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The use of active learning methods with deep learning frameworks has been investigated for applications such as image classification {{cite:f4384d564a298c428df0e1f3b20adf616c9f0ff8}}, {{cite:abe6dcd1576b0d99097b584b5c21fc273f6f0474}} tasks and natural language processing (NLP) tasks such as named entity recognition {{cite:44cb13f90ae3c628945b82954598b758158d40c7}} and hashtag segmentation {{cite:3a545d393eaa84b67a50c8cf1b1eaf6cfc68fbcf}}. However, this work incorporates active learning techniques with deep learning models for time-series prediction applications.
| m | 6b901f22d7755341339988f54c500f60 |
Approaches to quantum signatures of chaos fall into two categories. One involves investigating quantum variables that distinguish between quantum systems whose classical counterparts are integrable and nonintegrable.
These approaches typically look at energy spectra properties {{cite:763892cb62fdb85808393d5c47e7d1fb2d956c96}}, {{cite:c082b71b52dfcf6fd2719b0898769be9d3e2c022}}, {{cite:a89c16d623b2c18b54055a95d42e990a3169a543}}, {{cite:ea53ca94f03fcf570f204a2aa004456bbd337344}}, {{cite:a9929333cd2195d88a13155a26a5ba7cb77a928a}}. A second class of approaches seeks intrinsic quantum definitions of quantum chaos.
Examples of these include quantum parallels of the Lyapunov exponents and entropy measures {{cite:126894482b688917fe819382c3d16496b98fe03a}}, {{cite:5c9767f57792697c525ae78c8dc97d867b73d57f}}, {{cite:6b2ca30dd9962e9cd0d8473d8121e9268c6e1ebd}}, {{cite:5c9767f57792697c525ae78c8dc97d867b73d57f}}, {{cite:8c8a86106b9f775afdac5b1f598097ecbd9ed81b}}, {{cite:5e6ca15ae08921ee6641d3be8c439c34214df7aa}}, {{cite:3ef025ea1ea29c8f8f9344ca38c7f5cc1e6f62d7}}, {{cite:cce3d34cdc686a4e7c845ed81815e72402d65b54}}.
There have also been attempts to develop a quantum analogue of KAM theory {{cite:fca2a8b8c618818ab302e864943e0c8f96583dbf}}, {{cite:83fe6da608829a378bdef802cfe2b9ec08002dec}}, {{cite:7d44ca16b5c8d7cdd47ead4b510f6a174a1af074}}, {{cite:5fba561acb0b6d99e9d7a895aa9132e8f556a6b2}}. In this paper we will look at the linear entanglement entropy (EE) as a signature of quantum chaos.
| i | cf073292ee64a147c010202fb4ce75c3 |
where {{formula:86c69b25-a64b-4329-bf29-e5b944f65e5c}} is the inverse temperature and {{formula:bec722d8-62e5-4a69-a792-49b55f4597b7}} carries the information about the primary operator perturbation of conformal dimension {{formula:9b882976-f087-4ded-8526-86b2224e74ed}} . The parameter {{formula:e96083ae-d9db-4886-b901-7e17b927a0a8}} represents a UV cut off for the local excitation, so that the excited state is localized around a region of size {{formula:4ecc3f7d-3cfc-41fb-98a9-f3a061aadaa5}} of the operator insertion. This makes the energy of the perturbation {{formula:a09d8cbc-02af-413c-b49e-4bfd25686e91}} finite. In the limit {{formula:8a41d32a-2697-4fa8-a9f3-17176222fd62}} , which is the relevant one to match the butterfly effect discussed in {{cite:1c83c288e64e28bf17b2a53c8844b101c9903163}}, {{cite:fe135be250c07d2ebdc00c642c39af7c3fd0fe93}}, this reduces to
{{formula:96fb2e53-36e0-4740-9321-c8c76f51a6c6}}
| r | c291e62e2ccf70c54fb6322f33c36dbf |
A close look at the temperature expression of Lifshitz-dilaton
black holes (see {{cite:6241fbeebb760c348fcc2ba34c7b2983b7f915e1}} and Eq. (REF ) of the present
paper), shows that it is nearly impossible to solve this equation
for {{formula:927cc957-cb7d-48fe-842a-6eb8e1d815d5}} (or more precisely for {{formula:8be4aff9-5683-4708-8cb7-bd0731d46e37}} ). Therefore, we cannot have an
analytical equation of state, {{formula:b0c85e49-3e48-4437-8a9b-d0178dd20f46}} , to investigate the
critical behavior or calculate critical quantities of Lifshitz
black holes. Another way to investigate critical behavior of the
black holes is to use the method of Refs. {{cite:d3ca601238121f8b42548b48180f56c4ad8e732d}}, {{cite:213c157abeefafda4d6260b6d8e541f5952a6c3d}}, but as
shown in {{cite:0f77268df4035e045d8794815e20d76ee39f352f}}, such a view of thermodynamic conjugate
variables ({{formula:de61be16-52e9-4d9c-afbd-fabd0ce32c28}} and {{formula:558ea5f4-9832-435c-85c6-fc6158ffc680}} ) which are not mathematically
independent can lead to physically irrelevant quantities such as
{{formula:a3c53f5c-42ae-45c0-958e-43d6cb2adcf8}} which is supposed to be a
thermodynamic response function, but mathematically ill-defined.
| i | 6f95a7a245eceb7c962e32d9e82bc66c |
Proof of Part (a): As {{formula:308cefaa-b4c3-4538-82cd-ec5bb565f4f3}} for any {{formula:935fa3ae-8c10-49fd-bb59-fb95fb7b8ef0}} by Assumption REF , by applying
Theorem 2.1 in {{cite:1505a7628db1b9709f3923a69ebdd89752b1d85b}}
with {{formula:15b3c43d-7187-4f18-83f1-c8691f392f1d}} and {{formula:7e0a2935-cb0b-4bf8-80c0-1a081efe81ba}} , we find a ReLU network {{formula:a7d447ae-e35b-4df3-ba1d-36767176d4a7}} with depth {{formula:c78bf746-770b-476b-ba4d-50061a4bee3b}} , width {{formula:a3e3330e-0137-45b2-8cb2-da29c0755562}} such that
{{formula:d72aac0d-a6cc-4787-96d6-703af174f4b5}}
| r | 8d36de929540b1a6969d25f43557f2c0 |
A major drawback to the edge-on perspective is the more complex
geometry, which implies that each position {{formula:78b9eb08-9259-4530-9197-60c1a1aba401}} along the major
axis is a superposition of light emitted at a range of radii {{formula:074387f6-e27c-4d95-97a4-b2ceb5a9c38c}} .
Various authors have therefore set out to disentangle edge-on
galaxies and extract their radial structure.
One approach to this is to deproject the edge-on image using
the inverse Abel transform {{cite:700a5c4442e722d9a630b65a1cad4c4760dda635}}.
This method was first applied by {{cite:eca8aff7681062f853c9a527c79858aba6f6e3c8}}, {{cite:0eea30e7ee81f37404a02f46ed683629ff86e353}}
in a study of the mid-plane of edge-on
galaxies in the near infrared.
{{cite:7fbfb353b87b1ec28a9c8273577ec40d4ef51889}} extended the method to study both the
radial and vertical distribution of eleven edge-on galaxies.
UGC 7321 was studied in this way by {{cite:eac66f9cf8b2c2f6071eeb144f8d138047bbf536}}.
| i | e9cd28f61b367a1ef9723e9a802f862a |
NPs sample two sets of observations, for the context {{formula:995c2a46-60f7-4cb9-9e00-395d96031f3f}} and target {{formula:3914e647-ec05-4b32-a125-bd12cf06fab8}} sets. The context set is used to generate the representations and the target set to verify the predictions of the decoder. Our objective is to learn the underlying representation {{formula:9824b9b9-dcfd-40b4-ad47-f7bc25dd2cee}} that best represents the input in the latent space. Our approach works with any framework from the Neural Process family and any type of input. NPs aim to learn a distribution over functions such as {{formula:465063d9-6f15-424a-9452-14f5efee5b1f}} and approximate them using out of context sampling in the target set. For our specific implementation we use the convolutional conditional neural processes (ConvCNP) {{cite:75ff9ff12b03437e9460021b0ce7072ed185be2a}} because of its advantages when extracting time series representations. Compared to its predecessors {{cite:6b37cd1ff9c7f0c3edc0e08c9556da9bd515e808}}, {{cite:439c751094c81a2c64c81b16105422190235f5aa}}, convolutional CNP is able to initially map the inputs {{formula:53dffe70-258c-4bac-99db-a8909b5ffab2}} individually from {{formula:9a2dda4c-e345-49fd-b77d-849015d9586a}} to a functional representation that corresponds to the difference between two inputs, which guarantees translational equivariance {{cite:75ff9ff12b03437e9460021b0ce7072ed185be2a}}. Then the signal is discretized and passed into a CNN that is used to extract a latent space representation {{formula:587cc43f-2ebe-4da0-80ae-eff3d6db7151}} . The motivation behind using a convolutional neural process is twofold. Firstly, time series tend to have a periodicity and secondly, we are predicting samples that are outside of the context range which makes translational equivariance a useful property that allows robust predictions outside of the normal range.
