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Theorem REF (large {{formula:01c9fb27-a834-46cb-b642-bdeea2bb1faf}} ) follows from Theorem REF and a result of Lenstra {{cite:777a3b8df3d6ec3e09d4c9acea50ee64b6ea53f4}} (cf. Kannan {{cite:75b1fa7773c98ff81f8b1c5d63cfb64effc60c47}}), that shows {{formula:606f3f46-8e3c-43d8-8d6a-da106d59de0c}} is fixed-parameter tractable. As {{formula:f9d1a91d-3227-4372-8fed-dd7b9c9ff4f1}} can naturally be formulated as an {{formula:8c6c9662-3d83-42ea-8d62-d7dbef221c8e}} integer linear program, we conclude polynomial-time solvability due to the assumed magnitude of {{formula:b9f8ae91-d056-4993-b22d-528d1abc1165}} (see Appendix, Section 7).
| m | f210d10b56c6bb1748f56a00af492e36 |
We extend this framework to work with high-resolution histopathology images by making several adjustments. First, for our generative backbone we use StyleGAN2-ADA {{cite:b7872aef23b2b1eb828ab8af23053a0f99614c7e}}, which has been proven to work well in limited data settings with histopathology images. Second, unlike {{cite:1a80ca675487df7fb39ac9ee63f139a2fe2eec16}}, we choose to only extract and upsample latent features from the last 5 blocks in the synthesis module of the generator network, as shown in Figure REF . This yields feature maps which contain more fine-grained semantic information. These later features are sufficient for our pixel-wise segmentation task, and drastically cut the amount of computation and upsampling required. The computational burden is still too high, however, to fit the entire feature map dataset into memory while training when dealing with large histopathology images. We therefore use memory-mapped arrays during training, which allows for only those portions of the feature map tensor which are currently in use to be loaded from disk and into memory, reducing the memory requirement of the framework. This allows us to scale our framework to 4096 x 4096 TMA tile segmentation, with samples shown in Figure REF .
| m | d11d33e5267fce298f371d09e8a5761c |
Recently, a lot of substantial progress has been made towards research on automated radiology report generation models. Most frameworks adopt the encoder-decoder architecture {{cite:4256c9be9f2ce8ebcfe358443be65bd508bd68f5}}, {{cite:0685f86ca3c1bf529e5711985feb32f2bba8efef}}, {{cite:e06d887e00311b8ef89c7ddc09b466e24880ecd3}}, e.g., a VIT {{cite:80412c2cdb278f0f2acb676870d2ae753765fe31}} image encoder and then a report decoder based on transformer decoder {{cite:0964909bc8bd1274abfbbdf4ab5ea43ba03a806c}}. Nevertheless, physicians typically write radiology
reports through multi-granularity information, instead of only focused on holistic impression.
For instance, some sentences "There is minimal patchy atelectasis or early infiltrate in left upper lung zone" reflected some statements have a strong correlation with the anatomies(region features). However, some sentences like "No pneumothorax, or pleural effusion.", describing CXR from a global perspective is more likely to be inspired by global features.
| i | 3b90dd858a2adbffa98d310ad0229d76 |
In particular, extremal black holes play a key role in various types
of gedanken experiments that have been designed to challenge the
Penrose cosmic censorship conjecture {{cite:72ea27405021d36ebd54f2abd721f48709db02d7}}, {{cite:868c0a7d63b09e8d15497f29cc3d14080630055f}}, {{cite:395643d1e91f0a5552fb220d56477c46774a04ab}}, {{cite:f1ea84654407196d66fbbb953633469e49cd68cb}}, {{cite:16069f30b46eb54fa6be1e2772a9b835c78780a2}}, {{cite:6983412384c3098d0553da50c4654d6c67717127}}, {{cite:5105212cfefcd1df9449b1c65a2fdc9602e6134d}}, {{cite:e33def8ecc54b63c98962896f47cb2ab6621deb2}}, {{cite:b02b623ae29366a0de8d8cb73c8373267c201efc}}, {{cite:db1caf4abb345b2a4e3bcb453e2316c0635dff3c}}, {{cite:9cef0a59054712855eff3d96b5238cd92d68eccc}}.
Likewise, extremal black holes play a fundamental role in various attempts to prove the validity of the intriguing
weak gravity conjecture {{cite:b7fedec14efe05028dc91ac3eee41e4329996cb9}}, {{cite:2c5e237195a9d02d3856bd4493e2d60f82f2c129}}, {{cite:30b93f205e51cbecc3a5707a6bec11d50fbae268}}, {{cite:c4d11d9c81d75793c77834089f8c3d6b729a4c8d}}, {{cite:47a8d1324563633b1b6eba31c6f374e860bc36b5}}, {{cite:be35378bc23ece654531452e7ed4dc85b0e30779}}, {{cite:ec7756dce21d0a1bb7068e19e89667eb4bab39c8}}, {{cite:0955c723a1910d230456fcf09100c633debb18c3}}, {{cite:7774ff3ad1a83f99914df49c7f1f98e2a2b3724b}}.
In addition, the thermodynamic and statistical properties of extremal
black holes have been extensively studied by many physicists in
order to gain some insights on the origin of the Bekenstein-Hawking
entropy {{cite:e88d2f7756e780f6afe086155e92ee74aaf1e979}}, {{cite:d64a22c9632475a805a3d037a24d6f7a7cc89b86}}, {{cite:3ba4309ff3809cc17659f32725767b253615b236}}, {{cite:e52346838893e6d50a6b3cf27e0db20b8e69013d}}, {{cite:49b181ecfb346531b1e560de55dbf7258e7776f2}}, {{cite:60486820d91a350788c647a1e2379a8140eedb14}}, {{cite:c913cd9b7e8a01882f582a6ed05f2b8cb0c6e48a}}.
| i | d631920d09816d1a698739ea0dd9bf6d |
We employ an off-the-shelf pre-trained language model T5 {{cite:fd0b3ec211cfc78f72efb7c027304e992eb79861}}, experimenting with both the T5-Base and T5-Large variants.
For all DocuT5 variants, we serialized the database schema by enumerating the table and column names, similar to {{cite:13b834c70a142371b3bc3a56dba5eb209331d5b2}}.
We also encode database content snippets (anchor texts) by performing fuzzy string matching on the natural language question and the database entries {{cite:13b834c70a142371b3bc3a56dba5eb209331d5b2}}, {{cite:8d73558591d7449cee73d2efff3479d9abe0cb58}}.
Lastly, to reduce non-executable hallucinations, we employ constrained decoding to incrementally perform sanity checks at inference {{cite:13b834c70a142371b3bc3a56dba5eb209331d5b2}}.
| m | aa87629416df6c0297866ffc21743a48 |
In the X-ray band, we find that the luminosity of the soft Comptonization
component {{formula:a40fd357-cbb6-4d93-8a1b-7cdc1e599843}} correlates well with the hard component {{formula:44b75bf5-7a05-4d34-89f6-902140ccd750}} .
While there is some evidence that the high energy index
{{formula:f4e6d7dc-5f36-4634-81ad-191f33d7b80f}} correlates well with both luminosities, there is a seemingly
stronger correlation between {{formula:5414f7f6-886c-4701-86de-2832724f7fe7}} and {{formula:c6988cc8-4166-4668-b602-1a1c8f383c62}} in the sense
that null hypothesis probability is smaller. There have been several studies which have shown that the high energy index is correlated with the X-ray flux (e.g.{{cite:ecd417055000bb9426f9f752eb7deb96a3c4d610}}, {{cite:01f0dd35ea7f5a61b8b58c26ef3fe139f1fd3f2b}}, {{cite:8d0f45eaa67b591f9300be7959647f237887a63a}}). Recently, {{cite:64f147d6603cfc3eb00ca37095d591e3bff3c435}} have studied the index versus flux variation for
Mrk 335 and Ark 564 and have reported that while the correlation exists for
both sources, there is significantly more scatter for Ark 564. Our results
are broadly consistent with their finding and perhaps gives an explanation
for the difference between the two sources. Also the correlations obtained
here are consistent with the double Comptonization model used.
| d | 398c7f925893e38d6c6a092d9f505fb8 |
Graph matching is a term used in machine learning for the problem of measuring the similarity of graphs (e.g., {{cite:65c6517f133d0cc9302e06017a2c30f1e24e0a43}}), where it has its applications in pattern recognition.
However, there is no universally agreed-upon notion of similarity, and a popular notion, the graph edit distance, describing the cost of transforming one graph into another by adding and deleting vertices and edges, is not only hard to compute but also does not reflect the structural similarity of two graphs very well {{cite:def60f0d7debb5a45684ad81385be94b3c21d00a}}.
Restricted homomorphism vectors offer an alternative way of comparing the structural similarity of graphs since, after suitably scaling them, they can be compared using standard vector norms.
As demonstrated in {{cite:6a3b10755a00fbb970285c55fc08eddee094b89e}}, one can also define an inner product on these homomorphism vectors, which yields a mapping that is known as a graph kernel in machine learning (e.g., {{cite:b4d47cef6c1707954bea43c81751443ec7b4e7c2}}).
Graph kernels can be used to perform classification on graphs, and to this end, should capture the similarity of graphs well while still being efficiently computable.
Similarly to homomorphism vectors, state-of-the-art graph kernels are usually based on counting certain patterns in graphs, e.g., walks or subtrees.
| i | 073c418145254565d3e1d83ae24d83e5 |
Transitions as Features. The pattern of probabilistic finite state transition that the sr-RNN learnt can be used as a representation. Figure REF shows the t-SNE {{cite:01211e3503b38ca9c44d997cf0d86203233bf9ad}} of finite state transition probabilities for test samples. We find that the transition probabilities of categories are discriminative.
| d | 16c5dd51d1027b0627b72880d2974158 |
Table REF compares the SwinV2-G model with previous largest/best vision models on ImageNet-1K V1 and V2 classification. SwinV2-G is the largest among all previous dense vision models. It achieves 84.0% top-1 accuracy on ImageNet V2 benchmark, which is +0.7% higher than previous best one (83.3%). Nevertheless, our accuracy on ImageNet-1K V1 is marginally lower (90.17% vs 90.88%). The performance difference might come from different degrees of dataset over-tuning {{cite:8889215f9ac599132478d50ff8903815c092284f}}. Also note we employ much less training iterations and lower image resolution than previous works, while performs strong.
| r | 2794f7b8083d4ca8936932a4b378650d |
The timescale of Oort-cloud formation is probably closely connected to
the birth environment of the Solar System
{{cite:6e048ff130e4ea81307f8d037b358a27c7335a38}}. If born in a star cluster, as argued by
{{cite:8e98d7e03a5ee345e3a6f80fffbea03bdca9458c}}, {{cite:d0548fd8f2f7c5416715f018dca36c71998a6c84}}, {{cite:e165f9715f688a453f0bc704b14879836801e48e}}, {{cite:99602bfb8f6190c45f89b9310878168d34a8390e}}, with a characteristic size of {{formula:ecbe33af-c97b-44f9-912e-42023335b0ee}} pc and
with {{formula:757f6392-ed2f-47a5-88bc-e79b7d19a95c}} siblings {{cite:50ce75066c879136d9299e7908771fcc93b25e6f}}, asteroids in
wide and highly elliptic orbits are vulnerable to being stripped from
the Solar System by the cluster potential or by passing stars
{{cite:18b176559c5657538b79248debbb674351cb0cfc}}. {{cite:99602bfb8f6190c45f89b9310878168d34a8390e}}
on the other hand, derive an even higher density cluster with a
density of up to {{formula:08f1aa97-4c90-4211-b9a0-d15726221b95}} {{formula:7d87af3e-87ab-4b21-8cd6-2d57de621696}}/pc{{formula:04cd1321-f751-4575-82d8-bcb89f14d4d3}} . If formed too early in
the lifetime of the Solar System, the outer parts of the Oort would be
lost due to stripping when a small change in relative velocity
{{formula:271e5341-f135-4135-896f-f44615f11d2d}} O(10-4){{formula:eb609f0b-74fd-4b21-abdc-ce63ab1a6367}} e {{formula:dcafd69f-0f47-4f0e-a107-58804333b29b}} 0.98{{formula:3db07b06-248c-43fe-ac54-f8d85eab6c12}} a {{formula:bf51305b-b2b6-4c39-ab9c-9cf94f193bc6}} 2400{{formula:9c409a29-167a-4bf1-9411-4c41098a60f6}} a(1-e) {{formula:8b9f2b4f-76f1-4392-9294-055fc2df92cc}} 50{{formula:36d9fbb5-6789-4eb3-b65d-90e3eb716f7f}}
| i | fdb4418cb6611f2edd52a7d3bd929b80 |
In this work we investigate Borromean states in discrete-time quantum walks (DTQWs) {{cite:f87d51d425461b7121d545cb0e9cc17f313c43f5}}, {{cite:c58d58e982954d39149d430805b4f6ca01f92622}}, a basic model of quantum particle-dynamics that is known to simulate a broad range of physical phenomena and was already implemented on many experimental platforms (for a review see {{cite:a49265771083020bfc0883ae49ccb3944964e05a}}, {{cite:8a9efe78a073e8f2574b18a46167cbcc8b7fdb46}}, {{cite:57b34f8805f31c37daeccc09ddf609a42047e41a}}, {{cite:ec71c6bc703090db222ad438f1059582facbcb7a}}). To this end, we allow the particles in one-dimensional DTQW to interact and form bound states. In general, interaction makes quantum walks hard to treat analytically even in the case of only two particles {{cite:4ed2e65fa32d4e64c21894b986f183c0abe8b6d2}}, {{cite:abf999a96c438bf6a043a73a14d4022e8a63900a}}, {{cite:ae60239a290b1229a7ecb4ab3e18a09643b88da7}}. However, our model features Borromean states that can be determined exactly.
| i | d5ab467a1c1ab9f932ec08384effbb68 |
Efficient exploration in the absence of dense reward signals is a long-standing problem in reinforcement learning {{cite:26f3ca43baa7fc5d2e4f124b0803d1f69fd4f9cf}}. Without dense extrinsic signals, a promising alternative is to define suitable auxiliary intrinsic signals that can help the agent in exploring its environment {{cite:fbbff6ae47f5b7793f69c7fcbfdaba6dd1c35f08}}. Recently, curiosity has emerged as a promising computational framework for modeling intrinsic reward and has brought major advances in many sparse-reward domains {{cite:2667dc6a66f92f1097d2773961eb2534812f6f1a}}, {{cite:b4e632e6f814f4fc032600b85c4875c718708b15}}, {{cite:1288f364758ee869ada29339f70e2db1faa318b5}}, {{cite:06ce75c0f0e3833734b2025a2ae4c4ac64c032f1}}, {{cite:fea38a047f0c357b4133ec63926ceac519481bca}}. While the algorithmic details of different methods vary, the core idea is to use changes in the observed state as the intrinsic reward to encourage agents to explore their environment. Despite their strong performance on many sparse-reward tasks, these existing approaches tend to rely on a holistic view of state transitions and do not allow for a targeted understanding of specific aspects of the environment. However, not all states are equally interesting but such information is not available to the agent a priori. On the contrary, humans rely on extensive knowledge about the world when exploring the environment. Language serves as a powerful medium for encoding this knowledge. A particular type of language that humans use is question – in an unfamiliar environment, humans often start the exploration by asking what can be done in the environment.
Based on this observation, we hypothesize that language-based question answering may provide a grounded and targeted medium to probe specific knowledge about the current state in order to solve the task at hand.
| i | 6921284d7dd1495579cc00938a31c129 |
We use the pairing model to generate random {{formula:30129f0c-8104-4e94-8604-d558d4362f5e}} -regular graphs with {{formula:253059fa-dcd2-4f3e-84e4-1921bc4f6abd}} vertices, where {{formula:08f69838-502f-43fc-b4ae-5a39bed95ed4}} is assumed to be even. The model was introduced by Bollobás {{cite:9d1688bc90773b10c7625cfe4f53cd222cf97387}} and by Wormald {{cite:3f091a83cfd353471d4da2cf67be938a5ca069fd}}, see Gao and Wormald {{cite:7ec8d96b44e021d958a58acf971e8d1bfb697be3}} for a very efficient way to generate a random {{formula:fc4c71a7-a65a-46aa-b4be-a2d2cd9d5e25}} -regular graph. The basic working of the pairing model chooses a random matching on a set of {{formula:82c57ade-0281-43fe-9400-f6b806b3b23f}} points that are grouped into bags of size {{formula:9b1257de-c8bd-4109-8821-047615953062}} , each bag corresponding to a vertex. The resulting object is a {{formula:7a046a09-c3ab-4bd0-a62f-a20155c16a59}} -regular multigraph (it can have loops and multiple edges), but a basic result on the pairing model is that, with positive probability bounded away from zero, one gets a {{formula:5129c5b6-f73e-4a73-9776-b28eccbe25aa}} -regular simple graph with the uniform distribution. Therefore it follows that every property holding a.a.s. in the pairing model also holds a.a.s. for random {{formula:8b62d5a5-434d-4f13-97e1-4a5678630b16}} -regular graphs.
| m | 91cd8ed7f3962f57bd42089dbb98510d |
In lower dimensions, one observes a broader spectrum of string-derived supergravity theories, but these nevertheless show some intricate structures not naively expected from field theory considerations.
For example, the rank {{formula:a5ce5eb1-da1e-433d-8a6a-e42671f14755}} of the gauge group in known string compactifications is bounded by {{formula:ac5f9398-df3e-46bf-bc76-f947028cf90e}} in {{formula:d256890a-906d-406a-a18f-ca5a851c4138}} dimensions, and satisfies {{formula:fef46178-3840-4970-9ee3-0a2ed5520cf6}} and {{formula:0b4e82bd-f7f5-4abd-a21e-38b1bd0a7fd7}} in {{formula:50908bc3-b1d7-4f76-a021-852cb4610432}} and {{formula:ca66d781-1f12-4797-8903-cdab2174c8bf}} , respectively.
Likewise, not all gauge algebras have string realizations.
In particular, there are no string compactifications to 8d with {{formula:9dbaf060-c03f-47b9-bb74-f934a0513e2f}} , {{formula:3e0dd485-9309-475e-88d7-235a2d9b16ca}} and {{formula:8b41e8b1-6c4a-47b6-8e9b-50a8c54d6cdf}} .
