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Finally, let us note that much of the canonical approach to quantum cosmology is based on promoting {{formula:1e887fee-b4c0-4301-82da-50686e813e25}} (or some function thereof) to an operator, together with its conjugate momentum, and imposing commutativity relations. This is the basis of Wheeler-deWitt quantum cosmology, and lies at the heart of most of Loop Quantum Cosmology {{cite:97994790a60ce590377efef148e80c63f00a301c}}, {{cite:b1964333a1bfe677e5a6af64262fc843fb5c372a}}. In this and previous works, we have shown that this variable can be excised completely from the classical description. This points to an alternate quantization method, which should be based upon the contact geometry rather than its symplectic embedding. It is as yet unknown how to carry out this process.
d
d63954a620fb8975e0393c336dec24df
In this section, we qualitatively demonstrate the performance of RFCnet by showing some ranking examples. Fig. REF shows some retrieval examples of existing methods, PCB {{cite:15f598bb826f9bdfa22a749fd1e4c95eabf95d9b}} and PGFA {{cite:116566356c505718993e8ae64afeae68c6413094}}, and our RFCnet method on Occluded-DukeMTMC. The retrieval results show that PCB is prone to mix the information of the target person and obstacles, resulting in retrieving a wrong person with similar obstacle. Although PGFA utilizes the pose landmarks to alleviate the interference of obstacle, it still exists the information loss. As shown in Fig. REF , because of discarding the occluded regions, the characteristic of upper-body dominates the probe feature in PGFA. This makes PGFA tend to retrieve the wrong pedestrians with similar upper clothes. On the contrary, our RFCnet can complete the lower-body feature and form a full characteristic of the target identity. So RFCnet can work successfully in the case.
r
a5e7abb4d207e5992c740844d3bd48e3
Finally, we comment on the future research direction based on the present results. While Bi{{formula:d39f1b51-7eb2-4dc6-a024-17d991ff75a0}} Se{{formula:3735a3f1-0ccf-403f-bcac-61662b4a3739}} /CST is not suitable for realizing the QAHE due to the electron doping, it would be useful to fabricate (Bi{{formula:9d476f6f-4b52-433c-b784-136ac3dec471}} Sb{{formula:a97033db-0337-4a83-ad4b-0bc5c9c4948f}} ){{formula:3f480ade-b067-4836-ad38-a506f4765a07}} Te{{formula:681bd3ba-022c-4d22-8d9c-07e922d9ac29}} /CST where the Dirac point is situated exactly at {{formula:756be401-44f9-4e02-940d-a1fdfa22a39e}} to examine the possible QAHE at higher temperature. To realize a large magnetic gap by the FPE, the substrate is preferred to have a higher {{formula:a92aae49-dc8d-4983-8f8e-04b734e598b9}} and required to have an out-of-plane magnetic easy axis. In this regard, some van-der-Waals ferromagnets such as Cr{{formula:06efedae-451d-45fc-9d6e-2bef6f93f433}} Ge{{formula:cc7878f0-091d-4bc9-aff0-3ac37b73e573}} Te{{formula:35f1c095-6c4f-4e89-a531-5e5399cfc200}} (a cousin material of CST; {{formula:984570f9-50de-4e04-883e-9c397f2afcb3}} = 65 K) {{cite:cf22eab453dcc44997e61606d5403afdc088d5c9}}, CrI{{formula:4984289f-98f8-43b5-863e-ab1546f18c2b}} ({{formula:dcb98aa9-9183-4b88-9d2f-ecd101644adb}} = 61 K) {{cite:87c207f33e2a99ec01e805669f0fdfc53772ca81}}, Fe{{formula:9ed7d179-dd2a-415e-ad92-374e90cbdc0d}} GeTe{{formula:4f80699e-565e-4eea-a5f5-dd1fc2b37162}} ({{formula:b730cb0b-2552-454c-8919-e3913bfdf315}} = 220 K) {{cite:b4a4eb906812acb3223052743e36602f93597cb8}}, and Fe-intercalated TiS{{formula:a946ccb6-1762-4571-b9a2-38cb68d86956}} ({{formula:236a6007-9120-4689-8bba-e50ac4ef5de0}} = 111 K) {{cite:a0791299da60568aee47482e487e3c1a386f67fe}} can be the possible candidates for the ferromagnetic substrate. While we intended to create a Dirac gap below {{formula:93013a8c-fc2d-4cde-b896-8cf4bda94c35}} of CST by utilizing the spontaneous magnetization along the {{formula:52eb4102-2959-4f35-955e-c2f1a248502d}} -axis, it would be also possible to control the magnitude of magnetic gap by applying an external magnetic field and also by controlling the field direction using a vector magnet, as in the case of Kagome magnet {{cite:3a62c3899f139332348c9798ab8f2a9c71009bcc}}.
r
93619536a3ee3027a5ee833de83b31ee
From a quantitative point of view, given HI and H{{formula:0fb06b57-2e25-46f6-82af-bfdfe97c5e4a}} masses, cold gas is often quantified in terms of the comoving neutral and H{{formula:92bf1144-2427-4671-9455-eabdf3bff32a}} mass density parameters, {{formula:5dc8e364-399a-49e8-97d7-61362ad507e5}} and {{formula:1059ac56-f0f4-4beb-83e0-248fc4a2349a}} , defined as the corresponding mass densities divided by {{formula:5672050f-77b9-4ec2-8beb-d40abdafd980}} . Observational determinations (see e.g. {{cite:bc0d0c0c238cb3cc05969fed5ae2b73183cd159d}} and references therein) suggest that neutral gas at {{formula:84181a64-d83f-4dbe-9c8d-6d56b2e402b0}} features values around {{formula:0b02559a-7ed0-4995-8d5d-951cd3ce7c16}} , increasing smoothly towards the epoch of reionization. On the contrary, {{formula:0c8aa109-a6c1-45a5-875d-5fcc3554772c}} observations in the (sub-)mm and IR {{cite:bc0d0c0c238cb3cc05969fed5ae2b73183cd159d}}, {{cite:9f2d0e715caf56abf295b4f6fcf367a070e00134}}, {{cite:e3692a94233303b04f84dcf23ee2f4d34b5e2336}} give a more complex picture of molecular gas, with peak values of {{formula:ee959f31-33df-4266-88c1-bbfd230acd74}} at {{formula:a8cbc935-7c03-4ba2-855e-e4a88be4b6b3}} and a drop of at least one dex at earlier times. In this respect, impressive progresses have been made by recent ALMA data in constraining {{formula:64b0a96f-5d97-4939-9ade-a40ffa1f1bac}} gas up to {{formula:2843f609-fe05-4711-b41b-57bd54a06b71}} and in raising previously derived indirect lower limits at {{formula:fca3cdfb-b814-4da4-9515-c910de8b2ceb}} -3 {{cite:4e67a5541dc053e5d6daf09ca59ecc563347799a}}. {{figure:0e905b93-eefe-426b-8916-fb652691438f}}
r
86bb199a275ef9a447aa6fd80c78502d
For domain generalization study, we conducted leave-one-domain-out cross validation on the multi-domain fundus image dataset. We first considered all the available training domains as a single dataset (i.e., ignoring the domain shift in training set) and trained a U-Net {{cite:c3bc08184c32ba4141db2da1ccf707a03f6d6858}} using a standard Dice loss, and directly applied it to the unseen domain, which is referred to as `Inter-domain' and serves as a lower bound of the experiment. Then, for each domain, we trained and tested the U-Net {{cite:c3bc08184c32ba4141db2da1ccf707a03f6d6858}} with the training and testing sets respectively, i.e., no unseen domain involved, which serves as the upper bound for DG and is referred as `Intra-domain'. For DG methods, we compared our proposed CDDSA with four representative state-of-the-art approaches: BigAug {{cite:ae86897d3a60aff9ef151d28c7995ae135f135c5}} based on data augmentation, DoFE {{cite:fa7e98464ef42a64b768b55953fea1ddf862d707}} based on domain-oriented feature embedding, DCA-Net {{cite:2fd987fdf0c5be226d5d740f2530ca5cd80630df}} based on domain composition and attention, and FedDG {{cite:a074871cf5007993c7ac4a8bb065098709cdaa8a}} that is a federated learning-based domain generalization method.
m
9d6adc1faf7750bd01db5c9d7b6da4a3
Recent computational {{cite:a591c163473b07432eb2da282690ed42a9e3f1df}}, psychophysical {{cite:c25e9ff3186510a548fa7c7a41aa14d380a56316}}, and fMRI {{cite:abc8688c57504ade6c6393a03a48d5a4e2189de8}} experiments demonstrate that the informative intermediate complexity features are optimal for object categorization tasks. But the possible neural mechanisms to extract such features remain largely unknown. The HMAX model ignores these learning mechanisms and imprints its features with random crops from the training images {{cite:cafe1a2b9ea08e9e63d2d4e6ba7332a39bc0a9cb}}, {{cite:a9095acc179fa8470305a72993da0088ae188b1b}}, or even uses random filters {{cite:bb3483f4c30c2c9e6f33cd60e31f5940e9d56012}}, {{cite:948330c0055c70a292285cbf5837d608ff70dee5}}. Most individual features are thus not very informative, yet in some cases, a `smart' classifier such as SVM can efficiently separate the high-dimensional vectors of population responses.
d
9ba70203ad85dda33c9c678535161850
where {{formula:e7314b14-abc2-4a05-a212-648ec9b9e638}} is the decision variable and {{formula:85a16e83-2cf5-4418-8dd0-d48492f2f8c5}} is an uncertain variable. One principled approach to handle (REF ) is robust optimization (RO) {{cite:29449b8716a8fd11c0f5cbc933fea69884ea288c}}, {{cite:00a3957069f38b825ecd6a8d7c7d53c8e519548e}}, {{cite:5623529ecf2c891ad12f3fa506166a7f8baa0b5c}}. In RO, uncertain inequalities (REF ) can be written as their robust counterparts (RC) {{formula:2a89863d-3515-4183-8e3e-3b0b567eb0d3}}
i
343da86df5968e5a71ae69293617f840
Hard {{formula:1cf9dee7-4eaa-4d5c-a549-c8241d6f3763}} values also suggests that our line of sight is not significantly off the burst axis {{cite:be45261c88f112d8e082376b593d692fa32cb040}}, and that the central engine is active throughout the burst duration. At large off-axis angles and when the central engine is off, the observed emission would be dominated by high latitude emissions, resulting in a softer spectrum both in terms of {{formula:f0365d64-6e3b-4b47-8831-95690088d568}} and {{formula:f6f9c1bc-bd6b-4be6-8cfb-39510c598fb3}} due to lower Doppler boost and superposition of spectra respectively. This would result in an average spectrum with region below the spectral peak {{formula:529a0143-c9dd-4ac9-9424-ba5f77df310e}} {{cite:be45261c88f112d8e082376b593d692fa32cb040}}, {{cite:a8d42569aa317e4c5c497cd320c18b6f1ca2dc54}}, softer than what is observed here. Both the emission models discussed above, while being capable of generating spectra nearly compatible with those observed, find it difficult to explain the high degree of polarisation around the spectral peak. The observed high polarisation therefore results most likely from the viewing geometry, as envisaged by {{cite:4d51250af1d2436568937c3790cc076399113a6a}}, who showed that bright and highly polarised emission can be seen when the observer's line of sight makes an angle {{formula:ffca5f41-e0c6-498c-bfd2-7d7759f8920e}} from the jet axis, where {{formula:e2273a57-bf74-4cc3-aca3-22e23a637a39}} is the jet opening angle, {{formula:1dde7d36-e819-4986-9fb1-23f2c4f67063}} is the viewing angle with respect to the axis of the jet and {{formula:faafecbe-5bd4-4439-8ff1-fca8948cefb6}} is the Lorentz factor of the outflow. This also requires a strong asymmetry in observed emission within the off-axis viewing cone as could be obtained in a “top-hat” jet model, but not in “structured jet” models where emissivity drops slowly away from the jet axis. A sharp drop in emissivity beyond the edge of the jet is also suggested by the observed hard {{formula:ed2e3547-58b1-407c-8ccc-939fe01a31f6}} values. In case of structured jets, the emission viewed off-axis would be dominated by that from high latitudes, resulting in a softer spectrum both in terms of {{formula:00c9024f-2482-470c-9748-c0227f2c6f10}} and {{formula:8b07b649-dfea-44c5-bd68-476a74091bb9}} due to lower Doppler boost and superposition of spectra respectively, contrary to what is observed. On the other hand, in case of a "top-hat" jet, hardly any high latitude emission is expected and the hard spectrum can survive even when observed close to the edge of the jet. The hard {{formula:968c730e-b395-4296-9583-92f4eec74b8c}} then suggests subphotospheric dissipation to be the underlying emission mechanism. In this model Comptonisation can yield high polarisation since orthogonal Thomson scattering in the rest frame dominates near the edge of the jet. In contrast, regardless of the geometry, Jitter radiation cannot produce the observed high level of polarisation near the spectral peak.
d
4f911374265c6075a300f2ea47768daa
In this appendix, we discuss related work from two branches: training approaches for randomized smoothing, and data-dependent randomized smoothing. Both branches aim to improve the certified robustness of randomized smoothing. For tighter certification approaches leveraging additional information, a detailed discussion can be found in adxsubsec:more-discussion-related-work. For more related work we refer the interested readers to recent surveys and books {{cite:62d2185dec762b1131310cb6e53035c4c4e8b7d2}}, {{cite:ddd71e7dbdac97dfaf8e39d19a6216e2b42d05f8}}, {{cite:c0a33dfbff19d24b0cf580c0e46dd81191a96748}}.
d
c2d01aec470dd25245e9b27f83f8ebee
In spite of a caveat of double counting by including the data of {{formula:d3246f18-0b08-4a5a-93bc-5f82a7f81f47}} in the analysis {{cite:1c2c34d2ad07ea7101312b6fe055feaffe032136}}, the cancellation of systematic uncertainties in this quantity brings additional constraining power in the fit. The NRQCD calculations presented in this section are performed using the nucleon CT14nlo PDFs {{cite:15d9c48339cead96c916f56d46ede47f8f39523d}} and the pion GRV NLO PDFs {{cite:b4ab7215d686dc7bae926ffcc3baba426aa88e15}} under the LHAPDF framework {{cite:0d2867aa2e07b909444c28b98377cd5bf57030fa}}, {{cite:c2bc063d46e3fc4ec22a710efc7f42c56b6934ba}}. The cross sections are evaluated with a charm quark mass {{formula:758e1704-df32-486c-9f24-06a410a9df1d}} GeV/{{formula:a91a0c99-8b5c-49c7-8466-c5121055c551}} and renormalization and factorization scale {{formula:06c51ae3-85ee-47f8-abe5-b16a334d6b2b}}  {{cite:2ab04b45940a6fdade041e571d651bbf971efb32}}. {{figure:9229d7b8-a67d-4d82-aa8c-35d28edb8a1c}}
r
1565278a0605d56cbf0c109158874885
Another projection algorithm for solving eq:feasibilityproblem can be obtained by applying directly the FB algorithm to eq:minaveragedprojections. Let {{formula:d9b9967b-5a77-4888-b932-0c9fff07e4d8}} be given by eq:ffeasibility, and denote {{formula:08b0f275-8602-4173-bd7f-a76c57e85102}} and {{formula:9dce48eb-cfdb-4e70-9ffe-e3721247feb6}} . From {{cite:6982da160a3ee7bedf65ca0e527919da57c0490e}}, we have {{formula:26da953c-3bf5-4fa0-86ff-d4ccf01750b1}}
m
61512aa1d66cb36ae5e2fe76a7010b71
{{figure:7e94419d-113b-4d57-83c4-3df8566a9987}}Depth recovery by RGBD & Depth-only approaches. (a) Depth map estimated from ground-truth RGB-image using MiDaS {{cite:01b2bb32045bd1daaa4461228780cb7161208e42}}. (b) Depth channel of RGBD reconstruction directly from fMRI. (c) Depth recovery directly from fMRI, where both Encoder & Decoder are trained “Depth-only” – without using any RGB data for training. (d) Indirect depth recovery from reconstructed RGB-images using MiDaS. This approach fails to recover depth faithfully. (e) Depth reconstruction mean rank for (b)-(d) respectively by n-way rank identification experiments (lower is better, showing average over all 50 reconstructed depth maps and five subjects). {{formula:6fb9618f-7cf4-40f9-aba5-36e78288a32c}} Confidence Intervals by bootstrap shown on charts.
