:6af09a17-0861-4ced-a972-ff3a2e1b795f}} ;
{{formula:b85be3df-cbbf-4144-bc78-a9edac90c8d1}} ;
{{formula:d8edda93-35d2-4e51-a3ce-3bf16489977f}} is definable in symmetric Datalog.
If the above holds then {{formula:bfa3b305-d234-4e17-a274-220c40236138}} is in the complexity class {{formula:abed2f0b-179a-4380-89be-42d8f22fdd69}} .
| r | 353cf2ca2305c949485cbd25ad2e0d5f |
Ultracold atoms in optical lattices provide a fascinating platform for quantum simulations of correlated many-body physics {{cite:c480ed209279193a26bd439b17a4c88ed50ab86b}}, {{cite:cb1446434032cfeca1ccccb411e535bd1d951d03}}, {{cite:0c0f57e85e67939da50735adb0564641c3664c5a}}, {{cite:bebf470a4fdb6e1d9350dfc7eb269dde6868bf58}}.
Since the atomic tunneling and interactions are both controllable in these systems, they have widely been used to study quantum many-body phases and quantum phase transitions.
One main theme of quantum simulation with optical lattices is to investigate the low-temperature phase diagram of the Fermi-Hubbard model {{cite:d85df1753e6bd26e0fffaf19fdedbbcb6c2a0639}}, {{cite:005f46623e870f8b02623e2dee880a72426eeda1}}, {{cite:c7a6908717b331b2177d3062fe8d45e9c6011e9e}}, and help uncover the fundamental mechanism of high-temperature superconductivity {{cite:0a05dfdddb64e2de205c53736b8a11f57c0f9a36}}.
| i | 763cc99225b1599ee1da91af0392d584 |
IRAF {{cite:14636a3c2cc0f39c5e86dba7e6eee95a802b9e5d}}, {{cite:ac00e7a4f3facff7c4c121bc46a1c72fd6892276}}, IDL, python
| d | 12627a8a23beff5fa7a94acd76b125aa |
All the experiments were executed using a vocabulary of {{formula:fef35a97-cf03-4a27-adba-2a236b75fc54}} visual words, created on Paris dataset through the application of K-Means {{cite:106fee2de91476f00a5bceb422f92a85921c5fc9}} clustering technique, initialized following the K-Means++ {{cite:6f113a871f5edcd73925c8dc98ee4fa6b72fa432}} strategy.
At the beginning, the initial configuration was to extract features from the block4_pool of VGG19 with an input image of the dimensions equal to 224x224, that is the predefined input image of VGG19. Changing, the dimension of the input image, the results were improved. Also, the choice of the layer in which extract the feature maps is important: from block4_pool to block5_pool of VGG19 there was an improvement equal to 2%.
The breakthorugh was the use of InceptionV3. Thanks to the depth of this CNN architecture, the feature maps extracted allowed to create a more representative VLAD descriptor. The first experiment executed on InceptionV3 reached a mAP equal to 81.55%, which is almost 4% more than VGG19.
After we found the best configuration for the parameters: Network and Layer we focused on the other parameters. The application of locVLAD instead of VLAD for the feature aggregation phase allowed to improve the performance (improvement of 3%). Also, the root square normalization slightly improved the retrieval accuracy. Following the idea that features extracted on the image resized to square not respect the aspect ratio it is not a good idea, we modified the input image of InceptionV3 allowing to have an input of variable size, that was adaptable to the different dimensions of the images.
Finally, the application of PCA-whitening reduced the dimension of the descriptors and removed the noisy values, also improving the performance.
{{table:805ed3f7-fdf5-4a2a-a55b-29906091c756}} | r | 7aed83edce6187cc0afba16ab1751e58 |
Our structure learning algorithm runs efficiently on a standard desktop CPU, while providing structures with competitive classification accuracies and network sizes. First, we compare our method to the NAS algorithm {{cite:9395955fdc88672c95e0b1ac09996a04737aae7c}}. NAS achieves for CIFAR-10 an error rate of 5.5% with a network of size 4.2M. Our method, using the feature extraction of the WRN-40-4 network, achieves this same error rate with a 26% smaller network (3.1M total size). Using the same feature extraction, the lowest classification error rate achieved by our algorithm for CIFAR 10 is 4.58% with a network of size 6M whereas the NAS algorithm achieves an error rate of 4.47% with a network of size 7.1M. Recall that the NAS algorithm requires training thousands of networks using hundreds of GPUs, which is impractical for most real-world applications.