Again, novel Swampland constraints {{cite:59bc7a8f3e7720761ca4ec1adb04714b0a3c5875}}, {{cite:88060c0ced4ebd99aab49f443cbe846ba088354f}} and refined anomaly arguments {{cite:a9529096e35738ca3ec9893e57903c4b9d9712be}} reproduce these restrictions, thus downsizing the 9d and 8d Swampland considerably.As {{formula:b1a88bdd-78f9-4005-9b90-f0c81d3f656d}} does not suffer similar anomalies, it remains an open question if it truly belongs to the 8d Swampland.
| i | 706ccb1c794bbc51ff0146e618ddedff |
The class of almost periodic functions was introduced by the Danish mathematician H. Bohr around 1924-1926 and later reconsidered by many others. Suppose that {{formula:2a8fb4a2-2049-44bd-bcdc-4fabedddf073}} is either {{formula:5e22d9fe-2fdc-47b4-8847-be4bdeb2a44c}} or {{formula:2eb22031-b4c7-4c22-8584-f6ae46346542}} as well as that {{formula:e8bdbbbe-8fd4-49d8-9875-4c6a9e5c6983}} is a given continuous function, where {{formula:72226f2f-fcf8-42fb-9ee8-4c5cd1e4fe5c}} is a complex Banach space equipped with the norm {{formula:dbec9d29-316d-4c84-b1b7-ec3b035d3b57}} . Given a real number {{formula:d7ca4be3-6d68-4637-9d73-6733f837674a}} we say that a positive real number {{formula:a16d5063-a2ab-439a-aea5-f4bfd04e2ee7}} is a {{formula:9398e45e-a179-4d71-810a-f7a36a56957c}} -period for {{formula:626c7bb1-ce11-4f0f-959b-99c6a8a0f6fe}} if and only if
{{formula:aa7b2e2d-3e60-4643-aa9c-f4a650a23799}} {{formula:9bd0ced5-010b-43de-a331-bfcbe0457945}}
The set constituted of all {{formula:1a06854d-a515-4b42-a6aa-badda85ff7aa}} -periods for {{formula:adee0916-cf1e-43b4-8a90-c52b704b4046}} is denoted by {{formula:fa64efec-eae7-47cd-b669-fc6ecbc70714}} We say that the function {{formula:7dad598c-c506-4395-ab8e-c84282871ce5}} is almost periodic if and only if for each {{formula:d08c7b1a-fd45-4d20-b840-2ae0e3054116}} the set {{formula:1d10b47f-dc90-4b4b-a062-cde7cf194335}} is relatively dense in {{formula:ba109ddc-5bcf-4784-ae8c-cef486bcaed9}} which means that
there exists a finite real number {{formula:8b25fe5b-cf18-4463-8f85-99ad988b8c70}} such that any subinterval of {{formula:d5a521e6-26a8-4474-93af-aea04df09dbf}} of length {{formula:4df65a03-d56f-4dbd-a247-68f28519e1e0}} meets {{formula:3faae8c0-5d38-49eb-a7f7-c1d3b032a5d3}} . For further information about almost periodic functions and their applications, we refer the reader to {{cite:e6f3810276826f884f99c3721e66045ea82259eb}}, {{cite:fe3efc6a75762ac80e3755eecc9a7b90d3b368f9}}, {{cite:fc336eb1b7d757763f6378d37acb8ff285465f33}}, {{cite:04ff4fec02cc93554cc52d35f49674aca6444413}}, {{cite:a7094d7d10754003ce073974825c4a5235a61444}}, {{cite:907669c0fbb75923135e99d12a8d2907ce45ff48}}, {{cite:2f9485c52b1adc002d7db8761640cf5602e612b6}}, {{cite:1b13e136597f5bf53d168b77508065eae31a6269}}, {{cite:770d40910000087384f34a33020472946e4e41d4}}.
| i | 8389075a1bea00799a5c3715970fb6f5 |
What I did in my paper {{cite:d3643043a09d1753bd14babe4b289d33760f8d7f}} is realize that what Berry was doing was simple and standard geometry in the exact same setting as TKNN. I'd learned in the meantime that the TKNN integers were called the Chern invariant and the curvature {{formula:73fc5bb1-9ede-43ef-bf9b-15fc04d8b90b}} was called the Chern class and used those names for the first time in this context. The adiabatic theorem defines a connection, i.e. a way of doing parallel transport and Berry's phase was nothing but the holonomy in this connection. Berry had used (REF ) as an intermediate formula in his paper but didn't have the phase invariant formula of Avron-Seiler-Simon. Despite the fact that our independent work was earlier (dates of submission for our paper is May 31, 1983 and his June 13, 1983) and that the geometric ideas were in our paper (and more explicitly with the name curvature in {{cite:d3643043a09d1753bd14babe4b289d33760f8d7f}}), {{formula:1af79dcd-8ffa-4086-a452-7d1cad664788}} is universally known as the Berry curvature.
| m | fd910376c9e102a7781ed83047f2c276 |
We first compare with methods exploiting high-frequency features, i.e., SRMNet {{cite:894cf28b3bc78758d99c471be5dc6eeaf195a3c5}}, Bayar Conv {{cite:a9befb8e5e15423a14253ca788e9e24b501d6544}}, SSTNet {{cite:86e42b0c531f9bbf9d3e74c4074a60d7d642cd7a}}, and F3Net {{cite:6b084e1db955c4fd1024999f59b078d46b921f53}}.
The former three methods target video forges and share the same backbone but different high-pass filters, i.e., SRM filters, Bayar Conv filters, and loosely-constrained residual filters.
F3Net adopts Discrete Cosine Transform to estimate frequency statistics.
We follow their setting and perform video-level detection on the highly compressed (LQ) FF++ database.
Since our model is trained at the image level, we sample 1 frame every five frames to collect a total of 25 images for each video.
Then we average the predictions over sampled images to classify each video.
Results are presented in Tab. REF .
Note that we compare against F3Net with the Xception backbone for a fair comparison.
Our method achieves comparable robustness with F3Net and better performance than the others.
| m | 75c449509ccedbf12674b04eb2cc367c |
In the analysis above, we always assume {{formula:d764e60f-2535-42e1-ba70-3ae209df5485}} as expected in the realistic case for non-leptonic decays given their present sensitivity. This also provides conservative bounds, as any other final state (e.g. leptons) would be easier to detect. The most important caveat concerns the total width of the resonance. The typical detector resolution of the dijet invariant mass is at the level of {{formula:7f26e5fb-39a4-4f9f-893d-75bd9956c16c}} {{cite:70e82ef1369263d96cb70e65e919fc3dc790623a}}, {{cite:1fdb8a6e2359d8fe923ab1e71330fb2ef947362d}}, {{cite:7c94a7c64ec3fe6dc1e521ba4c769e1871cb2a69}}, {{cite:1ef8984fb3813f6b3c6432e278ac7d75bb946866}}, {{cite:d9891fdf1862eb5b4f063c5915a057b38fb15c4f}}, {{cite:d67cb6740fd2318d3417a0be24343334a3a825cb}}. Therefore, a narrow resonance is experimentally defined by {{formula:59a03067-e70f-41a8-81f5-71c9b7fea23e}} . This criterion has to be satisfied to apply the bounds from Fig. REF .
| d | eeb5b4b6b9c02ac816a9098fb120e5e4 |
For the NSFC population (a), time triggers from DECIGO+ will result in {{formula:31b4ee26-f78c-42d6-8a91-e8d6a67c7374}} . For Ult. DECIGO, {{formula:789894bb-e29e-4b5f-a6f5-5c6b96d4991b}} is expected. For the mixed population (b), the prospects increase substantially for DECIGO+, where it can help detect {{formula:f3694fdb-936b-4324-9a7b-3e8d6de99139}} neutrino events due to its increased distance sensitivity for memory in the BHFC scenario. For Ult. DECIGO the results do not change significantly from the previous case. Even DECIGO in its currently planned state, would help trigger and detect {{formula:d7c1ffe2-acfe-4334-9e84-c96f448f9272}} supernova neutrinos. We also show the background from the triggered-searches in Fig. REF (shaded violet area). This background associated with a triggered-search is, {{formula:702bf8df-c521-42b1-8f06-0db6e6afbfc4}} , where {{formula:cf2c8520-0bdb-4d11-9704-300f51d406bd}} events/year is the background rate in the detector {{cite:834653c06e0f0d6c09a42d882ad87a1691a8de57}}, {{formula:8b18f2a1-00af-4392-8d52-409493dc8017}} is the number of CCSN memory signals observed. It is evident right away, that the triggered-search background is orders of magnitude lesser than the untriggered background, thus highlighting the efficiency of triggered-searches. Furthermore, we see that even the triggered-background dominates the signal events beyond {{formula:b90034a9-7e13-4785-ac03-7faf898261ff}} Mpc and hence we restrict our analysis to {{formula:6cc1a650-7ead-4a44-8122-ced3297ecf68}} Mpc.
| r | c86d77bcb0cf291ff9eeedf4fa080346 |
Here the images of {{formula:6a9d4e81-c9d1-4911-8597-d5e2ba38d8d1}} in {{formula:1d1bcfde-c39f-4800-b4cc-feab5beff3d4}} are root vectors for {{formula:3cb96859-b5a3-447d-a41a-e6afd35bafdd}} in root spaces {{formula:ca91273c-0acf-4889-99ea-af5585d59fab}} and {{formula:6b367eac-c7e0-42da-aa92-216b2bda5815}} respectively. Thus the {{cite:5a42d972231e7cd984627c80b5d47a523787a5de}} action of {{formula:dcece44e-9902-4e03-bb57-783a2e16b13b}} on {{formula:03fbcbf4-9c79-499f-9e02-dc4fa21f149e}} induces an action on the set {{formula:8318db92-d2fe-4449-a388-29c3bf497397}} for each fixed {{formula:656b3c17-b663-4f5a-95d9-657e069a72f8}} . We have that {{formula:0d7bfcf8-76b1-451e-ad41-59874b6e616c}} (Corollary REF ), but we do not know whether equality holds.
| i | a95e2f9bb965083b616af7fbdd34221e |
Most existing datasets for training overhead object detectors are labeled with horizontal bounding boxes {{cite:dcb90fccfbdf85a50ca23e8c176172999bc2aa7e}}{{cite:47ae0025b84cb260bbf450e885aa59dd540b4b44}}{{cite:e5c10084ddc46433e03eb1ec8bc0e0d363cf76d9}}{{cite:707fded8c14abdf0ee823f2dec6ff2539ea718e9}}{{cite:a79bfde6eab9e70a01c02cb119dc6c657478d2c6}}, object-aligned bounding boxes {{cite:2dce921d9e21ea5ec42c56eebba732d286bb7d49}}{{cite:191dc7b9ceb7cb5a72b5aef6ea8a47004d021a60}}{{cite:727c850e3f074dc72edfd682af4c6af043bdba34}}{{cite:1ce79711ea567ade300fec12e10997630f79a52d}}{{cite:5e684d1a127efc102e3ad972d9c2f4cbac358bc2}}, or segmentation masks {{cite:5aa04342070029bcd1876b05498ad7ce81835da5}}{{cite:9a9b1a6daa79b7794eab703eae9fcaef79841bda}}. These methods of labeling appear to have been inherited from work on natural images – primarily cell phone pictures. Unlike objects in cell phone pictures, objects in overhead images are only seen in a narrow range of viewpoints and scales. This paper examines whether the extra work required to create such detailed labels is worthwhile in terms of the resulting detector performance.
| i | b1d8f87970ae65c7efc4ef8e2dba65f8 |
Theorem 1 ({{cite:6857d34904730f8ef972101fa2c87b5844512e5d}})
We have {{formula:e13fee8a-632b-4595-8bb3-5b9f4087a1da}} if
{{formula:9d8f09ab-0fe5-413d-98b8-9062438db2a1}}
| r | 6bde1317d9aa800f21f07ed02a61f491 |
Remark. If the Conjecture on the Finiteness of Central Configurations is true {{cite:4c964d0fa8d341704ba54c4cb23bd69047e6e4cc}}, {{cite:2c536a13005e1e2e36605586aed3a96f98307469}}, {{cite:b3e0c6675aa5661f74baa96709df96dc3aa88622}}, then the Corollary REF is obvious, but we don't need this hypothesis here, so the Corollary REF is not trivial.
| r | 69174ce4a6e70a011c75307c16c43223 |
where {{formula:7b86b362-26cb-4ca2-b529-e40d8a8c09f0}} and {{formula:c8cb7c03-fc61-455a-8a2f-1f0b867c37dc}} are independent variables, and {{formula:3bc7667f-d9fd-4ddd-956c-2e580e72fc33}} is the skew Schur function {{formula:f5f9aafe-8280-4d16-aa7f-3c1863ede031}} specialized to the case in which the symmetric power functions {{formula:873b9155-86f0-4174-8095-2d3eb6fcfab2}}
equal {{formula:6f59fa14-c763-4400-96d2-c2cb9ca84cc2}} . Similarly, {{formula:8d5deb39-519c-48fb-a616-a07ace39000b}} is the skew Schur function {{formula:6898a52b-1063-4460-b0d2-bc96f4a7263d}} specialized to the case in which the symmetric power functions {{formula:e56ce8cb-0a21-4b5a-aaa6-1bf8b3533e91}} equals {{formula:b9e67932-14f0-4997-ba9e-4cc5ff8cbcc2}} , [see {{cite:d984d8ab4f0aad90b10764241cdd007d7e0a6f87}} page 11 and 24, or {{cite:88cd91a2e68c04e64c6aeb45ef59e91876571ee3}} pages 25 and 70 for the notation]. {{formula:cd0c80d6-4379-4540-8184-aff5af698c6a}} is given by
{{formula:9a69b39b-f89d-4765-b37e-f938b75b938a}}
| r | ff1792e62dc8d0d3d6fa0f788df3b6ac |
One of the challenges in audio captioning is to address the lack of training data {{cite:21859a7ba9c2208db5dc5beb904b856646f7683f}}.
Typical datasets in audio captioning, AudioCaps {{cite:85fa197a97e1dbc0591bc080ba38f95ca43a84c0}} and Clotho {{cite:90517b0bfb9d9093daa72a3163e4d69d67429421}}, contain only 49,838 and 14,465 training captions, respectively, whereas there are 36M training sentence-pairs in the WMT 2014 English-French dataset for machine translation. It is due to the difficulty in collecting audio and the corresponding captions by crawling the web.
| i | d322f47f6af832e5d43743544411b0ac |
In our search for methods that model scientific specialties as networks of journal papers and enable the identification of thematic structures in those networks, we applied the algorithm developed by Lancichinetti, Fortunas, and Kertesz {{cite:19a28994d48c526bf0dfd9f5ad23b8397b4d35e5}}. This LFK algorithm is well suited to our problem because it identifies not only overlapping communities but also a hierarchical structure of a graph if there is any. Since we assume that thematic structures are of varying scope and that some of the smaller themes might be completely contained in larger ones, an algorithm that detects both overlaps and hierarchies is essential.
| i | bae27f62927d4ec5f74931be7fcb3f67 |
Due to computational feasibility (ExpGrad needs to store all intermediate models at
prediction time), we
combine Grid Search with FIFA for the CelebA dataset and ResNet-18 and use both
Grid Search and Exponentiated Gradient on the AdultIncome with logistic regression. Besides {{formula:cd45d7c6-c781-42f8-9808-f40b9254644b}} and {{formula:65c020b7-f2ac-4105-ac93-d45495e8273e}} , we also treat {{formula:8a2d2fd2-6fc0-4b86-93d2-f30730ab572a}} as tuning parameters (in Eq. (REF )). We then perform hyper-parameter
sweeps on the grids (if used) over {{formula:3a7c2242-2a3e-4c77-b469-4b550b756131}} , {{formula:b107cdae-d766-42a7-9bd2-6fd9c984665d}} and {{formula:9622750f-2816-4505-b2e7-88c5d7966605}} for FIFA, and grids (if used) for vanilla training (combine fairness algorithms with the vanilla softmax-cross-entropy loss).
The sweeps are done on the wandb platform {{cite:6106e44f614fbabc5ca2fcb2c9cf1f2c1cf6e061}}, where all hyper-parameters except for the grid, are searched using its built-in Bayesian backend.
All models for the same dataset are trained with a fixed number of epochs where the training accuracies converge. Batch training with size 128 is used for CelebA and full batch training is used for AdultIncome. More details are included in the Appendix. We compare FIFA with directly applying fair algorithms to NN's trained with softmax-cross-entropy loss, which is the most natural baseline. Also as a special case of FIFA, when {{formula:c48f1d9d-cf55-4a9e-b6e4-12b1bb829c47}} for all {{formula:e05f276b-3f36-4585-b5db-c663882424ab}} and {{formula:be7880e8-8c7c-43a6-b329-88039f7757d6}} the FIFA loss degenerates to the LDAM loss proposed in {{cite:e8b92b335d31c5b0e91bba5c275f494dea06284b}} that is not as fairness-aware as FIFA, so we briefly discuss it in Table REF too. FIFA further finetunes {{formula:df36c4ab-ac28-4f36-a7ed-16b797e32553}} and {{formula:baf04a44-2462-4f05-8848-a1b840da32d0}} , and to ensure a fair comparison, we set the same coverage for the the common hyper-parameter {{formula:28069028-099a-4e3d-9475-59704679f970}} in the sweeps, as shown in Fig. REF .
| m | ac659a6b3ffcb8d4a368915a4bd1fd80 |
For the first problem, inspired by compositional generative models {{cite:94e3fcb704ac3636096114adb2f150d0eddf486f}}, {{cite:e7c80ac82810e3a8e5f832e34c1e5715714b7a73}}, {{cite:e9e001fc27bbb088795ad3a60671f290b2a0883f}}, we introduce local generators and a compositional synthesis procedure as the inductive bias. For the second problem, we use a dual-branch discriminator {{formula:d77e1748-4991-48be-ba33-e33cbc96eb40}} that models the joint distribution {{formula:d04811f1-3881-4a02-804e-159d71f6c36e}} to supervise the shapes of local parts after composition.
{{figure:58dbf1f5-ec45-42d6-adcc-6a932fcf7498}} | m | 0571c4e445fc786cd146869a8b40c5f4 |
Moreover, one can estimate the value function terms {{formula:5ae58284-de1b-4d40-9996-52bcbc884ec4}} in (REF ) by collecting rewards from the Monte Carlo rollouts (as defined in (REF )).
This learning algorithm is called the Monte Carlo Policy Gradient algorithm, otherwise known as {{formula:2e664ee3-9ac1-4dc5-82f3-e0b96d559cbf}} {{cite:89da4353a4680344a3406cdf032995ce99a72ccc}}, {{cite:0b3c2f2542ce2a84cd1a6bbe54fce11bfd663470}}.
In the literature, there exist other sophisticated approaches, such as the actor-critic method {{cite:4c5adf9463c9b8cb3e25a07b97e21ade6051d300}}, where the value function is estimated using an additional approximator such as a deep neural network (DNN).
| m | 0e64b56ea45b649e414358a5f39e9e6f |
Firstly, we consider the case of adopting the differential cross section {{formula:0530c5cd-3da3-4c13-b877-7bd314c45edb}} at a near-threshold energy region to study the QAE contribution.
Combined with the predicted differential cross section from theoretical models and the VMD algorithm,
the QAE contribution ({{formula:3ea45ef0-0890-4aa1-b75a-51e1e8ee5317}} ) as a function of {{formula:c2fb6587-dd35-48bc-a7b1-3787300f4222}} is obtained as shown in the red-solid and green-dashed curve in Fig. REF . Besides, it can be extracted from the GlueX and Hall C experimental data directly {{cite:f276cbb3e832fc5294501dc41f0505b573a9f51b}}, {{cite:743f1de1bd6e33bf9ed9a252777bf29ecd6d63d6}}, as shown in the blue triangle and black squares in Fig. REF .