r
24882f58b4cadcdb38784841a42bf873
This paragraph introduces Bioformer, a Vision Transformer (ViT) {{cite:b95e7eb612fea2f5f660eaf537e3ce191fab21c3}} inspired architecture, which significantly reduces the computation complexity for sEMG-based gesture recognition, while reaching an accuracy comparable with the state-of-the-art. Further, we propose a new pre-training protocol to feed more data to our transformer. Finally, we provide few details about the experimental setup and the deployment of the networks.
m
ef40d89a0dd4fc53cd45af4ce7c83179
In the development of game theoretic models, there is a fundamental tension between constructing a model that is both simple enough to be tractable and descriptive enough to be useful. In cybersecurity, this tension is exacerbated due to the high-stakes associated with decisions in conjunction with the fact that the generation, transmission, and response to information happens rapidly and with little human intervention such that on-system activity is effectively instantaneous. In these games, a common simplifying assumption is that defenders are operating against some adversary that operates according to a fixed strategy {{cite:822999faa1facb74e01b237ff393184b55798be8}}, {{cite:1e91e27463dfb63bc34e1422bde5b334443366e1}}, often represented using the SIRE model from epidemiology {{cite:3769ff4b186eb559a5a5fc2bb6c605e249274982}}, {{cite:87b4a72c2960585c8cfdb930bcd35a963ef7ea27}}, {{cite:9dfaf3c735c23fe18b92327f58e17017bc8ab812}}. In practice, these sorts of adversaries are rare, and there are human decision-making aspects to how an attacker behaves within a victim network.
i
1cfad7208b22bf64a251360cb80dcc37
The IceCube data {{cite:200d3c7eb9f57d7ec765aec56c8505d2c1ea6a79}} are plotted in Figure REF . They are consistent with a spectrum given by {{formula:b6780c7c-bb35-4994-97e7-1b6df2edbc0b}} up to an energy of {{formula:535372e5-06f5-4eb5-ad5c-24b5f1507bc5}} 2 PeV, the energy of the so-called "Big Bird" event. No neutrino induced events have been seen above 2 PeV. {{cite:54124f86757452957ab18488202b91489b865601}}
r
92639507442935fe1c3c9f12cae203c1
Exponential moving average emsemble. Inspired by the mean teacher {{cite:bb0caa08259bbc55eebe680fdcab9894b75f24fb}}, after the pseudo ground truth learning, we ensemble the models from all 5 refinement iterations by exponentially moving average their parameters with a successive weight {{formula:7eded964-900b-4573-bfdb-3bf00b3b3bd7}} . The final ensemble model achieves {{formula:6a9ec56b-6efa-480f-8f94-d76c026125dd}} average mAP on the HACS validation set, and {{formula:9d850e89-7ef3-44ff-a2aa-857e4e52780d}} on the HACS testing set.
r
d32d2366c11fe226b4f6a7765cded0cc
Several comments are in order. First, in our preliminary study we assumed that the cumulants of the net proton number are a good proxy for the cumulants of the net baryon number {{cite:d2e92ee9f3e55da95ecb383791e231003505b1e1}}, which is likely too crude of an approximation (see, e.g., {{cite:e0519ee5dd8e81dd5c10fce326c855200aaf83e6}}). Furthermore, we assumed that the momentum space cumulants, measured in the experiment, can be used in place of the coordinate space cumulants, Eq. (); this is also likely incorrect. Moreover, we did not take the influence of the rapidity bin width into account (which can be done by, e.g., employing finite volume corrections {{cite:117693903e3ef7e0d06cd453c059602b67fa09b8}}). Interestingly, however, a recent, more in-depth analysis {{cite:ae01775a386f95eff22bfbc384fa8c5487aa3612}} of proton number cumulants measured at {{formula:da78ee24-812f-4271-8dac-52568a15cfaa}} , taking into account some of the issues mentioned above, obtains (using Eqs. (REF ) and (REF )) {{formula:8e00fbcf-f558-4548-9d2b-8b7e20b01304}} and {{formula:0176d7d0-9b61-4654-acc7-aaa13303ccba}} , indicating a behavior that qualitatively agrees with our analysis while being even more striking.
d
2c576e0233c1285db76ef3a35704da5f
An apparent downside of the proposed approach is the graph and its adjacency grows with resolution of image (number of pixels/elements). This issue is partially offset by sparse storage of the adjacency matrix, in general, and largely ameliorated by data that is on the same discretization, as in this work. In future work we will investigate low-rank approximations to the adjacency matrix {{cite:c57cee444f3809bb279fa5b43cc9d46b5805363a}}, {{cite:8523a322e2facb34b553761adf508b5d4225f4f0}}, {{cite:3a8a3fe077a0c18272c5d85898bdc9feac990188}}, {{cite:bf91888677d16cf7a603a91844518456a20d84da}}, {{cite:acb5ed66d82ba3762473ff363badfc338543ad10}}, dimensionality reduction techniques {{cite:4462d0038bdc6d23f4e794e4f36354f0595c1bc2}}, {{cite:1b549c446fb1641c5098710dede509908414a4ff}}, and the use of graph auto-encoders {{cite:822c681592ae085c9eb959af1d0577c312e7dba4}}, {{cite:ee1dd05950519bfb6b6d15e988d18649c69abdbe}}, {{cite:77d0e3706ed729b3e28f0381d6e41f2da884042a}}, {{cite:fc02fa0831fd5c924ef80266e69025254bf08b1c}} to reduce the mesh-based graphs in-line. We are also pursuing the larger topic of processing image with multi-resolution filters {{cite:beeb906bedcabc9a72a46ff25bb8189b5e420fde}}, e.g.  spanning the pixel to the cluster level.
d
9166da5e5f2068b0ce00b886dec2b82b
The idea of missingness-pattern-specific analysis dates back to {{cite:cca83aee23e59a149b91b14d8798496066b953d2}}, {{cite:e5bb10bf1a1538c15a5ecc3144ba6d72bac59194}}, and {{cite:16c5ca90fc3f1b0605dc047ef439c664082e9ac2}}, yet its use for analyzing experiments with missing covariates remains mostly unexploited to the best of our knowledge. A key intuition is that the missingness pattern acts as a discrete pretreatment covariate, and thus allows for post-stratified estimators by averaging over estimators within missingness patterns. {{cite:2232b6944a7401673168de83cb1b94fa94b57e0d}} demonstrated the asymptotic efficiency gain of post-stratification based on the simple stratum-specific differences in means without adjusting for additional covariates. The {{formula:48d3cb36-2951-4139-8334-86b4f8390b9f}} in (REF ) averages over regression-adjusted estimators within missingness patterns, and promises additional large-sample efficiency over the missingness indicator method by allowing heterogeneous adjustments across different missingness patterns. We quantify the intuition in Section .
m
3ea9cc2e80999d7e2e5cc4e364fa4744
In this work we apply the chiral quark model (ChQM) {{cite:5607bbf47a7fa1ab926e42ee0af2bf413de11e23}} to deal with the strong decays of the singly heavy baryons. In this framework, the spatial wave functions of heavy baryons are described by harmonic oscillators, and an effective chiral Lagrangian is then introduced to account for the quark-meson coupling at the baryon-meson interaction vertex. The light pseudoscalar mesons, i.e., {{formula:89e5ec32-2188-47d8-840c-1e0cec38bcf0}} , {{formula:eb9a21f9-9685-4280-90de-892d0756bb36}} , and {{formula:db7e687f-086b-49f3-b6c1-93ed03f1ed44}} , are treated as Goldstone bosons. Since the quark-meson coupling is invariant under the chiral transformation, some of the low-energy properties of QCD are retained {{cite:5607bbf47a7fa1ab926e42ee0af2bf413de11e23}}, {{cite:a949e97c3b9c1ebf359186d7d1ffe7bfe8cf9c36}}, {{cite:2dc56cb1ca8c28a62a812ec5f744b4ae780601cc}}. This model has been developed and successfully used to deal with the strong decays of heavy-light mesons, charmed and strange baryons {{cite:8b5d1a81a5bd88e80f60771b0f394fe0848493e3}}, {{cite:ca1d55ed57e63322cb13cbbd1e3c310b22c8dddd}}, {{cite:dc1e27200ecb7b07b143adfd82f71f24fe019b95}}, {{cite:afce3d44f2a06df3ba8e0f3885190a6922cc73e8}}, {{cite:0e906535b43ff40c8d8d4c313712c54d0ac36715}}, {{cite:ef65105ca97d5b1590b7c64832a70e1ca2570e13}}, {{cite:0f8af042d196f2dd1507d9938b403d494f71a43b}}, {{cite:2abeda99187e085ef5fdb2ec4347253ea4744de4}}, {{cite:6f8b2158a93fa2c08c9fc1c13cdc6f7d8f592cfc}}, {{cite:25749ba7b3e654ebfdaa27c7b14dfd2a18f65ae2}}. This approach is different from the often used {{formula:6d0bc4d9-b989-4085-b311-b1e752b08d1f}} model {{cite:7edfb3a2ca7e34c5c86c9e661e2080ddd077f69f}}, {{cite:07711c358166d0dd517de3cf9b61175f8d69fbe6}}, {{cite:94cc1955cc203ff849619651cb3cdeb9a3b0d6dc}}, {{cite:c601e17a027f40f08d5b10ca66bc696bed923ae5}}, {{cite:f4059f998fea963934681f5755e0c6fcce9dfe4a}}, {{cite:5ee72aa81d9eb8713f36bdc230cb998a4d9df9de}}, {{cite:2ecdab37629e6f2f56a1c39e14a45b42efc623e9}} since different effective degrees of freedom are involved. In the ChQM the light pseudoscalar mesons behave as pointlike particles which couple to the light constituent quark within the baryons via the effective chiral Lagrangian. In contrast, the transition operator in the {{formula:5ea9f301-a786-4e0c-88db-ee49569ef2bc}} model is obtained by a quark pair creation with the vacuum quantum numbers {{formula:65cdb093-1be6-44c6-938b-c5444c8228db}} . The created pair of quarks will rearrange with the quarks within the initial baryon to the final state meson and baryon. Thus, the hadronic transition amplitude will be described by operators extracted at the constituent quark level. Many other model studies of the strong decays of the low-lying {{formula:6f3e41f2-9a9f-4d82-be85-d5d4699d8dd9}} - and {{formula:648085b4-c0dd-42ed-9941-65651fc8931f}} -wave heavy baryons can be found in the literature. For example, for the singly charmed baryons, the strong decay properties of the low-lying {{formula:84dea876-2924-46f7-a8d2-6dd7fcabbae6}} - and/or {{formula:ae45c107-0179-4da8-9b65-2e5f8a66de0a}} -wave states were studied with the method of light cone QCD sum rules (LCQSR) {{cite:9de31ed6ca43b5febe3262a13e8a609ce2801056}}, {{cite:4f8b59654c397e3a9a36446a8339afbea16b65c5}}, {{cite:5b78d381906b08ce7849efca04521f536392901e}}, {{cite:1bc1f637d6af451bcc94b60886b55b280b8851a6}}, the {{formula:da15a5ec-7b34-49ff-8f03-60ee89801b19}} model {{cite:c601e17a027f40f08d5b10ca66bc696bed923ae5}}, {{cite:f4059f998fea963934681f5755e0c6fcce9dfe4a}}, {{cite:5ee72aa81d9eb8713f36bdc230cb998a4d9df9de}}, {{cite:2ecdab37629e6f2f56a1c39e14a45b42efc623e9}}, the heavy hadron chiral perturbation theory (HHChPT) {{cite:7382185211d90aa47920cba4666f4795dadb1257}}, {{cite:a4f764bbfc6984205c82bbf539f9b368e2fddbe5}}, {{cite:3a7f742b6d2579640ba45da7f2a151d20b708722}}, {{cite:668ad20c084b7dbef707d62eff6196110f4aee43}}, {{cite:e685402dc57826c0c71d71160a4c054121da56f1}}, {{cite:896bb56d47a45e9c1372d2ac8d6341178e0bc373}}, {{cite:4f4fe190f25e2d007896d5960801193095f7ad4e}}, the light front quark model  {{cite:e1946ff1c7c043cfff082187ab03bd615a8bfb08}}, {{cite:b2b67bba60cf3c4c1385d441c0507b35092239ad}}, the relativistic three-quark model (RQM) {{cite:d22161b8e78ec14ab4f8217f9739c62321a2710f}}, {{cite:d1834e5b9885e68fe8e1ae53012bf12ecfcca7b8}}, {{cite:f2382974c49b956be71916d2cd3d85157ecd5ff8}}, {{cite:cf7e14ccb3cdbcbc5e5c7118807992cae94cbc35}}, the nonrelativistic quark model (NQM) {{cite:adce71c74402ef83e5a6dff6584a2e4fb61007d8}}, the MIT bag model {{cite:c7e8bc87d7fe360d6f00ebd8b238cc5ae1d05d58}}, and the Bethe-Salpeter formalism {{cite:d6ddf81768a57fb9c7e55b33f6f9d1c7a07d4bcf}}. For the strong decay properties of the singly bottom baryons, only a few studies are found in the literature {{cite:19b4817fbeb31465498128be5a92c97b746f81f7}}, {{cite:d6ddf81768a57fb9c7e55b33f6f9d1c7a07d4bcf}}, {{cite:c7e8bc87d7fe360d6f00ebd8b238cc5ae1d05d58}}, {{cite:0e906535b43ff40c8d8d4c313712c54d0ac36715}}, {{cite:c601e17a027f40f08d5b10ca66bc696bed923ae5}}, {{cite:b952f28786703665f3221f46e5028e5fa9c09c62}}. While most of the discussions focus on the {{formula:4532616b-e92a-4bbf-a6c1-01f45b4c9e95}} -wave ground states, a systematic study of the strong decays of the {{formula:0e792d77-aec2-4440-82a3-b7990776371e}} -wave singly bottom baryons seems to be needed.
i
97e1dd5b9753df79a775eebc2152640c
To tackle the real-world data, which may not have a set of prototypical examples representing the data well, we can also utilize both the prototypical examples and criticism samples that don’t fit the model well {{cite:49969e13773d4f7dbdb013bc79d0f19209767587}}. The MMD-critic (maximum mean discrepancy-critic) method uses a Bayesian approach to select the prototype and criticism samples and to provide explanations that can facilitate human reasoning and understanding of the model.
m
59077ce0d354b2e3de00ab33cfbbdc72
Because of the specific boundary conditions {{cite:c07800ef2712261c7d29a90e8c0c96afb72a8de0}} and the importance of including the demagnetisation energy contribution, our predictions cannot be directly applied to other helimagnetic materials without repeating the stability study. For instance, although the size of skyrmionic textures in this study was based on cubic FeGe helimagnetic material with helical period {{formula:ce93f35e-86d4-4a51-9fbd-2e1cbf5bf291}} , in order to encourage the experimental verification of our predictions, this study could be repeated for materials with smaller {{formula:d9dc53b3-5909-4121-8a5d-d9b893b37500}} . In such materials the skyrmionic core size is considerably reduced, which allows the reduction of hosting nanostructure size and is an essential requirement for advancing future information storage technologies. Similarly, the ordering temperature of simulated FeGe helimagnetic material, {{formula:202e67ca-bbfc-408f-9719-d869ccef56a9}}  {{cite:831a7537aaeb413de4d358de184095f96e6ed4e3}}, is lower than the room temperature, which means that a device operating at the room temperature cannot be constructed using this material. Because of that, in Supplementary Section S4, we demonstrate that our predictions are still valid if the ordering temperature of simulated B20 helimagnetic material is artificially increased to {{formula:4735ab7c-d79c-4ae0-9a31-73930100988a}} .
d
9366837de71eb841547c0705ad90987b
One of the important conceptual problems in theoretical physics is the origin of a mass {{cite:67f4d61571e50555027ac5d7fcf1c98d9dc09161}}, and hence the existence of the mass gap itself {{cite:4d0fad8fe4d40492041753f7135d10b74b836231}}. Our findings provide new insights into its dynamical generation at the fundamental quark-gluon level. We have explicitly shown that the initial exact SU(3) color gauge symmetry of the QCD Lagrangian is not a symmetry of its ground state (vacuum) from the dynamical point of view, without mentioning its well-known topological complexities at the classical level {{cite:9c3a39fe36f09b28d5a5a8f78c916b4d7ae3e746}} (instantons, monopoles, etc.). Quite possible that just due to our claim that the symmetries of the QCD Lagrangian and its ground state do not coincide, QCD is a self-consistent quantum field gauge theory. It needs no extra degrees of freedom in order to dynamically generate a mass.