| m | b8acaf0a5af7aa92c0f37e54944f7248 |
Recently, convolutional neural networks (CNN) have achieved significant success in many computer vision tasks {{cite:74751fbc37c0bb2333445adc14fd9e2e28e6a4c9}}, {{cite:3010440e543e2d883f1e5c870e241e7a4d415eb6}}, {{cite:0fc0a98c1325d01ba325a941289d2c68ebdab6f7}}, {{cite:1d03b264abdc3fae40a26841c3f247bd6990e8b8}}. Moreover, many CNN-based methods {{cite:78dd3e27962a5ed425cfb4c6deb682a9461570de}}, {{cite:4fac7051ecb8704f1a87cb553bcce954bffb9970}}, {{cite:677b45361341756cb84d88931e23d1fe51e0316f}}, {{cite:b971229265b7ce0103bb270b94842175a52a85e4}}, {{cite:08f1b540752a43fddf7a125f9e8068cb051801ca}}, {{cite:f267daf447fb31f3a71a9b430a0700736ac487fd}}, {{cite:461542500f6ff3f9d113e1a639f3cf2004258503}}, {{cite:e3272dea2a642561930d3217d2b07b533c97cc6a}}, {{cite:f3393e7ec97a5b583c8b45687e0301e5445cd248}}, {{cite:3af78e5f383d03c7c267f401e1f3a0b1a84537e2}}, {{cite:1ab6466a3f183ecb84e9e76e16751ee0f0121631}}, {{cite:0cc3f2f1c7df59599e2a81ba7dd801ca44c91ad8}}, {{cite:dceaa5a61b2c0bad90858050d18e1d627f1d1dc5}} have been proposed for rain removal, such as DDN {{cite:4fac7051ecb8704f1a87cb553bcce954bffb9970}}, RESCAN {{cite:b971229265b7ce0103bb270b94842175a52a85e4}}, PReNet {{cite:f3393e7ec97a5b583c8b45687e0301e5445cd248}}, DRDNet {{cite:1ab6466a3f183ecb84e9e76e16751ee0f0121631}}, and RCDNet {{cite:0cc3f2f1c7df59599e2a81ba7dd801ca44c91ad8}}. Albeit these methods have brought great performance improvements, they are difficult to remove all rain streaks and recover the structural information of images in complex scenarios (Fig. REF ). This is because: (1). Most of them directly learn the mapping between the rainy image and the rain streaks layers. In other words, most methods predict rain streaks via the built CNN model and then subtract rain streaks from rainy images to get the final output. However, the density of rain streaks varies, which leads to excessive or insufficient removal of rain streaks, resulting in incomplete structural information of the reconstructed images. (2) These methods focus on learning the structure of rain streaks, but they pay less attention to learning the structure of objects and ignore the importance of image prior.
{{figure:d1d83657-b5a3-46dc-96cf-c74afb75cc41}} | i | 18527d32d49c3e457aabd0efb6978fc6 |
From Fig. REF we see that for
a {{formula:8f0ee860-7df2-49c9-a1e5-e843cda96d6f}} SN at a distance of 1 kpc, a 1-ton detector will yield, on
the average {{formula:8999e6ef-2e3b-46d7-89de-66d68eac8b0a}} 10 (20), 7 (6) and 6 (2) recoil events above 15, 20
and 25 keV, respectively, from {{formula:1058036b-fe44-466c-b2bb-edaa011b75b4}} In (CE{{formula:49edb21e-c5c9-47a5-a380-21d8ea7ccc27}} NS). The number of neutrons
produced within the detector volume through the {{formula:ebaf7a9f-18d6-4bc6-9acf-b64ca15cc12f}} In process will
scale as {{formula:af1f01c7-1ceb-4192-a59d-5a6eaf2d00f2}} , where {{formula:b8c69911-0b78-459b-a4bf-9fc0eaacbdec}} is the
active liquid xenon mass in the detector. However, the xenon
recoil spectrum and the total number of xenon recoils produced by the
neutrons will not simply scale with {{formula:34d709c8-5f8d-400d-bcf2-f680bd4e77b2}} , since the number of
scattering a neutron may undergo would depend on the
dimensions of the detector volume — larger dimensions would generally
provide for more number of scatterings. Nevertheless, a
rough (probably conservative) estimate of the number of events expected
in a larger detector may be obtained by
nominally scaling the number of events for a 1 ton detector to a
larger detector with the same aspect ratio of its physical dimensions.
With this, for a future large liquid xenon detector of the class of the
proposed DARWIN {{cite:61914d5b711bcb98b809904522d3bbdaa995651f}} detector, for example,
with an active target mass of {{formula:6305f8e2-8cc7-4f41-a432-f581910da735}} 40 ton, we may expect {{formula:fcf3c95b-2854-4846-ba9c-8249c2026f7b}} 16
(32), 11 (10) and 10 (3) recoil events above 15, 20 and 25 keV,
respectively, from {{formula:e32440a0-b78f-46f8-8c3a-83f74e3dd0f9}} In (CE{{formula:f266dffc-91b5-451b-944d-5c19ea4c2728}} NS) for the SN at a distance of e.g., 5
kpc, while the numbers would be reduced to {{formula:c37d9847-a8e9-4a1d-8e44-d8ed5288cc63}} 4 (8), 3 (2) and 2 (1)
for the same SN at a distance of e.g., 10 kpc. With the
capability to measure the energies of the
individual recoil events, and with the general expectation that
detection efficiency is generally an increasing function of the
recoil energy of the events, these future
detectors may offer the possibility of measuring the dominant
contributions of the {{formula:b9627ef0-aefb-44e3-ace9-2cdb9c9bfe27}} In process at relatively large recoil
energies.
| d | d987db77b54379c2e63076400069c8c4 |
Here, {{formula:7d5b5810-0bbe-4864-bf27-5c5a81ada6cb}} , for which we may utilize {{cite:6d70e55a61d4af874c6bb4b3dfef4fe3917d98de}}
{{formula:7c53db14-a712-42f3-8e81-c70cad2fbf8d}}
| d | 4d6c91d19bef093606eba9634e18536d |
Semiparametric model of ARPES intensity.
Now that the basic scheme of the Bayesian analysis is demonstrated for a single spectrum, we apply this analysis to the actual two-dimensional (2D) ARPES intensity through a semiparametric modelling of quasiparticle bands. For a testbed system, we have chosen {{formula:68306fa1-230c-4da7-b4a0-6c7f05ca9829}} ({{formula:0a929337-1355-4a2d-afef-1e27d7c1f442}} ) {{cite:49bc9a704adce50e5f2f329c5f532013ea720aa8}}, where a slight intensity suppression around the Dirac point is seen as shown in Fig. REF a, but the origin of such unusual gap-like behavior has been a target of intensive debates {{cite:c3a19e295382fcb335e8228da5d922d558fc404c}}, {{cite:edf03ae3d800761acdaa0cc267f59a57505d4a8e}}, {{cite:ae7e4deb5df3002054efa45653fa23e5b4418249}}, {{cite:9e6bc226239463b1e9388f9a85668e8ac79235d0}}, {{cite:0f494b5a0051b8b75f6bf02f058fc3c4fff2be36}}, {{cite:6e62a7c5bdd01c3e5cd1755020f015ef8a3d43cf}}, {{cite:77ea0c360853a145ebbcb783dc9fb773e4b66813}}, {{cite:1af45c252c1430a075bfe229c890a1fa8e3bb82a}}, {{cite:f93e04c062bd4b601fc209c2e771b3961741e93b}}, {{cite:033b86917b4b95940a4c32f4350e46c6b55d74d3}}. Since the Dirac gap is a prerequisite for realizing some exotic topological quantum phenomena {{cite:3ca7fa12fdb804855a114954be04beb6811bf0ed}}, {{cite:a4ab0e389f65f7e90bc128a2b4de496173d9028c}}, {{cite:55abf1c4bb5864237ef2a46e6e9f1c1b32be88a3}}, it is important to establish whether the bare band {{formula:5a362cf7-19f1-457c-97df-5e84176a616e}} of the Dirac-cone state is gapless (Fig. REF b) or gapped (Fig. REF c) to pin down the mechanism of unusual Dirac-band anomaly (it is noted here, if the chemical potential is situated within the gap, physical properties are mainly governed by the “quasiparticle band gap” which is a combination of the bare-band gap and the self-energy effect). It is worth noting that such absence or appearance of the Dirac gap is also critical for the classification of magnetic-TI and axion-insulator phases, as highlighted by a fierce debate on whether or not the surface state hosts the Dirac gap associated with the time-reversal-symmetry-breaking magnetic order in {{formula:c9f5de02-1d7c-4569-b6b8-7a9a8b6f1465}} and related compounds (see e.g. {{cite:87e9d47b33a7c478bfcf64c93951628c4d5a831a}}, {{cite:88c08884c4f7adeaf6f70152f76d2d0f3a9acb5a}}, {{cite:d44b1b36afceea797c3e502fa23836fb17cf84e3}}, {{cite:b2ee353b3f61a8650e46d2e5c1f63add7b2dc49b}}, {{cite:ab292a56418902a3fc6820157ab3dcbc0bf4b4d9}}, {{cite:0ee67f71b8198f3adbce159e689a8a98ae8235ea}}). In our Bayesian analysis, we treat such distinct gapless and gapped states as different model classes and judge the validity of the models for given ARPES data. As shown in the bottom of Figs. REF a-c, we assume that {{formula:32692e01-fa2e-4b52-a7a9-e700e3113b7f}} is represented by the function {{formula:d2ed7020-267f-4145-80e7-96ecc7e9c60a}} for the band index {{formula:ebe675a6-01ee-4ba1-97cf-90ba4c5c17c3}} ({{formula:49a75c4c-1017-4ab2-bc04-86937ef16ec1}} for upper, {{formula:2756a100-1d29-481c-abeb-cf8a89da74d5}} for lower Dirac cones), parametrized by the binding energy ({{formula:7903aa23-6fcd-4c94-b103-ee27d82b1818}} ) at the Dirac point {{formula:64c275a0-48d7-4c2a-8333-b168e5a44a89}} , the band asymmetry {{formula:715e2ca6-53e6-41a8-8977-9542280671e1}} (this parameter is associated with the effective-mass asymmetry of bulk conduction and valence bands {{cite:2dd7b6c07b7f9061622947b22733c14c1c71db5f}}, {{cite:7a750408286dbfb8862354cf292e6f4b316ee902}}), a band parameter {{formula:90d3eaff-b3c2-4456-b283-ce492ac2e84f}} , and the half-width of band gap {{formula:d49eb50f-daaf-4d41-bddc-0de5e39061f1}} ({{formula:4f561d00-53e9-4e48-bf74-bd35310ae55c}} for gapless, {{formula:d87605fc-ee98-4976-a23a-b3394145dc09}} for gapped). Our first goal is to extract the actual single-particle spectral function {{formula:e7d3c473-8057-46f2-b262-ec6dd632ea75}} from the ARPES data by estimating a parameter set of {{formula:bfac8168-bf6b-4d36-86f2-f0c412dbcafe}} ({{formula:2ad24087-d5de-410e-8d17-a2372934bc4b}} for {{formula:bf4ae015-4cb8-45bd-9d22-8167ab9d0d6d}} case) and also obtain a concrete form of self-energy {{formula:7ae7989c-3f80-4927-ae70-0c61c5997339}} (for simplicity, we assume that {{formula:870f241a-4f26-4656-9960-15460bd2270e}} is {{formula:b36d1fd3-dcf8-438a-ad1d-1b7f251441ab}} -independent because the {{formula:ac3a59ec-6f6d-44b8-8493-9ef1ba513cfd}} range of interest is sufficiently small).