| m | f26d160b86a5e2bec5fd9af3d4a60032 |
We compare our method to the state-of-the-art model-based RL {{cite:968fc361f3d9bcc0ac5320be713fd10e05232f90}}, {{cite:aa1134106de1c76ece6bf999840ba91cbc5fa223}}, skill-based RL {{cite:88dbfaaee604e3e8a5f248697b96835ef8eb01a4}}, and combinations of them, as well as three ablations of our method, as summarized in Appendix, Table REF .
| m | b6562fa84c7cddd7ad014ca351e2645d |
Previous work has shown that random seed is crucial in the performance of fine-tuning {{cite:2412f7a634b0ec0c7cff43da77e2cad75e10baf5}}. Fine-tuning also benefits from ensembling or selecting a few of the best performing seeds {{cite:8232e1ea9c70ef3e348446af8c7f9cd0c8f53d7f}}.
It would be interesting to study HPO's performance by adding the random seed to the search space for future work.
| d | c5f6850acdee1e81800a8692e2ee5ba1 |
All our calculations were performed within the DFT scheme, using the projector-augmented plane wave method (PAW) {{cite:e01f85c648b3d851f5cecf5b447279ce9edd4dfa}} as implemented in the VASP (version 5.4.4) code {{cite:87f6fe3747bb6c5c0ab5ff3321a49b976e2db760}}, {{cite:cb814a0a60b761b220164bd29d3d8b650ddd5b02}}. The valence configurations were 4s{{formula:b2328bbc-6bb7-4015-a502-3f165a024f75}}3d{{formula:8e6c8fb5-1c81-4db1-a36b-145ed5fb0c3a}} for Mn, and 3s{{formula:abc33220-3c57-4b62-8499-7f48e32f03e9}}3p{{formula:02055a42-d53a-4aeb-8c4c-2207aae27a9d}} for S, respectively. The exchange-correlation (XC) term in the effective Kohn-Sham potential was approximated according to the Perdew-Burke-Ernzerhof parameterization for solids (PBEsol) of the generalized gradient approximation (GGA) {{cite:067daf36d051f01bbf806d1c3b04fb39e2a22428}}. We also assessed the local density approximation (LDA) {{cite:3f01d7130781be8701f621936242cc54832c99cd}} and the standard PBE {{cite:c9c6d0e5c12892901e07467029c69b6bf036c3a4}} XC functionals, but we found that PBEsol produced more accurate structural parameters when compared to available experimental values for both AFM and PM phases of MnS.
Integration in the Brillouin zone was done on a {{formula:a6227f38-fd53-436f-9deb-87e5a3206eba}} -centered grid of uniformly distributed k-points with a spacing of {{formula:b9cecb02-95d3-4a76-a4ba-e8357b557b84}} Å{{formula:2f432b49-b2a2-486b-b538-8948ea242dcf}} . The selected plane-wave kinetic energy cutoff was 500 eV and convergence of our structural optimizations was assumed when the total energy changes were less than {{formula:2783b04d-7be1-4969-81df-36ed3e8da564}} eV and the forces on each atom smaller than {{formula:c2a5fcab-c942-46cd-bba4-caf8388a2517}} eV/Å.
{{figure:e9143016-30f3-47be-9912-df640109cbc2}} | m | d57e54333bcfe7bd0d28c2f01726a29f |
Miyato et al. {{cite:6630bedd8364cd1ec04dfc137701d5bc12d56ec5}} incorporated virtual adversarial training (VAT) in semi-supervised contexts to smooth the output distributions as a regularization of deep networks. Later, virtual adversarial domain adaptation (VADA) improved adversarial feature adaptation using VAT. It generated adversarial examples against only the source classifier and adapted on the target domain {{cite:c81524fb00bd541482bed606fb6a7624579488e4}}. Unlike VADA method, transferable adversarial training (TAT) adversarially generated transferable examples that fit the gap between source and target domain {{cite:dc2e2bfa2dfa42349840d2e4c7d21e7d0886f1c0}}. Xu et al. {{cite:aea7a70eeed476829b56669bd0ab2962bc8d513e}} constructed a GAN-based architecture named adversarial domain adaptation with domain mixup (DM-ADA). It maps the two domains to a common potential distribution, and effectively transfers domain knowledge. Zhang et al. {{cite:34d7ba7a5bc73da9a174d181520a643830ab7232}} introduced a hybrid adversarial network (HAN) to minimize the source classifier loss, conditional adversarial loss, and correlation alignment loss. A new adaptation layer was used to further improve the performance in the HAN model.
| m | 76a8cc8957614c9a2909656d33d6946a |
The classical model of communication complexity was introduced by Yao {{cite:b14bed259d7fbfdc61d563ce1da199a48b411190}}, who also subsequently introduced its quantum analogue {{cite:1388219b2821400b2c9ca582393c5ea33fd5908d}}.