d
fd555eeec5d0957441821f63fb41bfa3
where {{formula:2f6bcb38-97b0-4a64-b44e-eb4b5d98d0e9}} denotes the next state given the current state {{formula:3d4ee4a0-a2de-4f31-a9f8-c145021835fc}} and action {{formula:53d3c06c-cec8-4829-9f0f-3432ffc05dd5}} . It has been shown that {{formula:af641105-2c24-4d7b-a7e8-6519612f9382}} , meaning that the TD, i.e. {{formula:4721c955-0eed-4f71-8761-a238664844d2}} , can be used as an unbiased estimate for the action advantage {{cite:12c6389b8f34a3e37fb2544502220b50a7ac5ad6}}, {{cite:ff70d706906f993c8af3b7c98d27e5c5d886bda4}}, {{cite:f648731915ba9891e37b40f7c0195bbc53875563}}. Hence, we have {{formula:876c7aa1-1c44-46a0-b6ce-ad46bbb2d784}}
m
bde9b94dd5ee58cd4e850d771a2a10cf
Design choices of AutoCI. Dissimilar to generic algorithms, clinical algorithms must deal with unique challenges in terms of ensuring the safety {{cite:14f3595a6e553287c5e9cd817ff9beabb03ca256}} and robustness. Error-prone algorithms can potentially lead to critical errors in medical care. Driven by the need to develop safe-critical applications, AutoCI is carried out with a type-safe program synthesis method {{cite:5a7f865fd8d7f94e0ffde6b6067f14f09cd2e0ba}}. By further incorporating a newly proposed causal-aware module into this framework, we are able to synthesize a subset of differentiable type-safe candidates well suited for causal-aware learning. Compared to the laborious and error-prone manual function design, this implementation improves the efficiency and safety of AutoCI. Moreover, to achieve the robustness on the real clinical tasks, we introduce a novel causal differentiable learning scheme that utilizes the Fréchet inception distance (FID) {{cite:efaf38b3104d6d4f2ddfc883d680944e7dd76448}}. As a whole, the proposed AutoCI is the seamless integration of both components.
d
dc1fe17cf152ee81796dde0d0e49dfea
Supersymmetric theories with eight supercharges in five and six dimensions are a very rich subject that has been investigated over the past decades. Lots of recent progress in this subject have been made in the classification of 5d and 6d superconformal theories (SCFTs) {{cite:122a540b35112c6e06a76e4c1d9e590d40cd8500}}, {{cite:a1e638835b22ab7023ec8854dedd1f24866c19a5}}, {{cite:d6a3a8414a5455c4c7a38425dcf1cc9d26f44aa0}} and 6d little string theories (LSTs) {{cite:ef070c8c657e38c378e412d527d47c3a7a8d828f}}. Such classifications have been carried out based on geometric properties of F-theory compactified on local elliptic Calabi-Yau (CY) three-folds. Also, a large class of 5d SCFTs has been classified using gauge theoretic constructions {{cite:c12f456a8adfa1b6c8886f447900a1db2ca74a40}}, {{cite:bf2d1a350a71f28a24ddb5cf875accfe9496987f}}, {{cite:7de40e13ed98c69339eb6c3292c592fb65138fc1}} and M-theory compactified on local CY 3-folds {{cite:5906aa100b26123da8806fb850b7f4144dffecff}}, {{cite:bf2d1a350a71f28a24ddb5cf875accfe9496987f}}, {{cite:ec8e7ec19046bf8b977e529e31047af5db2a8a15}}, {{cite:c345cfb2a58e48d8f37c6d908f3570e685e31576}}, {{cite:f8d8b1f99b78466df3c1f48b4f62f6f857bfa109}}, {{cite:257e8a8a4d15133cbdd75edd7c69841b9ac6f5e9}}, {{cite:17d87c1c775cf39ef4fd9cfcb10bb246409678e0}}, {{cite:e99fe97f3831c1e082369a1324862fab8b363df4}}, {{cite:8ca1a4a701d04d2f46bd1ba8c155b0cfea466538}}, {{cite:ee26374c5689798e60488280100c40cd479e3166}}, {{cite:2e818a4ce50014aa0ec911b7aedeae8fec3cf610}}, {{cite:3bbd2687c30d9200c7f01ab78db4fea5a0daef66}}, {{cite:a621da913e046d497765dfa183e1f7da3b01f9ba}}. These higher dimensional theories turn out to exhibit several fascinating features of quantum field theories (QFTs) such as the existence of tensionless strings, dualities, and symmetry enhancements. Moreover, they have played a pivotal role in constructing and studying lower dimensional QFTs via compactifications.
i
6ebeb528b9c9cd88e8d2f7036e124c28
Particle filters often perform poorly for high-dimensional systems due to the fact that the particle weight typically concentrates on one, or a small number, of particles –see the work of Bickel and Snyder in {{cite:78c23b08f31d9f3a172b0fcaa20b3e479e4f9cbe}}, {{cite:2773b3c7f061022d5c23412912bea66af678da25}}, {{cite:62fc55687a730971af8c9331e6595fb0e4eb52fe}}. This is the issue that the optimal particle filter tries to ameliorate; the paper {{cite:461909c94e92bc858f5fff99191a27783b66b042}} shows calculations which demonstrate the extent to which this amelioration is manifest in theory. The optimal particle filter is discussed, and further references given, in the very clear paper {{cite:e0b5cfd91fa7f6c359499b7e6ec91d92cede1967}}; see section IID. Throughout much of this chapter we considered the case of Gaussian additive noise and linear observation operator in which case the prediction step is tractable; the paper {{cite:e0b5cfd91fa7f6c359499b7e6ec91d92cede1967}} discusses the more general setting. The order in which the prediction and resampling is performed can be commuted in this case and a discussion of this fact may be found in {{cite:fed0a3e221caf0c80cc9f33061630c80f1a81e5f}}; this leads to the distinction between what we term the GOPF and the OPF. The convergence of the optimal particle filter is studied in {{cite:fe0866abf8509338bb9fef09d84e9310ceeeb89a}}. The formulation of the bootstrap and optimal particle filters as random dyamical systems may be found in {{cite:194555ae3dfcdc54269dc8441ee5a48f0e9e1485}}. An attempt to alleviate weight collapse by introducing alternative update steps can be found in {{cite:62fc55687a730971af8c9331e6595fb0e4eb52fe}}.
d
17a3f9b11b16ebe27a89c1e97bbf4491
Generally speaking, the megastructure might be constructed by advanced Type-I civilization from extraterrestrial resources without launch costs {{cite:b0fb074c7f4bd66c6cb658c94e27788cab0a5250}}, but let us consider the worst case: the Solar energy is stored and then utilized to launch material on the orbit.
r
3c07bd9a66d240495def213257c76cb2
Conclusions.–Result 3 provides an efficient way for verifying special multipartite entanglements. This intrigues a natural problem to explore new way for general multipartite entanglements. While the entanglement is the weakest nonlocality of quantum states, one may explore new hierarchies in terms of the so-called multipartite steering {{cite:0e217c74f2f458e9de0b8f0c206ede468aba0c9d}}, {{cite:ea1ba38f2b1b95f30775963cb11245e2234c0357}} or Bell nonlocality {{cite:38c98cda9b1a9a71a83c7e0c9481447da07ee712}}, {{cite:4e1ca20e226ceaf6a0cc2df793c031cf17de290b}}. This is of special importance for recovering novel multipartite nonlocality beyond bipartite scenarios. Additionally, the present model shows the first example which shows converse multipartite nonlocality to recent quantum network model {{cite:a8d6bff230adb665131f1c3e0ef0d761bf04cefa}}, {{cite:bf2e5d633f615b2f1b229549582b10c05f418f0e}}, {{cite:59cba5c6c5429f8213d059555c6b4590e8fa3c1a}}. This intrigues a basic problem to explore the intrinsic nonlocality or the most reasonable model for multipartite systems.
r
7d158c65d5b5703af81e80a826821b2a
Assumption REF is required by {{cite:ed2ed217a6f73a2d24d35fda47a26df1c0ea2231}} to ensure that the iterates generated by randomized solvers converge in expectation. It can be easily verified for some sketching matrices. For example, in randomized Kaczmarz method, {{formula:c163c70f-ddd6-45ea-bd2e-a219ca352274}} with equal probability where {{formula:55735ee1-217d-4f3d-8a00-51b73be1267d}} is the {{formula:2af9bb35-4783-4746-9b33-5cae949424e7}} -th canonical basis of {{formula:4064b086-05fb-440f-92f1-5059bf4f7803}} . Then, we have {{formula:b4a2e43b-b1a5-4ad4-958c-088301e9041a}}
r
b6657d51c083698c9da198ebd5edf1da
In both our benchmarks, models based on RealNVP {{cite:26222d9ef4a3e31e218b2411d68914731a80228e}} and the standard autoencoder take the lead, while other invertible architectures seem to struggle in various ways. Success in our experiments was neither tied to maximum likelihood training, nor to the use of a supervised loss on the forward process.
d
2d1599f431f72e2fad4cef374ac13daa
The IPW estimator {{formula:cd93fb76-7c3b-4ae4-a6b1-4ff655c5b6c8}} is the same as the regression estimator {{formula:29e0e78d-2a54-4e53-b8ef-56b76461a1da}} when {{formula:abaabbee-6301-4c10-aca9-553ba9301a4e}} is discrete, but when {{formula:8ddeec68-df62-4886-b271-1ea9447232c1}} is continuous, generally, they are different. By taking a glimpse at {{formula:94edaa9d-4b5c-41fc-ab2a-de395227bb46}} , the estimator weights the observed data by the inverse of the probability of receiving treatment or control. Intuitively, a subject represents larger population if he/she has lower chance of being sampled. In practice, it is common to normalize weights to reduce the variance of the weighting estimators, leading to a more stable estimate {{cite:240a30271a37aa7af0c0699ee039bd561c058e32}}. From the perspectives of semiparametric inference, {{formula:18cf275f-3efc-47c2-a2a6-216939277c84}} admits asymptotic linear expansion and reaches semi-parametric efficiency bound so that no regular estimator can improve its asymptotic performance, in other words, {{formula:a125dc6b-3a44-4ff1-83fc-f1b6aece2539}} is an optimal estimation of ATE {{cite:240a30271a37aa7af0c0699ee039bd561c058e32}}, {{cite:06f93d93722686311cadde9f194fd523bd63fea8}}. Even though IPW estimator {{formula:4b38fb00-e153-4728-a3eb-3dfb12e7fcf6}} has good theoretical foundations, its unbiasedness and consistency highly rely on whether the propensity score model is correctly specified {{cite:48c1a2abc6cbf9c581bb9e711050a47b7b59a61b}}. Some researchers proposed using machine learning models to estimate propensity scores and {{cite:f3abe2aee3852e98f01d2c1401ce68f11655a150}} has also showed the improvement by simulation compared with traditional logistic models, however, {{cite:157c08cc0f24c645b084134bc100a7d7fa3a3613}} pointed out that black-box machine learning methods make little difference in real data. Additionally, similar to other propensity-score-based methods, {{formula:cb4ae4d1-22f5-4a23-92b6-e3474010388b}} does not perform well when the estimated propensity scores are close to 0 or 1. To solve the issue of unstable IPW estimator causing by extreme weights, {{cite:8d1bd0a626c6c950a1ec358ce06e487e95045ef4}} suggested further adjustment such as trimming the extreme weights to exclude subjects beyond the range of the common support region.
m
4b34f8ca65127cf12a323355754de0c8
State-of-the-art deep learning models in AI, approaching or even surpassing human's object classifying capabilities (such as {{cite:95d6c8784c4eb6c56cd620ea4f64a7819c44f3ef}}, {{cite:2e6363aee56f4c281256819b7d204d4eaadf33ff}}), require vast training sets comprising millions of training data {{cite:8c695aa8dea9c1ff265885ed5ad6817c5af68735}}, {{cite:969570727aa19bd521fcc1e3d31e233b34b946a1}}. These requirements are often necessary to ensure that the models do not merely memorise input-output relationships but also generalise well beyond the data they have been trained on. Indeed, in the simplest binary classification setting with the loss function returning 0 for correct classification and 1 otherwise, expected performance {{formula:20daba72-d839-403b-bd2d-ce3cb0ce317a}} of the classifier, expressed as a mathematical expectation of the loss function, can be estimated as follows {{cite:2d37ff70ced8b8f22241d0aea648a6ecf8a9af68}}: {{formula:9c80903b-0d4a-4961-81ab-0ed02d48b3d8}}
i
33e7cad11b79f3192fff13ca65b9c9d9
Theoretical analysis of transfer learning. Prior works on transfer learning mainly analyze linear probing {{cite:29507c8992f11738f3530f3b24405ede4d08ab3f}}, {{cite:c21f8f9c420eca05128bfa4c38b625ed21e44d45}}, {{cite:7d1c6e9d1c48fd7b308853c6d12cf33efed1d2c2}}. In recent work, {{cite:7ce828b38e6202d52eff409be11a9fba2eaaf09f}} study regularized fine-tuning in an underparameterized regime where there is a unique global optimum. In contrast, our analysis studies the overparameterized regime (mirroring modern settings of zero train loss) where we need to analyze the trajectory of fine-tuning from the pretrained initialization because there is no unique optimizer of the objective function. Prior works also focus on ID error, while we analyze OOD error. See Section  for additional related work on theory of overparameterized models.
d
242515d83ee839abdde3bdf5c47c3924
For the prediction of patient outcomes after treatment of brain cancer, most machine learning studies have focused on MRI-based prediction of progression-free survival or overall survival, which will therefore be discussed in more detail here. A systematic review by Sarkiss et al. identified nine articles on survival prediction in glioma, and two on survival prediction for patients after stereotactic radiosurgery of brain metastases {{cite:8857682e752b1a7b734a1c4c76dc9c0903da6cf6}}. A more recent systematic review by Buchlak et al. identified 17 studies on survival prediction with performance estimates (AUC or accuracy) mostly in the range 0.7-0.8 {{cite:4c4dfbbfd410f22ed1578b2c9ae2509d444c5fad}}. Among those, only one study reported results of external validation, predicting overall survival of patients with low-grade glioma, and obtained an AUC of 0.71 with a model combining radiomics with non-imaging features including age, resection extent, grade, and IDH status {{cite:11e2631b26b0a15fdb17e9c219b3878e1d517776}}. Random (survival) forests and support vector machines were most often used methods. One study used a CNN as a pre-trained feature extractor {{cite:117e8ab70b8432177b5aedd998d311b11c0b6544}}. Other recent approaches using CNNs to extract features that are subsequently combined with other factors into a final prognostic model include {{cite:41eeed4b8ac5a8412b9adc8fcb7f0a16943c308f}}, {{cite:9962cf77be66b2d2af8f7583f1a5947bd394b6f1}}, {{cite:5a9d66d7f93154ed2d26d02802595613e91d5b75}}. The 2017/2018 editions of the well-known BraTS challenges also included a task on overall survival prediction, with best teams obtaining accuracies around 0.6 in a three-class classification setting distinguishing short-, mid-, and long-survivors, {{cite:766a76f1934bbd9b2e52e9b6a6c8007a4d3b9fde}}. Here, it was also pointed out that conventional machine learning methods outperformed deep learning methods, likely due to the limited size of available datasets for training.
m
eae7ba6ea5e5267ba997872424897e7e
To directly evaluate the accuracy of the built correspondence, we evaluate the warped exemplars on DeepFashion dataset where paired data are available by treating person images under different poses as the exemplar and the ground truth. Hence, we can measure the distance between the warped exemplars and the ground truth with L1, PSNR and SSIM {{cite:d1202c3b14176dba1536bb22a9baf55801be7011}}. Specially, the margin parameter {{formula:c8263b53-cc45-48a5-8a66-1226c89e47b3}} plays a key role in MCL, we thus conduct experiments to investigate the effect of {{formula:48b41999-39a9-4449-bca7-93c91b33d4ea}} . As shown in Table REF , the vanilla correspondence is selected as the baseline. By varying {{formula:48c82043-dd30-4bc4-a75f-1f680dc7371a}} from 0.1 to 0.4, we can observe that the correspondence accuracy is improved consistently with the increasing of margin {{formula:12bd8f4d-a377-48d8-8052-adbc1f55c9bd}} . Although large margin {{formula:c975bcfb-d710-4e69-bafc-74bed6c3e272}} contributes to the correspondence accuracy, we find the model tends to be unstable and even fail to converge with a large margin, e.g., {{formula:c5bdc83c-7657-4ea8-b300-7e58725c037c}} . We thus select {{formula:18a4f16a-ad37-46ba-acd7-344e0a85fe3d}} as the default setting in our MCL. Besides, including the designed self-correlation map also improve correspondence accuracy substantially, and combine MCL ({{formula:7aaa7753-6792-4112-9e48-9dbfe09363e5}} ) and SCM yields the best correspondence accuracy.