| r | 48efb8ac62aadc546482319734f8e68f |
It is common to use actor-critic algorithms such as deep deterministic policy gradient (DDPG) {{cite:9cc297d9703b6a657db0dfc1acce3f9a0381a9e9}}, twin-delayed DDPG (TD3) {{cite:73f7bf68d113306e994d9bbfd018629257587f72}} and soft actor-critic (SAC) {{cite:6ad33aaee899e20cfa095d69d9629b22b836ac09}}, to solve multi-goal continuous state-action space tasks considered this paper. In DDPG, the critic {{formula:4ab231e3-2d5c-4341-bbfd-64f07e417f66}} is learned by minimizing the temporal-difference (TD) loss:
{{formula:48e106d4-d32a-46bb-88e5-ef98d454392c}}
| m | d161631e03f1f487b3f3eae27ee696e7 |
The distribution of the sum {{formula:fc951f49-eaf9-4586-922d-e9972883793a}} ,
where {{formula:53fc61b4-c2cd-4434-96a9-12689660989c}} for {{formula:3ea33162-8b9d-4290-93c3-03f0db47d45d}} are not all identical, is called (general) hypoexponential distribution (see {{cite:5e7e8341d1b0527317b8e80c1b1ae15e8bf92ab1}}, {{cite:4c84604ff5355de7c13fef0efa4da0b821fa0cce}}). It is absolutely continuous and we denote by {{formula:fa8d6d2d-9037-4ccf-ad77-51e3b6d43bbe}} its density. It is called the hypoexponetial distribution as it has a coefficient of variation less than one, compared to the hyper-exponential distribution which has coefficient of variation greater than one and the exponential distribution which has coefficient of variation of one.
In this paper, we deal with a particular case of the hypoexponential distribution when all {{formula:0fe228c1-7386-4032-8377-16d5aa4805df}} are distinct, i.e., {{formula:b9129748-b0ae-45d5-9f31-8bbd8f302ce7}} when {{formula:cfe2ef14-3acc-44a5-90c6-b64e04f53726}} . In this case, it is known ({{cite:41f665b721aeb92a63b36b3995fdc87bccbdd748}}, p. 311; {{cite:0811e0348800afa725726b58b39e1d210983a60b}}, Chapter 1, Problem 12)) that
{{formula:0efeba4b-712b-48fb-83b1-6b875c791b6f}}
| i | 91930562a79dec4f49af31fe7b7bb668 |
Another recently rediscovered exploration idea is Thompson sampling (TS) {{cite:24a7f3b7fc6a4b1183a060cc849dd6f0aba9eabd}}, {{cite:1695efbc4b941defa9952e64fcaa5872bb9a8e09}}. It is motivated by the Bayesian perspective on RL, in which we have a prior distribution over the model or the value function; then we draw a sample from this distribution and compute a policy based on this sample. Theoretical guarantees exist for both Bayesian regret {{cite:0d155b50f194d29d23b5b122e9895eb757808e24}} and worst-case regret {{cite:1463c656b66c37ed204b8bf2db40930731e0522d}} for this approach. Although TS is conceptually simple, in many cases the posterior is intractable to compute and the prior may not exist at all. Recently, approximate TS, also known as randomized least squares value iteration (RLSVI) or following the perturbed leader {{cite:b0962f8f78c2c48ec18b40279a49fc38c26d2326}}, has received significant attention due to its good empirical performance. It has been proven that RLSVI enjoys sublinear worst-case or frequentist regret in tabular RL, by simply adding Gaussian noise on the reward {{cite:4c1b08a834ffe7ea9ad99d85a4a06e3410c17728}}, {{cite:32e37e560405e07765f3d27f627a517bcd3fdb82}} However, in the improved bound for tabular MDP {{cite:32e37e560405e07765f3d27f627a517bcd3fdb82}} and linear MDP {{cite:57dcbb74f36ac7b4669c3213924f9a17453b5a13}}, the uncertainty of the estimates still needs to be computed in order to perform optimistic exploration; it is unknown whether this can be removed. Moreover, this computation is difficult to do in the general function approximation setting.
| i | 3fa24e763a64b69a8b7267656c9a9235 |
We now propose an experimental evaluation of DP-SGLD and compare it to DP-SGD on a classification task using logistic regression on two vision datasets, CIFAR10 and Pneumonia, a dataset of chest X-ray images of pediatric pneumonia published by {{cite:aa3428fd4dd207b38160a0bef89b504e435cafcd}}. Details about the datasets and models are available in Appendix .
| d | 36ca1067459d34138d70cf1d1eed7dd8 |
We will first introduce a couple of known results for vorticity equations, for further discussions on the topic see {{cite:6d84d778ff7a01bc377cfc6edb9e70ae9acd584e}} or {{cite:3f905592d32ab283ede2bc44286dc620d4a0d6fc}}.
The link between the vorticity and the velocity vector field in equation (REF ) is uniquely established using the Biot-Savart operator {{formula:61bf4aaf-6383-4b65-9033-3eb12393c278}} :
{{formula:69db98d8-31c7-411d-ac8d-0654f6f0b0b5}}
| m | 683c85ec4455761cabd4b5b201c3b358 |
Finite Volume Method {{cite:ec44ef2650a57204508085e12337bf10d8e17915}} adopts CNNs to generate coefficients for approximating spatial derivatives, followed by the standard finite volume method. CNNs are optimized end-to-end to best satisfy the equations on low resolution grids, and produce accurate numerical results: it can be integrated at resolutions 4-8x coarser than is possible with standard finite volume methods. {{cite:83348e24871b0b06a643e17b785d6cfc0dd6c637}} creates new PDE solvers based on the WENO scheme {{cite:0c0f269ffd94f1841d4470127d3c8f60c2f3633c}} via generating its coefficients from a learned policy network trained with reinforcement learning.
| m | 53848039aa020f150fd36aef1d8d0940 |
Since the papers above and our deal with higher spin interactions in {{formula:40b25b2a-9faa-494d-be80-f3d5de88f0a1}} and we used the notation close to those of {{cite:5c8adaf6e2cc3d5f4a22472594d1d94a5dc88ecd}}, {{cite:6730c65580e990e9bf0468d1f22da3fbcf658a74}}, {{cite:01186b096ba9946be2857a13d2a30f0e5382c2e0}}, {{cite:0ffd26b54e741865fb94cc3e7e16734a2cf139d6}}, it is easy to discuss the main differences that allowed us to make progress and to construct an actual theory. Let us recall that the spectrum of {{formula:8d67c034-8474-4a0b-b69d-700016826572}} and {{formula:3892dd3f-ef5e-4e91-bb21-f1e93c8c8355}} is the same, since it is determined by the free limit and all higher spin theories, loosely speaking, contain massless fields of all spins. The challenge is to construct interaction vertices, i.e. {{formula:afcb1bcd-e5a1-49a0-899a-146c1670e155}} -maps as poly-differential operators, that obey locality. There are several ingredients: (a) {{formula:e77bb62d-0046-4a8b-af7e-7992be83eb39}} star-product and contracting homotopy; (b) dual bimodule structure of {{formula:67ea708a-459f-4921-bddc-58be828f461e}} ; (c) duality map. (a) Our star-product (REF ) is different from {{cite:01186b096ba9946be2857a13d2a30f0e5382c2e0}} and {{cite:ea56aa923bb7d801ba62049c4e792d4e0ccb2998}}: it is fixed, well-defined and does not require any subtle limits, cf. {{cite:ea56aa923bb7d801ba62049c4e792d4e0ccb2998}}, it works as it is. An invariant characteristic of every star-product is the rank of the underlying Poisson tensor: it is 4 for {{cite:01186b096ba9946be2857a13d2a30f0e5382c2e0}} and {{cite:ea56aa923bb7d801ba62049c4e792d4e0ccb2998}}, 0 for Chiral Theory in flat space {{cite:a431a918b545c5a47cc42a86dc65f3fef60c6674}} and 2 for its {{formula:771af727-b3d5-4742-8d8a-025497d80181}} -deformation of the present paper (which is exactly what is needed to turn on the cosmological constant (REF ) and it closely related to the infinity twistor). It is interesting that the star-product of {{cite:ea56aa923bb7d801ba62049c4e792d4e0ccb2998}}, while different from ours, gives a local {{formula:a2ba4856-5982-4e2f-ba9d-bc4a64810828}} -vertex in the limit where the star-product itself is ill-defined. We use the standard contracting homotopy for the de Rham complex of a linear space. Ingredients (b) and (c) are completely new {{cite:a431a918b545c5a47cc42a86dc65f3fef60c6674}} and play the most important part. (b) Our zero-form {{formula:b2c11aff-da5d-4123-bf61-d8ed11a76450}} takes values in the bimodule dual to the higher spin algebra, rather than in the twisted-adjoint one {{cite:0ffd26b54e741865fb94cc3e7e16734a2cf139d6}}. In other words, {{formula:c29c36e6-e177-4a36-bdad-09a6e9841c12}} is not an element of the higher spin algebra and, for this reason, it should be treated differently and we use the general homological perturbation theory, which cannot be captured by {{cite:01186b096ba9946be2857a13d2a30f0e5382c2e0}}, {{cite:ea56aa923bb7d801ba62049c4e792d4e0ccb2998}}. In particular, this ensures the smooth flat limit or deformation to {{formula:5b355ebd-5409-4903-aa36-16a6167d1d2d}} , which is a counterexample to the general folklore {{cite:0ffd26b54e741865fb94cc3e7e16734a2cf139d6}}. (c) It is of crucial importance that {{formula:51bc6d07-a007-4226-b3d7-ed1f8def5fcb}} -vertices are obtained via the duality map from {{formula:8c9c28c9-c455-4469-9118-647628f442f6}} -vertices, which is an original idea born for flat space Chiral Theory {{cite:a431a918b545c5a47cc42a86dc65f3fef60c6674}}, otherwise they emerge nonlocal as in {{cite:6730c65580e990e9bf0468d1f22da3fbcf658a74}}, {{cite:01186b096ba9946be2857a13d2a30f0e5382c2e0}} and require a separate treatment {{cite:ccc260d5e64a51791bc989a469c159fdd564ac75}}, {{cite:492c1670c4e89ca72bcd9d67f0c0e8a74dc1761c}}. To conclude, while one can play with different (a) more or less successfully, it is (b)+(c) that are crucial for constructing a local theory. An even stronger difference is that our main result is a smooth deformation of Chiral Theory in flat space that is already known and well-defined, the deformation having {{formula:29beb24e-fc0f-4bd5-bd32-d4c74e0da9c8}} as a free parameter.