We note that the QAE contribution to the proton mass is sensitive to energy and varies greatly with energy, which can be seen from both the theoretical models and direct extraction from experimental data.
However, the energy dependence of the QAE contribution is not the desired conclusion. One can chalk up this energy dependence, in large part, to the rapid change of {{formula:9a4b03fa-d34b-4cab-b8a1-7526931ae1b9}} near the threshold, as shown in Fig. REF .
One find that this effect is less pronounced for the lighter vector mesons {{cite:f13bf90c67370d493b28a4ba4fef46761d1b2a4e}}.
{{figure:ccc7329c-70d9-422e-9e9b-3ed6ce31bd0b}} | d | 479cb4bf8ea1e1549b431a9ace647a50 |
Q-learning is arguably one of the most widely adopted model-free algorithms {{cite:aa300f79c075ca5969e410bca9f1f36644e4f8b0}}, {{cite:42450b150f2e7539c989886cab30bf810c78d490}}.
Characterizing its sample efficiency lies at the core of the statistical foundation of reinforcement learning (RL) {{cite:636a3f34f0830cc50bdf76eea5734492207594a2}}.
While classical convergence analyses for Q-learning {{cite:b702a54033a7deb1a8753ba85e1d2184bbe8172a}}, {{cite:932bd01aa1b38f84bd8c77aebda7046839efd158}}, {{cite:789e63d3a5f8db86211eb53142890a3c985b3b75}}, {{cite:91a05da8a20421596f9bad9ea1ecdc5df635aead}} focused primarily on the asymptotic regime — in which the number of iterations tends to infinity with other problem parameters held fixed — recent years have witnessed a paradigm shift from asymptotic analyses towards a finite-sample / finite-time framework {{cite:845957255d0881f12cb6d8d0215c9e887a9143bd}}, {{cite:62b88ac8244c633e24c48280248f68778ea456c3}}, {{cite:568f6b8559cc1f3929261f1206cfff70a23f9ea0}}, {{cite:fe5112756d9cbe26dc5c46ed67b859d7c0233c79}}, {{cite:717d2f04b64891bb63c10088651290b79c2cd364}}, {{cite:d9e6a9afdc18d2f0c92acb0d0b784b5b5928f396}}, {{cite:15301e294bbf981a95f31c53eea12946537a350d}}, {{cite:9e21b9c4517ff119106275d4dfe4c4c9f2b66f2d}}, {{cite:105a103a2e78067f01e4be966a98e7a3994710a0}}, {{cite:3bfd7a2578475014523227fa3c755c58895f2982}}, {{cite:248b0810503c00a59f0d49edef073df9a9d7488d}}. Drawing insights from high-dimensional statistics {{cite:4a7cfbb690910ce49a6a7c1221645b4c6e39bba8}}, a modern non-asymptotic framework unveils more clear and informative impacts of salient problem parameters upon the sample complexity, particularly for those applications with enormous state/action space and long horizon.
Motivated by its practical value, a suite of non-asymptotic theory has been recently developed for Q-learning to accommodate multiple sampling mechanisms {{cite:845957255d0881f12cb6d8d0215c9e887a9143bd}}, {{cite:568f6b8559cc1f3929261f1206cfff70a23f9ea0}}, {{cite:0bf10a24aee44675d553242f64822fb846066345}}, {{cite:717d2f04b64891bb63c10088651290b79c2cd364}}, {{cite:15301e294bbf981a95f31c53eea12946537a350d}}, {{cite:3bfd7a2578475014523227fa3c755c58895f2982}}.
| i | 7c4f8a3367fa26bb7119ff43dcb7ca16 |
In {{cite:8c7643298da192144cbf942bba1e68139b179e7b}} two policies were considered for the treatment arms: an “initial policy” based on the results of {{cite:24f8311fd792e4f51c9197c9ccb53a07977dd9db}} to incentivise exploration, designed so that: i) no message was sent on {{formula:69bd6c8a-a1fe-4238-a31a-3cc988fed3fe}} of days, and ii) for the remaining days, a negative or a positive feedback might be received by the user with equal probability based on their expected fraction of activity; and a “learning policy”, based on a linear regression algorithm with interactions and the Bolzmann sampling {{cite:57a3edbf95449e3c83002a6e9cce988f30750e7a}} on the outputs of the learning algorithm to choose the feedback message to be given.
| m | 2504f724d57266d1781b4027282eb0ef |
Recently in 2014, the LHCb Collaboration has determined the mass of the {{formula:35efc4cf-32bc-4c21-86ea-1658e08e1195}} using its radiative decays to the {{formula:bd061800-2254-4f95-a0e4-37b2a617af61}} and {{formula:2f0666b6-6dfe-4100-9293-89cd5adc9b05}} mesons and the measured mass of the meson is {{formula:15d8cf5b-0a71-4eee-9895-6e3d7d9dc436}} {{formula:d972d640-1f57-42ce-aba3-c458d37c1e90}}{{cite:51b9df19b8026dc36e59bbc964d24707f614bada}}. Many other states above open flavour have also been observed experimentally in the Bottomonium family but their association to a particular S,P or D state remains questionable. It is because of unknown couplings of the many channels that become available once the threshold is crossed. Two charged states namely {{formula:8c1f872a-74ec-4433-9cce-f123f9cbcf74}} and {{formula:469bc008-9a54-481f-b2d7-07008c2583ed}} were observed at Belle by {{cite:30022e4c440188223170447a9dd6966a99e3b1aa}} in 2011 in the {{formula:536edd17-1a53-4f7a-b0da-e2d32a2bd0ca}} decays to {{formula:d2a3d0c2-2056-4d20-a3be-5e22a72ca04d}} (n = 1, 2, 3) and {{formula:f054a34c-b914-49a7-b106-efaf7cef82de}} (m = 1, 2) with {{formula:a5c0448d-f92c-4c16-a889-1fbd944f2fac}} . Ref. {{cite:4bc46b631267056c86fa8a47a881fee9ae90b361}} suggested by considering molecular nature of these states all their properties can be explained. Recently, in 2019 one new state {{formula:d101f444-aba8-4946-8eeb-2948bc1ec579}} was observed at Belle by {{cite:0086af990e6b9ce3651eba961730fdb3b07545a5}} in {{formula:ca0515b6-3fcc-4ce3-9163-4a76f344fb08}} (n=1,2,3) with a significance of 5.2 {{formula:875c388d-6b0e-497a-8f67-fe44125f2757}} with mass of {{formula:60be827b-68ab-4015-a197-4c1542c46aea}} MeV and width of {{formula:bc3706d2-edf7-425b-a1e1-551efec119b2}} MeV. This new observed state can be a candidate for {{formula:c9dfbaec-a070-4d28-a22d-58a35aac6406}} state as suggested by {{cite:9c8f6fe0bd156cadc3eb8563f200a74050850221}}, or a compact tetraquark {{cite:99bfc5679f8e9ab4fa135f84f07febfb3c754f66}} or hadrobottomonium {{cite:ce31089dfef850720cca9e1419274dc9054d7e36}}.
| i | bca55b0f4c69f48599f01a122acb7a0c |
Clearly, this `malfunction' of sieving through {{formula:475b3dd2-d7ac-4ce0-b602-c7ceb4d2d1bc}} -spaces is due to a lack of some kind of hereditary/hierarchical structure in spaces in this category: no particular collection of subspaces of an {{formula:b952f7e0-61c1-48c1-a10d-0f1ccf4ab01b}} -space is forced to inherit the {{formula:7178c848-cb5f-45a7-b669-e1c1a3dc582e}} -space condition. This motivates the introduction of the notion of {{formula:6f71d0cc-ceec-4169-ac1c-d6a03b458851}} -spaces, best viewed as a relaxation of the hereditary class of ultra-metric spaces — {{formula:0efffc90-ab2c-4a25-ad27-21a32b8cf13a}} -spaces being of particular interest, in view of the key role of 4-point conditions in the metric clustering literature {{cite:0151189360b1643e001459255119038e9457c316}}, {{cite:0f288da5d877f54b7c1608c58c8da53e5edc574f}}.
| d | 5ba54f3fd62ddb7adc40bf3f080c0d80 |
It is of fundamental interests to study the quantum control of
spontaneous emission which inspired the development of the quantum
electrodynamics during the last century {{cite:cd5df9dbf60cdf11a114146516432d994275b837}}, {{cite:9550d0d746031b5c17c26ea199c5b6fdea0c76f7}}, {{cite:990e5af4f2d5b5aa975bb38f552e6852a142e964}}. The unwanted spontaneous emission often sets the
ultimate limit of precise quantum measurement and many proposals
have been made to suppress it {{cite:89bbdb2047f6be9625cb2ada1ab1a2a701278b65}}, {{cite:240a3c34d9bc20bb522476d7c8b81d9b55326d6a}}, {{cite:92247cea0d9b73679e9ffbab5b810b633786b6c5}}, {{cite:f435159cf7df88b0c9321640a33ac069b1eaeb67}}. One way widely applied to control the
spontaneous emission of a small quantum system, such as a neutral
atom, is to place it either into or nearby a microcavity such that
only a single mode or several modes of the cavity are resonant to
the eigenfrequency of the quantum system {{cite:2899941d44d016109d836b065a4997974df73f47}}. In this
way the structure of the vacuum is modified and the spontaneous
emission could be controlled by the properties of the cavity.
Another way to control the spontaneous emission is dynamical
control of the quantum system such that the coupling between the
quantum system and the vacuum is effectively modified. For
example, dynamical decoupling of the quantum system from the
vacuum via either phase modulation or amplitude modulation could
in principle extend the coherent time of the system {{cite:b235ac51bae7e804806a4c427dc78b174c002690}}, {{cite:5395cbc80d7d1090fd5cd422f8f5fe5f08896bf8}}. Analogous to the quantum Zeno effect (ZE) which says
frequent measurements of a quantum system would prevent the decay
of an unstable quantum system {{cite:3b781f57df0181b148a4c04208e33c63b7f07c8c}}, {{cite:b235ac51bae7e804806a4c427dc78b174c002690}}, {{cite:5395cbc80d7d1090fd5cd422f8f5fe5f08896bf8}}, the
extension of the coherent time through coherent modulations of the
quantum system are often called ZE as well. Under some unfavorable
conditions, it is also possible that frequent modulations lead to
acceleration of the spontaneous emission, the so-called quantum
anti-Zeno effect (AZE) {{cite:74cd3bed0440991a3e67ed3c84a455ff2f72f93e}}, {{cite:6128f17686a603b966a6ab0b263950fc6027c823}}, {{cite:4fec2da3667c47e6c63afadaec6e09cf838e8cbd}}, {{cite:e624789bf49bf9d663084e6ad81732f778c194f8}}.
| i | 8c4c1a29e50d6c464161e942d031802c |
The LSTM baseline used in our Omniglot experiments have a hidden size of 128 and use {{formula:d0e92624-2887-456b-a021-7324549bd270}} latent modes.
The input is first projected into this space using an embedding layer, which is identical to the one used in AutoBot.
All input sequences of sets are encoded independently using a shared LSTM encoder.
During the decoding phase, we autoregressively generate the next stroke step using an LSTM decoder.
In order to ensure consistency between the predicted future strokes, inspired by Social LSTM {{cite:ebf7b1d51201548d7c306c217e2510abc634d105}}, the LSTM baseline employs an MHSA layer at every timestep operating on the hidden state of the different strokes making up the character.
We concatenate a transformation of the one-hot vector representing the latent mode with the socially encoded hidden state at every timestep.
The output model is identical to the one used AutoBot, generating a sequence of bivariate Gaussian distributions for each stroke.
We performed a hyperparameter search on the learning rate and found the optimal learning rate to be {{formula:7eb8043c-599a-4813-85b1-b9b320194bb4}} .
Furthermore, as with all our other experiments, we found it helpful to employ gradient clipping during training.
| r | da41e0396049290457c6113b67139b40 |
For {{formula:560fd828-2136-4d59-a3ac-a6a72872193c}} decays into {{formula:efda2d3f-fb7a-48d5-80ff-3074357df546}} our estimated results without radiative correction are consistent with {{cite:99ef74cd0c5ccb8862b7da08f9fb56a59638df16}} and considerably lower than that from the {{cite:f9787c69670173e0e5ab3fe909bc055ed5adb46f}}, {{cite:97b657bc476c4a49caf41e566d0e0fcd804c65af}}, {{cite:4ef207a6cd834b828ab39df16c8434784d119e43}}, {{cite:1b5bf290589cce5cfee61b6799d677ac1c1bb790}}. For {{formula:02b055c4-97fe-4e33-a904-55c9b6a1f921}} states, our computed results agree well with the {{cite:97b657bc476c4a49caf41e566d0e0fcd804c65af}} without QCD correction while they are in accordance with results of {{cite:f9787c69670173e0e5ab3fe909bc055ed5adb46f}}, {{cite:1b5bf290589cce5cfee61b6799d677ac1c1bb790}} with radiative correction. For these states estimations of {{cite:99ef74cd0c5ccb8862b7da08f9fb56a59638df16}} are comparable with our predictions. For the {{formula:d167af63-c62f-44eb-97fc-3093a95fb19e}} our predictions are in line with that of {{cite:1b5bf290589cce5cfee61b6799d677ac1c1bb790}} and {{cite:97b657bc476c4a49caf41e566d0e0fcd804c65af}} . For the S wave vector state decaying into {{formula:26de1aee-f2d7-4f36-96c1-a7878896f216}} our results are in agreement with the decay width listed by PDG {{cite:4806a585f85da3f95dc5920230c91f9c22e95883}}. Also they are comparable with the {{cite:f9787c69670173e0e5ab3fe909bc055ed5adb46f}} especially for {{formula:be738e38-a08c-4ed3-91e6-fe5ef0a9dad4}} state where our prediction is 0.040 MeV without radiative correction and their prediction is 0.041 MeV. For the {{formula:80ab0791-cebe-41d5-8787-6152442beda0}} , {{formula:2942050c-bc30-4c2a-94b2-7e7a391cd00a}} and {{formula:92df5341-0d49-4ca3-a71a-f929b618713f}} we do not include the radiative correction because such correction will be very much lower. The results are consistent {{cite:f9787c69670173e0e5ab3fe909bc055ed5adb46f}}. Intrestingly, for {{formula:a50e714e-6e35-4079-a905-0353e20e33f7}} state our predicted tri-gluon decay width is 0.035 MeV which is the same as reported by {{cite:f9787c69670173e0e5ab3fe909bc055ed5adb46f}}.
| r | 2ef08a458e362b2f4e1536ce38a4f808 |
Table REF shows additional results on xGQA.
We outperform multi-lingual zero-shot baselines on all non-English languages, without access to English GQA labeled data. This further confirms that our unified approach to mVQA is effective. In addition, unlike on {{formula:672ca82b-36e4-4f7c-8a35-0f006accdd1d}} , VQA2.0 is the best pre-training data source. We attribute this to the fact that VQA2.0 and xGQA share COCO images {{cite:cb24c022f8c34f93e1944e1a78fb8e42bc53de0f}}. This highlights the utility of {{formula:e3d297dc-4910-41aa-ab67-7f3de8422018}} as additional out-of-domain test-only VQA evaluation data.
| r | e58a4c7a1f2fbedc417806990cce93ab |
Remark 8.13 One may want to compare statement () with {{cite:1651f80085ce69c068b5fa2a762d0d04f3446b61}} in which
the product is replace by multiple harmonic sums. Furthermore, Au
showed that the level of the CMZVs can be lowered to 2 in that case.
| r | ed9acc7d48b6bf27be644f792d0f64dd |
(1)
For the neutral {{formula:bf86bd0f-0ea0-4eda-8884-45099ab0dc68}} mesons, the wave functions (and the distribution
amplitudes) and the decay constants are same as those extensively utilized, for example,
in Refs. {{cite:b34645621b2823a33a0665f875f6978332932362}}, {{cite:382e226e9b897a3eed4df88f112c4bae16627429}}, {{cite:44b82ee3f07348079d956351f4c7532878778261}}, {{cite:0bad9fabee374bac1638e58ec088c202566e6e64}}, but with the updated
lifetimes {{formula:8ba0caad-f9dc-4c18-8739-4a3b4cfc869c}} ps and {{formula:5330fb13-e077-48f0-abc0-38be0c0a930c}} ps {{cite:1fae8d50ff788de8609bf34a4d1386971439f3e9}}.
The masses of {{formula:9be2d8ac-bf58-4441-8e51-0e7e07c39b0a}} and {{formula:2408b1ae-fba3-4839-80fa-a5d6fc361aba}} mesons are
{{formula:1b4e69da-4d3e-4336-81ee-ad9bc24656ab}} GeV and {{formula:54172019-16f5-4656-8e75-337c019d5f45}} GeV {{cite:1fae8d50ff788de8609bf34a4d1386971439f3e9}}, respectively.
The recent developments on the {{formula:7556c7b8-17b0-4bd3-b08f-c6661082494b}} -meson distribution
amplitude could be found in the literature, e.g.,
{{cite:ac35e7141d6db56746022c60749e434c309219c4}}, {{cite:1d986bcb87807b1bd77f0db01835c33fdc63602d}}, {{cite:f446dc7ded24d7520315ae92f77d721a868811af}}, {{cite:14dd5ec82730b799468cb181037dfa15bc108aa2}}, {{cite:9c8425087f5711f4e0675c5c36ef4f3a1fb1fdb0}}, {{cite:7ef85c5ec4812fbd08fe5bae601c823052cc4b70}}.
The effects induced by these mentioned
distribution amplitudes could be left for the (near) future investigations with definitely
precise data.
(2)
For the light scalar flavor states, namely, {{formula:451f4a20-366d-415d-95b3-171db60bd93b}} and {{formula:933be867-5073-401a-8c76-05aea0552875}} ,
the decay constants and the Gegenbauer moments in the distribution
amplitudes have been derived in the QCD sum rule method {{cite:6206c641f7bcced81ce6a59dd074869209a7800c}}
and their values at the renormalization scale {{formula:a05eac08-7ee7-440d-8a71-863937b4d3a2}} GeV are adopted
same as those in Ref. {{cite:869c870c55b1df141c9bb8440a55794f1bf6275b}}, specifically,
the scalar decay constants {{formula:5ebad673-f3ee-4273-a1ff-fff0daa9cedd}} GeV and
{{formula:b6cf158b-41d3-4de9-901d-a71c8286a19d}} GeV,
and the Gegenbauer moments {{formula:ab37f2ef-5775-4833-b9bc-a497d370557a}} , {{formula:c383836c-ef10-45da-b194-c6ac9a834703}} , and
{{formula:f85dcb46-5d07-4613-ad93-e08190c068b1}} {{cite:6206c641f7bcced81ce6a59dd074869209a7800c}}.
Notice that the vector decay constants {{formula:2558570e-1f25-4f02-af72-162616d48d25}} and {{formula:fcfa5183-cbc1-48de-a741-d7a3a45d767b}} are naturally
zero due to the neutral scalar mesons with the charge conjugation invariance
not being produced by the vector current.