d
9c72b69ce56bc8f090e2c189e096eb0c
By introducing a periodization procedure in momentum-space we were able to analyze our result in terms of experimentally observable quantities in the nodal and antinodal points of momentum space (section ), making contact with recent spectroscopy experiments{{cite:823e21a0849de8137b21ac6e48ac302e61e037f0}}, {{cite:afdce62ad4a682dee263cf0f3f3281f80ceaccb8}}. In particular, we were able to interpret the two energy scale in terms of a pure superconducting gap (dominant in the nodes) co-existing with a normal component gap (related to the pseudogap of the normal state and dominant in the anti-nodal region of momentum space at low doping). We complete in this way the work presented in the short publication of ref.{{cite:d9ebb90d934063d236f1d30aa01d01ead5430d85}}.
r
5fd919f1779a8955b77b921e52fad26f
Assuming the finite entropy of de Sitter space implies that the microscopic quantum gravity description involves a discrete spetrum of energy eigenstates, that are presumably most effectively captured by a holographic theoryRecently, some properties of such a holographically dual description have been investigated by considering a de Sitter version of the Ryu-Takayanagi formula {{cite:5424bfa21a2ab7ee531c6d41adc33d12d3d4edbe}}, {{cite:953c8e6ca4dfff84e6729fb78eb75b62b628db1f}}., on general grounds one expects that the late-time behavior of correlation functions should be quasi-periodic. This is obviously analogous to Maldacena's original observation in the context of the AdS eternal black hole {{cite:5e6664522dcc69ee69569388d43753edb196a5a0}}, and also closely related to the incompatibility between the absence of a finite-dimensional representation of the de Sitter isometry group and the finite de Sitter entropy {{cite:6c385960a6f16938f8ec7b12213b55de82f8a9d5}}. Using a geodesic approximation we have seen that the two-point function (REF ), besides an oscillating part, is exponentially suppressed at late times, related to the timelike part of the complex geodesic. We note that this is strikingly different from what happens in the AdS eternal black hole. In that case the exponentially decaying behavior is related to the exponential growth of the spacelike geodesic probing the interior of the black hole {{cite:5e6664522dcc69ee69569388d43753edb196a5a0}}. For de Sitter space the exponential decay is instead generated by the timelike part, which does not probe the region beyond the de Sitter horizon. We believe this difference is important when considering non-perturbative corrections that could halt the exponential decay.
d
83229e9cfa8d40280f0393b22c7043d6
In this study, we empirically demonstrated that the final BN layer could still be eliminated in inference without compromising the attained performance gain. This finding supports the assertion that adding the BN layer makes the optimization landscape significantly smoother, which in turn renders the gradients' behavior more predictive and stable – as suggested by {{cite:a4b287bf93a36edefdd68afa0524b7bb109e28c2}}. We argue that the learned parameters, which were affected by the addition of the final BN layer under imbalanced settings, are likely sufficiently robust to further generalization on the unseen samples, even without normalization prior to the softmax layer.
d
868b11cfe4c1e78a289a2ba4f4a94a92
The fundamental matrix solution {{formula:351a6d49-7cb4-4e58-af84-5d5be0bdfbd8}} of (REF ),(REF ),(REF ) in the {{formula:924ee01e-37e9-4b03-ac49-c0dada23ab9a}} -periodic problem, such that {{formula:357dd7e5-be81-4730-81e8-073f7ee06494}} , where {{formula:c3453638-5286-4502-9b22-c56a3449abbd}} is the identity matrix (see {{cite:e5390442fed759a3e405e61ffd53f8f80e9251b3}}), is an entire function of {{formula:38e8fe2f-6488-4c4f-aff5-895f92780b31}} . The eigenvalues and eigenvectors of the monodromy matrix {{formula:19e38106-3ca6-4fcd-85d2-92dcd5b4d509}} are defined on a two-sheeted covering of the {{formula:ef0f70e8-0fa1-434a-a98b-fffa1571aa7d}} -plane. This Riemann surface {{formula:fcd6f005-df6f-4013-95f5-4c93abf1dccf}} is called the spectral curve and does not depend on time. The eigenvectors of {{formula:4521850e-f93a-4166-9282-90585b94675e}} are the Bloch eigenfunctions {{formula:8cfb0e37-b754-499e-a287-dc93f5b2eece}}
i
04db991e2aadaf4a2b7211063d001fd6
We view our study as bridging recent deep learning advances in semantic representation with educational applications. Predicting, characterizing, and ultimately, optimizing the quality of a learner's initial encounters with content has many potential applications for both human and machine learners. Our results showed that 1) our attention-based deep learning model can be effective for predicting the instructional aspects of contextual informativeness, 2) that our model can also provide interpretable results on how context words are used to infer the meaning of the target word, and 3) identifying low-informative sentences and filtering those out from the training set can significantly improve the quality of word embedding models, as measured across various sentence sizes and similarity tasks. For human learners, contextual informativeness models could be applied to diverse sources of classroom-generated text, such as video transcripts or class notes, to find the most supportive lecture contexts that help learn or review specific terminology. Search engines could emphasize the most contextually informative educational Web content examples for a given term or concept. Using custom pre-trained models, like BioBERT {{cite:50b898bd88db120965065ad3a486c5a432a7d57a}} for biomedical terms and content, would enable more domain-specific applications.
d
3e57c86360f3b6eaf231dd6293607708
The dimensionality reduction techniques used to generate the projections are principal component analysis (PCA) {{cite:4506eb0c18319848c8245fe2c72166740df25a2d}}, multidimensional scaling (MDS) {{cite:5502c5e2df23bc13e7d6977740f750169685d560}}, isometric feature mapping (Isomap) {{cite:a326d0794969c58d3a372f0b90656a2446232c81}}, {{formula:23ddf57f-5b06-4813-8336-b16b6c7c1780}} -distributed stochastic neighborhood projection ({{formula:4a21fe2e-f671-4d23-99c9-4eb86b04787b}} -SNE) {{cite:e3dc833f18c873a63c147f2ea73489508e96f48e}}, uniform manifold approximation (UMAP) {{cite:f68befbd9e71bf1056bfa5fea926d81392d47e8e}}, locally linear projection (LLE) {{cite:8b66611cdd91fc8b3cf5997fb1f509ed122f5c1f}}, Spectral Embedding (SE) {{cite:47960143b061c1e7b450b95861f3b6b088ece683}}, and Gaussian random projection (GRP) {{cite:be445ce6d5c55cfe622a98a95e378b9083fdc957}}. For techniques with hyper-parameters, multiple projections were generated. One hundred projections were initially generated for each dataset and, then, 25 projections for each dataset were uniformly sampled based on the metric space to be used in the user experiment. Finally, we manually down-sampled projections that appeared very similar, e.g. rotated variants, or duplicates of one another. This process resulted in 15 to 20 distinct projections per dataset. An example of the selected projections can be seen in Figure REF . The parameter settings of Isomap, LLE, {{formula:a09e8a47-d9f2-486c-bf17-e5a6a638765c}} -SNE and UMAP can be found in Figure REF (right side). In the next step, we showed these projections to users in an online experiment as detailed in the following section. {{figure:c4248ede-f251-4f04-ad4f-5f0eac3cdb2c}}
m
a3709ec6d4c3e10d90c54b5f0d75f712
Remark 2 Note that the singular set of our area minimizing surfaces comes from self-intersection, or more intuitively, of crossing type. In real analytic metrics, immersed minimal surfaces are locally real analytic varieties, so they cannot possess fractal self-intersections. Thus, if we strengthen Almgren's Problem 5.4 in {{cite:25d8e87c82357b49e7db8961170aa848dac88fc2}} by imposing the restriction of real analytic metrics, then the stronger statement still remains open, no matter how we adapt our method. In particular, we still do not know if minimal surfaces can possess fractal singular set in the Euclidean space. (In Simon's work {{cite:dbc371982960c0c8d72489fc0ce856c62ddd7a61}}, he also needs to perturb the metric smoothly and non-analytically.) Moreover, around any singular point, the surface is locally reducible into two smooth pieces. It would be very interesting to get locally non irreducible examples, for example, with true branch points being the singular set. In some sense, the locally non-irreducible singularities are the more genuinely singular points. One can compare the situation with Theorem 1.8 and Conjecture 1.7 in {{cite:41238fc23df06e92dbcdfd0385741492652083be}}.
i
0f582bc13bc9e40f629e077881b617de
The present model given in Eq.(REF ) is derived from the distributed settings of entanglement generations {{cite:4b820b4d0a409593e5d41a39d750cd30d9f4221e}}, {{cite:9404d668f2ebc4e76326d417762f9b2aaacddf63}}. All the entangled states that have the decompositions in Eq.(REF ) are not symmetric from Theorem 1. This geometric feature has a strong restriction on the resultant from a generation procedure based on quantum networks {{cite:992aa76f6ee24aefaf46dc288458b2e9f78d0d96}} without classical communication. Interestingly, this shows a new kind of genuinely multipartite entanglement going beyond its verified by all the previous local models {{cite:c270483cbfbd4d105d9b870fcbd095d2052384ba}}, {{cite:cc59694ebfbcda348d2850f8d86d80601bb5ee13}}, {{cite:9a90ed92af6afc9579bd445ddfc2b161849c95af}}. Specially, the present model in Eq.(REF ) is stronger than the previous biseparable model {{cite:9a90ed92af6afc9579bd445ddfc2b161849c95af}} that is used to verify the genuinely multipartite entanglement, as shown in Fig.REF . It means that all the new genuinely multipartite entangled states in the present model in Definition 1 are genuinely multipartite entangled states in the biseparable model {{cite:9a90ed92af6afc9579bd445ddfc2b161849c95af}}. The converse is not right, see examples in Fig.1(b) and (c). Theorem 1 presents some interesting examples includes all the generalized GHZ states, Dicke states, and generalized permutationally symmetric entangled pure states which are new genuinely multipartite entangled states in the present model.
d
18619b15ab0f75c4abaa6728c440e1f1
Fact 3. (see e.g. Feller {{cite:89b5ecf5693f1f5f6c12308271174383119799cb}}) For {{formula:22db4469-6803-4e25-a81e-81b43e5dd9b2}} we have {{formula:ed283848-dc61-40b7-b2e8-ef6a0e554c9e}}
r
5a43a60bfbe8fdf1d21ed4988d229d34
Before showing the results, we briefly mention the parameters involved in the discretization and the numerical setup: on the gravity side the bare coupling {{formula:ef5518d4-896a-40d5-bdcf-3cf01277dad9}} acts as a cosmological parameter in front of the total volume, since the path-integral is weighted by {{formula:e2ce055e-a0b4-4620-95cb-3456745612e9}} ; in this respect, {{formula:bf8141f5-b860-4b86-b34c-daef458d1236}} can be interpreted as a chemical potential coupled to the total volume {{formula:afcd5934-0f81-4ea6-8b34-44cd1ca0a5de}} : lowering its value results in an increase of the average volume {{formula:33ea60df-b6c7-4309-a0ba-805da9bfea8b}} , up to a certain critical value {{formula:7ff0ccea-757a-4b12-bfb8-b79b6b1ca604}} below which the average volume is diverging. For two dimensional CDT, this treshold has been computed exactly by analytical means and has the value {{formula:34a44be8-df35-4a80-8496-b58c9b31d333}} (see Refs. {{cite:3a7a3a96d11e28cb5fc115f4fa52fac91d1f2354}}, {{cite:8ad119e1169c4b5077eb3204bb756cb3403ddb04}}, {{cite:afc2cd436208b703eaf16fbaa66780b370e8263e}}). In general, close to the critical point, we expect not only the average volume, but also other observables to present a critical behavior which can be fitted to a power law scaling of the form: {{formula:5dec51ae-638b-4f24-8cf1-231c1a51d28b}}
r
eb540b2c12c678681b8aae0ba8d77b95
where {{formula:dc5ab39a-c986-47b5-af85-02719756f4de}} denotes the identity matrix. Note that we allow the variance {{formula:a3a820de-01b6-447c-b0e4-2bf9f1b1240c}} to increase with each step {{cite:9a2b3bb40bd2009007322170860ee9076cecd229}}, {{cite:a34ff1d9e69d1408e5b1a33e443f1097db2ac0a0}}. The forward diffusion process is repeated for a fixed, predefined number of steps {{formula:2167deef-803a-49dc-bd81-b9607e6ab913}} . In our case, in line with the literature, we set {{formula:50e69d3d-5f81-4b30-b6a1-35e7f229fe3b}} .
m
9d8419c0569aa2aaa38367e5d8d7d9f8
and the coefficients {{formula:623ddd56-a4e0-449c-923b-003c33abe609}} are given by three-term recurrence relation {{cite:10674d66d78c8b53f1a035687b40ba41794bfcaf}}. This solution can be reduced to a confluent Heun polynomial of degree {{formula:d0279821-eed0-4632-9393-d674954cb1f1}} provided that the following conditions are satisfied: {{formula:743e49c1-9e32-4dca-8d61-0ed9e8545456}}
m
5be9e66081e4581ce98b8349ef25ef88
Experiment 2 aimed to explore how the dataset size used to fine-tune the models affected the overall performance. The findings from this experiment showed that, although a larger amount of samples will guarantee higher correlation and lower error rates, the performance gap is not necessarily large. This behaviour, where wav2vec 2.0 models report stable and moderate correlations, was also observed in {{cite:a240d97e8ab3fda0719fbc95b10af86649f20742}}. In contrast, the performance of NISQA baseline models, trained with different architecture settings, showed noteworthy differences across the evaluated datasets. These baseline models show the best and worst performances for several datasets. A similar fine-tuning experiment using NISQA would allow us to explore and understand how is the size aspect affects NISQA.
d
e2e2bfedcf96c5a8ad4c9c31406a7eb1
Different social networks have been working to identify fake news and warn users. It is pointed out that these actions may increase social welfare {{cite:e8cca4835b7e66b5610216a29c344d372de2fced}}, but identifying fake news sites and articles also raises important questions about who becomes the arbiter of truth. Notice that the more an opinion meets one's expectation, the more it is likely to be approved and shared.
i
84dd4381045b511fd3016b903073d9a2
Recent advances in wireless communications and smart device technologies have promoted the proliferation of Internet of Things (IoT) with ubiquitous sensing and computing capabilities to interconnect millions of physical objects to the Internet. Nowadays, IoT constitutes an integral part of the future Internet and has received much attention from both academia and industry due to its great potential to deliver customer services in many aspects of modern life {{cite:cebdf5453f440cc998fc9eed22b003f972dc0c6d}}. IoT enables seamless communications and automatic management between heterogeneous devices without human intervention which has the potential to revolutionize industries and provide significant benefits to society through fully intelligent and automated remote management systems. {{figure:8b0f603e-966a-44dd-b5dc-e92a4c4212cc}}
i
11130db141a2c1efed75cece7674d6ce
We extracted different hand engineered features like word {{formula:7296a516-421e-4b1a-bdb0-b39c9beffeae}} -grams, sentiment polarity, punctuation frequency, word frequency, emoji frequency and profanity level from tweets. We weighed {{formula:c499ad8c-2930-46fc-981a-30d49758f398}} -gram features using their term frequency - inverse document frequency (TF-IDF) scores. We then built a Logistic Regression classification model using Scikit-learn {{cite:50d381bfbb9c5c36af383b3a7d079d74bd018e6e}} library.