| d | b4e1c9a8b59107d77a389ae6ca3ad0f9 |
In our experiment, these changes in the ways participants integrate information when receiving prompts about unobservables did not translate into an overall improvement in human predictive performance. When interpreting these results, it is important to consider several characteristics of our study. First, the number of features available to humans in this initial study was relatively small (eight features), which means that it was possible for them to scan through all of the available information in a short period of time. Yet in many real-world settings where AI-based decision support tools are used, the total number of model-observable features and relevant unobservables is significantly larger. For example, call workers tasked with screening child maltreatment calls have hundreds of features available to them {{cite:aac92896c68fe15053ad732051b99134072e8d3f}}, {{cite:e8709adc5494c1eb1d912b2b62f8d14017bcbf9c}}. In settings where a larger number of features are present, it is possible that highlighting the pieces of information that are not available to an AI model would have a greater effect in improving their predictive performance. Furthermore, our experiment included a training phase in which participants were provided with immediate feedback on the accuracy of their own predictions and the model's predictions (cf. {{cite:fb51df054334c48b57bb4e4afd64ed2fef2be20c}}). Combined with the small number of features present, this may have facilitated participants' learning of what information held complementary power {{cite:e852f50c04865c65fabdb5c4ec2bf9e588667edd}}. In domains where decision-makers do not receive immediate feedback {{cite:1a3eca2079cb4a655ba25faaafdb28a7b3d0a80f}}, {{cite:147caa98bb2857ca6878e442150c2a1a6733004c}}, prompts emphasizing unobservables may have a greater effect in enhancing complementarity. Further research is needed to investigate how the number of features present and the availability of such granular feedback may mediate the impacts of interface prompts about unobservables.
| d | e90bd887441097dc9753cd07f689ec4b |
Finally, there is no reason not to apply our method to sets of phrases or paragraphs, by replacing CLIP with a summarization engine, such as those based on transformers {{cite:def00e720759e123719ee8eb60aa60310de728e9}}. Distancing ourselves even further from the current work, we note that with the advent of powerful image generation engines {{cite:8995b27c30281880a044a44b3e87c345ebc8e8a4}} the role that images and text play in our work could be reversed. Images can visually capture the common theme of a set of phrases or paragraphs as well as their modes of variation.
| d | 6adc0c84ba335b5c0de92d39be171983 |
Although the prostate gland is represented in the image FOV center, since the organ to be imaged is always positioned approximately near the isocenter of the principal magnetic field to minimize MRI distortions {{cite:e5cdbb0abceb65b29a4d46fb0242a405c52f2184}}, sometimes it may appear shifted from the center or the patient could be not correctly positioned.
This fact could affect segmentation accuracy especially in apical and basal prostate MRI slices, when the MR image center is considered for prostate gland segmentation.
To address this issue, a rectangular ROI selection tool is dragged around the prostate by the user {{cite:99474ec4faf886629dd7e90d1f08ddaae57f258d}} for more reliable and precise delineation results {{cite:814ea6c1439c80a70768737f99b3c26e5ad4787f}}.
Interactive segmentation is becoming more and more popular to alleviate the problems regarding fully automatic segmentation approaches, which are not always able to yield accurate results by adapting to all possible clinical scenarios {{cite:aeb82dcdca98e7e7041db534281dbe792fc9fc6d}}, {{cite:d89333224dc0d7565f40f81ac385a52d2d234ee1}}.
Thereby, operator-dependency is reduced but, at the same time, the physician is able to monitor and control the segmentation process.
Accordingly, computerized medical image analysis has given rise to many promising solutions, but, instead of focusing on fully automatic computerized systems, researchers are aimed to propose computational techniques to aid radiologists in their clinical decision-making tasks {{cite:32fa17cbc3b863cbdebb916a6d71dbda492bcf0f}}.
| m | 9a9f1ef24a0be73bd0f0e48756f11a6c |
{{cite:2a7468024d38888bc098d7b1295c0e8bbe5bfc46}} also analyzed observations taken of a field positioned along the plane of the Galaxy. These observations exhibited a hot component somewhat similar to what we see for our CGM fields, but {{cite:2a7468024d38888bc098d7b1295c0e8bbe5bfc46}} interprets this high temperature contribution as stemming from M stars in the Galactic plane. They include no such enhancement in the XQC field that overlaps with the HaloSat fields studied in this paper. {{cite:fc85e7b8a950cbff9b523e41c4c283b4933f705e}} also studies the X-ray contributions of M stars along the Galactic plane, modeling the excess emission as an APEC, somewhat similar to what we observe for the CGM. However, that work notes that the M star contribution drops off steeply, diminishing exponentially over just a few degrees of latitude. Previous investigation of stellar contributions to the HaloSat spectra {{cite:18ff893e67eb1ff7a1cfeb573d62eefa41445216}} has not supported a significant contribution from stars. The fields studied in this paper are even higher latitude than the fields from {{cite:18ff893e67eb1ff7a1cfeb573d62eefa41445216}}. Due to the selection of only high latitude fields for our CGM analysis, it is unlikely that M stars are a significant contributor to our hot component.
| d | a9b367ae11c7a954d43322f8183a507b |
Understanding fixation processes and their probabilities is essential to the analysis of evolutionary games on finite populations. In this context, {{cite:4c3d245502ba7d6d1edce8c4fb237b65e2cda687}} observed that even if individuals are interacting via the same game, the size {{formula:64fecc18-3e27-41e3-8e6d-548b25611b8a}} of the population where they are included could lead to different evolutionarily stable strategies {{formula:0c4c6bc7-70ae-4871-908e-fe4880c7c56e}} as defined in {{cite:11fe97c7ce65c3d4f4bd84d7d740e7fdef4672d9}}. This is an emerging feature of evolutionary processes under frequency-dependent fitness, since stability under the fixed fitness Moran process never depends on population size. Here, we provided an extensive analysis of the dependence of single mutant fixation probabilities on population size, focusing on the simplest {{formula:70d3b682-0c0b-4de8-ba6a-98dc7f1defdd}} games in well mixed populations.
| d | ead0e1d9c151b4c8112fedc6e00a464e |
Differentially private federated learning (DP-FL) has received increasing attention to mitigate the privacy risk in federated learning {{cite:a22112eb4b4173cbf38a6792488424e1f8dce3c6}}, {{cite:ff8fd2517ed333ee8add4ec28435f888ff798eea}}, {{cite:25a85584a113b3eed8294b244e69fc8bd78a7061}}, {{cite:3faff14f289dcedf9b25d59d10d2aebf8626618d}}, {{cite:73429a7662f46eeb5ad411d8f53ba80752eb0fb6}}, {{cite:e52cddbda16c42ecb10742811ddf73113338a17f}}, {{cite:d76446719b4999c1e0d9140d0e59a23f04f6eef0}}, {{cite:efee10b34ad44968577424ee4fdfe6f39081a5d9}}, {{cite:c9a3e0d81d143a0a1f8f0d5b81c8b454ed4f55c7}}.
Differential privacy (DP) {{cite:9e674dc2aa90ecf82a82441e38ed585ea0ad2c0d}} is a formal privacy definition that requires the outputs of an algorithm should not be significantly affected by different inputs.
Researchers have explored different schemes for DP-FL in order to strike a good balance between trust model and utility as shown in Table REF .
In CDP-FL {{cite:a22112eb4b4173cbf38a6792488424e1f8dce3c6}}, {{cite:ff8fd2517ed333ee8add4ec28435f888ff798eea}}, {{cite:25a85584a113b3eed8294b244e69fc8bd78a7061}}, {{cite:3faff14f289dcedf9b25d59d10d2aebf8626618d}}, a trusted server takes the responsibility to privatize the aggregated global model under central differential privacy against malicious third parties.
CDP-FL guarantees that it probabilistically indistinguishable whether a client is participating in the training or not.
In general, CDP-FL provides a good trade-off between privacy and utility (e.g., model accuracy) of differentially private models even at practical model scales {{cite:ff8fd2517ed333ee8add4ec28435f888ff798eea}}, {{cite:25a85584a113b3eed8294b244e69fc8bd78a7061}}.
However, CDP-FL requires the server to access raw gradients, which leads to major privacy concerns on the server since the original data can be reconstructed from the raw gradients {{cite:4b9cb695bc32e6104a663237cbcc0ed7d97c9e04}}, {{cite:364a43c5042fa9ddbf92625dfe16f96233e99ddf}}.
In LDP-FL {{cite:73429a7662f46eeb5ad411d8f53ba80752eb0fb6}}, {{cite:e52cddbda16c42ecb10742811ddf73113338a17f}}, {{cite:d76446719b4999c1e0d9140d0e59a23f04f6eef0}}, {{cite:efee10b34ad44968577424ee4fdfe6f39081a5d9}}, the clients perturb the gradients with local differential privacy before sharing with an untrusted server.
LDP-FL guarantees formal privacy against both malicious third parties and the untrusted server.
However, LDP-FL suffers from lousy privacy-utility trade-off, especially when the number of users is not sufficient (i.e., the signal is drowned in noise) or the number of the model parameters is large (i.e., more noises are needed for achieving the same level of DP).
To improve the model utility, recent works {{cite:c9a3e0d81d143a0a1f8f0d5b81c8b454ed4f55c7}}, {{cite:4092a7607d86744aa26b07644049b7326a6e04c4}} proposed a scheme for DP-FL based on the shuffle model of differential privacy {{cite:2f603bb82a73805c3373574119262945ca726cf5}}, {{cite:ae7d0a36f2fb6eb7c7eb2b903c3f5c4f6abfa5d5}}, which we call Shuffle DP-FL.