Communication complexity has important applications in several disciplines, in particular for lower bounds on circuits, data structures, streaming algorithms, and many other complexity measures (see, for example, {{cite:d3f19e01ec31a2e11425d4e47e182e62e222e72c}} and the references therein).
| r | fad9ad4e85007cf8bae4448b9f8b425b |
In the bottom left panel, we show the rate of change of configurational entropy ({{formula:57831098-e319-4b45-884c-23c1803767d5}} ) where we find the minima transpire at a larger scale factor as {{formula:57c353d1-d21f-45ff-b146-2cd5c2bbb327}} decreases and {{formula:d2f198b8-38e6-4110-a0d3-b8ea9793c269}} increases. For the {{formula:024c34d8-d5b3-4e24-880d-3a68a9500961}} CDM model, the minima occur at {{formula:a64b541a-588f-4143-ab3b-742b93c983a8}} which correspond to a redshift of transition of {{formula:8a9152a2-74e3-4ea2-b32f-513c7ebf3e94}} . For {{formula:5b716c9c-65d8-410f-b75b-8c43fa6c1d2b}} = {{formula:c6d94ba8-839a-49a1-bc95-0636eef60168}} , the minima hits at {{formula:fba5acb9-99f7-4a6f-9400-d151f548a203}} or at {{formula:1333e148-73bd-48f3-a089-da90084de531}} which is not consistent with observations {{cite:2f4fca311b7e518eab3e044b325159191f017a4f}}. Similarly, for the {{formula:f01f247a-02d8-4c07-a08e-6a6db9832d73}} = {{formula:4d8017ee-f1e0-40aa-9910-067069a53551}} , the same transpire at {{formula:16235603-3089-465d-be8f-300cf6498e98}} which is again observationally unfavorable. Nonetheless, for {{formula:89a5de0d-a856-4bab-b11e-17bbcfde9593}} = {{formula:3eaae52e-f66f-41f3-9c71-8b12378397df}} and {{formula:f962484b-f39e-4056-8830-1a78d8657ab8}} , the minima occur at {{formula:7825932e-1b9c-4e20-852e-e8f4c144d568}} and at {{formula:14a423a5-d20f-4516-87da-9d113c10d60a}} respectively, both of which are consistent with observational constraints {{cite:2f4fca311b7e518eab3e044b325159191f017a4f}}.
| r | 31e8b1f4e3f5097a3af5b142d5752c82 |
Data and Models.
We use the publicly available Breast Cancer Wisconsin (Diagnostic) dataset {{cite:0b60030b3ec13a49a9947a7d5b62b01ff69aae52}}.
It contains 30 numeric features which we standardized by removing the mean and scaling to unit variance. We explain Scikit-learn {{cite:a584617c269d0dc82bc686572c2f674dd8959a04}}
random forests, trained with a 50% train/test split. Our model consists of ten decision trees of the maximum depth of ten.
{{figure:dd5979b6-af09-441c-b7e7-fe9d0e05f54f}}{{figure:50a74b45-c80f-4752-aad3-4683f2680326}} | m | d7ccae2be13f0bad6baafee7461c9c77 |
The QCD light-cone sum rule for the magnetic moment of the {{formula:42ed095f-d1c2-4e36-b547-94385d836d72}} states contains many input parameters whose numerical values we need.
The values of these parameters we use in the analysis are given as follows: {{formula:c5b7d5fa-0623-4c11-a929-0fd89b564c90}} , {{formula:e11fa599-7838-4c3f-8c30-82c06f3cc483}} , {{formula:52ac8e95-9e10-4bf5-8d94-108e9a6c7eae}} {{cite:cd7d5564ce5b9518f8d62303a49d15aeb3b21d47}}, {{formula:ce2fa17d-cd89-4cf8-9c88-322cebb913d9}} MeV, {{formula:532e0eb9-82bb-4f76-934a-25e67dacd305}} MeV, {{formula:8e6f134b-5224-4198-a13c-263d9e8fd98a}} {{cite:a8fa09ff91d1e218fc1a2ae8d5283183aac23342}},
{{formula:06afc09d-9d4d-4e30-b6d1-d5366129e8af}} {{formula:ce42f385-a52d-4c29-9623-10480da3ba92}} with {{formula:d098c170-47f1-43e5-80d5-fc4c7e397095}} {{cite:41624bc302c7bf6f45c7b29dc48a3cee247a1599}},
{{formula:013184b8-79b2-41b0-b861-87389457076d}} {{cite:41624bc302c7bf6f45c7b29dc48a3cee247a1599}},
{{formula:0b4d7182-5c40-4a91-9876-bafd0b04650d}} {{cite:7a310bb4ed1607bf5118568a1338860351b58b66}}, {{formula:70d53a1d-361f-45a9-b358-09c3d90d2871}} GeV{{formula:b284802a-6f64-462e-9e8b-2d67f96f8f6e}} and {{formula:e55039f7-ac1c-4fd2-a91e-60fe4ca4eb22}} GeV{{formula:8b2249a0-1b4c-4b02-806b-a3daf03301ca}} {{cite:f4be2eb03b08d487302f986659755398f49a4050}}. The photon DAs and explicit expressions of the wave functions used in these DAs and their input parameters are borrowed from Ref. {{cite:a8fa09ff91d1e218fc1a2ae8d5283183aac23342}}.