m
2f7a1104e7ae650a333d53abf94c34bf
These methods aim to directly generate images of a person in novel views and poses using image-space rendering. Earlier methods treat the problem as an image-to-image translation task. Given an image of a target person with image representations of keypoints or dense meshes or semantic labels, these methods use an image translation model to directly render the target person in the style or pose of the source person possibly in different views {{cite:0d2e699be176034acc5fe1c75388998b0ef95de8}}, {{cite:8351ba30ea6bf912a37a5f0859c4b80bbffaa1c0}}, {{cite:6d002aa3524237180f7068982a691161f497316d}}, {{cite:84bfac6a670c76a2023e0c59844ea3fe8bf67496}}, {{cite:a040b9719b050ce9f92d035babd13178287a5885}}, {{cite:3345d783ec05269d37e6e18cf4d798c41ffad108}}, {{cite:77b179b26228068ad232b5d17b53a942a5049384}}, {{cite:4cab2097793b7a11c94eea89c98c7fab44a0b506}}, {{cite:c827dc2a613216d0d9336a70f57e7405c312e400}}, {{cite:f6333625548cfd8f1fee327f51220611ba5d45f8}}, {{cite:b4df585e0095872ede3c2951013a09e58329b515}}. The main limitation of these methods is that they lack multi-view and temporal consistency under significant viewpoint and pose changes since these 2D-based method generally do not learn any notion of 3D space. Instead of fully relying on the image-space translation network, Liquid Warping GAN {{cite:10b886ee76c79b46de42d077cc1282a073ca62f9}}, {{cite:769d232469ceaef2e3b171793c6b419e3e65be26}} uses UV-correspondences between the source and target meshes to explicitly warp the source image to the target pose and then uses an additional network to refine the warped image. Given a target pose in form of 2D keypoints, Huang  {{cite:b368cd885674c154e8b94d4d006e673ac1d87bcb}} predict the UV-coordinates of a dense mesh in image space and then generate the target image by sampling from a learned UV texture map. The main limitation of these methods is that they require some exemplar images to be available during inference, limiting their semantic editing capability, such as fine-grained control of the target appearance.
m
204fc15f489e223e89b0564d145d2a13
where the constants {{formula:f85ba908-45cc-4af5-a00a-3b85629a2262}} and {{formula:827b332c-533c-41c4-a085-841452549827}} (see {{cite:9618b8d27dd0d87a282d0d1efd63bce6eaa98249}}). Note that the function {{formula:b79d70aa-e421-447a-b816-a3e0b6360574}} has {{formula:8bd1efbc-b60d-4740-a54d-d3c64650f16f}} simple zeros in {{formula:efe3966c-d19e-4c7f-9864-c8db2fda02d8}} given by {{formula:252400c5-ec89-4f54-8bd1-8d271df95446}}
i
18156b5119b841db0f10473edaabfdb6
The tBLG used in this study were fabricated using a dry-transfer and “cut-and-stack” technique (Fig. REF ) instead of the “tear-and-stack” technique{{cite:fb66cae56d10e4b1b11f09558c2d82e9f211e2f6}}, {{cite:da16dda330ed8ce59b8f8f1d39b71c4c56d9295f}}. Prior to stacking, we first cut graphene into two pieces using AFM{{cite:2e56bd81978f76a3c0863696bfda083ca5368ed3}} (Fig. REF a) to prevent the unintentional strain in tearing graphene. We used a poly(bisphenol A carbonate) (PC)/polydimethylsiloxane (PDMS) stamp mounted on a glass slide to pick up a hBN flake (typically 30{{formula:71fe409f-759b-420f-b44d-41c35f0971fb}} 50 nm) at 90{{formula:c0bcd723-a122-46c9-97a1-998953c8ae3c}} 110{{formula:e0ffeef1-520b-4d86-8254-0007c9f2ec36}} C, and carefully pick up the 1st half of pre-cut graphene piece, rotate and pick up again the 2nd half of graphene piece in series at 25 {{formula:089d1d87-60d2-4153-a8fc-417920449709}} C using this hBN flake (Fig. REF b for details). Here we rotated graphene pieces manually by a twist angle of about 1.2{{formula:4c35d26d-72dd-483a-8cea-1ee30b93b25c}} 1.3{{formula:201e70f2-dd65-4e42-8d9b-71ef5ff5b006}} . Finally, the 3-layer stack (hBN-tBLG) is transferred onto another stack for the bottom gate part (hBN-graphite or graphene gate), which is prepared in advance by the same dry transfer process and cleaned by the typical solvent wash using chloroform, acetone, methanol and IPA followed by vacuum annealing (400{{formula:c875c8b6-a8d1-4748-8834-f8090aea8e69}} C for 8 hours) to remove the residue of PC film on the hBN surface. We did neither squeeze the bubbles nor perform any heat annealing after the stack is completed to prevent the relaxation of tBLG. We selected a bubble free region as a channel area to prevent inhomogeneity. Electrical connections to the tBLG were made by CHF{{formula:bd73b5d1-afa8-40e6-b378-f9344ef43826}} /O{{formula:d492f710-04d8-407c-8802-0b037a9ae3d6}} etching and deposition of the Cr/Pd/Au (2/15/180 nm) metal edge-contacts{{cite:048c6a89105cb7c64ff06f9f6fb83007737f1f71}}. Following this process, we got 5 superconducting tBLG devices (presented in this paper) of about 20{{formula:e843a394-8d82-4efc-a0b8-6443b2b1293c}} 25 stacks.
m
d34efecdf12ed0476287aa52b7ee956b
This paper examines work began by Borodin, Gorin and Rains in {{cite:8a378f808ab69fdfc46de637e7aa8e9e0bdbc9f5}}. In op. cit., the authors examined {{formula:713dbcb7-81a2-4680-9fa9-f2e4dbba3404}} -distributed boxed plane partitions from several perspectives, but the {{formula:6e922c85-3cf7-43b5-969d-9783fffa60c9}} -distributions were obtained as limits of the elliptic distribution briefly appearing in the Appendix. The present paper takes the Appendix of {{cite:8a378f808ab69fdfc46de637e7aa8e9e0bdbc9f5}} and expands upon it, following the steps in {{cite:8a378f808ab69fdfc46de637e7aa8e9e0bdbc9f5}} and {{cite:06d68b39a81949753e6f0c3e206c02e888d7de01}}. However, since we are working at the elliptic level (rather than a degeneration as in {{cite:8a378f808ab69fdfc46de637e7aa8e9e0bdbc9f5}}), new tools are needed to generalize the results of {{cite:8a378f808ab69fdfc46de637e7aa8e9e0bdbc9f5}}. These tools belong to the area of elliptic special functions, an active area of research in algebra and analysis generalizing, among other things, the Askey and {{formula:31dfc815-c272-4de2-ac21-b4982f6432a1}} -Askey schemes of orthogonal polynomials (as described in {{cite:2bf17ab18a58873fdabe87d60c504ff6f40bb777}} for example). Thus, in some complementary sense, while being a generalization of {{cite:8a378f808ab69fdfc46de637e7aa8e9e0bdbc9f5}}, the paper is an application of multivariate tools introduced by Rains in {{cite:8d9e27d8b6d58a2a6f2723f85460dc6f735bde30}} and {{cite:e45aeb770602a540fb1066f45c0ce1cee5804b65}} (the first is more analytic, the second being more algebraic) which build upon univariate elliptic biorthogonal functions found by Spiridonov and Zhedanov a few years earlier in {{cite:043d7cd702dae5359a535ab94e33770753dab1a9}}. Work in the area of elliptic special functions started with Frenkel and Turaev's discovery of elliptic (theta) hypergeometric series ({{cite:f8ce0fd3c1c39b7e6e5f7ac12bdcc748fc7c14f2}}) - the authors of op. cit. cite Baxter's work (see his book {{cite:90f03e5f44742eb1c2b8e92a2206c1d2ea531be3}}) as the genesis of the theory.
i
9b60d0990b56dcf7214756caae83f23b
Our work opens several doors for future research. We could either add an extra hierarchy to model the size of the larger cluster {{formula:62ee8d2a-f53c-453c-9452-feab07fb39d6}} in a way that microclustering is preserved or consider a different joint distribution for the corresponding allelic partition {{formula:8e5a4adc-1993-4b04-b159-049ce3f05380}} . Lastly, it also may be worth considering other fast approximation techniques in the flavor of variational approximations ({{cite:dd3257979d72b6ebbd5b9bf42aa13fe67f981e33}}, {{cite:53a201c3599e2ad296589f5584c3906e19ed6bcc}}, {{cite:87a7508994b5c1b443ab496911c84e71e3453b90}}, {{cite:d9976df25762457d4d2c2689a3e7ef5f3da8b26f}}). This would allow us to consider bigger datasets with even millions of records.
d
75aa69d42dee8c1779210b756891f81e
We also evaluated the DP-SGD and subsample-and-aggregate methodsOther private prediction methods cannot be used here because deep networks violate assumptions REF and REF . on the CIFAR-10 dataset {{cite:dad19fa41ca428df26d3d061983e6266e24732b2}} using a ResNet-20 model (with “type A” blocks {{cite:de86c9be1c6202954756a399f79d2d7f97124809}}) as {{formula:ae2c5bff-0574-4247-a82d-4c35d6651c60}} . To facilitate the computation of per-example gradients in DP-SGD, we replaced batch normalization by group normalization {{cite:6b9f5480edd609371d79508098abe8ecf1115dc4}}. A non-private version of the resulting model achieves a test accuracy of {{formula:eff4824f-c43b-49e6-989f-51eba03fef2d}} on CIFAR-10. All convolutional networks are trained using SGD with a batch size of 600, with an initial learning rate of {{formula:ab12dd27-9c16-47b3-a932-b7c7412538c8}} . In all experiments, the learning rate was divided by 10 thrice after equally spaced numbers of epochs. We use standard data augmentation during training: viz., random horizontal flipping and random crop resizing. The {{formula:e46b96bc-f31a-47c2-b47a-8f2e1cc3bfa1}} models used in subsample-and-aggregate were trained for 500 epochs. Because privacy loss increases with number of epochs in DP-SGD, we trained our DP-SGD models for only 100 epochs. As before, we set the clip value {{formula:ed5dd24e-c01b-4a9c-addb-353eda3d9b79}} in DP-SGD via cross-validation.
r
79a6c257f483b826b1629e7382f3af5d
In the vicinity of a second order magnetic phase transition, the spontaneous magnetization {{formula:b8dfc722-c9b0-4bd2-a6c9-998578374378}} and initial susceptibility {{formula:114c5e09-136e-48e6-afae-7ab2923c5d33}} can be described by a series of functions {{cite:af4d8767b116457c30baf23bb660f26bf852a7e2}}, {{cite:3eeae180a30efe88d3ad24517a4a34962d1cd655}}: {{formula:57e290f8-e047-404e-934f-f4f72a5880e0}} {{formula:ee3b059e-af67-4ba8-b14b-edd94a689cfc}} {{formula:6ecb2efe-01d6-4fac-b4d6-dad8714d0b2f}}
r
04bd5a629ed8d089a20fb04037025c35
(1). ODIN: Researchers have proposed several methods to improve the OOD detection performance of a trained network by post-processing {{cite:0cd4a5f3521089bcc15d4595e4c57a7a24054f58}}, {{cite:82135a332b759f83afee0051ff6e741d0dae362c}}, {{cite:f060915e7cf7a96def969c319b5138c6c1b5e467}}. ODIN {{cite:0cd4a5f3521089bcc15d4595e4c57a7a24054f58}} is a representative method. It adds perturbation to input and applies a temperature scaling to the softmax output of a trained network.
m
3c66dffeb64042f8b5414bee0832fd3f
for all {{formula:1ea3cec4-a5b3-49b1-8c86-83aa2c981b42}} , see also {{cite:544415e7fbf81af2ceafecc7cfa9a70027e06200}}. Similar to Definition REF , we define classical Wronskian Hermite polynomials as {{formula:577496f1-fd41-4b18-955b-606dbce52816}}
r
9891cd4febbf57db879996b20efd9c81
In Section , we argue that there exists a discrepancy between over-smoothing based theoretical results and the practical capabilities of deep GCN models, demonstrating that over-smoothing is not the key factor that leads to the performance degradation in deeper GCNs. In particular, we mathematically show that over-smoothing {{cite:59ac497eac00f61c8776e5f7a751a38f9d8af09d}}, {{cite:7233c022ceaf2d2dc149b6d38069627b99fdf530}}, {{cite:6dfa5704e67de0b4aad952d9bff4488a464a43c0}}, {{cite:8a7631cd8c5a80d22c830cec3ff6322b6e6437a6}} is mainly an artifact of theoretical analysis and simplifications made in analysis. Indeed, by characterizing the representational capacity of GCNs via Weisfeiler-Lehman (WL) graph isomorphism test {{cite:55072f0295ce11250e67482a0fea524ee8ff951f}}, {{cite:c1639b81590e9ccf3187e373e05de383ea58739f}}, we show that deeper GCN model is at least as expressive as the shallow GCN model, the deeper GCN models can distinguish nodes with a different neighborhood that the shallow GCN cannot distinguish, as long as the GCNs are properly trained. Besides, we theoretically show that more training iterations is sufficient (but not necessary due to the assumptions made in our theoretical analysis) for a deeper model to achieve the same training error as the shallow ones, which further suggests the poor training error in deep GCN training is most likely due to inappropriate training.
i
7def89dab53f412019fac6772ad35b53
Few-shot learning methods can be divided into three branches: metric-based, optimization-based and data augmentation-based {{cite:2c7414512157206e51518e198f386f3f509b60e0}}, {{cite:5f75053bd4620e1312da8ad2d5ca1dd64cf9f026}}, {{cite:e26ad0e04df7d5c2a7a72288e3ddb84f1a65ae9c}}. In this paper, we mainly focus on metric-based learning. The metric-based methods could be categorized into inductive and transductive, and two representative methods are prototypical network {{cite:6513b5fb417905a2043190416963e1d35ddda08b}} and transductive propagation network {{cite:614020b395edb26df2c43ad6d9a398ae08783716}}, as shown in Figure REF . Given a {{formula:bad7457e-a61d-466c-922f-cfef27b724de}} -way {{formula:9d8f0448-dee7-41ec-afaa-b55c7c4efde0}} -shot task {{formula:ba6afb27-e84b-4617-880b-30a131f05f75}} , and the feature encoder {{formula:a2bbf602-4e3e-4595-bbe7-bb2f83f7d9b2}} decided by its internal parameter {{formula:32939bf2-c28e-4d04-94ec-05273e704e34}} .
m
1c80a4d5b2f2fbd7e3b6a3ae34844e96
In this work, we have experimented with both image-based and 3D-based methods. Image-based methods includes TSN{{cite:af768c80fc5f5c79239f9afde3476d7df11cd26e}}, TSM {{cite:4e986a15545a34f0130d444bde2080c76ae8474f}}, TRN {{cite:8ac81a09d3e2ca7031c7a6722476a9b1065f8eab}} and TIN{{cite:27983aff8ef06850cc8b1d9cf75bfdb7911d53b4}}. These methods all use 2D convolution kernels instead of 3D convolution kernels to capture the temporal information. The number of their parameters and FLOPs are small compared to 3D-Based Models, but most of them don't have better performance than those 3D Networks. For the 3D-based methods, we conduct experiments mainly based on the SlowFast{{cite:3d5ce30e522380b134b34e169c25c77a7f9c7761}} and several of its efficient variants. In following sections, we will first introduce the image-based models, then are the 3D-based methods. All the experiment results and conclusions are given subsequently.