This scheme introduces a shuffler sitting between the server and clients, who shuffles the locally-perturbed gradients and then sends them to the untrusted server.
By the mathematically-proven privacy amplification effect of such a scheme, Shuffle DP-FL can achieve good utility that is comparable with the CDP-FL setting but without the need of a trusted server.
However, the privacy amplification effect for FL {{cite:c9a3e0d81d143a0a1f8f0d5b81c8b454ed4f55c7}}, {{cite:4092a7607d86744aa26b07644049b7326a6e04c4}} is limited when the number of model parameters is large, such as deep learning models.
Hence, there is still a utility gap between CDP-FL and the state-of-the-art Shuffle DP-FL.
{{figure:54bc9009-005b-4332-988d-c3436db60f9c}} | i | 1612656bb013fa46672a3ef07ac95dbf |
While decentralized learning is typically studied with heterogeneous datasets across workers, sparse (decentralized) averaging between is also useful when worker's data is identically distributed (i.i.d.) {{cite:fa3281097d9345cd88eed5dea4432f9664dca7a7}}.
As an example, sparse averaging is used in data centers to mitigate communication bottlenecks {{cite:06aa2f5f4192e02226038bc834c1ab9a2a8849a6}}.
In fact the D-SGD algorithm {{cite:dce0cb41e285a8c339cd2fbfd74ac0effac1fd52}}, on which we focus in this work, performs well mainly in this setting, while algorithmic modifications {{cite:9b2a0e5e07b83e59f380551dea5d6cdd94cf6c66}}, {{cite:97cca4b62eed472c508129732a982a345620ffc7}}, {{cite:e4f8c101468ccd0c6ce2d046d2183883af124a7d}} are required to yield good performance on heterogeneous objectives.
When the data is i.i.d., the goal of sparse averaging is to optimize faster, just like in centralized (all-to-all) graphs.
| i | b95e728e0c9b7429e8718861ab31d995 |
Case sensitive BLEU scores are reported in Table (REF ). Our model brings in an improvement of 2.3 BLEU over the LSTM model. When tested on lower-cased text (without altering the training procedure), we obtained a higher score of 26.2 BLEU. One major limiting factor of this analysis is that we use a small, fixed vocabulary (17k and 7.7k words), with no way of dealing with out-of-vocabulary words. For future work, we intend to experiment with an open-vocabulary encoding scheme such as byte pair encoding {{cite:2a94f2246b7a7e48dd0d30af7a2af13aede67cb9}}.
{{table:6a48ddc2-99fb-4e80-899d-5c45c4149bd9}} | r | bcbb7a90ee787b246629e542fecd7591 |
It is interesting to think about the scenario studied here to the arguments put forth in
{{cite:5d4682998aa44cfca3219ce91b26f04139d88fdf}}. In that work, it is conjectured that a CFT with a large-{{formula:8d8f96d2-8c51-4d82-9648-a645c3b7be17}} expansion and a
sufficiently large gap has a local bulk dual description. In the case at hand, the bulk is strongly coupled and
the boundary operator dimensions and correlators do not have a large-{{formula:d45fe9f0-4f20-4338-8f7b-9dbf2f6434e4}} factorization. Therefore, in a
sense holography is more general than the requirements of {{cite:5d4682998aa44cfca3219ce91b26f04139d88fdf}}.
| d | a99dccae0a85ea2743022d8a18309e80 |
In principle, the matrix elements {{formula:7450d68b-1174-4dbe-a69a-53a593f38026}} contain full information of the cross-correlations between stocks,
but carry also strong noises.
To sketch the backbone of the interactions between stocks, the edges should be greatly discarded with
respect to the complete graph. To this aim, the graph should be kept as simple as possible, but
important correlations should remain. The MST tree
is therefore the
simplest connected graph {{cite:c848e079014ac6f9d11ff89189fb1be92571188d}}, {{cite:98fecb3ad8e64ff4b1d70b17586e0925e1eac308}}, in which there are no cycles. Moreover, the MST tree may give
the simplest subdominant organization structure of individual stocks in a direct scheme.
| m | 21278f19d721d14c8d2b78b7cbdb1b3f |
In particular, here we are interested in leveraging the EOB approach {{cite:1641edc6f1555183c749a42fe2009d2c7f499989}}, {{cite:c50b33e460bfa6c6d8a6f651b991bbd52ec263e9}}, {{cite:e5455ae04e76f1bd8a0ef36095d50e4cc6ab82f2}}, {{cite:b1243a128b97848d91451c3f0c2ebf0998cb50dc}}, {{cite:5f76b9f3294d307de453d219d51e88b7e5a81e48}}, {{cite:756e3fd82802aec4f0f46df1a4eaa78c4a1681d5}}, {{cite:17fcee17efab4d9d0719a8c0a0fb8cb8452e7a4f}}, {{cite:6a496a6f87548c78f0fe365ad2276e5f09b80665}}, {{cite:183f5ddfbee6bf25bc7fcd95ec3c19c844756f88}}, {{cite:ec2333f6582c9e7e5936f96ecaebb5dd28438e18}}, one of the most accurate state-of-the art frameworks for waveform generators.
In this framework, the Hamiltonian description of the two-body problem in GR is mapped to an effective problem of a single body orbiting in a Kerr-like deformed metric.
The effective metric potentials are determined by suitably resummed PN expressions that make the model predictive in the fast-motion and strong-field merger regime.
Gravitational waveforms are natively generated in the time-domain using the solution of the EOB equations of motion and a particular factorized and resummed analytical expression of the multipolar PN waveform {{cite:cff766c0875532e3c2e95fdcf5d326aede4b9858}}.
The EOB approach has the advantage of being both accurate to Einstein's equations, and flexible to the addition of analytical (e.g. PN) information.
The faithfulness of inspiral-merger-ringdown models is increased by suitably informing them with NR data, see e.g. Refs. {{cite:fe9201bcfa792def40ac71d1b1bdd4114d467d07}}, {{cite:843db8c7db52491e177a40f1863523989167b3db}} for recent work targeted at XG detectors.
Analogously, BNS inspiral-merger waveforms are obtained by augmenting the effective interbinary potential and waveform multipoles with tidal terms {{cite:315abec6727cc5754af9082390c24b70e5be5134}}, {{cite:37d0335e43d92a2d563bd6172f2a10ea1d6b6f91}}, {{cite:28ae53113f7e839f1ad66031f7319a3cb17403cc}}, {{cite:b60439d13e68a9bf69b331735dcac1d5629cc317}}, {{cite:4cec920a14c9892acce71d7ab910e1281f1664b9}}, {{cite:025cfe75a0b17926e37ecdff9498f98a3cbbf403}}, {{cite:bcbcd94373ef89670a50e6bd5e0338ddb1341f91}}, {{cite:0daba9f315516763651e4dfbc5c230a491f22816}}.
Full inspiral-merger-postmerger BNS waveforms can be constructed by hybridising the model with NR-informed post-merger models {{cite:b3b707baa54d7cb6a6ae1cc8a19679ecc2934eb9}}, {{cite:f2f6a25561650ae8596b6d566e8856f91f7301ac}}.
| i | ea1aad3a8d36a128f4efb5a229373c32 |
Finally, we show qualitative results across different benchmarks, namely the noisy point cloud variant of SHREC'19 mentioned in our main paper, additional qualitative examples of scanned point clouds from CMU Panoptic dataset {{cite:199f96fcc6f4ac3d8341a8de0b8647994db2b8df}}, animal shapes from Deforming Things 4D {{cite:64500a35005d7e515b22c65dcd1606ac233a4c6b}} and real-world scans of humans in clothing with registration artefacts from CAPE Scans dataset {{cite:d8cc960b320ec4aa3e42d7bce6aa9a1ee3f7ddb5}}.
| r | f92aa60ec607b6e9e92f1d53da2dbf0e |
Consequently, the estimate of {{formula:69cea750-d3ff-44bf-b7d2-5a9d8dec046c}} requires the source term to be bounded, which is not the case in general because the velocity field is not Lipschitz in the framework of Yudovich solutions. This suggests that all the scenarios of well/ill-posedness are likely possible for this model, a fact that was confirmed by some recent works. Indeed, on one hand, according to Elgindi and Masmoudi contribution {{cite:a5d142bcb82bfa73b19c38d7ff0698a74bf61057}} an ill-posed result connected to some instability estimates in the Yudovich setting can be achieved with special initial data. On the second hand, a well-posedness result in the smooth/singular patch class was obtained by Hassainia and Hmidi {{cite:cfb6807e9aa2ace1f28fd77af0f80e055987f962}}. Although the patch structure is destroyed during the dynamics, one can still take advantage of the flexible vortex patch formalism developed by Chemin {{cite:566f29ba2339c77b3585c836697655856dbb52e0}} and prove that in the smooth case, the velocity remains Lipschitz for a short time. However, when the patch is singular, a compatibility condition was required in {{cite:cfb6807e9aa2ace1f28fd77af0f80e055987f962}} stating that the density should be constant around the singular set of the boundary. This property is conserved along the dynamics due to the transport equation, and this was a key observation in their proof. It was left open the question of whether local well-posedness result can be performed for the partial viscous case (B{{formula:372c3620-1237-448a-9005-dc548b881877}} ) uniformly on the vanishing conductivity when the initial patch is singular. The presence of the dissipation induces a smoothing effect which unfortunately alters the compatibility condition affecting seriously the main ingredients in their arguments. In the smooth case, it turns out in view of the recent work of Meddour {{cite:7e0c1063e0e23ba6b6f37318cbf25cd7c2317e4e}}, that a positive answer for the local well-posedness problem can be obtained using the same lines of the proof. More results and extensions to different models can be found in {{cite:93b90c909e745e1f189b558ccb33904440d84755}}, {{cite:37a80907c6453b7242c6cab79b72a15c0c10669e}}, {{cite:6953dfba5cad045582d2a4807b8c28b709657d0a}}, {{cite:fb294e669953ec85ad6954bf868d1b906d629457}}, {{cite:cd97e4377bea93472b73a8603e7d36aa2ddabc96}}, {{cite:df7b99a4932e5ddd7b450017b64625ec46b71149}}.