Moreover, the masses for the physical states {{formula:e6547d44-80fb-4e0d-843e-03dbc4d3ea09}} and {{formula:2f0e35ad-bd49-492f-8440-0ba5c097b4d6}} and the flavor states
{{formula:5ad4cf0f-f29b-43fb-a189-c5299e4de16e}} and {{formula:331b3a6f-880a-4c03-890c-58631cbc9ea3}} are same as those utilized in Ref. {{cite:869c870c55b1df141c9bb8440a55794f1bf6275b}}, i.e.,
{{formula:7c10cebe-0bd5-4525-b407-1507355a9828}} GeV, {{formula:715bb2ce-2f4a-44c2-abb4-297c62362972}} GeV, {{formula:f7065902-a0fb-419c-9a85-9c359f3adb96}} GeV, and {{formula:8268c918-7167-47a3-9048-eb4c86ae3688}} GeV, respectively.
(3) For the Cabibbo-Kobayashi-Maskawa(CKM) matrix elements, we also adopt the
Wolfenstein parametrization at leading order, but with the updated parameters {{formula:42e7a64c-d8bd-4cd2-a986-bbade8492989}} , {{formula:44492bcf-0eaf-427d-9e88-adaf3bace5eb}} , {{formula:9a258d2c-7032-4424-9eb0-a86818ce8e2e}} , and {{formula:0c0ddf70-cd3d-479c-90f4-186548b1d10c}} {{cite:1fae8d50ff788de8609bf34a4d1386971439f3e9}}, in which
{{formula:90b61e41-8f2d-4db5-a396-ae10009a2602}} and {{formula:29275ac5-18dc-4048-a87a-1cdab510a80f}} .
| r | bb7085d0f9ec70320df5f7ce7c93b232 |
As in {{cite:b9be41b272987160318e969024ba751dbfe1ed34}}, define {{formula:7e07a67a-3ef7-4898-8843-ca1d1e84f862}} where {{formula:06d14797-54bf-4982-9bfe-b753255d80d7}} . Then {{formula:48c496d6-bef8-42f3-82bb-96a3a1991fce}} satisfies the hypotheses of {{cite:74d61847af7df43332440f681ce2bede8be25016}} from which follows
{{formula:41b76a0a-3f50-4714-973d-e2d816e3520d}}
| r | a76e664540c3914230c186ec723408ff |
To deal with the inaccuracy problem in smaller deviation ranges, we adopts a multi-stage prediction strategy. Previous BIQA approaches adopt a one-time strategy to predict MOS, with a feedforward structure. However, the way neglects feedback mechanism of human visual system (HVS) as is important for perceptual learning{{cite:93185ed3f213f24289a28fc4f3c9ce3ea6d5bda3}}. Neurologically speaking, feedforward hierarchy underlies implicit processing for initial vision at a glance, and feedback connections add details to explicit vision with scrutiny{{cite:6ff047f39fd1c2f357f78cc7edf64b6c4bfcde73}}. The same applies to BIQA that fine-grained cognition of image quality is achieved through a feedback processing where high-level and low-level features are recurrently integrated by HVS. Moreover, feedback-based learning approach has been proved more effective than the commonly employed feedforward paradigm in prediction tasks. In the proposed method, MOS prediction is constantly refined under multi-level tolerance constraints through a feedback structure. Besides, coarse-grained metric is fused into the structure as the prior knowledge as it is easier compared to fine-grained prediction from the perspective of curriculum learning{{cite:436126bc27b519e5ca6df9daa24842c1153277b5}}.
| i | b8ae3ddc61c15baf1a5a368ec2c77fca |
For the parameters in the light neutrino sector, we adopt the current global fit values from Ref. {{cite:cfe89ff1d84bf30625b56818678f24bbcd62d78b}} and show them in Table REF . This leaves us with only three unknowns: the lightest neutrino mass ({{formula:d9f29cfc-d2fb-468a-8e50-ab8a0ecd1e7f}} ) and two Majorana phases ({{formula:5cad277e-a5a8-4a17-93ff-551c16fdd59c}} ). Our results are compatible with the low-energy observables in neutrino oscillation experiments with such a choice of input parameters.
| m | eda375210c62f81f1e4be2fc35fe8795 |
where {{formula:fa5bf4b2-e9d3-4317-89f6-06a8fbf06c43}} are the DFT eigenvalues, {{formula:ab03d446-b6c6-4f42-afed-487fb64d11f6}} is the electron self energy operator, {{formula:22e27651-2767-4947-933f-da3480a60d8c}} is the exchange-correlation potential and {{formula:58295554-cac8-4b00-91bd-2f224a091dd9}} is the quasiparticle renormalization factor expressed as {{formula:fb7278d6-4b08-42a9-a474-9c78c1fb97b9}} {{cite:c1113d8e249ca296a81174489119e28918c74ecb}}. The electron self-energy is calculated in the {{formula:14805536-3be2-496c-ace4-d99dc9d75844}} approximation as the convolution of the single particle Green's function, {{formula:1b77a7fa-b4d9-45a7-8ff5-70b1eff68fb6}} with the screened Coulomb interaction, {{formula:c3668f7b-7a7b-4b49-8295-81e641435e37}} , defined below. The single particle Green's function is calculated starting from DFT as {{cite:5bdc8866a4f59eee47342aa0e204fec62342b4ef}}:
{{formula:85b60cd6-e2eb-4fad-a4fc-8278af66cc44}}
| m | 8365644d639c7eab312acb3a2bbda3db |
which are consistent with the one obtained in Ref. {{cite:0c6b338d6e9317503007ec04b307a640c09efe36}} very well, {{formula:bf08ec44-0c44-42aa-aad9-f49a1579881b}} , with a bit difference to their former results, {{formula:f3b5aee3-0b51-4df4-a6ed-ce8dae1a0004}} {{cite:e98615543023d6a96403bec0816d3eb0fd162d31}}. Furthermore, using the framework of resonance chiral theory, a value of {{formula:86170290-cf04-4fe3-8d21-90ad25b06b3b}} (Fit I) and {{formula:a1af8418-fad9-4fb9-a710-ac1012f6b43e}} (Fit II) was obtained in Ref. {{cite:1d8717eef0a2844dc09e1dedd7dc39ce1702af04}}, which are consistent with ours within the uncertainties.
{{table:75b09805-2de4-41b0-ad67-fbb65199b7b8}}{{figure:1547f068-315e-4345-ac44-7ff02f84c8b7}} | r | c7597777c82214513d7961b3cc677c81 |
The Zak phase formalism that needs to be developed for the soliton metacrystals
should reflect on two features - (A) nonlinear interaction between the phonon and crystal and (B) the discrete sampling of the states in the Brillouin zone.
In order to make our derivations transparent, we first neglect (B) and, hence,
take the limit of a large number of unit cells, so that {{formula:d23712cc-3e6d-4bf4-8235-29f2b6a808d2}} is
continuous in the Brillouin zone. {{formula:72da84fb-14e3-4313-adf9-113a02e8a1d4}} is now assumed to vary adiabatically in time, {{formula:e116eb9d-d436-4d47-bbb9-cc75545cf0b9}} .
The equation of motion, Eq. (REF ), for the phonon wave function,
{{formula:16a00003-a59e-424c-a66a-0f9d48a27bb4}} , is solved by the substitution {{cite:ab6f19beef525086fd820a8f21f95b219103a9b1}}, {{cite:b1ca0d0969bfad7b262634699f10a5661f6cfbe4}}
{{formula:765a7099-2fb6-4721-8d16-85e4989cbd66}}
| d | d1647d4874636c864490ba7f15d9b519 |
Establishing a solid theoretical foundation for deep learning is greatly desired. A core challenge is to prove
that structured deep neural networks used in deep learning can outperform the classical fully connected networks
and automatically extract features when the data or target functions take forms involving some special features. The main difficulty lies in
the approximation theory of structured deep neural networks like DCNNs which is totally different from the nice theory
for fully connected networks developed about 30 years ago. For example,
a typical approximation rate in {{cite:ce3d138d515c7b97518be87fc9c0dd6c44d37945}} obtained by a localized Taylor expansion approach
for shallow network (REF ) of width {{formula:245241a2-a6cd-4782-8b28-cad805f4a001}} with {{formula:b28c504c-4e09-4fbb-84c3-4e3a14d3c30e}} is
{{formula:db63e2c2-6fcd-4ebd-926e-614a7b5a5af8}} for {{formula:d6b7862b-d13b-4c50-960c-dd27e57070b7}} ,
when the activation function {{formula:b78b7f88-e9dd-4b7c-8c8b-7a664a40fd10}} is {{formula:9013ffd5-98d9-43a7-979f-bad3d891a49d}} sigmoid type satisfying for some {{formula:486657d1-27a3-4434-a104-2df8e02a2cf2}} and some integer {{formula:488a0e76-9b60-4e49-81cc-96cb1db73805}} ,
a restriction {{formula:c7a88df8-c877-4aa0-b904-11b8cf0471f8}} for all {{formula:d44541d6-1d26-4dd0-9276-900d0c1ff180}} and an asymptotic condition
{{formula:ec5531d0-3797-4104-9759-60f767a5d9b0}} . Such approximation rates were recently proved for ReLU shallow networks
in {{cite:059e2e230da204d858ab0aac851b65d0c5c272ff}} for functions satisfying a decay condition for the Fourier transform {{cite:687d9a45277245664aeb79dfe4337879198877d0}}, and were extended to ReLU deep networks
in {{cite:782978827aadac36ea3a7afadd18ed1a2c381db4}}, {{cite:c9309f713e497e4b37e30fb4677dcef6a3c8c8be}}, {{cite:f5a19f7210bd7a7f776df7b140686937ae2b4dd1}}, {{cite:55079d8fc475231ea279ad91f53e4966d5dfc1ff}}, {{cite:e0b6958d70aea18f3325708ab5ae3ccc4470d212}}, {{cite:e932c5b28b65e3fd8078c2eb2f0589351dfd7514}}, {{cite:80275280b305f2a3347b3be03edb494fb2f5b3a7}}, {{cite:84c9f6e0bf731015a76bdefc9ccdc0746f3d32ee}} for functions from {{formula:5cadd0d9-ca82-491b-82b7-16b0029844dd}} with {{formula:117d0274-ad17-46d4-a0ad-ce7e7beccd3e}} ,
and in {{cite:37efc8e9a93dee766a65fabbca47c07084731368}} for approximation on manifolds, all for fully connected networks.
In particular, it was shown in {{cite:782978827aadac36ea3a7afadd18ed1a2c381db4}}, {{cite:f5a19f7210bd7a7f776df7b140686937ae2b4dd1}} that an accuracy {{formula:f476ce76-d70c-49e0-81fd-b69e17ae30e3}} for approximating functions from {{formula:4f40cbf1-d9e2-4541-95fb-2e842da14356}} can be achieved
by a deep ReLU fully connected network of depth {{formula:f99536ae-5086-4ad9-998b-06d380759e95}} with {{formula:c5230f63-d17e-460c-8b96-7beb89bb86c4}} and
{{formula:da086ff7-729b-40e6-9745-ab161392e931}} free parameters which has the same order of complexity as required by shallow sigmoid networks.
| d | cc3a5f7ae03228cec3c5e26889fbb00a |
Besides the improvement in the accuracy, ensembles are widely used for modelling uncertainty on predictions of complex models, as for example in climate prediction {{cite:e50c5282626946b4c38f58be842da69907f46ba7}}, {{cite:5a9c4532932dfb3ef6435211bf56c0c2efebfe42}}. Accordingly, ensembles are also used for quantifying the uncertainty on a deep neural network's prediction, and over the last years they became more and more popular for such tasks {{cite:d4be62a2180a1f902b0e57057035d4bac9d4dd94}}, {{cite:981e8ba04f8900ce39f2a83a88ec58a8f8d5ed0f}}. Lakshminarayanan et al. {{cite:d4be62a2180a1f902b0e57057035d4bac9d4dd94}} are often referenced as a base work on uncertainty estimations derived from ensembles of neural networks and as a reference for the competitiveness of deep ensembles. They introduced an ensemble training pipeline to quantify predictive uncertainty within DNNs. In order to handle data and model uncertainty, the member networks are designed with two heads, representing the prediction and a predicted value of data uncertainty on the prediction. The approach is evaluated with respect to accuracy, calibration, and out-of-distribution detection for classification and regression tasks. In all tests, the method performs at least equally well as the BNN approaches used for comparison, namely Monte Carlo Dropout and Probabilistic Backpropagation. Lakshminarayanan et al. {{cite:d4be62a2180a1f902b0e57057035d4bac9d4dd94}} also showed that shuffling the training data and a random initialization of the training process induces a sufficient variety in the models in order to predict the uncertainty for the given architectures and data sets. Furthermore, bagging is even found to worsen the predictive uncertainty estimation, extending the findings of Lee et al. {{cite:c747ebd6425f7537533d84d1ed6d3b640d0d76f4}}, who found bagging to worsen the predictive accuracy of ensemble methods on the investigated tasks. Gustafsson et al. {{cite:62813142f05923784d6518ad5bfe63bff436a921}} introduced a framework for the comparison of uncertainty quantification methods with a specific focus on real life applications. Based on this framework, they compared ensembles and Monte Carlo dropout and found ensembles to be more reliable and applicable to real life applications. These findings endorse the results reported by Beluch et al. {{cite:6c9127963271db1362d33fb051c475b5088bf2f7}} who found ensemble methods to deliver more accurate and better calibrated predictions on active learning tasks than Monte Carlo Dropout. Ovadia et al. {{cite:59495d439aa07d6b185730a4475b19a7aef5c8fc}} evaluated different uncertainty quantification methods based on test sets affected by distribution shifts. The excessive evaluation contains a variety of model types and data modalities. As a take away, the authors stated that already for a relatively small ensemble size of five, deep ensembles seem to perform best and are more robust to data set shifts than the compared methods. Vyas et al. {{cite:982dfd6968587114cad52b8bb49c8fd24cf2ccfb}} presented an ensemble method for the improved detection of out-of-distribution samples. For each member, a subset of the training data is considered as out-of-distribution. For the training process, a loss, seeking a minimum margin greater zero between the average entropy of the in-domain and the out-of-distribution subsets is introduced and leads to a significant improvement in the out-of-distribution detection.
| m | e08540c335527e490abb876f430e4cbc |
Data-driven discovery of dynamic models has recently picked up much attention as there are revolutionary breakthroughs in data science and machine learning {{cite:3e89d60c67fd34fe171700cdb8dc1dee494730dc}}, {{cite:d0e1fd55cdd931574e034e618a3e38250c4f566b}}. With the increasing ease of data availability and advances in machine learning, we can delve into analyzing data and identifying patterns to uncover dynamic models that faithfully describe the underlying dynamical behavior. Though inferring dynamic models have been intensively studied in the literature, drawing conclusions and interpretations from them still remains strenuous. Moreover, extrapolation and generalization of models are limited beyond the training regime.
| i | 7e70ed9b0af96bce15fbeaeaa033984e |
Fusion Module:
Outputs {{formula:df131921-37ba-4621-8ea4-48a79d3e6b68}} , {{formula:03605ccf-978a-4c4b-8966-f5a1b44d27ab}} and {{formula:cd43d6ce-4cc5-429e-8bac-ecfc7f8c8302}} from both modules are fused via the Fusion module from Zhang et al. {{cite:824332804ea9e3446d319720406dae0c33acae7b}}. The fused vector {{formula:826792c5-df4a-46d9-bda3-6da57f978355}} is generated by implementing the following operations:
{{figure:919040e7-6cfe-4acb-802f-e0258c6f64b3}} | m | 211fb46f9144a105f3387a7261c68508 |
A single peak is also observed around 2670 kOe for {{formula:a0464d21-23e7-4cbd-975f-08c221662538}} {{formula:686af903-7b19-49c3-9542-4781937494f4}} to [001] direction.
The oscillation frequency provides the extremal area of cross section ({{formula:6b653af8-697f-49a0-93ed-2f22786a3110}} ) of the Fermi surface (FS) according to the Onsager relation, {{formula:2177aaba-7560-44db-952b-dbd2b4ad971d}} , with {{formula:953cdffc-e492-4867-b967-cc953c84ad14}} . The difference between the {{formula:b1f1cf58-5fbc-40d8-90c2-e00578a7f3f6}} and {{formula:8065a6f8-3440-45a8-85f1-365ad05554eb}} component in {{formula:8ea953dc-47d3-42f4-a11d-4d34d7de8c1a}} points to a highly anisotropic FS, analogous to Bi{{formula:cb159084-d47e-4caf-a051-c0d0ef7b0c35}} Se{{formula:fe185496-af58-4773-ae5c-fc135e2e6c74}}{{cite:f437c4ae09bf0f043af13295fb8f42e681a5eeb2}}, {{cite:5f5052529d7867ebbbae78ca83ad742c2c70a6ae}}. The values of {{formula:8316b10d-6233-465a-9126-2b0e20e32f4e}} provide the values of Fermi momentum ({{formula:1050e1e1-fff4-4b1c-9abe-c23105bd0b85}} ) {{formula:bd875f3e-d861-406d-a040-fe242eaac4d0}} 2.5 {{formula:105ecf4d-a7bd-4b22-ba1f-35a473431e6f}} and 9.0 {{formula:bebcd6dc-e359-4ef2-9d9f-84bb6f836c94}} {{formula:501bd5d3-2ef1-4ca5-8ace-f7f56f2a1237}} for the {{formula:da130ff0-d0e9-4493-80c8-abdc80f49f11}} and {{formula:bd9bb26f-5ec8-411a-ba90-ba5fe2006864}} components, respectively.
| r | b703425839c9d9ccaf65a0c21ed6475d |
We find that {{formula:e91caf13-6ae0-4808-8959-fcef41d5d16d}} can be enhanced in g2HDM to
experimentally accessible values, even for exceptionally small
extra Weinberg coupling {{formula:c864e663-cad0-42a6-9116-066c2b7c02b0}} .
This is in context of using large {{formula:70ce52ad-800c-4069-a542-b0b59e3989c0}} coupling to explain the muon {{formula:3e3e57b1-2115-4ec2-a6ca-720ad334b9df}} anomaly.
A diagram similar to Fig. REF with {{formula:39aa67ca-e854-4f44-9d87-59ec553d265f}} and
{{formula:1129830c-1c45-4379-b581-0ba5417e52e4}} in the loop can contribute to electron {{formula:ffce3901-bfe3-4803-b651-846094e0d914}} ,
where recent measurements of {{formula:97d06997-ec1b-442d-8978-7142816caed9}} suggest some tension {{cite:1d93a78756d3f4846d9440e6d0b759926012b468}}.
But since large {{formula:b1d11ecf-75b3-4842-85f6-fae896512285}} constrains {{formula:8a02346b-2eb0-4975-b4b6-e021558764a8}} ({{formula:bf2aeb99-ee7b-461c-9d3e-6a344f66b81a}} ),
through the MEG bound on {{formula:7eb2a74e-648e-4629-aa99-1fceb35fede9}} ,
to be consistent with Eq. (REF ),
we find the contribution is negligible and the electron {{formula:570640b3-c4a5-43f9-8675-ee7bb6acc9fe}} remains SM-like.