m
d0e868269e55fcee3001f06767f546ef
The resolution of the Abraham–Minkowski momentum controversy for the electromagnetic momentum and the energy–momentum tensor in a linear medium is multifaceted, complex, and nuanced. It is not sufficient to simply derive an electromagnetic momentum or energy–momentum tensor from the macroscopic Maxwell equations. That much is apparent from any examination of the scientific literature. After a century of study {{cite:4e86077401ede939bd0378e45156025997d3ede3}}, {{cite:3704dd6804274c49b1d7a240bebf407bb8620ee9}}, {{cite:d1269c2159b99dc75cc4eccdf08b65b7205404a9}}, {{cite:06d105977ecd09e55fcc87944eb3b58244a963ad}}, {{cite:62cb720f89e799dbf1cc45e319a887e59a8e325f}}, almost all aspects of the Abraham–Minkowski momentum controversy have been carefully scrutinized, yet there is scarce mention in the literature of conservation of linear momentum. None of the well-known forms of continuum electrodynamic momentum, Minkowski {{cite:852bd5d3fa6e26f4ecd1fd5ae9313bdd93b698d7}}, Abraham {{cite:dfd291934cbe301b9b300031325b6ea12bbfde3d}}, Einstein–Laub {{cite:2d95f9d372a2105f96afaac2e72c8ca9105548cd}}, Peierls {{cite:d6cc8ee9dc9587791402d7254684b86c68461c0e}}, etc., are conserved and each one is generally regarded as the momentum of some unspecified or arbitrary portion of the whole system {{cite:4e86077401ede939bd0378e45156025997d3ede3}}, {{cite:3704dd6804274c49b1d7a240bebf407bb8620ee9}}, {{cite:d1269c2159b99dc75cc4eccdf08b65b7205404a9}}, {{cite:06d105977ecd09e55fcc87944eb3b58244a963ad}}, {{cite:62cb720f89e799dbf1cc45e319a887e59a8e325f}}, {{cite:d6cc8ee9dc9587791402d7254684b86c68461c0e}}, {{cite:39ad7906fd5cc2a36ac95da53e51a68385ca7456}}, {{cite:967f16d9eb79570b8191596309a18159e842bd9a}}, {{cite:bcdc788d231f531ca7b4e1757fbce72cf485888d}}, {{cite:0a87fd59b8743b7fd367bdb05dba84232b1930e2}}, {{cite:a7f36acb9cf15f9fa1729fe8c290c3096f2de7b0}}. A number of composite momentums have been constructed from the Abraham, Minkowski, or other momentum for the field subsystem with a momentum for the material subsystem {{cite:4e86077401ede939bd0378e45156025997d3ede3}}, {{cite:3704dd6804274c49b1d7a240bebf407bb8620ee9}}, {{cite:d1269c2159b99dc75cc4eccdf08b65b7205404a9}}, {{cite:06d105977ecd09e55fcc87944eb3b58244a963ad}}, {{cite:62cb720f89e799dbf1cc45e319a887e59a8e325f}}, {{cite:d6cc8ee9dc9587791402d7254684b86c68461c0e}}, {{cite:39ad7906fd5cc2a36ac95da53e51a68385ca7456}}, {{cite:967f16d9eb79570b8191596309a18159e842bd9a}}, {{cite:bcdc788d231f531ca7b4e1757fbce72cf485888d}}, {{cite:0a87fd59b8743b7fd367bdb05dba84232b1930e2}}, {{cite:a7f36acb9cf15f9fa1729fe8c290c3096f2de7b0}}. With the exception of the Gordon {{cite:0a87fd59b8743b7fd367bdb05dba84232b1930e2}}, {{cite:4dd716affbe7b081efd064b33a709ad9a1e0deac}}, {{cite:ac97854b0406e59ed7c312ae278a444a58860d3b}}, {{cite:440d713016864de92744d5d9a20e84ffcc050481}} momentum in a dielectric, conservation of the composite momentum in a thermodynamically closed system has not been explicitly demonstrated.
i
befe666762fbec5d17f43ebe83101ec8
The artificial intelligence (AI) techniques can efficiently solve massive data, mathematically difficult non-linear and non-convex problems. Deep reinforcement learning (DRL) as one of the powerful AI techniques has been considered as a promising candidate to handle the dynamic adaption problem in complicated environment. Compared to the deep learning (DL) approaches, the DRL technique does not require a large amount of training data, which might be very difficult to obtain in wireless communication systems. The DRL based approaches can continuously seek for the optimal combination policy of beamforming design by observing the reward value in time-varying environment without the priori knowledge, e.g., the channel model and the user movement pattern. Thus, the DRL based approach is more capable of handling beamforming design problem in time-varying wireless communication systems {{cite:d936438ee5fe56a2cff5ef07cf8ec7b01cbe03e5}}-{{cite:cb423d3666114de1ed52648745734d811dfe3c28}}. In {{cite:d936438ee5fe56a2cff5ef07cf8ec7b01cbe03e5}}, the authors proposed deep Q-learning (DQN) algorithm with its greedy nature to joint design beamforming, power control, and interference coordination. The authors designed the binary coding to execute the action of agent, control the BS power and the beamforming codebook. In {{cite:d1e7de19134c08f4efa523cbb2f046d703d48bdf}}, the active beamforming and passive beamforming are jointly designed to maximize the sum rate utilizing deep deterministic policy gradient (DDPG), in contrast to solving the discrete action space. The action space is simply designed by the beamforming matrix and the phase-shift matrix. In {{cite:d79c6ec6e4ed3dfa6cb3be700bdbee8237799340}}, the authors proposed a distributional RL to learn the optimal passive beamforming of RIS in the imperfect CSI scenario. In {{cite:070a167ba0bee0ff0789d9335b42491f805072cf}}, the authors introduce DDPG to optimize the passive phase shift at RIS. Furthermore, the authors in {{cite:cb423d3666114de1ed52648745734d811dfe3c28}} formulate a robust power minimization problem considering the RIS's power budget constraint and receiver's signal-to-noise ratio (SNR) requirement. When part of actions are generated by the DDPG algorithm, the rest of actions are obtained by the model-based convex approximation. However, the above algorithms are not effective in optimizing large-scale continuous variables.
i
0e858a0a51c534f65ac44f4a25654921
One particularly interesting result of our investigations is that for sufficiently extended gaseous discs, capture is more likely than disruption (see end of Section ). Consequently, there are implications for how debris discs are recycled on timescales much longer than the {{formula:ab13830d-aa3f-40f7-ad39-6bbc67e83127}} Myr upper bound suggested by {{cite:f9d9c458ed4c5865590d51fd535e8cf15a325129}}. There are several important consequences. The first is a new source-sink relationship between the dust and the gas in the disc. Another are the geometric signatures resulting from a captured planetesimal {{cite:c98735348519469d3ecfb6f5f60810e68d5bec62}}. A third is the possibility of capture of multiple large planetesimals which could gravitationally perturb one another as well as the disc. A fourth is captured objects which could reside close to the locations where second-generation planetesimals may form from a massive disc {{cite:d354be3e7c413b62e82f139fcf486e06721f949a}}.
d
2a792ebd3ef86d4a16a2911e83dc9e7c
Given a claim {{formula:8e65d342-4b9f-4c5d-b077-a1735b575b68}} , we first extract all entity mentions from {{formula:37c9beb7-1663-493c-9820-8155cb0f57d6}} by means of an entity linking tool {{cite:742b27957689d6fed555ae21505ad4fcd935f59c}}. We refer to the set of entity mentions in {{formula:df90a7d8-c031-420b-9996-8e311c04dbba}} as {{formula:8b8cc83c-70a8-4be1-9276-cd945e1c0774}} . The evidence can be traced by extracting from {{formula:5b9fb88b-274f-426b-8785-9c74ed7e5d27}} all paths {{formula:4bbe8635-25d6-4478-9eba-8a187f446666}} that satisfy the following conditions:
m
925d4848239f9d09633c202049de2924
To ensure that the results in the previous subsection are not confined to a specific weight initialization scheme, we repeat the PCA projection process on fully-connected policies with two common and two uncommon initialization methods. Figure REF , below, displays networks initialized with He Normal {{cite:060be8a095328414ed32fb8735448a21581d91d4}} (top left), orthogonal {{cite:8d21a798ca9119c2fc72364d181d29bd1eb11b2b}} (top right), a one-sided distribution with a long tail ({{formula:f3fef0b5-b89b-4956-ae2a-ee55f3dee6ea}} ) (bottom left), and a U-shaped distribution ({{formula:83fc0909-57fb-4e11-94cd-677691ce6ee3}} ) (bottom right). We note that, across all four weight initialization schemes, each hidden representation retains an organization that relates to reward. These results suggest that the innate internal organization that is gifted by a well-learned latent representation is robust to differences in weight initialization method. {{figure:ccacb1f5-47bc-4b34-9e99-db473e41f835}}
m
3d5d0f5ecd623114f5c8745cf75e917f
Thanks to recent advances in data acquisition and computing technologies, data-driven control has attracted considerable attention in the past years. Designing control laws directly from data without resorting to any system identification step, offers an appealing alternative to the traditional model-based control paradigm {{cite:974500147ec31087ecd2163280d8641299cddfa0}}, {{cite:d0cf9591cc3e0e9bba0593ed73ffa9eb2e75e396}}. This is because in real-world applications, it is always difficult or even impossible to acquire an accurate system model {{cite:7480c5725424c2953a9899b3d51734fa81f8fe60}}, {{cite:888ed6773304c5206ecaebd15f6a66a36b25ab26}}, {{cite:6fc7fe219e751fa55db01302dd37c326b6f82cc6}}. Indeed, a number of publications are devoted to studying data-driven control. These were mainly inspired by the celebrated Fundamental Lemma proposed in {{cite:a00487bd8ad02354163041caa06f1fa3fbddc61a}}, which lays the theoretical foundation for data-driven control. Several control problems have been addressed under the new framework, including stabilization and optimization in {{cite:f69431593261fceedf77c8e4f30069e46fb2634d}}, {{cite:b9e2e1fd68569cb605482716ebcc35b0fe45bf17}}, {{cite:acd3d4e81fcb06890c045735cfb933eea4564c58}}, {{cite:97042b078f97e2fdc0fcc25571a1724f91525846}}, {{cite:875251d2eac59ce9eed6bd8ab6f3200de6c4b657}}, linear quadratic regulation in {{cite:d128133096ea0e8bc6d567dfd1067f849672f7d9}}, robust control in {{cite:e7548139ece626e02bf7c2cf67509ad17e56d589}}, quantized control in {{cite:ba3e55c376c166ba0fe125d16a72b4ff07290e6b}}, model predictive control (MPC) in {{cite:ac361b12ce6df14fc939942ea4a973cff0f317cf}}, {{cite:5834a570a75faa76c188007512527497ed409621}}, {{cite:2205cccf979e944adb51b90899d22a34a2f864d3}}, {{cite:7e2b07ad11b35ec2be73863dc83009c7246fc657}}, {{cite:91706dff077a2dc18a5714b610630cff9a4dc88a}}, and control of complex networks in {{cite:3a96d139ef9d92ff26df371b727813b642a2cdc9}}.
i
2b6f783eb2c0e5e0463b5afa2274f44a
When a Brownian particle diffuses in a geometric confinement, its encounters with the reflecting boundary can be characterized by the boundary local time {{formula:06f96ccc-c4f2-418c-ab71-6e0217586cb9}} , which plays the central role in the theory of stochastic processes {{cite:3419f6ea8eb022e138f952e5fb8a6d087399b497}}, {{cite:4161e464251fbf2bd7e8d5f18c09eb113a899e42}}, {{cite:155d4e01da9e141977dca32ea890c5888d93968a}}. In the basic setting of ordinary diffusion, one considers reflected Brownian motion {{formula:2bff5739-ed58-41e5-ae4b-86c000d42dec}} , released at time {{formula:8da60f85-a0f3-41c5-975c-6d31f38ae61c}} from a fixed point {{formula:307e0d43-5820-43ac-a9cd-280399d96f00}} and diffusing inside an Euclidean domain {{formula:68076d47-1cbf-4b10-ad98-9440911af6be}} with diffusion coefficient {{formula:925347ea-caba-4dd5-9f99-51a0e661ee7d}} and normal reflections on the smooth boundary {{formula:87367df3-aac3-41d9-b471-aecc1fba6f14}} . The boundary local time {{formula:07cdd53f-a3b3-4fa7-8ad5-39eb9bec1ab2}} of this process on a subset of the boundary, {{formula:a985156a-41b5-4b86-9dd3-14c4e8b9f554}} , is defined as {{formula:7c7b54d1-87d1-4fe8-94d9-f80e6db3f018}}
i
d3058177bdc9ea446c4536a03959aa74
Remark 5.3 (An alternative proof of Theorem REF .) {{formula:ad3a35a8-d43c-4faf-823a-ee434abc8245}} In order to derive formula (REF ) for the kernel {{formula:0c1e1b66-b107-4570-9334-f71773801d20}} of the integral operator {{formula:a2e94a3f-a493-4818-a39a-66c3354223e8}} in eq. (REF ), one can replace the calculations in our proof of Theorem REF above by applying first the Fourier transformation to the homogeneous parabolic problem (REF ), () to calculate the Fourier transform of the kernel {{formula:b8bfe662-a810-4cb1-b723-c834e6935cf5}} with respect to the variable (difference) {{formula:57e087e7-2e4e-4999-86e4-a401674d5fa5}} , followed by a standard application of the inverse Fourier transformation to obtain the desired kernel {{formula:8e79933f-8638-43bd-9c5f-7b7b125d0491}} for all {{formula:781d4c52-8a07-4535-b984-01baebb99bc7}} and {{formula:363768d3-49c3-4bae-b9ab-f4dab77ad99d}} . This procedure is analogous with the derivation of the “diffusion kernel” {{formula:a24c9d6c-c710-4661-9ee1-f0e434265022}} (defined here in eq. (REF )) by Fourier transformation in F. John {{cite:38c40daa04d31fe6fc269440e99724c352fc9342}}; see Eq. (1.10d) on p. 209. {{formula:4f7ed08f-1cb3-4cec-8144-7f7fcfb4b348}}{{formula:12048726-32ac-4e68-bc58-f95a7a5e7af1}}
m
c6f40ad832ee0fffbeb2a392bd05126e
If the observed H{{formula:e51f82bc-6fef-4942-89f3-67aec1b8062d}} emission is indeed from an accretion shock, the shock also produces strong optical continuum emission that reduces the line-to-continuum flux ratio. Follow-up characterization of this source to measure ultraviolet and optical excess emission would provide useful comparisons to model SEDs and enable a diagnosis of the accretion shock interpretation {{cite:7a3315f00ffe6619db00424947c52ac2efa287a5}}. Assuming that the observed F656N flux is entirely produced by the accretion shock of AB Aur b, we can determine the instantaneous mass accretion rate of the protoplanet based on the observed H{{formula:c6ce2f28-df1e-477d-9419-2d8296ab323c}} luminosity. Adopting a line-of-sight extinction of {{formula:0a160739-a175-477c-b7b1-9475a669d37d}}  mag (the same as the star, {{cite:787aed3e5cf10e6673e6b8f20c2a7d493ca2ff6b}}) and assuming no additional extinction opacity, we find a H{{formula:0bfb372b-6af4-4c52-b787-48387c2956eb}} line luminosity of {{formula:a14ae91b-43c7-4d6d-828d-06cddadbd9ad}} . At this {{formula:a08a9e95-ccf9-46af-8251-0d0257021e27}} , gas in the accretion flow should not lead to significant absorption {{cite:13ddd19d65beffa52a995dcf278d17b8a754cad8}}. The {{formula:9b6fdab4-55dd-49d1-9d82-5bb0f1e3dc1d}} value corresponds to a total accretion luminosity of {{formula:979fe251-44ad-46f3-9f97-63cff7fe1148}} by assuming the planetary surface shock model {{cite:af6a97da4a2bf6839d691873677ad03f7ec707f2}}, {{cite:255571003c531d2b4223672aa4d21b72ba6b0759}} or {{formula:44ab352a-c0f9-4615-ac2b-ecfc32c335e3}} using the empirical relation for classic T Tauri stars {{cite:74e4e3785d318dd3e17dccc17b39fbcf0d876caf}}, respectively. Adopting a planetary mass of {{formula:97a082d8-5573-44aa-95bb-e7bd5f8d0df2}} and radius of {{formula:0d232290-1a9b-409c-8be9-36aa0aea1f52}} {{cite:497301211fd4e9677236627a7839fdffe614a4de}}, these accretion luminosities can be translated to mass accretion rates of {{formula:9c1fdf27-9e3a-4d0f-aaa9-70f932d5b650}} between {{formula:0b5e0188-e9b7-41c3-8ddf-98014f3eaacf}} and {{formula:6befa519-ca36-427e-b710-cf9361ceb63a}} . These estimates roughly agree with the result {{formula:c46f6705-8afb-4620-bf20-63ba1f49c55c}} obtained from SED fitting {{cite:497301211fd4e9677236627a7839fdffe614a4de}}.
d
f348c6d3ee41c07a740b56749ff5df65
Two methods have been proposed on how to jointly provide highlights along with classification. (1) an extraction-based method {{cite:2484ae40cddcd50b32df7ebcfdc1a90cf79dbcf1}}, which first extracts evidences from the original text and then makes a prediction solely based on the extracted evidences; (2) an attention-based method {{cite:7b49e9c047202f2995c902fb84f98052e533fa02}}, {{cite:b26a9f35fd5df6e4099ab31a5269d4e89b3bf5cc}}, which leverages the self-attention mechanism to show the importance of basic units (words or ngrams) through their attention weights. {{table:ba11b99f-e882-48d0-bde3-68f864460c15}}
i
6bb0b800bab755fcf86ebcc1dd07fd66
Then we only focused on the first channel of our new images, the luminance values of each pixel, channel L. Following Bychkovsky et al. {{cite:e4c9057fcc23c3b5035263eb163b48d65780d85a}} and after experimenting with these values, we created the curve of luminance by computing its cumulative distributive function (CDF). This curve was sampled 51 times, as our values went from 0 to 100, it means simply taking one out of two.