| i | 2479c9700494a841417972f84c0c8fa2 |
Lemma 2.4 (Lemma 2 of Section 3 of Chapter VI in {{cite:3993601a78740a917c3356f9a709a4d1513a4b75}})
Suppose {{formula:3a2cf547-49fc-485e-b158-8858044d2656}} , where {{formula:da8ed8be-3cf2-4a70-9b7f-2740f7be07dd}} is a Lipschitz function satisfying: {{formula:dc61a554-870c-492a-9020-20fae575c317}} , for all {{formula:3218f3f9-2fda-4b1c-8944-dc4d57a8b3b4}} . Then there exists a constant {{formula:c640948b-b30b-426a-bdea-dac04179726e}} ,which depends only on the Lipschitz bound of {{formula:6873ea78-e9bc-41ce-a836-f0f72bed982c}} , so that if {{formula:d0a07a3b-5edf-4e0b-b200-ca08d0e37421}} , then {{formula:d97ad09b-30e7-480e-8c1c-6e5ad908fdc9}} .
| r | 8d8f22fe2a97e6c39d73594e7cd403c7 |
In this work, we propose a NeSD framework to address the sound field decomposition problem. The NeSD approach is inspired by the neural radiance fields (NeRF) {{cite:3d505af889ca04f684822b1c75dfd97d848c75da}} for view synthesis in computer vision. NeSD has the advantage of predicting the locations of wideband, non-stationary, moving, and arbitrary number of sources in a sound field. NeSD supports any layout of microphone array types, including uniform or non-uniform arrays such as planar, spherical array, or other irregular arrays. NeSD also supports the microphones to have different directivity patterns. NeSD can separate correlated signals in a sound field. NeSD can decompose a sound field with arbitrary spatial resolutions and can achieve better directivity than FOA and HOA methods. In training, the inputs to a NeSD system include the signals of arbitrary microphone arrays, the positions of all microphones, and arbitrary queried directions on a sphere. In inference, all sound field directions are input to the trained NeSD in mini-batches to predict the waveforms and the presence probabilities of sources in a sound field.
| i | d93737791e1d0984d6a5f0cf8fa2670a |
Mobile edge computing (MEC) provides a promising solution to enabling cloud computing services in mobile edge computing-based Internet of Thing (EdgeIoT) {{cite:acd38b004458438e281da161df29c6b0f12761be}}, {{cite:274e8719becddb0cca9d372cb94d9c766352c850}}. The IoT devices can offload their local computation-intensive tasks to computationally powerful edge servers {{cite:b9d50a4b876a3472dc9b216904fe6e7988c68737}}, {{cite:5167d504986c4ef2186954a47bf61e1c0b3a4e1e}}. In EdgeIoT, offloading the source data of the IoT devices to the edge server is vulnerable to eavesdropping attacks {{cite:7a7807e496f645d53c8c5e6ede689129804331cb}}, {{cite:5bcd01239b501096552718b58309955e31c7c342}}. To prevent private data leakage of the IoT devices, federated learning (FL) {{cite:28b0c266ecaf65836e4cf29f43f3a621195ce742}} is used to train a global data learning model at the edge server by aggregating the data structure parameters of the IoT devices, while the source data remains at the IoT devices.
| i | 9197ebbc9beaa3c788e459ea74eb4261 |
Quantization of the weight and activation of the deep model has been a promising approach to reduce the model complexity, along with other techniques such as pruning {{cite:328faa6f0adf950400f9bc87f2d2c6521d9c9cd2}} and distillation {{cite:d10c2f4802d34c5dfaaa39286af384e9b55c45cb}}. Previous studies, both on weight-only quantization and weight-activation quantization, have achieved meaningful progress on computer vision tasks.
Especially, the scalar (INT8) quantization provides practically applicable performances with enhanced latency, and has become a new standard technique for the deployment of mobile-target lightweight networks on edge devices. However, the actual amount of performance gain that can be obtained from quantization varies greatly depending on the network architecture. From the results in Table REF , we can raise an issue regarding effective quantization of current lightweight network architectures: What is quantization-aware architecture design scheme?
| i | 07b79767f96d0c82b57551c915801eb3 |
Datasets. We curate natural backdoor datasets from two popular open-source object recognition datasets: ImageNet (released under a BSD 3-Clause license) {{cite:fd402fb4bb8094876821937376bbcd9d489a2d08}} and Open Images (released under an Apache License) {{cite:bf67c90670c433c84620c6a22579a22fe4d2d7b2}}.Note that approximately 20K of the original 1.7mil images are no longer available. Table REF in the Appendix provides high-level statistics for both datasets. Open Images includes human-verified annotations for each object in each image, providing native multi-labels. We use an external library to generate multi-labels for ImageNet (details in Appendix REF ).
| m | 38141982615dd5759ca4dd73d4252d1b |
Verify the Certified Robustness: We run experiments on synthetic networks to verify the certified robustness; the synthetic networks include Barabási-Albert (BA) {{cite:3abb1967b972b571aa503e4e88814665ce55bb6e}}, Watts-Strogatz {{cite:e28edbbd10d60d072f1b0cb595ef6460f4ed04ea}}, and Block Two-level Erdős-Rényi (BTER) networks {{cite:ce62cba5cc9e76c6ebb14d51d51f322da27de439}}.
We use the same experimental setup as described above.
Fig. REF shows the difference of infectious ratios on the modified and original graphs (within targeted subgraphs), as a function of the attacker's budget {{formula:8f1c8646-2043-43d4-9a2f-07104ed8f613}} .
The vertical dashed lines are the lower bounds on the budget computed using Eq. (REF ).
Note that when the budget is less than the lower bound, the differences are close to zero, which means that the network is robust against targeted diffusion.
{{figure:29610853-3257-4ded-b524-d9b9665da39b}}{{figure:af3fba25-2349-4dd9-9534-3c4eaa4553c2}} | d | edb06d3dae501202c6c5de6f72b68f1c |
(2) The content preserved style mixing aims to add style noise of the other domains to one image while preserving the content information. While there exist some popular mixing methods (e.g, mixup {{cite:ea77f72fa3ee1d21ada51062695df85768348c91}} and cutmix {{cite:0ec428abef24efa818ba91602246daa73ba12230}}) able to mix domain styles, they also add content noise to the image. Our experiments find that the content noise will lead to a significant performance decrease in our cross-domain reconstruction task. Therefore, we propose a new non-parametric content preserved style mixing method to take advantage of the cross-domain reconstruction and avoid the undesirable performance decrease by content noise.
| i | a8aefb77471aa4cea0a5fa85cdb36628 |
The total corrections of exciton-LO and SO phonons coupling on exciton binding energies for the monolayer MoS{{formula:d3b4ed38-517f-4651-ad17-ee52bf3c9cce}} /SiO{{formula:b992e906-f4f4-4fc0-a89e-8c533358e041}} system are presented in Fig. 4. It can be seen that the magnitude of exciton binding energy can be tuned in a very large scale due to this two kinds of exciton-optical phonons coupling, which not only provides an potential explanation for the divergence of the exciton binding energy between experiment and theory, but also proposes a way to identify the variation of exciton binding energy by controlling the polarization of substrate, the distance {{formula:1da1aa25-dd62-419f-b7d3-3c37e41e060b}} and dielectric environment in experiment. In fact, many-body mechanisms have been assigned to result in these discrepancies in several works{{cite:7dc406f03e1f8a70ef23495e2bf9bd0254819506}}, {{cite:4563bc3577580d76f6e64b5b53819bf276033893}}, {{cite:9625b5c214a55c42d8f1c22e7771f60afaa50ec2}}. The present model proved that exciton-optical phonons coupling is an effective many-body interaction affecting exciton binding energies remarkably as plotted in Fig. 4. Especially, the SO phonons induced by the polar substrates have potential influence on the properties of excitonic states at certain distance {{formula:6c395390-fea9-46c8-885d-8381c5fde900}} . These SO phonons modes generate a series of novel quantum phenomena in the van der Waals heterostructures based on these monolayer TMDs materials and arouse more and more interesting in recent years{{cite:6b8764018dfb6fd465937bbcb3b10b8472639f34}}.
| r | 00088dc5c26a8563416607c3e6cfb84b |
Most of the work done on sparse linear regression solves (REF ) heuristically by replacing the combinatorial condition {{formula:76974997-71f5-47b6-b52d-13b36e6cc3e7}} by a {{formula:1bd05cd0-684b-44bc-b891-0a4621e7caca}} -norm constraint {{cite:65b4a70e0d3c2c5cb2ccce5a651fa05ed23766c6}}.
Elastic Net or Lasso is usually favored over solving (REF ) exactly because of its computational feasibility and scalability.
However, they possess innate drawbacks as the {{formula:889662f0-82a0-425d-bb51-99784708bcab}} -constraint penalizes both large and small coefficients while, in contrast, the {{formula:98277540-f10d-4b9c-8086-a48a840bf05d}} - constraint does not, and thus the sparsity pattern is not well recovered {{cite:992875e4e2b746b6c06fdffd95229150465f69c6}}.
Despite the NP-hardness of (REF ), Bertsimas et al. {{cite:ab96eebdb76782542477488a9ad64fdda6cfcb71}} have recently developed a cutting plane algorithm for solving (REF ) in a matter of minutes where the number of data {{formula:67d9cdb8-de15-4936-9a76-dcfa52b4327d}} and the number of features {{formula:98dcc30a-00c3-4dd9-8e96-f88c1a4b7bb6}} is in order of {{formula:d872e7d0-dd35-4398-84ea-2ff66eeb736c}} s.
With the ability to solve such a large combinatorial problem, we can compare the performance between Elastic Net and sparse regression. As shown in {{cite:ab96eebdb76782542477488a9ad64fdda6cfcb71}}, the solution of (REF ) is superior in both accuracy and true support recovery.
Moreover, it has been shown both empirically and theoretically that the new cutting plane method requires much less data than Elastic Net to attain phase transition - the phenomenon in which the true support of regressors is recovered with enough data with high probability {{cite:ecca5957e1fa94da31538e4453700529fb169cc6}}, {{cite:c69bc83a7684180b06743f2dec1dbfe908a5e4ae}}, {{cite:d736656c2e181807e4c768cb0a1ff00106cb0aac}}.