| d | f19a6ded13ad55ef99ff4f8fdf01455a |
The act of fuel cycle benchmarking has long faced methodological issues
as per what metrics to compare, how to compare them, and at what point in the
fuel cycle they should be compared
{{cite:484c4accbcb455a84af6c17d836125a59c3e6d65}}, {{cite:5b18ab0832e2cf3c6b27d8f662eb1593ec92d444}}, {{cite:1536059c48a8f3c66d0a28d06cbf0dd738580eed}}.
The benchmarking mechanism described
here couples Gaussian process models (GP) {{cite:18c21812505e48b429fcbbfa751ccaaf1ef26ddd}} to
dynamic time warping (DTW) {{cite:352c122df181de8d4a6ba999d87495ceec585e32}}. Together these address how to
generate figures-of-merit (FOM) for common nuclear fuel cycle benchmarking
tasks.
| i | 8e78afaf1988c877aa8403fa04e450a5 |
The systems level approach taken here means that no individual component stands in isolation.
Rather, the properties of each component are shaped by the system architecture and operation. In our case this lead us to make important assumptions regarding the features the individual components provide: disentanglement and invariance.
Bengio et al.{{cite:340ba8839be6433a91313d90402cd15a732a2c5d}} state, as is often the case in the context of deep learning methods, that the feature set produced in training may be destined for use in multiple tasks that may each rely on distinct subsets of relevant features.
The authors conclude that the most robust approach to feature learning is to disentangle as many factors as possible, discarding as little information about the data as is practical.
Disentanglement has been the subject of study of recent work and various approaches to learning disentangled features have been developed {{cite:bc6017777062f102730a869764f037a3ef096a28}}, {{cite:88377dc59c8f982160fa58a17c157976bdb28cf7}}. The property is useful for memory as it allows for matching on subsets of the features but also because it allows for composable representations.
Models that extract disentangled features remains an open research topic, as are methods for evaluating the quality of the representations. In Locatello et al. {{cite:5adf38ec5877341f50619dce8db5461b7c6f00e7}}, the authors argue that unsupervised learning of disentangled representations might only be possible with inductive biases on both the models and the data.
While methods for producing disentangled features is an open research problem, we nonetheless believe this property of features is useful as it allows for search by partially specified queries.
| d | 42d48133c15bd9cb49194cf1edfd0f9b |
One of the hallmarks of language is flexibility, which contains two aspects. The first requires that the generated language should be a variable-length sequence, but many previous works {{cite:3b5e518340d206fb70ee476ce39969ec8f5bcb16}}, {{cite:13ee73de26102c61601b8b2fc0cbd61e0daebb04}}, {{cite:51eefb9f5e3cd2a935e53f9457598be80e535e29}} use fixed-length representations. Although works in {{cite:7fb53f313d550f3b497def4454c687f4e6382fb7}}, {{cite:efd47d3efcbc97a4d448791faa7bb897fac87d69}} leveraged the idea from image caption and generated a variable-length sequence during communication, they did not match the second aspect of flexibility. Humans can describe a picture using the language of any length. However, the current model only learns the optimal length of a particular picture, and cannot describe it diversely. On the contrary, our method has taken the two aspects of flexibility into account. Even for the same picture, we randomly give a length to the network as conditions, and the network can output a description of the corresponding length. As shown in Figure REF , we show examples on the Animal dataset. Moreover, we found that variable-length descriptions can be generated under different vocabularies. It is similar to human language, i.e., Chinese and English have their own vocabulary to constitute language. Different vocabulary sizes (e.g., binary, decimal, alphabet) could lead to a different language. Although the length and vocabulary of the sequence are different, the listener can understand the language and guess correctly. From the result of the experiment, it proved that the machine language generated in SGD game has the nature of flexibility.
| r | 1555d0ff77c913808083eef802f71ef9 |
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