The {{formula:25231004-b785-448d-b191-7252e3744cdc}} , {{formula:7968bde8-b8f4-4354-87d6-513d8caa2bf8}} couplings, together with {{formula:1dda7593-b050-493e-997c-c1c1f15dd0e0}} ,
induce {{formula:334aa8a7-d4fa-4d97-8902-9b5f3967e769}} decay.
But again with Eq. (REF ) and with {{formula:cdb59dde-f54a-460e-89b5-0b27e483446e}} ),
the induced {{formula:ff906c32-ba14-4ccc-b95f-6892b24046e6}} is very small.
Putting it differently, the current bound of
{{formula:ff654c7a-59ac-430f-87dc-cd1f3014f6db}} {{cite:871aa7c06f12a808c93dafae05591914785384ad}} sets
only an extremely poor bound of {{formula:b27791fa-be46-4a5b-b882-7397bcde81bb}}
for scalar masses considered in this work, and far from probing Eq. (REF ).
| d | d88b13433ef57431407dd61514f259b8 |
In Fig. REF the same points are plotted in the {{formula:880ae417-9b15-4568-a72f-09e48a280670}} plane with the oblique parameter {{formula:37d4cdc3-dc2c-4dc4-bae4-8ccae91ac273}} in the color code (left panel) and in the {{formula:3f9c09fe-6b4b-4dce-abc7-744d05c8f10f}} plane (right panel) with {{formula:09cd7e3d-49af-4d6f-b993-cbe26bcdf8d2}} in the color code. Points located within the 1{{formula:d1b4e99e-efe0-4853-85a6-09a66c58fb1d}} interval of the {{formula:e91fb132-bac6-4ff5-881a-8eaf449abc0c}} are coloured in orange, while the points within the 1{{formula:636e6f6c-af4f-4e70-9ebf-3c11a237322c}} interval of the new {{formula:9de56523-7057-4783-ab52-1dc728d7664e}} measurement by CDF are denoted by the red points. The light red band indicates the {{formula:2c816ce9-250f-4619-9cca-63beda48dcd5}} value with the associated 1{{formula:72ad8ea3-25f7-4995-adde-d2fdcc1b0dfa}} uncertainty measured recently by the CDF collaboration, while the light orange bandal shows the world average for {{formula:0e3a4b2f-719b-422d-8c5e-fc17472fe21e}} with the associated 1{{formula:260f1720-9c1c-4dfa-ad57-3fef666cc012}} uncertainty {{cite:72676aacac4f336613da53bfd393e271d1d349ad}} that was obtained by averaging over the results of the four LEP collaborations and the SLD collaboration, we also display the result for {{formula:830114ff-b3e4-42e4-ad76-747878ee3e6f}} and its associated 1{{formula:8ae69a4b-14a6-42a8-bc53-3ef424b2bf38}} uncertainty that is based on the measurement of the left–right asymmetry by the SLD collaboration {{cite:72676aacac4f336613da53bfd393e271d1d349ad}} as a light green band. From the left panel of Fig. REF one can remark that the dominant contribution comes from the {{formula:de762363-29c2-4d3c-aa04-631e26ee3243}} parameter which is almost a linear relation. An interesting observation from both panels is that the point that describe the 96GeV excess (orange points) are in good agreement with the new CDF measurements as well as with the SLD measurements.
{{figure:ed5c7965-bb58-4a00-8087-61d92542bbf9}}{{figure:b3814ca1-44cc-49c6-a53e-f8e3c2fd1655}} | r | 9d44134372987b292ed3273fed530df6 |
Character Variational Auto-Encoder (C-VAE) generate SMILES string character-by-character {{cite:2b58ed4ad26785af2b1c242908d7c4adffb6ba8b}}.
Grammar VAE (G-VAE) generates SMILES following syntactic constraints given
by a context-free grammar {{cite:2f5addae7aa9dd0d70b1b3a3458e089fdfbe3ed9}}.
Syntax-directed VAE (SD-VAE) that incorporates both syntactic
and semantic constraints of SMILES via attribute grammar {{cite:2c3d945c2f211faa5187cafa3cf3c5b284855430}}.
{{cite:2fe0d3c3cd5ff036b58cb9bab8e5e1441eb51d95}} proposed a method that is able to control the properties of the generated molecule based SMILES string generation.
| m | 5c5aa576c2a4d1a3565f88d1ab5e8541 |
Iron abundances relative to {{formula:7dc8c2b8-7393-4340-a8c2-4005a7f49ff9}} -element abundances change as a function of time and with the galactic environment {{cite:176b0b13cd89980b423d0fef62c9180a6b3644b6}} and this systematic variation of [{{formula:2e9e29e3-df39-41d4-a74f-2ef6a6af7965}} /Fe] needs to be taken into account at different metallicities. It is not just iron that changes with metallicity – a complete census on the chemical history of other elements and their evolution with overall metallicity is critical to determine accurate metallicity measurements in galaxies, especially at high redshift. The [NII]/[OII] ratio is an ideal abundance diagnostic {{cite:abadcb89f7a2ba3e49e5c24d2126c99eb08a9a11}}, but at high redshift the [OII]{{formula:8389f0de-2cc8-47ca-a223-4406f89c9b48}} 3727, 3729 doublet is often unobservable, relying on calibrations based on [NII]/H{{formula:1902f458-12b9-47b0-83d1-1b3ae9cf803f}} {{cite:18de12e3b7831ce9bb182ee42ad77ca5dfccf717}} and/or the [NII]/[OIII] ratio {{cite:958d0e50b603934303eba67daab4d44d23055ad9}}. Often yet, only red line ratios are available such as H{{formula:4e712f95-6672-4354-ad22-c133980a694c}} , [NII], and [SII], and the O/H ratio relies on indirect methods using combinations of these line ratios {{cite:a7febd84f161f50f107bd1e90ad4f93fbf8cf827}}.
| i | f121a3ca5d0db409f0e3e282e16cc947 |
It is well-known that {{formula:190e4fee-60e4-4b0f-a0a5-a6db8064db11}} . From {{cite:345c8bbb0d141271b9a2e77db710158f41396bf0}}, we know that
{{formula:97970f9c-5a64-4910-8c93-1e676e6acf93}}
| r | fcfa618372080ca1b8c477a426050d64 |
Weyl semimetals show a number of interesting transport properties, such as
an anomalous Hall effect{{cite:b3a8fb3839a936561d04e6ac421bf5d6d9ad2a3a}} for a WSM with broken time-reversal
symmetry, a chiral-magnetic effect{{cite:3c8a812293f3edd0e2345dabc7f905bc23677a81}} for Weyl semimetals that break
inversion symmetry, gapless surface states called Fermi arcs{{cite:fa4ecfee42a9a85de4bf26a551d9ca5b058e5039}}
and a chiral anomaly leading to a negative longitudinal magnetoresistance{{cite:764b09fe870ba6246a73c1b7a3423718d5bc143d}}.
| i | 901671beef7d0899243e5f9088a652d6 |
Reference images is extremely important for evaluating images generated by GANs. Evaluating GAN-based IR models attracts lots of attention in recent years {{cite:ea43621365d481349c27a4c70a5730bfcc0d39a2}}, {{cite:61caf3a0991f7bb0c7b447c6ce18215cbb301244}}, {{cite:87f54bd88a46aee486ad01c10b9f58569c931c04}} as the artifacts generated by GANs yield new challenges for IQA. We study the performance of our model on GAN-based images in Table REF and find introducing reference (e.g., full reference or degraded reference) can significantly benefit assessing GAN-based images (with 0.3101 SRCC gains). Such a result is reasonable as the textures generated by GANs may confuse NR-IQA models on distinguishing the artifacts and image contents. Thus reference images can provide strong guidance to disentangle quality-sensitive factors from image contents.
{{table:ef97bdff-d42e-4962-9a4c-2a5bcd5238a9}} | d | ccc5170cfd5102b1321f014e07d259bd |
Furthermore, no significant variability of the optical coronal lines in Mrk 335 was detected {{cite:3f4c1f0df46bfcdf247abd014d3d3ffed96f216a}} despite
strong changes in observed X-rays. As those lines are driven by the EUV-to-soft-X-ray part of the SED, the
observations indicate that the emission lines saw a different (less variable) continuum.
An absorption scenario can also explain the lack of intrinsic variability of the photoionized soft X-ray emission lines
{{cite:20e204c9bc79492bb94353d961155d83ec7d824f}}, and is consistent with the lack of IR variability of Mrk 335 {{cite:fbdb9ca84c1cf6e11248b6040f0848ebf0e67115}}.
| d | 60cc66fa8491e4d83ab5fdc8b0a469c9 |
We begin with an account of the contribution {{cite:5e3b64768473760aeb9d9efa17f515dff457aa2c}} make in the context of reinforcement learning and describe how decoding can be used to query the information stored in the network. We then describe our hand-crafted representation which records information about the angles between pairs of visible points and about the extent to which these change as the optic centre translates. It is hardly a surprise that this representation performs well on geometric tasks, and we are not making a claim that this representation is in any sense `better' than the learnt one - the representations are, after all, utterly different. Nevertheless, it is informative to compare the performance of the representations side-by-side in order to inform the debate about improving learned representations in future in a way that incorporates information that is particularly important to animals.
| m | 97d2b98c574614bf3b3023ab2bc54347 |
We considered the impact of active speed fluctuations on a {{formula:60f7a0e2-67c6-4492-a096-2cc620e12b69}} -dimensional active Brownian particle (ABP). We utilized a Laplace transform method for the Fokker-Planck equation, originally proposed to understand the worm-like chain (WLC) model of semiflexible polymers {{cite:d5aafcdd81e9bea3554d353f899c1d9327c9cf60}}, to find exact expressions for dynamical moments of ABPs in arbitrary dimensions. This method allowed us to obtain several such moments, including the mean-squared displacement, displacement fluctuations parallel and perpendicular to the initial heading direction, and the fourth moment of displacement to characterize the dynamics.
We found several dynamical crossovers and identified the crossover points
using the exact analytic expressions.
They depend on the activity, persistence, and speed fluctuation of the ABP.
| d | 6ea00f820ce66f6121211de6b1653a2d |
In the recent years, since the first observation of gravitational waves {{cite:188c3ce795a42b2ce103c6366e5b476a150f1070}}, there have been lots of new investigations on compact objects in theories beyond Einstein's GR. One of the key feature of many exotic astrophysical objects is that they are horizonless. In particular, ultra-compact objects which still possess a photon sphere can generate echoes during catastrophic events like binary mergers. See Ref. {{cite:d44efb93fb26961c6912e512d4980d5be9bc8afa}} for a very recent review on theoretical and phenomenological aspects of exotic compact objects.
| d | 4dd7cbc25138e4c3653b769422f596a5 |
Two-step estimator.
To go beyond {{formula:0ba38a1a-67cf-4768-bd23-532dd9db73e2}} statistics, we consider the set {{formula:e6bf5939-4f8f-431d-8a0f-136b36538ca9}} , containing the rates at which two successive transitions {{formula:0fbbac16-9550-4aa0-bc2e-6170633c8746}} occur for all triplets {{formula:c5f60797-a15a-4785-a000-4a63e501f327}} . Knowledge of {{formula:96d04b6f-01b5-4d94-878e-245bd337c861}} imposes stronger constraints
on the set of underlying Markov processes {{formula:b93dca86-be8c-4997-9484-a2aa95040a85}} , promising a better bound on the entropy production rate.
In practice, performing a direct numerical minimization to obtain the corresponding estimator {{formula:56526b2c-5084-4269-8d80-0878ada288bf}} is not possible due to the arbitrary complexity of permissible Markovian
network topologies {{formula:1dd8ba73-db30-4663-b720-a21a2cfa2d84}} . However, two exact analytic results, proved in the SI {{cite:f8e89a983d4092716164d91555505a3372376e71}}, enable us to find the best possible bound
for the combined entropy production across all edges connected to a state {{formula:8f0d21db-ea3c-49bd-b4cb-08f510c8d478}} , whilst preserving
the {{formula:e1a24997-e32e-4b7e-a8c8-7c700974b3e5}} statistics {{formula:6a9cd1ed-8306-47e1-9a6b-9bb2d0bf8bb6}} , {{formula:f9b46f39-85df-4805-8ff3-85fd64e35e79}} , {{formula:dd95ec32-c228-4ff6-afe9-d24c7e86d662}} for any distinct
neighboring macrostates {{formula:0a4e6432-6170-483b-b048-ad73dc62016d}} . Specifically, our first result enables us to
take any network {{formula:e9290e7f-af5e-417b-bf97-32eeb7d3a168}} consistent with {{formula:e11a4ea1-2f26-4bc1-a180-5c29fe86d196}} and simplify its internal topology so that only {{formula:17f476aa-d564-4706-bca4-833b074d5937}} has hidden states,
and further, that {{formula:4bbe4150-3351-44f3-929b-6c145dfe9c1e}} has no internal connections. We show (SI {{cite:f8e89a983d4092716164d91555505a3372376e71}}) that one can always construct the simplified network in such a way that
the entropy production rate is lowered while remaining consistent with the {{formula:11c0cfb9-6841-4fef-bd96-36c9b317e2ca}}
statistics involving {{formula:6bb15301-a662-4cb9-abb9-7c4acbeda0a3}} . Our second result proves that minimizing over this simplified topology, with arbitrarily many internal states of {{formula:6665c9e9-0809-4af7-b39b-573f71a1ab79}} , yields the same bound as minimizing over a system with 6 internal states for each pair of neighboring macrostates {{formula:47f53928-c6e9-41db-87ec-e28304873921}} . This fact makes the problem numerically tractable {{cite:ff887429bb016d48586c8e25fe964d2911d75231}}, {{cite:31868b1c4688bba92bafa0e31756df8c90a156f5}}, {{cite:f8e89a983d4092716164d91555505a3372376e71}}. By bounding the entropy production rate across connecting edges
for every macrostate in this manner, we get a {{formula:8c54a575-8945-4c2d-a746-27d5eb6f87ee}} -bound for the total entropy production, This new estimator satisfies the
hierarchy {{formula:a6185076-f7ef-4340-a6e2-442941a663f7}} , and can be computed by observing the states visited by a suitably long
trajectory without measuring conditional waiting time distributions {{cite:d06270ac5c15670b1d1cc66117afad9376fcb0e7}}, {{cite:f8e89a983d4092716164d91555505a3372376e71}}.
| r | c6dee67f62dded23e62ec43bad5ca5c2 |
For text-to-image synthesis, current methods work well on datasets where each image contains single object such as CUB {{cite:0e5aad108430eea98790ceaed1c8605e7d3faf8c}} and Oxford-102 {{cite:accdc0794f678c4174ebc6eb731af4004a412ffc}}, but the performance on complex datasets such as MSCOCO {{cite:98a52b8d533bb69160ef9c026bed35ee51a96871}} is much worse. Although some models can produce realistic images of rooms in LSUN {{cite:316da778aec82486a01b46b1f2b2828fcfa64985}}, it should be noted that rooms do not contain living things, and a living thing is certainly much more complicated than static objects. This limitation probably stems from the models' inability to learn different concepts of objects. We also propose that one possible way to improve GAN's performance in this task is to train different models that generate single object well and train another model that learns to combine different objects according to text descriptions, and that CapsNet {{cite:e680098848a72f0c5652625bf0eb56718a92a52b}} may be useful in such tasks.
| d | 220b5a2041aab79725661a6f917bfff3 |
The epoch folding method was also employed to prove the QPO signal further.
This method is mainly unaffected by the irregularity of observation data and the modulation shape of periodic components {{cite:3303a855c7c15724146b5fda2fa67a129acf7338}}.
In Figure REF , one can see that this folded light curve varies with the phase, indicating substantial variability in the source brightness.
Nevertheless, the light curves of AGNs are mainly affected by red noise, which results from some stochastic processes in a jet plasma or the accretion disc {{cite:79a9197592570b52dc7600a882955b0f230d4936}}.
Emission from an AGN is usually autoregressive, so the first-order autoregressive (AR1) process can evaluate the red noise spectrum reasonably.
The calculation formula of the theoretical power spectrum of an AR1 process can be found in equation 2 of {{cite:b811edbd7b597eaa1d520a12532a798e4d58d126}}.
We use the program REDFIT3.8e to complete the calculation, in which the parameters are set to {{formula:2379d0d7-3f8e-4789-806a-b88f74a182da}} and a Hanning window is selected {{cite:3a8c0e83ae8af82052bd3725aaf5c0b15e76e5e0}}. The resulting power spectrum (black) is shown along with the AR1 spectrum (red) in Fig REF . It can be seen that in the periodogram a distinct peak stands out around the timescale of 1086 {{formula:9e814f4c-49b6-446c-87bb-50874c8d1b5a}} 321 days with significance {{formula:8033a297-8362-4704-a546-7850ffc0bd48}} . It is worth noting that the REDFIT method can only give a maximum significance of 99 per cent. However, the significance of QPO detection based on the temporal spectrum is usually affected by the bandwidth penalty effect. In order to evaluate the impact of this effect on signal detection, the 6-dB bandwidth {{formula:003cf44f-7270-4988-83c4-be29675cb512}} is commonly utilized: {{formula:bcc358bd-3f24-4edf-b836-587210084511}} , where {{formula:74a44234-4b35-43a4-a56f-6c163b2e6ddd}} is the normalized bandwidth that depends on the spectral
window and {{formula:1087f430-1d1e-45bf-8c06-50978ed9a074}} is the fundamental frequency associated with {{formula:d98d865c-1c9e-4a5d-900b-58dd29a93e0c}} {{cite:b0bd19cbb7b8065c4495ccf5b675485ef7a0a5ee}}, {{cite:ea5aaa6a9577581130eb29dfb93d35384469571e}}. Considering different spectral windows (e.g., Rectangle, Triangle, Welch, Hanning, Blackman-Harris) and {{formula:95b0dbce-6639-47dc-89cb-5c7ec2297c7f}} (0,1) values, we estimate the significance of QPO detection again. The overall results show that the quasi-periodic signal ({{formula:6950f81a-33d2-443d-860c-7ec51063fb6f}} ) may exist in the {{formula:ce7191cd-65ef-4987-9425-651c47021e97}} -ray light curve, in which the 6-dB bandwidth ranges from 0.00025 (only {{formula:b1684519-6bb2-4ca2-8ff0-09f62bf8ba49}} of the relevant frequency interval) to 0.00071.
| r | 99cb61389b0fb5e23b607f9af7113286 |
To investigate the relationship between skilled control and the variability of actions and states, we analysed the aforementioned time series measuring the performance and estimating information-theoretic measures of variability for each participant in each experimental condition. To measure participants' performance we employed a mathematical framework commonly used in models of sequential decision-making and control {{cite:cd9f41f4e2eed3498333fee0f54600d328b38736}}, {{cite:e033b5bef3f808d599173d98e8832d790c2c76af}}, {{cite:f8318a82f30a41123d272af8c66b67b113ee679c}}. We first defined the reward as a function of the state space {{formula:5dc9e22e-f668-4293-934d-9648653dff2e}} , which measure the immediate worth of a state with respect to the given balancing task. In the experiment we defined the reward as follows
{{formula:fd230070-aa83-49ed-8e42-aabf080cbd97}}
| m | dbaeaba4c856f592c1fc75c6224bb9ed |
To this end, we also note that Mauring et. al {{cite:6efa58c0409194ca3bd7af8bf7779eeb961c4e39}} observed fluorescence enhancement of the blue fluorescent protein (BFP) with hydrostatic pressure. The coupling of BFP chromophore with the rest of the protein is different as compared to GFP because of the His66 substitution, which leads to smaller number of hydrogen bonds {{cite:0e3e4f46f81329065bb2f2f8c0e01bf006563553}}, {{cite:aaadcf2eca459e3046e63a4e82a4221a873d11ea}}, {{cite:c64c3cd60e104101a54734643a42c012259950f2}}. Due to smaller number of hydrogen bonds, the fluorescence lifetime and the quantum yield of BFP is much smaller compared to GFP. They find that the fluorescence quantum yield increases with pressure without a change in the shape of emission spectra, results very similar to our results for GFP. They further attribute the increase in fluorescence quantum yield with pressure to the inhibition of fast quenching processes due to stabilization of hydrogen bond between the chromophore and the rest of the protein. We expect that the decrease in anisotropy may reflect the effect of pressure on the radiative and non-radiative decay processes arising due to pressure-temperature effect on the H-bonding environment around the chromophore. Our current experimental setup does not allow us to perform time-resolved experiments, which on the other hand, would have been an ideal way to resolve these issues, and should be explored in future.
| d | 41f99200f0b56ac0fe28e34720a10a8c |
Currently, the state-of-the-art method for dealing with multimodality is parallel tempering (PT) {{cite:cfae5d287de1cb567320fa69ebcb6e1dbf361608}}, {{cite:5356cb1d0d1fee87440d02b018d7dbf97d55c933}}. PT is based on several interacting chains that converge to a product of tempered distributions, one of which is the desired posterior. The chains interact via a series of swap moves that in principle help exploring multiple modes. The challenge, however, is the computational cost involved in the algorithm as one usually requires a large number of tempered distributions and iterations {{cite:3fe52cbb91c93ab2af0f4778cb81cca8b55e4cbe}} for the method to work correctly. Hence, this and similar approaches might not deal well with multimodality as the computational expense will render the approach unfeasible. The t-walk can sample from posteriors with several modes with different scales {{cite:8d1e964521ffc1c21764b2f9d6f5a02e90c7d421}} but, as with most other methods, once these modes are separated by areas of very low density, then it may get trapped in one particular region of the sample space.