Interestingly, in contradiction to the common intuition for the complexity of (REF ), solving times for (REF ) drops significantly as the number of data increases {{cite:ab96eebdb76782542477488a9ad64fdda6cfcb71}}.
| i | 1bd5ffae7bd6320188e783486041e6be |
This study focuses on pruning for the increasing need to accelerate the application of DNNs. Pruning accelerates DNNs by deleting the trivial elements in the weight matrix. The importance of each element is evaluated by the importance score {{cite:b130dd7ddef94503c487e5840a0b911a9b2baaa4}} so that the elements with small importance scores will be deleted. Furthermore, to quantify the result of pruning, we calculate the loss of pruning based on the importance score of the deleted elements, generally summation. As the goal of pruning, we hope to get a minor pruning loss, which brings higher inference accuracy, with a certain sparsity of pruning.
| i | d0f3344b062b6776fff2c2b22bd6fccf |
Direct training methods were proposed to address the aforementioned issues in biologically plausible training algorithms and DNN-to-SNN conversion.
These approaches, which are based on supervised learning, use surrogate gradients {{cite:c9512eab7b159361029306dbe70bdef853440027}}, {{cite:28256ceeabad4e363c32a1378fc1be8c3d471205}}, {{cite:451b1da1b67e62661600362d8524472eb583caf4}} or surrogate models {{cite:83eebd0f641e9a045a7d6f1a37fd0c6f74445ae8}} to overcome the non-differentiability and bring DNNs' training algorithms to deep SNNs.
Surrogate gradient approaches successfully train deep SNNs with SGD, but they demand tremendous computing overhead according to the spike activations, which prevents efficient application to deep SNNs.
To train deep SNNs efficiently, surrogate models have been studied {{cite:83eebd0f641e9a045a7d6f1a37fd0c6f74445ae8}}.
These methods have shown successful training results on deep SNNs.
Thus, in this paper, we adopted the surrogate model approach.
From the perspective of neural coding, most studies have focused on rate coding, and only a few have trained SNNs with TTFS coding {{cite:172c0bb3d682f6716c59a4a9385d1dafe52efa60}}, {{cite:439f5f87167e3f7691b733355ac82f1b9a9e5d9f}}, {{cite:9a26aecc23751f9f770733d66831881bb332aa96}}, {{cite:5d414b44a8757b430dd537182270d9fab02d46c0}}.
Despite the efforts to improve the efficiency of TTFS coding in deep SNNs {{cite:9a26aecc23751f9f770733d66831881bb332aa96}}, {{cite:7648cc793f778b6762544cd0e5335b54aa78d6a6}}, their improvements have been restricted by the conversion-based training algorithms.
In several studies, SNNs were directly trained, but their methods were not validated as applicable to deep SNNs {{cite:172c0bb3d682f6716c59a4a9385d1dafe52efa60}}, {{cite:1d3ef83b0d010bd3e37894829748efae50b73644}}, {{cite:2cb6134f251d64b7e439ae6ac79590ede00ddf26}}.
A recent study suggested direct training methods for deep SNNs with TTFS coding {{cite:5d414b44a8757b430dd537182270d9fab02d46c0}}.
However, few previous studies considered the efficiency during training process.
| m | 77210822452c2af4bc456d6ad91ada5c |
Naturally, this paper is also related to the rational inattention literature pioneered by {{cite:32247a9ff4ad041819663aca5c873cea9f8848b1}} and furthered by, e.g., {{cite:48862b45b21d0b1cc74ec504a838cb61f97c3cac}}, {{cite:6684ecb70e99c34d60aac455899d4cb7a02802fc}}, {{cite:5c6c99dc715a1c5af54cdb826a82bb022c41aca5}}, and {{cite:44b78f59e9e9a90da1a9e47f9da5044e58db5102}}. {{cite:d2d43b2b1040968e79d32c559d98f5c111c540e2}} is especially similar in spirit to this paper. There, they formulate a (binary) relation between joint distributions over actions and states: one such joint distribution dominates another if for every utility function, every experiment consistent with the former is more valuable than every experiment consistent with the latter. In this paper, we construct a binary relation between value functions–one dominates another if information is more valuable for the former. In this spirit, our paper suggests an easy test for Bayesian rationality: give an experimental participant with some initial endowment of bets an additional extremal bet; they should be willing to pay more for information as a result.
| d | 4ad2fa4f6d7c01ec77f37db353031758 |
There are several mechanisms that could drive the eccentricity evolution of a SMBHB. For instance, at sub-parsec scales a binary formed by a galactic merger may be embedded in a dense stellar environment. As discussed in {{cite:db0e35f8028328bcd4245e7e1892c65a154bee9e}}, if one assumes an isotropic stellar distribution, the interaction of a star and a SMBHB with semi major axis {{formula:4177c118-cb7f-49a1-84ef-ed2060da9b22}} can have two possible outcomes. Denoting the semi-major axis of the binary formed by the star and the SMBHB by {{formula:e6854c8a-c7cb-4998-b533-cda708947fd3}} , encounters with stars with {{formula:2a80c608-91f3-41c0-b92d-787c82b84029}} tend to circularize the orbit, whereas those with stars with {{formula:813c910c-9d2e-4f96-b258-d4216f192aa6}} tend to increase the eccentricity of the binary.
In non-isotropic environments, co-rotation of the stellar distribution tends to circularize the binary. Counter-rotating stars tend to extract angular momentum from the SMBHB, causing the eccentricity to grow {{cite:dab85cdaa773678670130878176b126fbb3b59fc}}. Several issues still remain to be explored regarding the evolution of SMBHBs at sub-parsec scales in dense stellar environments, but most models seem to favor a growth in orbital eccentricities before these systems enter the frequency band of PTAs {{cite:19e3c8899c575ad9e94a39d09d86403c42414afd}}, {{cite:509ca83b0abf4ea63eb79b6fdada4f3a0120fb0e}}.
| i | c9bb01b6e463c9df6f46966086a1ae77 |
The failure of this model offers insight into the ability of new physics to resolve the Hubble tension. In this case, the pressure fluctuation drives the growth of the heat flux on subhorizon scales as shown in Eq. REF . This sets off a cascade of effects, softening the gravitational potentials, shifting the acoustic peaks in the CMB, and ultimately exacerbating the Hubble tension. A few ways around this result are suggested. For example, if we abandon the scaling solution and use a model that spikes just prior to recombination and then decays faster than the background, then the pressure source decays, too. This is the method employed in Refs. {{cite:acca2ca01224aded17a2cebdede25263bcf97154}}, {{cite:cc519138605fcc3a1e56a87ba6d3fb060f558f3f}}, {{cite:5d49010e0596889b7d498de92b12d100c9b24bf1}}, {{cite:cdd5f51bb1573b1b97dac3692b956d7df998cd39}}. The price of which is an additional parameter, which may require the fine tuning of the initial conditions. Another solution would be to introduce an additional term on the right hand side of Eq. REF to damp or diminish the pressure. This might be accomplished by coupling to another field {{cite:ac16bd5c0db9880c87d2d3f925a9f5fb90bc8884}}. Yet neither of these fixes do more than soften the Hubble tension.
| d | 30bb1849712be050a9c271380deb44b2 |
Table REF presents the performance of our approach across all phases along with several ablations. We find that our approach is able to consistently solve the tasks, is robust to observation noise, and can recover from failures (i.e., dropping the object). However, there is still room for improvement. We often find that executing our planned motions only takes the object near the goal pose. This is because the grasp was invalid at the exact goal pose, planning failed or took too long, or the object slipped while executing the plan. Robustly correcting for these errors could improve our performance considerably. Additionally we accumulate a lot of negative reward while the RRT is planning, and failures that trigger another round of planning can lead to a large variance in rewards. Using a Probabilistic Roadmap (PRM) {{cite:6440f940217287cd2e1e6a6c484d055c841c0e9f}} would allow us to precompute many paths and thereby speed up planning significantly.
| d | 9f435e9fff2c9232de850a41f4f5d6a4 |
where the eigenvalues of the Jacobian of the vector field {{formula:95156ea6-1638-40ea-818e-1f5c87b97dbb}} are located in a narrow strip around the negative real axis. In order to study the stability of Runge-Kutta methods, it is common to consider the linear equation (see {{cite:1c4391f55f46648ccb85f3ceec84bf8cd0eb088e}})
{{formula:ba63c8c4-c7ad-4bfc-94a2-a5698dd53b7f}}
| m | 7bcde859427d252545483dd1178d001c |
Most hypothesis-driven neuroimaging analyses depend on specified models when proposing a statistic and fitting parameters of the GLM. This is a major advantage when data (nature’s mechanism) is drawn assuming a Gaussian distribution (model’s mechanism), and the inference drawn from the experiment may be misleading {{cite:621b39fed48afea53f69217925a8238128076a24}}. In the synthetic example, we assumed a known covariance matrix and a set of noise realizations for the formulation of the GLM. This experimental setup is imperfect in neuroimaging applications and the statistics following on from the best guess can fluctuate around the ideal value {{cite:a310b688f364857319a6c8ae56723340966979ba}}. Frequentist and Bayesian analyses are strongly grounded on model selection and parameter fitting stages where in complex scenarios with a limited sample size heuristics are the common solution {{cite:2feb4714c0faf1dbbcee3fe08369d4065078bc96}}. Finally, limited samples sizes and the selection/estimation of any specific model remains an issue in neuroimaging. This problem potentially deteriorates if the model, and the interaction between model parameters, becomes too complex for an accurate posterior probability estimation or a feasible numerical computation of Bayes rule. Given the relationship between the GLM and MLE-based regression, we propose a conventional statistical inference based on the optimum estimations derived from MLE from limited amounts of data {{cite:e3f08b895f2d6daaeb0796c47328598d5837f9a5}}, {{cite:583258094b9f5b4234801ad962f44a9ca3a650e8}}. The SVR-iGLM is not limited to linear regression since the main regressor in the design matrix could be replaced by another non-linear function; a common approach in fMRI data modelling. Moreover, SVR-iGLM could be incorporated in novel statistical tests, e.g. the P-tests {{cite:f074b330ac23a9279de2e7fc58042538a3046e99}}, to highlight between-group differences in patterns of imaging-derived measures.
| d | f116b48fe732ac193777e4c3efec44c9 |
Considering the variety of coupled-spin-chain compounds, including the other materials in the {{formula:9fe484c0-ff06-468f-ab00-a1810e022d6d}} -type hexagonal perovskite family {{cite:0daaec1d6d69875cedbe5aa2a9ecc1b0a70b79e3}}, {{cite:ec3de9b6fce655594a131f618ef52f9b55de7eb2}}, {{cite:089fa9f58a9456ca751c7b94f91e78c497ce2f45}} and those with different lattice geometries, this concept also provides us with a unique opportunity to study the continuous classical-to-quantum crossover of the ground state and the elementary excitations in a wide variety of 2D frustrated quantum antiferromagnets.