m
820ce45b6467b21d39e8a337d6a9f80e
When {{formula:3f1f38f2-d01f-4575-9c79-a4925a0cfe0a}} , the equation (REF ) is widely used to describe some fast diffusion phenomenon under stochastic perturbations (e.g., {{cite:24f834114bc10c75ae3c9883e4c6817efcc93437}}, {{cite:ae5312a23156512ebf9cc6fefde8b4675847a6b4}}, {{cite:c6e72c4de25758f4f116d95d3669251c8a87e5d4}}). Further, it is the linearized version of stochastic Cahn-Hilliard equation, which is used to model phase separation phenomena in a melted alloy that is quenched to a temperature at which just two distinctive phases can exist steadily (e.g., {{cite:99736483f6881fb0aaef8f1f011fcadfa748c208}}). By acting control on the system, we aim to modify the diffusion of the material. It is an important goal to drive the state to the rest. This leads to the following definition.
i
1a033fcdc5d95ef4f6950b668d3c25b0
Some previous work on implementing the moment approach can be found in {{cite:a787f7f1b8f42687887b1a7429466b998b9a0e23}} (based on {{cite:93ae56131db9b5c7cb50ce7c8ff682419b6a62f2}}, {{cite:59c5076fcc0b12668aef125c2edacd96da120758}} and described in {{cite:53813fbb8faabea87421ca381863c8d47592c710}}) where an explicit implementation (based on matrix inversions) was implemented in SOLPS; {{cite:148b3d21956a7a4a9c278c8f36e1a7fb506a8fa0}} where the multispecies closure was implemented into 3D turbulence and transport codes based on {{cite:6ebe03fb39fa5e246e49ec00b21c2d098fda42a5}}; and additional work in {{cite:e1c534221337da8bcb773d466f3bd49e63c1206c}}. Some of this work assumed {{formula:fb3cf8a2-a2aa-45ca-9d93-b3d01ad71e24}} and so could not be applied to deuterium, tritium and helium mixture cases, while in others the closure for viscosity was not considered. In addition, there is a difference between definitions made by Braginskii {{cite:5b07b871330c8635bfd7d9a4a447549102a5d28b}} and in {{cite:6ebe03fb39fa5e246e49ec00b21c2d098fda42a5}}. Thus, for the application of the closures discussed in {{cite:6ebe03fb39fa5e246e49ec00b21c2d098fda42a5}} for the Braginskii equations, special corrections are developed in this paper (see Section ). Some typos in {{cite:6ebe03fb39fa5e246e49ec00b21c2d098fda42a5}} which directly affect the results are corrected in appendix . In {{cite:a787f7f1b8f42687887b1a7429466b998b9a0e23}}, a full closure (including viscosity) was implemented into the transport code, though the heat flux dependent part of viscosity was not considered and this higher order effect plays an important role in toroidal systems {{cite:25b377a15bd9e9da9e34656a38bbacfc56e715ac}}, {{cite:1c6782f0ee33ebb9ff0a1eda1ce3108d178867c2}}. Such viscosity was added by Rozhansky et al {{cite:39ede0539bb470f32712064da6e89dea7c5c546f}}, {{cite:25c17cc578fb8e0fbd35a4df4a5c9181dbca5fba}} for correct calculation of the radial electric field in the H-mode pedestal in tokamaks, but only in the single fluid case and can be extended to multispecies cases.
i
224afff5dabed675620998a7e13bfc60
Quantitatively (tab:compare:appendix), our method outperforms all other monocular pure VO baseline methods in the kitchen sequence and achieves state-of-the-art accuracy in the snoopy sequence. We did not include comparison with USLAM {{cite:707104ef63f77819bdd1f834d008dca8086209f3}} in tab:compare:appendix since it requires an IMU, which is not available in these two sequences. The beamsplitter device (see sec:supexperim:bs) has a better sensor quality than the DAVIS240C in {{cite:8823f8078db1f63fe6768921de7b76c086e011a7}}. It produces events with less noise, which makes the EGM more accurate (see multimedia material for details).
r
3526583d75730c8225b196cb7f856172
The adhering state was previously studied by means of a general multipole-expansion-based singularity model for swimming microorganisms {{cite:0a7ca33473b0b603d278ad142c6c5b3e17d1c179}}. Both pushers and pullers were predicted to accumulate at an oil–water interface, giving rise to large density inhomogeneities in many-particle systems. The collective dynamics of microswimmers strongly affects their motion {{cite:a0d200370ff648dba08e269f68d55d413157b091}}, {{cite:db1b71462522e025292a4aa89576074fb58ed958}}. They can exhibit highly organized movements with remarkable large-scale patterns, such as networks, complex vortices, or swarms. In the present work we analyse only a single swimmer. This might help to explain why we predict instead that only strong pushers can be trapped by an interface. Li and Ardekani's work {{cite:5f3c31eb43259553ae42e89d4ff7bbdd6debe2a1}} is probably the closest in methodology to work, although they studied the motion of microswimmers near a solid wall. They found that a swimmer that was initially oriented toward the wall can escape (bounce back) if the strength of its squirming is sufficiently weak. However, they also reported another swimming mode, in which very strong swimmers ({{formula:c3cd5b0f-a924-4598-a1e9-000831967b76}} ) were observed to repeatedly bounce at the wall, which we do not observe in our simulations of a soft interface, although a harder interface would be accessible within our methodology.
d
34eba8fb9b6da0fd42f5f9cd7eb7fada
The theory becomes trivial in the bulk, in the sense that the Euclidean partition function on any (oriented) closed 3-manifold equals 1. After all, this is what we expect from a holographic theory: the degrees of freedom only live at the boundary. Given a (possibly disconnected) 2d boundary and a boundary condition, the Euclidean partition function on any 3-manifold with that boundary gives the same result (this follows from point 1). Chern-Simons theory is a generally-covariant theory {{cite:531d36dfab62ba29e831c463cea6aa32f9cae4e4}}, {{cite:28f35cb734f07e20f6edb5eeddc0c923c50baacd}}, in the sense that its partition function on closed 3-manifolds does not depend on a choice of metric — but it does depend on the topology. After gauging, the theory becomes independent from the bulk topology as well. The partition function of the gravitational theory is defined as the one on an arbitrary 3-manifold with the given boundary conditions (not as a sum over all possible geometries, or some subset thereof), because of point 2). Factorization in the case of disconnected boundaries immediately follows. The partition function with boundary conditions equals the partition function of a single and well-defined boundary CFT. The details of such a CFT are encoded in the bulk gauge group and in the specific chosen gauging of the 1-form symmetry. What we described extends to correlation functions of the boundary theory, and hinges on the fact that all lines are transparent in the bulk (because of point 1).
i
d44dfacd92dbfb7b92cb033fa0f1eb70
We conjecture that BiLSTMs and self-attention have complementary strengths, which become apparent in small models: BiLSTMs can capture sequential relations, while self-attention is able to perform cross-checking between query and title tokens. Motivated by this, we show that we can improve over {{cite:576774acb57f750bcd148833e7e07bebc0d23d80}} for QTR by training deeper but more narrow models, as well as cascading BERT-student and BiLSTM layers in the proposed BertBiLSTM model. Combinations of RNNs and Transformers {{cite:a1c0e2a25614ccd587d8621a79eea6b317df4196}} have been used before, e.g. for deep models in machine translation {{cite:b94bc28f9e818db0be9f7a59cca6895c65eec90c}}, speech recognition {{cite:babb6645385acc688c13cbe5c9e9ea156f1e518a}} and text classification {{cite:0cce36fff1a742f07825dc56cf383f417753c79a}}. To the best of our knowledge, we are the first to apply such a hybrid model for the purpose of training small and production-oriented models with KD from pre-trained BERT models.
i
459f0db3901cbcced77d6f82294aea6e
Future Directions. Currently, we only focus on the object-level task. However, the instance-level task is more difficult and may be suitable for many image-editing applications. In addition, as described in {{cite:327edf0067ba236f26e3323c24f9f92d1a6b61d7}}, studying non-salient objects will provide rich context for reasoning the salient objects in a scene. Finally, in this study, we only provide sparse annotations for the proposed dataset. However, dense annotations like those given in DAVIS {{cite:43a181e0d8df8df0f43752c881be36350628ccef}} dataset can provide more valuable information (e.g., sequence-to-sequence modeling or audio-visual matching) for both traditional I-SOD and PV-SOD models. {{figure:b1a3222f-e99e-4578-988c-e75abde76949}}
d
f4af631d3b2d46d0b64a2827f7b46113
After its introduction in {{cite:52e282d89a32f85a00c871095fc54fd9f36521d9}}, the Master Equation was studied in many papers, almost always in the periodic case {{formula:ce35a717-2856-42c4-9de2-ccb0201c8a59}} or in the whole space {{formula:1972c408-0323-4df4-9221-7a9e3913b631}} . In {{cite:908999e9cc589599ee6b722e72d254778867e51b}}, Buckdahn, Li, Peng proved the well-posedness of the first order Master equation without coupling terms, by means of probabilistic arguments; whereas a first exhaustive result of existence and uniqueness of solutions was proved by Chassagneux, Crisan and Delarue in {{cite:13e82119a6f258cc6b8db0073c843a837507b568}}, also here without common noise. Gangbo and Swiech for a short time existence of the Master Equation with common noise, see {{cite:c5b9bd246c5c78fc51a8dd04579855ec9f7241a0}}.
i
22750d6307ab51c7c54aaf15fc884b76
In this work, we gave a finite-sample analysis for heuristics which are heavily used in practical Q-learning and showed that seemingly simple modifications can have far reaching consequences in both tabular and linear MDP settings. We also resolve some well known counter-examples to Q-learning with linear function approximation {{cite:38083d63697c811049dbf4ae6ac09473835871e4}}. Further research is needed to extend these results to the most general setting of {{cite:d95b4a9460f4335fb1113e7b1ea5052916e70701}}, {{cite:a6205d61b6bae7a2cd3c624361093d1fe4da36c5}} where linear approximation maybe highly misspecified, which often leads to instability of the algorithm. Since Q-learning is mostly used in practice with non-linear function approximators like neural networks, it would be interesting to analyze such scenarios {{cite:785670c412cbc6e2fd0b530071830a33405a5637}}, {{cite:bdc783c35f9e735fc4f9420905230b175567c990}} precisely without simplifying assumptions like in {{cite:30e43c6215ca351118ef91c8e978657a36ab205f}}. Another important direction is to understand on-policy algorithms (like SARSA) with the modifications suggested in this work, where the agent has the additional task of exploring the state-space while learning the optimal policy and obtain a regret analysis like in {{cite:f6abda4f4c3982e10f05d293ebc44ea7ad43e23b}}.
d
5f2bea86412ac7358222d866e870950e
In this section, we depict and discuss the analytical results corresponding to the uplink performance in terms of CE and achievable sum SE of an IRS-aided MU-MISO system with imperfect CSI and HWIs. Monte-Carlo (MC) simulations ({{formula:aa8c6094-8a60-43a1-96ad-ec49a5cfd454}} independent channel realizations) represented by "✕" marks in Figs. REF and REF below, corroborate our analysis and the tightness of the UatF bound. For the sake of comparison, we have modified {{cite:6a9236cf1efc1155b3b93883f28c8ced4abf1a76}} to describe the uplink transmission.
r
29a97257f2f16cb5cc56ed5f95e114aa
These questions can be addressed by tying the properties of the Higgs-like scalar to those of fundamental fermionic states, which do not suffer from quantum sensitivity to large scales. The two time-honoured avenues realizing this idea are supersymmetry (SUSY) and compositeness. In SUSY scalars are associated with fermions via a new symmetry extending Poincaré invariance of particle interactions. In compositeness models scalars emerge as resonances of underlying bound fermions. In this contribution we follow the composite avenue. The basic idea is inspired by QCD but realized with an extended symmetry of the condensing theory to allow for a misaligned vacuum {{cite:b7a9a5a0749931b30a2659510893f9e4e9b236a0}}. The large top Yukawa coupling can be explained via the mechanism of partial compositeness {{cite:a4777681646fe84f9b5ca73af6161ffa8d5024bc}}. At the price of a moderate tuning, this class of models features a limit where a light Higgs-like state emerges as a pseudo-Nambu-Goldstone boson (pNGB). This idea got boosted in the early 2000s thanks to the holographic principle {{cite:1c8e052b4254324c2fca4736e04b6f24869a938c}} linking near-conformal theories in 4 dimensions to gauge/gravity theories in 5 dimensions on a warped background. Based on the symmetry breaking pattern {{formula:2dfcac69-bb8b-4d30-abba-dea4ab9bf65b}} a `minimal' model was proposed {{cite:0106ad5d3a156d9545da3464a373a0fe1b24c616}}, where the number of pNGBs matches the 4 degrees of freedom of the SM Higgs field. The phenomenology of this model has been widely explored, see e.g. the reviews {{cite:0dd24f0fe15e93f6291a86686d59f857da1c7a89}}, {{cite:ffcd71aa0e51655cb40ee6855c66a56845cc27e4}}, {{cite:aea21b853cb598045493bdbec3d746a23a0cff7c}}.
i
8159e0c2daa1f16acdf0d015f51563b0
As for potential limitations, our contribution 1, in general, could be applied to any object detector, including RPN-based ones like Faster-RCNN {{cite:3ef52ae0489655126d8de7ddc24c47bcdff609c0}} and Mask-RCNN {{cite:283e0031dc05e47a59dd504976c7ba89209f9852}}), point-based ones like FCOS {{cite:00f81d47445236b1257ff57a105f9fc90dd65b68}} and Center-Net {{cite:879869921a4f7cc19a1e4b79be537feffe12fc8d}}), and transformer-based ones like DETR {{cite:cd8f29c5ec75073bc8a9a469ea09612b16d71e8a}}. However, in our experiments, we have succeeded in applying it only to the RPN-based detector. This might be due to the pre-selected balanced training examples of background and foreground classes in the second stage of Faster-RCNN, which is absent in the other two detector frameworks. Also, while our estimation of uncertainty of box prediction and our new uncertainty-weighted box loss have enabled significant performance gains, our contribution 2 lacks a theoretical underpinning as to why our formulation outperforms a Gaussian-based uncertainty estimation.
d
ef8c0009689bfc5077cbc9f65fb62df4
To perform the experimental analysis, TPPD is implemented on a full system cycle-accurate simulator, gem5 {{cite:7142a61986d8cab6c4d71dcab43c45a7cde07fdb}}. We consider a 4-core system setup with two levels of the cache hierarchy. Each core has its private L1 cache, and the L2 cache is considered a shared LLC. Other parameters of the setup are shown in Table REF . To simulate the CCA attack, we have developed our own trojan and spy applications. These applications are written in C++ and can be executed on gem5. We considered a generic Prime+Probe attack as described in Figure REF in this application. The ability to perform CCA attack by these two applications have experimented first on gem5. Parsec benchmarks {{cite:204e739aa3f54532c8945c742181abcc763c3b4b}} are used to measure the performance of the innocent applications in the presence of attacker applications. From the 4-cores, two cores are assigned to the attacker processes (spy and trojan). A multi-threaded Parsec benchmark is binded to the other two cores. We have considered all the Parsec benchmarks as innocent applications. To measure the worst-case performance impact, the attacking applications are developed such that once the attack starts, it continues during the execution of the system. Different configurations of TPPD (TPPD-{{formula:5567a968-0b60-4a7b-bc5f-4ec156405af5}} ) are considered in order to fully analyse the performance behaviour of TPPD. The value of {{formula:ae0aac50-5795-4425-8750-c9774cfc3fbe}} varies from 1 to 4 (8 is the associativity of the LLC). TPPD-0 means baseline design with no defence mechanism.