Various staring points should always be used in the practice of MCMC, increasing the chance of finding how and where our chain got trapped in different modes. How to join these samples from different regions into one that has the correct target is not obvious.
| i | d08646cecdf5cf53ca3ed23710be9c6f |
We conduct experiments on CLEVRER against several counterparts: TVQA+ {{cite:59efdf1ebde5868de83302bff50badf4eef61865}}, Memory {{cite:c8c9158f5dc31cb60827b79b3d90d5210374b2fe}}, IEP (V) {{cite:91076eb00982d754c075c470550b5860a55732ca}}, TbD-net (V) {{cite:1c0e74ca12fc24b77a0f99b047d44e3910d4d135}}, HCRN {{cite:d85d60492da6a1add54b8a3d301d520b306fd030}}, MAC {{cite:e06352c4f2e29dd47caf91042c22889877efa177}}, NS-DR {{cite:ebcdde029c450a72e7f15752fd95fb3b7f6cf5c6}}, DCL {{cite:93d03420d88db638f9c9bcff3e1c6e4fba3c3724}}, and Object-based Attention {{cite:841879059739a3ab6365e401bc5ec4c1519d5dd8}}. Among them, NS-DR {{cite:ebcdde029c450a72e7f15752fd95fb3b7f6cf5c6}} and DCL {{cite:93d03420d88db638f9c9bcff3e1c6e4fba3c3724}} are high-performance interpretable symbolic models, while Object-based Attention {{cite:841879059739a3ab6365e401bc5ec4c1519d5dd8}} is the state-of-the-art end-to-end method.
| r | 380bad8a754ed8c8fcb4737a12e65a36 |
Two recent and popular approaches have been selected to guide the explanation of the proposed protocols, which will also serve as a baseline for the aggregated dataset: 1) the Color-based face-PAD proposed in {{cite:048c27b88c170c2d836ff33bf9a80b58707e5648}}, and 2) the Quality-Based method proposed in {{cite:ba4958caebe67e8bbd70f9fb07b972c4d1a37324}} based on a concatenation of quality measures (IQM) introduced in {{cite:4c9f48c8597e335d5ca9dfba85829e40b5285c36}} and {{cite:b0ec09b49948f2a841ed44ded685ef59a5cf0a1a}}. The code for these algorithms is publicly available in the GRAD-PAD framework based on the reproducible materialhttps://github.com/zboulkenafethttps://gitlab.idiap.ch/bob/bob.pad.face/ shared by the authors.
| m | 46b3405bbbc7ab984ddd21316d3beeb5 |
In the best case comparison (Figure REF ), it is clear why a sufficiently large, yet not overly large, eligibility trace time constant for the non-replay case gives best performance – it must store a suitable amount of the trajectory history for learning. If the eligibility trace time constant were too small, it would not store enough of the history, whereas too large and it stores sub-optimal or unnecessary trajectories that go too far back in time. Yet the non-replay model became more unstable as the number of trials increased, as shown in Figure REF . One explanation for this is that the eligibility trace time constant necessary for learning in non-replay had to be large enough to store trajectory histories, but doing this increases the probability that sub-optimal paths may be learned. For the replay case however, since the trajectory was replayed during learning, it was not necessary to have such a large eligibility trace time constant. Sub-optimal paths going further back in time are therefore no longer as strongly learned. Furthermore, replays are able to modify slightly the behavioural trajectories. By looking at the effects in the weight vectors of Figure REF , it is apparent that the weight vectors closer to the start location are shifted to point more towards the goal in the replay case. Reverse replays could help in solving the exploration-exploitation problem in RL {{cite:4d5d9f95942e7ed1208e896b7e2e9d649c1c0987}}, since they could simulate more optimal trajectories that were not explicitly taken during behaviour.
| d | eba29c7e802e74e19590a9ee5249bb83 |
Given we now have weight-shifting operators that both preserve and raise the spacetime dimension, is it also possible to construct operators that lower the spacetime dimension?
One approach we have explored, explained in appendix , is to find so-called Bernstein-Sato operators which act to lower the powers to which the various polynomials of interest are raised. In this case, the relevant polynomials are
the Cayley-Menger determinant and its minors appearing in the parametrisation (REF ).
We found, for example, that replacing {{formula:5f84e377-ca83-4479-b845-9d9a31adfcb3}} in the Kirchhoff polynomial {{formula:3678f79d-63ef-44bd-abc8-c7bfc25eca97}} yields an operator
{{formula:237d36bd-93ac-4d11-b936-a661a81e7d43}}
which lowers by one the power to which the Cayley-Menger determinant is raised:
{{formula:f0bb1310-b6ca-498d-9a19-4339a73f181d}}
For the simplex representation (REF ), {{formula:f91b6ed7-1e59-4ddd-a11f-06f28a27b631}} is the parameter {{formula:c806eca3-bd99-40e9-a37e-46ed459412cd}} given in (REF ) and so lowering {{formula:9841388b-769c-4e21-a42f-f7bbbb524917}} by one corresponds to sending {{formula:a3541b45-d1b3-46d7-9f95-243b5712154d}} if all the operator dimensions are kept fixed. In principle, one would then integrate by parts to obtain an operator acting solely on the Schwinger exponential, which, due to its diagonal structure, could be
translated into a differential operator in the external momenta.
In practice, however, this approach
is complicated by the presence of all the
remaining powers of Cayley-Menger minors present in (REF ).
In sections and REF , we saw how the action of the special conformal Ward identity on the simplex reduces to a total derivative. This followed directly from the scalar parametric representation, without any recourse to the recursive arguments developed in {{cite:264f0e7ab38c6f2965d9123589500d8af2e062e8}}, {{cite:27b515ef78fa42b7a1f99ec301250a07a77d55ee}}.
Nevertheless, these arguments, and the recursion relation between {{formula:c95f43c8-e626-4b6f-90f6-a866ef1dc93f}} - and {{formula:322e92e0-7db8-4e4f-9a79-582d07673e14}} -point simplices on which they are based, are of considerable
interest in their own right and could be reformulated in the scalar-parametric language used here.
The deletion/contraction relations of graph polynomials (see, e.g., {{cite:0cb5925914a065c908cff8c07baf8ff79e8849b9}}) and Kron reduction, corresponding to taking the Schur complement of a subset of vertices in the simplex Laplacian (see e.g., {{cite:4f922de9398495a605e48a626bf0531a1df1164e}}), may also yield relevant identities.
Starting from the general simplex solution, the arbitrary function of momentum-space cross ratios can be restricted by imposing additional conditions of interest: for example, dual conformal invariance {{cite:88a76a72f10391e85ae2c7c0d789612b76e4abd4}}, {{cite:0347248db648dc75eddbb283820f6fd85040c19b}}, {{cite:8eb30b663d6a21a40208de48b23ffc5d2f69383c}}, {{cite:d4f7f6f6578c30356c8bd65c62fae5ee7324d714}}, or the Casimir equation for conformal blocks. For such investigations, the connection with position-space developed in section provides a very simple link between the action of a given differential operator in the external momenta or coordinates, and its corresponding action on the arbitrary function of the simplex representation.
For holographic {{formula:9f056f70-6061-452e-82f2-fe118fd028ce}} -point functions, bulk scalar Witten diagrams have the interesting property that their form is invariant under the action of a shadow transform on any of the external legs. In momentum space, shadow transforming the operator {{formula:b70724eb-2baf-4580-aec1-d566c1480d96}} corresponds to multiplying the correlator by {{formula:1199c863-9df9-403c-a90a-9388faa6a8da}} , where {{formula:880bbb4c-596d-4cf4-adc9-7d9e59ffbe1b}} , which has the effect of replacing {{formula:23c8791f-7168-40d3-92ed-577f853c756e}} in the bulk-boundary propagator
{{formula:86dadb53-c061-4369-a148-ac4379f192b2}} .
It would be interesting to understand the restriction this condition places on the function of cross-ratios appearing in the simplex representation.
Finally, the parametric representations we have developed may provide a useful starting point for the construction of general spinning {{formula:d40e106b-f761-40c5-9f05-466b0f9adb44}} -point correlators via the action of spin-raising operators {{cite:7af4fcf6f705aaa7d65d7205d190d2e8f1272b4e}}, {{cite:daab72d622f93697f7e39e444153c17dc96d0516}}, {{cite:dd4c1614d845f088675ca00f9277556cf7e6edfb}}.
| d | a334ec67a2d32bfe5446db79844f003d |
where clip function {{formula:c7de4fec-6aaa-40c5-99a1-e2acc63e98fb}} . The choice of {{formula:da9a5071-10e7-482b-982d-697890af9706}} affects the bias-variance trade-off: when {{formula:082f31c9-d959-4356-bc60-4ef3a8d1adc8}} , {{formula:abef2906-4a57-414e-8a11-c9e293a1523c}} converges to {{formula:3c482986-7a12-42a5-8dee-5036efebb5ac}} ; with a smaller {{formula:5f9a579c-3e01-4a33-b785-cd31fce040d8}} , the variance is reduced at the cost of increasing bias {{cite:02196fe977d57c57baa096c7691b6995aec26e66}}. The improved MI estimation via variance reduction techniques is benefit to the optimization process in Eq. (REF ) and thus leads to a robust final optimal design {{formula:77451c99-04cb-4ee0-b6d8-d15a597135f2}} .
| m | 6c2a1105ccd7e90de492a3202ca6f1ce |
There is a general expectation that the smoothing of the singularity {{formula:869fddf4-94d1-4908-9ebd-7a71069d337e}} (i.e. its Milnor fibre) should be mirror to a resolution of this singularity: Brieskorn–Pham singularities fall into the framework of Berglund–Hubsch {{cite:a1b0dbadcecdd25ac5108a541f74c9256efcd3a0}}, and are their own Berglund–Hubsch transposes; some versions of mirror symmetry have been proved in {{cite:45fa7b69e68323aca7a721956de2f7f52bb5a554}}, {{cite:256c6dc95ec35d99f7c11ac985ec00d3d841f9d4}}, or {{cite:531648b2940577ee35604ca753ded91dd1eb6715}} in the case of {{formula:373d9c9f-965c-4b50-b31f-2766233b4499}} .
In particular, one might expect the (wrapped) Fukaya category of {{formula:b7b7f63a-ad7e-4fea-8d53-c77455795c58}} to be mirror to a category of coherent sheaves associated with the resolution of the singularity {{formula:5bf0d0ae-b0de-4f8e-b5bc-2591169d0b0c}} .
The mirror-symmetric counterpart to the statement about mutations is that given their Floer-theoretic properties, the family of tori we construct can't correspond to cluster charts on some (fixed) mirror variety, or more generally to structure sheaves of points of {{formula:3079429c-cca7-49d5-8f23-df00814bbcb0}} affine charts inside such a mirror variety.
This contrast with what we understand of a number of families of tori in two-dimensional examples, e.g. in the
case of {{formula:6767b50d-a521-4574-aebf-a7f2ef7846d8}} {{cite:bf9a653937f5dd8102ec1154476770c76b497739}}, {{cite:531648b2940577ee35604ca753ded91dd1eb6715}}, {{cite:da1573753f2094ebd8946d0f49a0059c653e5db0}}, for {{formula:a4e390b4-3cee-464e-b610-a12916adf72c}} {{cite:bf9a653937f5dd8102ec1154476770c76b497739}}, {{cite:828de8f68d8895cf29186d91f4aa24b9ca5710fd}} or del Pezzo surfaces {{cite:c58892855b143f60fd821ed15936f5a00a9c826e}}, {{cite:40c6c7295b42885659c556c11131e36198df8b65}}, and arguably most remarkably for log CY surfaces {{cite:a2304f3f77469b0092539427a4facb1e742c015b}}, {{cite:7d8b15aea373148ac75755ee505aaba02290566f}}, {{cite:35bca837b2b8652e95282a6e806c46f2304c17fb}}; cluster structures associated to Grasmannians have also recenty been used to construct families of exotic Lagrangian tori in them {{cite:24d7804a595dfcaa0a3f2f5d0f10cccd4b209d9f}}.
| d | df618138757a15f77a3122c411bc88a9 |
The achievable precision of an actual RV follow-up campaign depends on many factors, such as weather, observational windows, the number of RV observations that can be acquired, the properties of the target stars (e.g., magnitude, rotational velocity, effective temperature), the resolution of the spectrograph ({{formula:fd290d53-a8df-4362-bb6f-eead78d8a5c6}} ), the exposure time, etc. Therefore, we find it impractical to incorporate all these factors into a generalized simulation, but these results can be used as a set of guidelines for real-world follow-up efforts. In future work, we intend to explore how the fitting of the RV signals can be improved with other software tools such as EXOFASTv2 {{cite:395abecbd02e6ae44a63dee2181437b3c0ba7058}} or Juliet {{cite:e12176ec162bad56b8173f5654d0471e48cae00d}}, as opposed to RadVel.
| d | 48bbaacc3ad361e93e46c9ab149ab529 |
Thus, we can use Lemmas - and the Brenier's theorem {{cite:342215a29c2d54de7a853c71ab45a59baef40ab3}}, {{cite:70724b3057448cbd455205fed13631f35bf3630e}} to define a mapping
{{formula:6a89c249-4cfc-4556-a695-9375e2e7f592}}
| r | 0bc08cdf49ba613d02e11d9ffe60a9b2 |
For a non-homogeneous linear form with two integer variables, we use a slight variation of a result due to Dujella and Pethő ({{cite:c43742fceed33171018c40a30d6bfdd775cd476f}}, Lemma 5a). The proof is almost identical to that of the corresponding result in {{cite:c43742fceed33171018c40a30d6bfdd775cd476f}}.
For a real number {{formula:27e69a0c-43c8-452b-b604-7620f1fbb71a}} , we write {{formula:8a5c15d6-e300-445c-87ec-a279a289c882}} for the distance from {{formula:4783b4f3-e0e9-4d72-a8e2-e50422cc61ab}} to the nearest integer.
| m | 9c54db27042205beee0352b8a077c9cc |
The boosted decision tree is an example of a relatively modern
development in Machine Learning that has attracted substantial
attention in HEP. Support Vector Machines (SVMs) represent another
such development and will no doubt also find further application in
particle physics; further discussion on SVMs can be found in
Refs. {{cite:5a47350b105fbbaea99a63dfa30b3dcab2adf179}}, {{cite:bf5c144cddb2f814f5f77c97f8644ee50e821845}} and references therein. Linear classifiers and
neural networks will no doubt continue to play an important role, as
will probability density estimation methods used to approximate the
likelihood ratio.
| m | b786b161aa63363d5a2cbb6579312ed2 |
The disjoining pressure {{formula:40c4b3e1-8944-4d5e-a8b3-1fec363a1c6d}} was computed from equation REF , and is shown as a function of the slit pore height {{formula:154c7aa6-92e8-4d92-b882-0f1252830a71}} in figure REF . The disjoining pressure was here defined to be equal to the integral normal pressure minus the normal pressure at infinite separation. Because the integral and the differential normal pressures are the same and because the normal pressure at infinite separation is equal to the bulk pressure in this case, the definition contain the commonly used definition of the disjoining pressure {{cite:f586d3a0d8bc5b8884163a33d598be641c6c2e60}}, {{cite:f3d1f277b13c289b1a2488fee882e96cf90a7e9b}}. The normal pressure is constant for slit pore heights {{formula:3d1ff6b1-b6fc-457c-877b-b48bc8c41b92}} . Consequently, the normal pressure at infinite separation can be calculated as the normal pressure when {{formula:5bc4a04c-3be9-4135-b918-d0d89a5223e8}} . The normal pressure at infinite separation is equal to the pressure in a bulk fluid with the same temperature and chemical potential.
{{figure:a53ed36e-04b5-4d04-89a2-b24c10c753b9}} | r | 9f13365450abbaf4e321064fccb761e8 |
In the classical version of the Prisoner's Dilemma, two agents can choose
either cooperation or defection. Hence, there are four payoffs associated with
each pairwise interaction between the two agents. In consonance with common
practice {{cite:70fc8e2a93bedc10d50a607a3035a586451b2283}}, {{cite:f4fb9de40f5e084e26b4788a8696601dcdc4afb4}}, payoffs are characterized by the reward
for mutual cooperation ({{formula:28c47e70-1bd5-4bfe-9fdf-617c679acc27}} ), punishment for mutual defection ({{formula:cc8bfacb-9639-481b-8655-ba91371b06bd}} ),
sucker's payoff ({{formula:569b071c-3e7f-48d0-bb8f-429edaa5cff9}} ) and temptation to defect ({{formula:dce3bac7-5c14-441f-bb8d-4c4b4a274df6}} , where {{formula:c3c2e95e-0ea0-42f1-9dc8-b0a1e4a970e3}} ).