r
27cbd62bac13bfa0e511f10640371fc7
However, the RIS is commonly assumed to be nearly-passive. That is, no power amplifiers and baseband processing units are available at the RIS. Besides, in order to compensate for the additional path loss in the reflection route via the RIS, a large number of RIS elements must be employed. These make the channel state information (CSI) acquisition difficult to tackle in practice, since the channel estimation (CE) can only be performed either at the base station (BS) or at the mobile station (MS). As RIS phase control and joint active and passive beamforming are sensitive to the CSI accuracy, the full potential of the RIS cannot be achieved when the CE is poorly performed. Therefore, accurate yet efficient CE methods for the two individual channels (i.e., the MS-RIS and RIS-BS channels) or the cascaded channel are of vital importance. In our previous works, we took advantage of the inherent channel sparsity and rank-deficiency features of the mmWave multiple-input multiple-output (MIMO) channels and we applied the iterative reweighted method and the atomic norm minimization (ANM) method for estimating the channel parameters of RIS-aided mmWave MIMO systems {{cite:3b053ba2b237abf04eef476b2f92d5351f226f2d}}, {{cite:7c18158a97a39815aceca5ca6fcf13e7bd882075}}. In another recent work {{cite:d210ade3586933fe5bfaacd3c4ab35d01a690c94}}, sparse matrix factorization and matrix completion were exploited in a sequential manner to facilitate the CE process. These works fall into the category of conventional model-based approaches, which suit only for a small- or medium-sized RIS, BS, and MS.
i
eca7350b43bb5657a992c1142c5ffc1a
The latter approaches appear under various names in the literature, such as optimized perturbation theory (OPT) {{cite:d2793536ff6a6397a2c6c074d4d0bd74530394e9}}, {{cite:6f2444ceb79286421fcbe903c7286411f4828530}}, {{cite:3b7e740eb11a5948765e6b4018c0d316fd34a80c}} (as we dub it here), linear {{formula:b4565347-55ae-4dd5-b929-57003b6875fc}} expansion (LDE) {{cite:2445b5d8a3adc68617bb702d2e0f8b79742a66c3}}, variational perturbation theory (VPT) {{cite:2172bf0f980328a281ab865d14aec149ad6429b1}}, or screened perturbation theory (SPT) {{cite:163bd6b74dca3d9cba61a08f3f1d82dce2194f51}}, {{cite:ca5df5085821e5e693f130964f7e305219283d74}} in the thermal context. Remark that adding a Gaussian term does not change the polynomial structure of the theory so that the process is compatible with the usual renormalization procedure. Already at NLO one usually goes beyond the simple Hartree approximation since the variational mass is “nonperturbatively” dressed by incorporating different topologies (exchange terms, vertex corrections, etc) order by order. Moreover, at leading order the OPT has the welcome property of exactly reproducing large-{{formula:8697281a-24e0-4e3d-902e-ef97ba5ad23c}} results {{cite:39754dfb0993bbc6fe4874091e169cf922d4230f}}. As discussed, e.g., in Ref. {{cite:f276baa83c745a8698559777f02209f711b753aa}} this technique has been used to describe successfully a variety of physical situations, involving phase transitions in different models. On the other hand, for thermal theories, the SPT method has been generalized over the past two decades in order to be compatible with Yang-Mills theories. This generalization was made possible thanks to the hard thermal loop (HTL) gauge-invariant effective Lagrangian originally built by Braaten and Pisarski {{cite:679b3256a9ac69f4e20471f7c8584b8cd2a2bae8}}. The high temperature expansion based on the HTL Lagrangian, known as hard thermal loop perturbation theory (HTLpt) {{cite:e836b6d5b4dc981e3a696d913df102a1b1279580}}, has been employed in a series of applications up to NNLO (three-loops), to describe the QCD thermodynamics, considering both the glue {{cite:51dac7895631cb5ae11e47c1a4f14f23b19ab733}} and quark {{cite:6e7a2381058570c8c7a7523a5c1721638a3cd28f}}, {{cite:3562c99a76fba34ef767acabf5e299fed3a4a88e}}, {{cite:d5353285c3334f1451d215a8eee6aef88711b92b}} sectors at finite temperatures and baryonic densities. Given the intrinsic technical difficulties associated with the HTLpt evaluations, the NNLO state-of-the-art calculations performed typically in Refs. {{cite:3562c99a76fba34ef767acabf5e299fed3a4a88e}}, {{cite:d5353285c3334f1451d215a8eee6aef88711b92b}} represents a remarkable achievement. Unfortunately it is worth noting a serious remnant issue, also plaguing standard PT but not sensibly reduced in HTLpt: namely the sensitivity to the arbitrary renormalization scale is observed to substantially increase when higher orders are considered. More precisely, as compared to PT the NNLO HTLpt predictions in Refs.{{cite:3562c99a76fba34ef767acabf5e299fed3a4a88e}}, {{cite:d5353285c3334f1451d215a8eee6aef88711b92b}} are very close to the lattice results for temperatures down to {{formula:c08ab8d4-be33-475a-8c8e-552d493386eb}} for the commonly chosen “central” renormalization scale choice, {{formula:e408b506-576f-48d9-a621-8b73bf735759}} . However, even a moderate scale variation of a factor 2 dramatically affects the pressure and related thermodynamical quantities by relative variations of order 1 or more. It has been argued {{cite:d5353285c3334f1451d215a8eee6aef88711b92b}} that resumming logarithms may help to improve the situation but, as explained in Refs.{{cite:357071f0374f936f32f9a5e793f2a47fc2ca3e2b}}, {{cite:2a77d9c2cd40e9122125513f8ca96cf62827af0d}}, it appears that the lack of renormalization group (RG) invariance is more basically rooted within the HTLpt approach.
i
fc3a09203eab4badea1175b8282e23ed
with the best constant {{formula:28c7515d-214a-455b-b104-a73a3570e542}} . The qualitative properties of Hardy inequality and its improved versions have been studied extensively, see for example {{cite:97a0867f1d1204530612b8ad46c6dfc85bae45a3}}, {{cite:939d14954a03826567e0b3a6714366e5181508c5}}, {{cite:f31e726c0650b1a247d22c7f07ab252af4e5b60e}}, {{cite:dc0a19a7c2249f1add2be8abb8e70eb57473c467}}, motivated by great applications in the study of semilinear elliptic Hardy problem by variational method, see {{cite:76c15c85cd3bd041e9d887d10b4312fed4b744d8}}, {{cite:85c2ceb141e5de75e21188689a9e53c777100763}}, {{cite:8f29468cc90cf5634b03eeb443b3b2b7279ebd1d}} and the reference therein. Due to the inverse-square potentials, the related semilinear elliptic and parabolic equations appear various peculiar phenomena and attract great attentions, such as parabolic equations {{cite:3e9a0184f97822f23b0c3b125cf6fa98cac94fc7}}, {{cite:25f0eb151ade5dc995f2e606ec44338cdb1a877f}}, {{cite:5b87bfe2db4ef2c00557038fbe7a21222f7fa822}}, singular solutions of Hardy problem with absorption nonlinearity {{cite:ed1151aaa059989109d12656ad64d974b3f44665}}, {{cite:5b2395471f548f8cc5d1b11a62f8333af3bcfcdf}}, {{cite:90c9b6a19004e32c7596c876d96795130403c349}}, {{cite:80c228c1c0c29ffeb3c83c0935a9a897e5302f68}}, Hardy problems with source nonlinearities {{cite:e5151ff7b11000ebeb324e8e046254b84afcd75b}}, {{cite:05f486e6e929cc7d9788843cf93ae2dacf37a153}}, {{cite:2537c7bdc82712ca69f1340efd8a8535d38fd264}}, {{cite:fbaf68f1d59c27ba5446f8b176b53fa12de32763}}.
i
ba4a1dd4ef7a3dd4d9ca6a8435b76510
We recorded two sequences with our beamsplitter device to prove generalization of our method to other (and newer) visual sensory data. The sequences were recorded in natural indoor scenes and we used COLMAP {{cite:e5f233cd91a73745000767124547833964a5c85a}} to provide a ground truth trajectory, since external motion-capture system (i.e., Vicon or Optitrack) was not available. fig:sequences:trajectories shows the reconstructed 3D map for EDS in the kitchen and snoopy sequences using events and frames. The colored points in the central part of the kitchen correspond to the 3D locations which are active (i.e., generating events using the event generation model - EGM) in the current keyframe. snoopy points cloud used RGB color for a more appealing visualization of the Snoopy reconstructed house. {{table:f932beb6-02a1-4a42-a94c-485f4bb32e23}}{{figure:d907e4ac-464d-4c0c-b222-d4fad6c7c54e}}{{figure:f162b049-14f8-45a0-a8b0-d9cff5a6549f}}
r
87f37b074ac40ad8bc06eb5f25b17e37
CodeXGLUE {{cite:db4cf2cba284e13fae8e2d915d0efa7ac026fec3}} is a benchmark for programming language understanding and generation tasks. In total, CodeXGLUE provides datasets for 14 tasks, in which the dataset PY150 is for code completion task. Table REF shows the experimental results. Note that we fine-tuned PyCodeGPT and CodeParrot on PY150 training dataset. The results show that CodeGPT is worse than the fine-tuned CodeParrot. However PyCodeGPT wins the CodeParrot with {{formula:4b7487a2-7824-477e-85e2-04282092c439}} % higher score on token level completion accuracy. On line level completion, PyCodeGPT also achieves {{formula:7f0fdc7c-c3e4-4723-a85e-45bbf5bd63fb}} % and {{formula:c1d9a4a3-7cbf-4b9e-bf12-817e2b6769cc}} % higher accuracy on exact match and edit similarity, respectively.
r
03b227078e6ad39afc923568d360e65a
In this paper, we have proposed a centrality measure derived from von Neumann entropy (VNE) to identify and rank network edges according to their impact on the spectral complexity of information diffusion over a graph. Our work complements prior work {{cite:16bc804737966306dab0599cc77210cfe46e2469}} that similarly uses VNE to obtain a centrality measure but which only considered the importance of nodes. In Sec. REF , we developed a measure for the importance of each edge {{formula:39e63758-46dc-4184-b3c9-f128e8478121}} by considering how VNE would change upon its removal. We rank the edges according to these VNE perturbations, and the resulting top-ranked edge is the one such that its removal would most increase VNE (and subsequently, most increase the spectral complexity of information diffusion at timescale {{formula:3075caba-c360-4734-a0eb-b064b5dee4d9}} ). Our approach complements existing centrality measures that are related to information spreading {{cite:a2c064ca660c3faf318f5e0a22ffcc9fc4069c95}}, {{cite:7c8acd918675c9099241cbe3dc28580a0f66a994}}, {{cite:d6c14a39fa04a04ba839f1da2e0f85a901d345ab}}, {{cite:4b7144efba1cec86bd3712866e4ebda2719a04f7}}, {{cite:5fb3e92937bfa631dc053e0127a71bd576768260}}, {{cite:beb0a951cfff3fe552f88fe656ab01e48a1cc272}}, {{cite:d6c1f7e93cb8b4b05a60296c1a2530800a8d06ac}} but which do not consider the spectral complexity of information diffusion, as measured by VNE.
d
e07147e6de76306cf02eb48f2fbc20e1
The presented analysis is based on the exact solutions to the related problems; see, e.g., Ref. {{cite:737ab1dca2b8d88f8bbd6cd774dedcf37c0071ca}}. The symbolic and numerical calculations, as well as the visualization of the results, are made with the help of the Wolfram Mathematica software.
m
4f8dc3d4bf65d0fc0e42ff9f98478c4d
In Section REF , we experimentally demonstrated that our learned binarized regression model is robust to random label corruption. Under adversarial settings, the data corruption problem can be formulated as a bilevel optimization problem where the attacker tries to optimally corrupt the dataset in order to degrade the test accuracy of the machine learning model {{cite:5849553816c9e629acee2846a654df128da5733d}}. Under such adversarial settings, the ability to provide formal robustness guarantees {{cite:f70d3570ec80e1e5e68e8a67ec5b2a6ab444171c}} presents an important venue for future work. Similar to this paper, the robustness study of other interpretable machine learning models (e.g., decision lists {{cite:6ec1df1b70e79ee593d4106e90407327f86cfd07}}, decision sets {{cite:88875f4e71f991ff5dbaf53c25629341683f61e2}}, decision trees {{cite:54204a1cc5a187fc188411a56c0a0ae30bfd59d2}}) can potentially yield important ideas for future work. {{figure:64f61222-14f0-4b57-b975-385b7b642a8e}}
d
0dfd625d9efa93be017a02b3cf5f82f4
In the static limit, both Faraday and Kerr effects are often considered as manifestations of the axion electrodynamics {{cite:78605b9a98343d41a6f56ed0d288ae4ca78648f5}}, {{cite:fe381330bd49c338a9e7ea870564fe0c2b1204ac}}, {{cite:7c4b704792730180ad61df6f909bdaf33838d527}}. This is because the systems under consideration have finite net Hall conductivity. The same sign of the Hall conductivity is induced on the top and bottom surfaces of a {{formula:ec86b9dc-b935-4070-a90e-52c6711f906c}} topological insulator by either external magnetic fields {{cite:78605b9a98343d41a6f56ed0d288ae4ca78648f5}}, {{cite:fe381330bd49c338a9e7ea870564fe0c2b1204ac}} or coupling to ferromagnets {{cite:7c4b704792730180ad61df6f909bdaf33838d527}}. The main focus of those studies is the manifestation of the half-quantized surface Hall conductivity, rather than the magneto-electric response of antiferromagnets.
d
c9f5776141bd3cefc504fe2f2c997a78
In the following, the root mean square error (RMSE) of the estimated DoAs obtained from the proposed algorithm is compared with the Cramér-Rao bound (CRB) {{cite:8ebbcbda2ee4da8ba9c5b83fadd000f79e8104c8}} and those achieved by the state-of-the-art DoA estimation algorithms, including the sparse signal reconstruction (SSR) algorithm {{cite:8f6c93096e6aa4681d66c6aabaf369e6d50cd177}}, the NNM algorithm {{cite:06cdbafd182212c47f9bce6f7c07a7dfca2c56d3}}, the NNM with PSD constraint (NUC-PSD) algorithm {{cite:7cedf1658dc8df246836b542848faf015b68ee4b}}, the maximum entropy (ME) algorithm {{cite:7cedf1658dc8df246836b542848faf015b68ee4b}}, the ANM algorithm {{cite:1436b4e8acac6982b792253a395a26a4aea212c1}}, and the covariance matrix sparse reconstruction (CMSR) algorithm {{cite:23369d76a2f8979965338e30169e8d968ef440c9}}. The direction of the incident signal is randomly generated from the Gaussian distribution {{formula:066449bd-f091-4439-abc0-c6ebd8dbe566}} , and the results are computed using {{formula:6c7bd845-7dae-456c-9a2d-da76b32b067c}} Monte Carlo trials. We first fix the number of snapshots to 500 and let the input SNR vary between {{formula:bad92077-e8ec-48c6-805e-3520be0705ad}} and {{formula:d03ac7ec-8fb6-42f9-9f79-a53d54f884f8}} . As indicated in Fig. REF (a), compared with the competitive algorithms in the case of low SNR which varies between {{formula:7d7badad-1e4a-434a-b0c4-057eef1d29a3}} and {{formula:66173d05-d761-4611-8e8b-af3802c15b46}} , the RMSE of the proposed algorithm is significantly lower and much closer to the CRB. As the SNR increases, the RMSE of all the algorithms, except SSR and CMSR, gradually decreases, but the proposed method provides the lowest RMSE results. The floor of the RMSE performance observed for SSR and CMSR is because these methods are grid-based algorithms and thus suffer from performance loss due to the basis mismatch problem. When we fix the input SNR to 20 dB and vary the number of snapshots, the results depicted in Fig. REF (b) confirm again that SSR and CMSR render high errors, whereas all other methods achieve similar RMSE performance with the proposed algorithm slightly outperforming others. {{figure:767688de-8260-4a33-9ce3-fd2fdeabac04}}
r
8cb5b0519fdd530bbc18801104682f7d
Moreover, see {{cite:7f216b0ba91b4cd0369d48a78ad6ed145aafa3be}}, we obtain that for any {{formula:11fa1e62-7b7c-4e03-9ab1-cb0259550d8b}} {{formula:5e3ac815-3c12-482c-817d-4c043bdabf36}}
r
092c7d5205831e25bf5e3dcacff175f8
Let {{formula:13423c86-0a72-4812-a5bf-00084790f742}} and {{formula:1bccad89-99c0-45d4-8999-a1bc43a23a3a}} denote the Chebychev polynomials of the first and second kind, respectively. Keeping in mind the representation {{formula:4ce8ee48-90a7-468b-92e0-244f25352d94}} and {{formula:876ff00a-1abc-4e66-9e47-0c856bf2693d}} ({{cite:1a400810d3bd11767002aa154ef5f14bc2198e2c}}) from the conditions (REF )-() we get {{formula:fc68da88-91c3-44f2-a879-255d42cce6e7}}
r
2857538e5c1cb0942eeb40096b84deed