Note that this parametrization refers to the weak version of the Prisoner's
Dilemma game, where {{formula:171869c6-8976-45bb-8477-d826bcdde019}} can be equal to {{formula:5e964a12-06fa-4a6b-a3ff-558d22feb9a7}} without destroying the nature of
the dilemma. In this way, the constraints {{formula:da396cb2-0d73-45ba-98e8-702a0feff89c}} maintain the dilemma.
| m | 6f9fb6c445562743aa60d87ba36c72e6 |
This letter addresses the long-term localization problem, where the aim is to localize a robot within a pre-built map across varying levels of appearance change induced by time of day, weather, seasonal or structural changes. We focus on topometric maps which do not require metrically accurate reconstructions of the environment, thus enabling large-scale mapping. Topological maps consist of a discrete set of nodes or “places" connected by edges which encode spatial constraints. Incorporating relative pose information provided by odometry within these edges yields a topometric representation. Each node within the map stores an appearance signature by applying appearance-invariant visual place recognition (VPR) techniques {{cite:eedc87ca4b685ec359573c61a741626760702f53}}, {{cite:0d7fd840f3d785e439a44616c249bce3868df436}}, {{cite:1b03f9adee3d3e289e815b1129057caa989b9474}}, {{cite:8156995b96cf38354e7c5983a89915b65d123003}}, {{cite:876f620926e8e92d8b006db05b0d4457c6e66d8e}}, {{cite:36eb646fd6771ecdf04273a13abf5ba6d638834a}} to an image captured at the corresponding place, enabling persistent localization.
| i | 8f0fa85f3c0ab78a4b2880aebf35fc62 |
Did the halo stars form in situ or were they accreted?
This is not yet clear, although it seems that at least a fraction of halo
stars have been accreted, since they show lower [{{formula:e22c2223-2358-4c04-8e10-7f2334708453}} /Fe] ratios. In fact,
the best tool
to ascertain this point is represented by the abundance ratios versus
metallicity relations. A recent
important discovery has been the realization that 10 Gyr ago a massive dwarf
galaxy, called Gaia-Enceladus or Gaia-Sausage, has fallen into the potential well of our
Galaxy. The stars of this object might represent a large fraction of the
stars accreted by the Galactic halo.
How should we explain the large spread observed in some abundance
ratios in halo stars?
The abundances and abundance ratios of neutron-process elements show a
particularly large spread observed in halo stars relative to other elements,
such as {{formula:a2ec3ad6-3338-40d9-9d17-f77d7213fecf}} - and Fe-peak elements. The first explanation for
the spread is to assume inhomogeneous evolution of the halo, but then the
spread should be visible in all the elements. A tentative explanation was
given by {{cite:006b4c1e995fef8aa5a283d8f5abc1f6c6880be0}}, who suggested that the different extent of
the spread in the plot abundance ratio vs. metallicity is due to the
different nucleosynthesis and stellar progenitors of different elements,
coupled with inhomogeneous mixing.
How did the two disks form? Thick disk formed fast whereas the thin
formed slowly? Did the thin disk form inside-out?
The two Galactic disks could have formed in a sequential way but
with a halt in the star formation between the two, and by means of different
gas infall events (e.g., {{cite:e576c28b9c229a3a93c0b521d8e363c5406a9263}}). Alternatively, the two disks could have formed in
parallel, out of two independent infall events but occurring at the same
time and at different rates (e.g., {{cite:b93eb642fee97bd425337c465641e9fdd1c48eb5}}). In both
scenarios, the rate of chemical evolution must have been different in the two
disks, with the thick disk evolving faster than the thin disk.
Most of chemical models as well as chemo-dynamical cosmological simulations agree that
the thin disk should have formed on a longer
time scale than the thick disk and the halo. Late time major or minor mergers for the
formation of the thin disk seem to be excluded since they would have
cancelled the abundance gradients. On the other hand, abundance gradients
are favored by an inside-out formation of the thin disk, although other
processes such as inward gas flows and decreasing efficiency of star
formation with the Galactocentric distance should also be present
(e.g., {{cite:11143b8ceafc519e1246e6c0f8f6d88178f11894}}, {{cite:925a98476e5e649878bee0def07a2444c2009b5c}}).
What is the cause of bimodality in the [{{formula:92236e24-af22-4562-b910-ef9107148fbc}} /Fe] ratios in the
thick and thin disks, if real?
The cause of bimodality, if confirmed to be real, is certainly a consequence of the mechanisms and timescales for the formation of the two Galactic disks. The bimodality shows that thick disk stars have larger [{{formula:9610dbe6-fa52-4a5d-a8dc-c258255dc08b}} /Fe] ratios than the thin disk stars and part of them lie in the same [Fe/H] range of thin disk stars, so that these abundance ratios appear in two sequences. The sequences look parallel in Gaia-ESO and AMBRE data, whereas in APOGEE data the low [{{formula:f110979b-dbb1-439e-bed5-7cd37a90f88e}} /Fe] sequence appears rather as a plateau. This bimodal effect is indeed interesting, and it seems to be a common characteristic up to large Galactocentric distances ({{cite:fd270b310846d3cc5157ff0e9e05b743ad4ea768}}). In any case, many have been the explanations suggested for the bimodality. Several authors suggested that a framework like that of the two-infall model can explain the bimodality, since there is a stop in the star formation between the formation of the two disks with consequent dilution and decrease of the Fe abundance. This effect had been found first by {{cite:e576c28b9c229a3a93c0b521d8e363c5406a9263}}, who showed that a gap in star formation of less than 1 Gyr was expected because of the second infall coupled with a threshold gas density for the
star formation. In order to explain APOGEE data, {{cite:6433c7f1e0c4a45db333abafcc28f63554654dcc}} proposed a longer gap of {{formula:b1011fd6-85b0-4a59-a6ec-d2ad58d0f69b}} 4.3 Gyr, while {{cite:b93eb642fee97bd425337c465641e9fdd1c48eb5}} proposed a parallel disk formation to explain the data of AMBRE survey. Other authors (e.g., {{cite:208b9fff9506f56255c6071dc5bf9ed91fcfeaab}}, {{cite:e71ed705a5962d50df7581f90434baa39d189701}}, {{cite:2ec46db7a0c8886f8465ce24b581c1e22558e3fc}}, {{cite:7ba1f068b65e8de1661404c6020e3c6d79981861}}) have suggested that the bimodality is due to stellar migration. Also a late infall event occurring in the thin disk has been suggested (e.g., {{cite:064f460d951a6fcc1800cd990449a7bef9f8d3b7}}),
as well as the possibility that Gaia Enceladus can have influenced the evolution of the thick disk ({{cite:522c231de3d939c24225a3659d43b0cbe7a3d0aa}}).
How important is stellar migration?
Stellar migration seems indeed to exist and most of the studies suggest that it should occur mainly from the inner to the outer Galactic thin disk regions. However, there is not a general agreement on how really important is stellar migration. It has been invoked to solve several problems including the observed spread in the abundance patterns observed in the solar neighbourhood, the [{{formula:83636668-3f57-43e8-b17a-75a44b3b655e}} /Fe] bimodality as well as the existence of the thick disk itself. On the other hand, models without stellar migration can still reproduce the majority of the observed features in the solar vicinity, except for the presence of stars with super solar metallicity, for which a 10–20% of migrated stars could be enough (see {{cite:ead64b730dce2376ccd4053a2214490b0a7414bd}}).
Anyway, the exact amount of solar vicinity stars which have migrated from other regions is still difficult to establish.
How did the bulge form? How many different stellar populations are in the bulge?
Most of the chemical studies, including chemo-dynamical cosmological simulations, relative to the Galactic bulge have suggested that
it formed quickly, as a consequence of a strong burst of star formation lasting less than 1 Gyr. With high star formation efficiency, short infall timescale and an IMF with more massive stars than in the solar neighbourhood, it is possible to reproduce the MDF and the [X/Fe] vs. [Fe/H] relations for a large part of bulge stars, as first shown by {{cite:21a2e65f9c3fe56b70658b8a654e7442f3541ece}}. However, there is a fraction of bulge stars which are more metal rich and associated to the Boxy/Peanut X-shaped bulge ({{cite:50aca6f3cf6bdf67ad71e60892825f45842f86aa}}), and might have been accreted from the inner disk. The true bulge stars seem to be old and the fraction of stars younger than 5 Gyr to be no more than 10% (e.g., {{cite:100c15fe302a6b455d6cf2f8c3ec8f386743c03a}}, although other studies have suggested a larger fraction of young stars, such as {{cite:68e0b181093e833ecd4e881251e6fcd431807b43}}).
How did abundance gradients along the thin disk formed? Which is the role of radial gas flows?
Abundance gradients are present along the thin disk: they have been derived from young stars, PNe and HII regions. The abundance gradients generally indicate the present time abundances along the disk, except perhaps for data of PNe which can refer also to older objects. Chemical evolution models predict abundance gradients if there is a gradient in the SFR along the disk. This can be obtained in several ways: i) by assuming an inside-out formation of the disk by means of gas infall, with the infall timescale increasing with Galactocentric distance (e.g., {{cite:82e1236e9195e1f7de2e3d81062c7c5d83f8909c}}, {{cite:7da0052208bc9e3cd5c05aa52a17e2d73164ec3f}}, ii) with an efficiency of star formation decreasing with Galactocentric distance (e.g., {{cite:15b8304cfeab570b7f297c9ba759c5e6719fe25f}}, {{cite:e9bf69ef2dc19c20372f0f4125f36d9d9edb1f5a}}), iii) by assuming a gas threshold for star formation ({{cite:7da0052208bc9e3cd5c05aa52a17e2d73164ec3f}}), iv) by varying the IMF with Galactocentric distance, although this variation should imply a smaller number of massive stars at larger Galactocentric distances, at variance with the {{cite:bf7353c4cb2eea05909b370d382361d9df81167a}} criterion for star formation; v) by assuming radial gas flows (e.g., {{cite:387e9203aeacef64f2464f36fabfd7f4ec3c7645}}, {{cite:f7f4ab726ff4427ff46fbead2d20d72043c741c2}}, {{cite:9c6b996233f295db988938b9abdcf6f95b75fb1d}}, {{cite:925a98476e5e649878bee0def07a2444c2009b5c}}). All of these processes can be at work at the same time but while we could avoid ii), iii) and iv), we cannot exclude i) and v).
In fact, radial gas flows and inside-out formation seem to be unavoidable physical processes: in particular, the inward radial gas flows have a strong effect on the formation of abundance gradients and they are the natural consequence of gas infall. The inside-out process derives from a faster accretion in the inner denser disk regions relative to the less dense outer ones (see {{cite:506a4b296008c6a6ed0e31d24c2f4bc50128833a}}).
In addition, most of the chemo-dynamical cosmological simulation found that the disk of a Milky Way-like spiral forms inside-out.
Another still open question is whether the abundance gradients have steepened or flattened in time, depending mostly on the assumptions on the SFR. For example, by assuming a constant star formation efficiency leads to a steepening of the gradients in time while a variable efficiency as a function of Galactic radius induces a flattening of gradients with time. This problem will be solved only when we will have more data on gradients shown by old stars.
Which stars are the main contributors of r-process elements? Merging
neutron stars or supernovae or both?
The r-process elements, such as Eu, are mainly formed in massive stars either by means of explosive nucleosynthesis during the CC-SN events and/or by merging neutron stars. The second channel seems to be favored, as shown by the heavy elements which arose from the merging neutron star event associated to the detection of GW170817 ({{cite:b8294891d74882dcc8c0a486b6dc26fb8aa18cac}}). Chemical evolution studies have explored the possibility that Eu can be produced only by merging events of compact objects (neutron stars and black holes) as well as by CC-SNe or both. In fact, CC-SNe alone seem to be not able to produce the right quantity of Eu to reproduce its solar abundance. The plot of [Eu/Fe] vs. [Fe/H] clearly shows that Eu behaves like an {{formula:28e53c19-d731-4276-bb19-548cd4143130}} -element, namely it shows a plateau of [Eu/Fe] at low metallicity followed by a decrease of this ratio at higher metallicities. This behaviour is interpreted by means of the time-delay model, in which elements formed on short timescales (by massive stars), such as {{formula:6ee12bc8-296b-4198-b920-fb28eac7a524}} -elements, at low metallicity show an overabundance relative to Fe, which is mainly formed and ejected by Type Ia SNe on longer timescales.
Therefore, from a chemical point of view, the mergers of compact objects can be the main source of Eu, if the merging timescale is very short. {{cite:db3d4dc6bf3c3c394880b80bfb809374c6244efd}} suggested that all systems should merge in a time of 1 Myr, otherwise one should assume a distribution of merging times together with CC-SNe also contributing to Eu. This conclusion was shared by papers in the following years (e.g., {{cite:d021af6a5bc3ed02c6488681d98ec474f58a3bca}}, {{cite:fcb79de316b1a7029de89884acc367b4dbf8eedc}}, {{cite:8688b587daa37f4829378a0f2b176867818b107e}}, {{cite:11e281e59bfcd894679aafff1fb3b0766b8f94b4}}), unless one assumes that the fraction of merging systems should have been higher at early times (e.g., {{cite:7f482614881fb764c127a189f5e5a53b93570ba0}}, {{cite:f325752470b1b2423934f01f177d5d2ad53d5165}}).
Why the origin of some elements is not yet understood?
When we compare the predicted [X/Fe] vs. [Fe/H] relations with observations in the solar vicinity and bulge, we find that for some elements there is no agreement and these elements mainly belong to the Fe-peak group. Some of them do not behave like Fe, as one would expect on the basis of the time-delay model, and this fact suggests that we have not yet understood the nucleosynthesis of such elements, which are {{formula:bd3cfb57-4c60-44f4-80f1-fa7faed79355}} V, {{formula:ad7a6fc2-a5f1-4b54-ba83-2fbb2ddc0609}} Cr, {{formula:01185ad6-6e0f-45dd-ac5b-7ef29989a905}} Mn, {{formula:34f3cde1-60e4-48f0-a85d-cc14b0663601}} Co and {{formula:43bee904-f444-4678-b012-83e029c98c0b}} Zn. Other elements, which do not belong to the Fe-peak element group, and whose nucleosynthesis is not yet well understood are {{formula:4231284a-3d41-4bee-b05c-966eb8317d03}} K and {{formula:ef8fb0c7-00f8-4193-8468-ca42e6066991}} Ti. Generally, in chemical evolution models, the yields of the above mentioned species need to be changed (increased or decreased) relative to standard nucleosynthesis calculations, in order to reproduce their abundance patterns (e.g., {{cite:b794e4966fa143f7590705ee12f4f441aed8f841}}, {{cite:61d84c5127c2ab1f6b5f2818709a9f9acf4733d5}}). Future improvements in stellar and nucleosynthesis models are expected to shed light on the origin of these elements.
| d | 386e197674a02c21629236349f183674 |
The energy spectrum near the ground state is shown in Fig. 2(b). The magnetic quantum number
of the ground-state changes as for the semiconductor quantum rings {{cite:ccb70222324591127d81661a93b42d7f265cb276}}, {{cite:c1d9e65e787216234c4ba9bbf753daf956b398ef}}.
For a strictly one-dimensional ring of radius {{formula:cc991d58-f7ba-41f7-9c1a-6ed17fac7dae}} , the energy spectrum is given by
{{formula:ba1ab390-1953-4272-88bf-de6c58b822d7}} , with flux quantum {{formula:9c12c74f-72ec-4c8b-8ed9-48362b75c46b}} ,
and {{formula:cb6a5642-3e25-429d-810b-ae3af40687c4}} the flux threading the quantum ring {{formula:a664ba85-68d5-4e2e-ac92-d739c8747030}} .
In Fig. 2(b) we observe the changes of the ground-state angular momentum
from 0 to -15 as the {{formula:4e8df8b5-a002-4fce-85af-76af40eab0d7}} changes from 0T to 0.12T. The angular momentum transitions appear with spacing of {{formula:80b63da4-ee1e-4094-9db1-999e1dbcf4ee}} mT.
The radius that corresponds to the magnetic field flux through a one-dimensional ring of {{formula:51d004c4-e168-48bc-811c-c5c6aa1f26b0}} nm, that agrees with the confinement potential geometry.
| r | d1d4ac6046b43d58090198eca39c8a6c |
see e.g., {{cite:d403fbc4a4ed533553980590ee0b732de5e73060}}.
| r | 07bfc5350650ef209a5a4d675abee16d |
2018 {{cite:5a4c2ec184d7b27a5e275500c2868c94fc03d9d6}} YOLOv3 Improving accuracy
| m | e40394d101bcf50a79150e87e33bc910 |
Adopting the theory described by {{cite:d0106ce4cec8e8350babaac4afc537bac2502c48}} and used in {{cite:cb888f99e6b21ad79458b6cdee52ed2aa1c08eae}}, the predicted source sizes of a Type IIIb striation are much smaller than what is observed. The most probable cause of this discrepancy is a combination of radio light scattering in the solar corona, propagation effects in the Earth's ionosphere, and limitations due to angular resolution.
With this observation, we accounted for and corrected ionospheric effects in the calibration step {{cite:cebac0787ce91c0737496198c6f15840766f521f}}, thereby removing the largest uncertainty in source size and position. By fitting the source size directly in visibility space, we can directly see the power at which different angular scales were observed. The uv coverage of this observation allows angular scales of {{formula:3bcfa8a6-d22a-4544-8a7e-0c7749607533}} to be observed (Fig. REF c); although this is larger than the predicted source size of {{formula:c8e60936-6a13-43d9-a73a-667758f87c98}} , the amplitude of the observed visibilities does not increase until {{formula:1744f32d-b33e-437d-88cc-4f9f36a8b29c}} , indicating that it is, in fact, the smallest source size observed in the visibilities.
| d | d1bd1a12f5a8a67c3f8b0c104a8b2303 |
Not all relational networks are restricted to have only pairwise relationships, and polyadic relationships are also ubiquitous {{cite:ebf112c91b57846ec89a9a9c1e3b46950fe9403f}}, {{cite:6ec3852798bb043e3e3a2eb0c8628f347298adc4}}, {{cite:4db67b2875c81971401fea7e6dca375d9d9af595}}, {{cite:3befc045d4237f8246a74aa7895c2895e0c93be9}}, {{cite:16aae8b5c0de2df41aa0d8626354b24caf6b04b7}};
for instance, publishing a paper may involve three or more authors, and an online group chat may involve tens of participants.
| i | c3f6e6131e7cecfecfe1270028c297f0 |
In the top panel of figure REF we show the annihilation cross section as a function of dark matter mass {{formula:23da43c9-4959-4ab5-8787-6d580fa79443}} . The solid red line correponds to the predictions of the inert singlet DM model . Bounds from FERMI-LAT {{cite:d2b693a69037da50a331ae6c42200c9a7c3e1b50}}, MAGIC {{cite:8a0f1d02e14a84073eefd9b441bc7e18c107b952}}, and HESS {{cite:77f198ae6868d5ecaef2be503c7db1d866e40e7e}} are displayed in dashed lines. The color scale correponds to the value of the degeneracy parameter {{formula:bb35c14f-d429-4755-b942-73bb9563a0c6}} . Smaller values of {{formula:40d43428-e0fc-4d3a-8feb-8057152e9b09}} lead to enhanced annihilations due to more Kaluza Klein modes were involved in the early universe.
In the bottom panel we show the spin independent cross section versus the dark matter mass {{formula:b6c4e3fb-a3b0-4b3d-b9b1-df4d2325ca81}} . Bounds from XENON100 {{cite:edbc0176ee4e6bea833d1c28d09020e5aed79931}}, LUX {{cite:dcb52ec185d2be186fe71218abc01684d1a2df61}}, CDMSlite {{cite:79e744e4679b57dac9012308265ed30ae539df77}}, CRESST {{cite:fe6597c3a59970b8da2a6897fba626b0e8e5b923}}, and DAMA/LIBRA {{cite:81a41ddd260bdf2b9f52a1006b6593f1445a4adc}} are also shown.
The color bar indicates the value of {{formula:76053c59-c8e0-4864-bbe6-2c25a72076b9}} where for lower values there is an enhancement of both cross sections due to coannihilations.
On the other hand, when {{formula:fd7bb605-ee14-4b7a-a99f-f1fae3ebb848}} is large most of the points fall close to the predictions of the inert singlet DM model.
{{figure:3eb43355-2063-4112-a4e5-94047541dbdd}} | r | 99a523595eb127bfc3d7e6e91c126932 |
Our tagger is a hierarchical deep neural network consisting of a bidirectional Gated Recurrent Unit (GRU) network at the upper level, and a CNN or a ResNet at the lower level, including an optional novel residual bypass function (cf. Figure ).
Bi-directional GRUs and LSTMs have been shown to yield high performance on several NLP tasks, such as POS tagging, named entity tagging, and chunking {{cite:c4f9a27c9ef28ad2ae328e8a9368813e15137ddb}}, {{cite:066d9bc23f6f755ca3535d31e8ad9245dca86c08}}, {{cite:5ee982da21cb3392e83aaf09d59e3923710eadf3}}.
We build on previous approaches by combining bi-GRUs with character representations from a basic CNN and ResNets.
| m | e8c68f747e8e20c346e81678a48654c3 |
A new proof and generalization of the Mass Transference Principle of Beresnevich and Velani {{cite:b85545ac615a11e9eccc64e0664f44fab759cc75}}.
There has appeared quite a substantial number of works building and generalizing the work of Beresnevich and Velani. MathSciNet knew, in 2021, of 97 references to their work; see e.g. {{cite:c79d0ac54e6c5d9ace04e1418e6051cb35ada6c2}}, {{cite:7a2a6da12781bfb7b73bd412370684372a10155d}}, {{cite:3ff76b4c737f94da7c2c1e27fe5fa4aa63f8c0be}}, {{cite:570f379f58bf401abd2ee7bbb2b0d0d5a0845034}}, {{cite:8142552dada6233318c5c7e9ca17c08a28ad5024}}, {{cite:f803d7d74d8d33c9144e844e2c667d4504a51f5c}}, {{cite:3e51722f0456b732829e7206fa44095f73079181}}, {{cite:4cee7aa25276165b092d00e4339922add675436a}}. Many of these are various generalizations. A comprehensive survey is available in {{cite:e965fd89e5ce1fee9d1322b2c0d5fefeee7c2dd5}}. While most of this work assumed some Ahlfors regularity, our theorem does not require this assumption. Further, our approach uses substantially different techniques.
A new result on the content of random limsup sets. Our version of the Mass Transference Principle together with new covering lemmas yields strengthened and simplified bounds for the dimension and content of limsup sets of collections of open sets. The proofs yield also that, in Euclidean spaces, such limsup sets are sets of large intersection in the sense of Falconer. For prior results, see {{cite:6f3fb3cf79c69b2180ca185bbaa729c9a7231756}}, {{cite:cbc20493946b0706b1983a670e9a024f5485ef09}}, {{cite:6aee00615cefa0d782e9aea0214667e528f9e913}}.
A new proof of a geometric characterization for sets of finite perimeter in PI-spaces. Sets of finite perimeter in Euclidean spaces are classical, see e.g. {{cite:227fe8d9ddbf10deb3027b1aa922768611c7be97}}, and their theory has been extended to general metric measure spaces {{cite:72e13ba5b49b8a6f0b5dea6c713b1d4cda79fab4}}, {{cite:6613bf02b7ca6ee597eabdc18993e5d83c77c4f6}}, {{cite:96934115a325b0c570f797a594d3c373274b7cae}} . A natural problem is giving geometric characterizations for a set to be of finite perimeter. The Federer characterization is one of the most natural ones and involves a Hausdorff content bound for the measure theoretic boundary; for the Euclidean version see {{cite:2084ffd07c5feb5b6e6b3a0a84b46426780b19bd}}. Lahti extended Federer's characterization to spaces satisfying doubling and a Poincaré inequality {{cite:e360cbb578dac5f01f613e310652220cb39fc818}}. These spaces are called PI-spaces. We present a much shorter proof for Lahti's and Federer's claim, which uses less machinery and leads to better bounds on the constants involved. This proof is new even in the Euclidean case.
A result that generic curves in PI-spaces pass through the measure theoretic boundary. For {{formula:82484bbb-6e05-419d-b1df-3e4aa271c5b2}} , the modulus of a curve family {{formula:b0cd7f54-3656-421c-a146-54f52bf3db6a}} , denoted by {{formula:b97c5908-7c68-4807-823a-0ca2eb16487f}} , is a measurement for the size of curve families. Specifically, ({{formula:3dbc5a99-4ffb-4142-acff-59d8ae8aa43e}} -)exceptional curve families {{formula:e849af4a-37fb-45bd-b325-349502b1410d}} are those for which {{formula:53bd99e8-f0b6-40d8-bca4-c68fa1f44606}} . Interesting analytic properties hold outside of {{formula:7e56dbbf-8941-4496-bf30-12d8371792b0}} -exceptional curve families. In other words, they hold for {{formula:fa51182e-aa2e-4006-909a-dc6c8f565993}} -almost every curve. Our covering lemmas and proofs yield a new proof of the fact that in a PI-space the following hold: If {{formula:1087b779-503d-41c0-88ff-99a77154dcdc}} is a set of finite perimeter, then 1-a.e. curve going from the measure theoretic interior to the measure theoretic exterior passes through the measure theoretic boundary. This is a fundamental property, which was first proven in {{cite:6b2c48a6046dbd2e0040f6380d4a6616fbbc3e12}}. Indeed, it is closely connected to the Federer Characterization, although our proof does not utilize this fact; see {{cite:6b2c48a6046dbd2e0040f6380d4a6616fbbc3e12}}.
| i | 290972b3108d82d18d5642cede56dc3b |
The ratio of the pPb relative to the pp distributions increases
with pseudorapidity from the p-going to the Pb-going direction for
central collisions, suggesting a scaling of the pp distribution with
the increasing number of participants as the lead nucleus is probed by
the incident proton, indicative of independent proton–nucleon
scatterings on the lead-ion side {{cite:32973d6e698588dd49005deb074bdc706742a805}}, {{cite:21e1baabac468d6e6dbd8cb9d99cde5f0704524e}}. A
similar scaling, however, does not hold for the PbPb reaction. The
ratios cannot be obtained by simple scaling of the elementary pp
distributions. Instead, the ratio of the PbPb relative to the pp
distributions exhibits an enhancement of particle production around
midrapidity for the more central collisions that is indicative of the
formation of the sQGP {{cite:d9b4990eb0e07d23066517489fd9a2842726393c}}. Likewise,
{{formula:483d1492-7936-421f-b5ef-2c58018ab3e0}} increases for all but the two most peripheral
centrality classes as {{formula:00f8ca38-1fb7-4ea4-bdb1-0580628cf838}} , suggesting that the
various mechanisms behind the pseudorapidity distributions are more
transversely directed in peripheral pPb than in pp collisions (the
same observation also holds for PbPb with respect to pp
collisions).
| r | 219a2bf9d216215b2f77704b2884c63c |
The wide distribution of EM values (see Figures 4, 6, and 9) between fields points towards the warm component being clumpy in distribution. The hot component also exhibits this wide range of EM, and thus is similarly clumpy. This supports the interpretation of {{cite:ddbf8e427af559d47b8d50760e4dec47d2b89539}} that the CGM has a clumpy distribution, and is consistent with the localized distribution of the hot component in {{cite:82cd37b28094b36b0c93d2e320208b5d113ceaae}}.
| d | ced6aaf405a137203d2f13863561cf88 |
In this section, we first apply the approach described in Sec. REF , i.e., MAP, to predict riser displacements in uniform and sheared flows. In particular, we conduct a comparison between the present method and the state-of-art multi-fidelity approach, MF-DNNs {{cite:9aeb1e5f92d4bc91a988b93d5708c7faab627b12}}, which is capable of capturing nonlinear cross-correlation between the low-and high-fidelity data. We then employ the method described in Sec. REF , i.e., BI, to quantify uncertainty in our predictions. In MAP, the Adam optimizer with an initial learning rate is set as {{formula:44ac3f31-a254-48a8-b504-51ddcbd83137}} , and the number of training steps is 10,000. In HMC, we set the number of burn-in steps as 1,000 with the leapfrog step 20; also, the initial time step is set as {{formula:d549b8b1-4f2c-4acb-a194-2d0772f83feb}} . Finally, 1,000 samples are employed to compute the mean and standard deviation after the burn-in steps.
| r | 698017efec1fa57693f207134135740b |
We study the collisional regime in Section . There we apply the Mott-Smith ansatz using the BGK collision term {{cite:74f34b20f3c4fd52351304e5e1f9ccbe46b9e49a}} as a collision operator for {{formula:350a6ab9-37db-45d7-87b3-1e10037b1801}} in Eq. (REF ), with {{formula:32794707-20ba-480a-a77b-34de9e04dfd8}} . Notably, {{cite:74f34b20f3c4fd52351304e5e1f9ccbe46b9e49a}} presented 4 different collision operators through their Eqs. (3, 4, 5-6, 15-19). Those given by Eqs. (3, 4, 5-6), like {{formula:f9ae0c49-e111-46c9-8feb-d9f36269c66d}}Here {{formula:7843cbb4-dbd0-4f2a-9b92-964db29e685f}} is a collision frequency, {{formula:7bff6d3b-6a22-48e7-a426-ce01493815e2}} the distribution function and {{formula:c1b9b93e-b4ff-478f-8f83-a6a3e36987ac}} the equilibrium distribution function., have been widely used although they do not conserve all 3 quantities: particle number and/or momentum and/or energy. In {{cite:74f34b20f3c4fd52351304e5e1f9ccbe46b9e49a}}, only the operator of Eqs. (15-19) does conserve all 3, hence this is the one used here.
{{cite:7279f972ab374a76dd30fc6ef203fa6755c3cedb}} used the Fokker-Planck operator to deal with the problem, considering Eq. (REF ) with {{formula:28e9fbc5-8afb-4624-a6d4-5c0a72157192}} and,
{{formula:8941e4a5-82bd-4958-bc62-f3f24ec31cd7}}
where {{formula:769a0f6e-fe12-4c00-9510-1e35a5068104}} is the Fokker-Planck collision operator, {{formula:32f23a17-3328-4329-80b4-9445cd740427}} the ion mass, and {{formula:37c76cfe-76cc-49d3-8e3a-a201856d3f72}} the number of particles in the Debye sphere, that is, the co-called “plasma parameter” which measures the coupling of the plasma. As we shall see in Section , the present treatment provides a more adequate bridging to the collisionless regime than {{cite:7279f972ab374a76dd30fc6ef203fa6755c3cedb}}'s Fokker-Planck result.
For the collisionless regime we follow in Section the collisionless result of {{cite:b4933ea04efa2d72fee2ddf682597dd9158974ec}} who also used the Mott-Smith ansatz. In recent years, the correctness of this approximation, namely that the distribution function is well approximated by superimposed drifting Maxwellians, was validated numerically using Particle-In-Cell simulations {{cite:50f9dc92896766b7c56d57fcf7d02d473259d7bc}}. {{cite:b4933ea04efa2d72fee2ddf682597dd9158974ec}} considered Eq. (REF ) with {{formula:a8a0ed3b-a09d-4a72-b79b-69c6f7e17969}} , describing {{formula:31944f43-bc36-495a-ab2d-38a744112cc2}} by the quasi-linear operator.
| m | 31f8e79d361d2e2baa55a350c8ebc751 |
To stabilize training, the natural policy gradient method {{cite:ea11b3832a3211e7750d680d4b50a9b262edb9ce}} restricts how much the policy can change across training iterations by adding a Kullback–Leibler divergence constraint ({{formula:526f8bb6-c9ae-46a1-8371-689b9d43da6f}} ) between policy iterations:
{{formula:bf193f47-628a-4fe2-a83f-5398b14ae7e9}}
| m | e18cfb3c2669022b92bf97ffd82e5822 |
Diversity-aware Queue.
The number of negative samples is critical in contrastive learning. Short queue leads to inhibiting convergence {{cite:032419f54f2a6d0f3ea6b46305782e7a3d08b4a9}}, while long queue suffers from redundancy and inappropriate negative samples. Empirically, length of the queue is related to the size of dataset, such as {{formula:0cc1adb6-63d1-4419-9042-d7dfe16d1300}} number of the dataset in MoCo-v2 {{cite:a86d1797d2d6a31bc2fd7c039c63fc210bb86174}}. However, this empirical hypothesis does not seem to hold up in GANs due to the continuously changing generated images over training iteration. As described in Sec. 3.1, the optimal queue size may be related to the diversity of samples in queue. Furthermore, the diversity of fake queues is indeed higher than that of real queues and decreases gradually accompanying with training due to the convergence and stability of generator. Therefore, a diversity-aware queue is required for contrastive learning in fake images. Generally, {{formula:34ecc335-e67b-4aeb-ab56-d553f3b77270}} , where {{formula:a390e8ce-8cc3-4e45-8fef-fd9b8bd7e052}} is a diversity estimator. In this paper, we also adopt a simple implementation that is {{formula:dce9497b-bf34-41ed-a632-4a5e5d07c3d7}} to reduce the computational complexity, where {{formula:07adfdd1-840f-4ac1-b180-0e4c0dbcdfca}} is a negative coefficient and {{formula:bb1a33c6-abd3-448d-a8fb-fcd61cb2e9af}} is the iteration of training. Therefore, queue size in FakeCLR decreases linearly with respect to the training.
| m | c593b635091bd725cfcb4c6c323deb62 |
For CIFAR10, to fairly compare with {{cite:b7b89d5027d592300e9d3cd00752a522b7bd0545}}, we crop each image into two views to construct the loss (REF ). For ImageNet, we follow CLSA {{cite:e2ab45883028a6e09f36588eaa50d55a5bc9a1c9}} and train SANE in two settings. SANE-Single uses a single crop in momentum mixup loss {{formula:f69e349a-738a-451d-8c18-2804c25a2f2a}} in (REF ) that crops each image to a smaller size of {{formula:aa729da4-afb8-4395-8ad5-4880541c1a86}} , without much extra computational cost to process these small images. SANE-Multi crop each image into five sizes {{formula:d062c67f-e217-4e69-ab1b-a522ff65f048}} , {{formula:b26b6eb3-fb8a-45e1-a291-2032d8ba1fb6}} , {{formula:4e26f227-c2fb-4132-9867-564558934c9c}} , {{formula:237d29c1-66d7-4ece-9515-431032ee6ef1}} , and {{formula:67669c3a-9fc0-4196-9f6d-873d1896263a}} and averages their momentum mixup losses. This ensures a fair comparison with CLSA and SwAV. Moreover, we use strong augmentation strategy in CLSA. Spefically, for the above small image, we randomly select an operation from 14 augmentations used in CLSA, and apply it to the image with a probability of 0.5, which is repeated 5 times.
We use “(strong)" to mark whether we use strong augmentations on the small images in momentum mixup loss. Thus, SANE has almost the same training cost with CLSA, i.e. about 75 (198) hours with 8 GPUs, 200 epochs, batch size of 256 for SANE-Single (-Multi). For vanilla contrastive loss on ImageNet, we always use weak augmentations. See more details of the augmentation, loss construction, and pretraining cost on CIFAR10 and ImageNet in Appendix .
{{table:c215a44b-b9e5-4759-8e5d-f4704d3bb096}} | r | 36ea9ffb63f4904755288c232fc87fe8 |
It can be easily seen that Eqn.(REF ) is a special case of Euler’s method when the step size {{formula:4f46b7cc-168d-448a-bc14-0f41e91f8c84}} . The iterative updates of ResNet can be seen as an Euler discretization of a continuous transformation {{cite:84212ac81b27ad61d77c54dea1a89c5f11012360}}, {{cite:e9d708bf3b7ad2b7702c293865e537d9d92fe785}}, {{cite:8f413ea134279d6afd2efd4b0ad57cf0022df49d}}.
When the input data is perturbed by adversarial noises {{formula:16716370-ca28-4d36-a6a7-e8b63c6c19c6}} , we denote the adversarial example by
{{formula:36b821b3-a58b-4ff6-a2a4-b10be35bc93b}}
| m | cf6036e7320f0387e4c69572130448e4 |
BFT-SMaRt {{cite:679311a1fed49b8e9c92b1c49ad655adf534b659}}, {{cite:a23def029389743dfd6e4b954e9b21345b80e8f2}} built on the ideas
of {{cite:f58958ab8c000fd2484f43df806297051c704bbf}} to propose an abstraction of validated and provable
(VP) consensus, which allows its clients to control leader changes.
Although the overall BFT-SMaRt protocol appears to be correct, its liveness
proof sketch suffers from issues with rigor similar to those of {{cite:f58958ab8c000fd2484f43df806297051c704bbf}}.
In particular, the conditions on how to change the leader in
VP-Consensus to ensure its liveness were underspecified (again, see §).
| d | d1e77bb82109ed49c7bc6027bb649755 |
The other parameters are the gravitational constant {{formula:767f66ae-59c2-4994-b962-19ba527c7300}} , moment of inertia {{formula:52c712fa-a99d-4900-ae8a-4b9fb34bcadc}} , speed of light {{formula:c2a218ce-3632-4b82-899d-d94ea9bc9d57}} and angular velocity {{formula:efd847e7-4e9d-4cba-88d9-97dc34067003}} .
Similarly, we use an effective dipole magnetic field strength on the NS surface, {{formula:c96c5bc7-9b1f-4777-b1db-d24e0d4c71b9}} , to include the deviation from the actual electromagnetic radiation, then the
power of spin-down wind is (e.g., {{cite:fb0e769d0d2e8e2ac1b2120f13001dc1fc0062a6}}, {{cite:8af5d24571837fa980e6077d06e794efd4d77611}})
{{formula:fd9ff9be-34c1-43fc-a871-1197cc2795c5}}
| m | fe8296dd9f7cd477e5c535d3658aeb5c |
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