For example, the spatially-anisotropic TLAF model has been extensively studied in the literature {{cite:25855b54de2b18bbd03634644da307648e91198c}}, {{cite:682dc81a20d212b1cbf81276a8ffaf2c66feea06}}, {{cite:3694f9cc82e502c484478b92b5dc771eff527258}}, {{cite:57e02d999b922ea4d0486c0c0fd12ed9656af905}}, {{cite:c4bc7f50c96a9537c15add65947c9a0350ea8bf5}}, {{cite:0ec96a42a16c8d25aba0273642e01533a822e864}}, {{cite:f7c50c36f6f142117856fa5a0c58ae37e6a2d590}}, {{cite:26830c91648c87ec9aebed009d5f6644f182a5b4}} as a model showing a rich phase diagram including quantum spin liquids. High-pressure experiments on a coupled-chain compound, e.g., RbCuCl{{formula:afa8d110-b24d-432b-84f3-fbcea57f5dd6}} , in which spin-1/2 chains form a spatially anisotropic triangular lattice {{cite:089fa9f58a9456ca751c7b94f91e78c497ce2f45}}, could enable us to simulate the theoretical phase diagram with active and continuous control of effective spin {{formula:29519837-38de-4093-8ab6-7650cf390e0c}} . Such an experiment may allow access to the spin liquid quantum critical point via the melting of magnetic long-range order by tuning pressure (or the value of {{formula:781020b3-574f-4394-b064-4107eea1d000}} ).
Future research in such a direction would be promising to shed new light into the connection between the semi-classical “magnon” and highly-quantum “spinon” descriptions of magnetic quasiparticles {{cite:00624b5f92e3990ab3b8c8fe41167a07dd5ad4c8}}, {{cite:b94a25daa64ae14efeab8d1f9f764e16e5ff8fac}}, {{cite:3a2db3a59289d33d6fcdef22be16a48939e77568}}, {{cite:e5abbcac82d4ceeb49c98e9a1074bbddcb3c95bf}}, {{cite:25855b54de2b18bbd03634644da307648e91198c}}, {{cite:570fabc72f3b0ae361198d84cb52d1a0125cddcb}}, {{cite:9543db2f74b4b0713640457e555f55b3aec571bf}}, {{cite:1908fff1338bd4e6d40986e2aa1d870a54c1e529}}. Finally, note that although not a few compounds in the family of {{formula:f682f9f0-3fe2-4dbb-a95a-013588c52241}} -type hexagonal perovskites have antiferromagnetic intrachain coupling {{cite:0daaec1d6d69875cedbe5aa2a9ecc1b0a70b79e3}}, there is still every chance that the pressure application changes it to ferromagnetic one, allowing for the squashed model description we proposed here.
| d | ae4e6eceb655d267c62b85c4a303b1cd |
Within the model-based Bayesian framework for causal inference {{cite:748e1939e9f812cddfd61781309003a70f8a1686}}, {{cite:b4ceb4f8c67e3078613fdbd3ee41f7e6839ceebd}}, the {{formula:5034e08e-c3d0-4651-80d8-0fbdf46806bc}} are considered unknown parameters. The goal is to sample from their posterior predictive distribution conditionally to the observed data defined as:
{{formula:100406d3-6445-4120-9b33-f92673fba484}}
| m | faaa96f62b54e9b1974fe176cc03699b |
Inspired by Domain Adaptive Faster R-CNN in {{cite:2b0d62471471eefa1004c545fcb993cb413f0356}}, {{cite:b390166a55629fae76c921d3f60b80da09cf2e48}} adopts a similar idea and designs a Domain-Adaptive Mask-RCNN (DMask-RCNN). The source domain takes the clean images in the MS COCO dataset, and the target domain takes unannotated real-world hazy images in RESIDE dataset {{cite:9a266245f00253aea7c0c772e1adc2390584206b}}, and their dehazed output images by MSCNN {{cite:07e4bc3d78d34a7099c33f2be162b60ff133eec8}} respectively. And DMask-RCNN adds a domain-adaptive branch after the base feature extraction layers in Mask R-CNN architecture, aiming to mask the generated features to be domain-invariant between the source domain and target domain. The experimental results in {{cite:2b0d62471471eefa1004c545fcb993cb413f0356}} {{cite:b390166a55629fae76c921d3f60b80da09cf2e48}} demonstrate that the domain adaptation method can enhance the performance of both Faster R-CNN and Mask R-CNN models when tackling the object detection task in the hazy environment. Moreover, this enhancement can be more effective when feeding the target domain with images restored by a robust dehazing algorithm.
| m | 3e923058a483fe446eab151cdefc8089 |
In this work, we propose to generate 3D portraits that can be explicitly controlled by allowing the user edits upon a group of semantic parameters. To this end, we try to make the best of both the explicit parametric model and the neural face representation: the 3D Morphable Model (3DMM) {{cite:272fd2ef3e40b411e1395135b566266dd2cd103c}}, {{cite:77d1e73ee6e2b5141ddae2db5cda15ae6409fbac}} provides the desired controllability in terms of face shape, expression and lighting; whereas the neural representation ensures multi-view consistency and offers photorealism. Specifically, the generation network is built upon the tri-plane representation proposed by {{cite:82e5e8b59ed2e016691488c03124dfe5a5a67e55}} which can be efficiently rendered, and the generation of such proxy representation is conditioned on the control space of 3DMM. The rendered images are expected to lie on the real face distribution as guaranteed by the adversarial loss {{cite:b8040da3ffd7c381c82e766e4e96b05bdebb2b74}}, with the appearance resembling the rendered face mesh.
However, the 3DMM guidance does not necessarily lead to disentangled control, since the latent sub-vector that accounts for a specific facial attribute may interfere with other attributes unexpectedly. Hence, we further improve the disentanglement by forming contrastive image pairs that differ in partial latent segments and enforcing the consistency for the attributes that share identical latent codes. As such, different latent sub-vectors bring independent effects to the final output and changing a segment of latent codes will not alter uncorrelated face properties.
| i | a518c9a48c0d23051593567866becef7 |
In a cooperative interaction, the environmental noise is usually expected to lead to a detrimental impact on the emergence and stability of cooperation {{cite:3a0390a583208aa121c4329cccfc0f0ab79a2179}}, {{cite:55666dcb902b844c45cf9850139e203a16a1bdc6}} and thus requires additional supporting mechanisms such as apology and forgiveness {{cite:3e95ccd5395eb1c2e42933c233e1f4de5eaebde0}}, {{cite:54588ed200a2f49182b1516633e36619ba863c1b}}. Surprisingly, we have shown here that the presence of some noise that causes errors when deciding to participate in a prior commitment, can stabilise commitment compliance and cooperation, enabling ACD to become an ESS and risk-dominant against all other strategies. A non-negligible level of noise enables ACD to break ties with the commitment-accepting unconditional cooperators (ACC), who cooperate even when a commitment is not formed and thus can be easily exploited by non-committing defectors. In SI, we also considered execution noise that happens during the PD game. We showed that it has insignificant effects on the evolutionary dynamics and ESS analysis (e.g. none of the strategies can be an ESS for this type of noise).
| d | 08edfde3c7d7775b5f198698a6473db0 |
Combining optimism with MD and FTRL yields their
optimistic counterparts, optimistic mirror descent (OMD),
and optimistic follow the regularized leader (OFTRL), respectively.
OMD and OFTRL both provide tangible benefits when problems are not quite adversarial. For example,
faster convergence to a saddle point on the average {{cite:e6af40275906f9623ff56e08bea97d8dbb51523e}}, {{cite:f95705c74a5aa6a73f925ddab6b04b32cf127e2c}}, {{cite:b68bb54a84cf62778f09f94a7a442509057998ee}}, {{cite:82ebe7bea078bfff0d808bb66d1e9922877ec4ef}}; faster convergence to optimal social wellfare in n-player games {{cite:f95705c74a5aa6a73f925ddab6b04b32cf127e2c}}; last iterate convergence
in games {{cite:09330c537ac4ed99d63ec4c41a62d52d75c8b4ba}};
acceleration in offline or online optimization {{cite:06332041b7fbebd7a1b4afa60b62657ac7d6cf96}}, {{cite:c3e0295356fbf6a4557061a3af21ed2a70372fc0}}, {{cite:ecb0d0b4c1be6dd1dcdd7534736b6401e1478dd9}}, {{cite:34844413875a6c550117de5edd99b9fd4c2430f7}}.
| i | 4e236c9a2fef100ce0e330abed19f4aa |
Carefully measuring accuracy allows us to disprove the claim {{cite:3da2c045623a836477878b46ca0f22c696162837}} that sampling simulation parameters from the posterior, as is targeted in a wide range of algorithms {{cite:285434220ac4b86978451cb28a07fd52734a5c91}}, {{cite:4e6271709a9690967a1f213a4eb8ef8e35b1deb0}}, {{cite:d2f98b637964f0bed9f33ee82dac315b164ecd2a}}, {{cite:aa8ebe20641a15f7a0b73d3046df8daa5e9b7e06}}, {{cite:c9e2ed80c91068a3a5c792ba0987ea552fb7009f}}, {{cite:f1d5e0c4794ddffde74c231b105658db9419c836}}, {{cite:eb416680271bae3891529108f94ffb346e878817}}, {{cite:40f10ec96f52a48096335195aa06168c86a8bdb8}}, is optimal for ABC, or even consistently better than sampling from the prior.
This complements earlier work arguing against sampling from either prior or posterior by comparing to maximum likelihood (ML) estimation in an informative-data limit where ML works well {{cite:3f8db654b92e35001c9a282ea76aed755d81a0d1}}.
The intuition underlying Eq. REF , that simulations should be concentrated where (1) they are required to learn the likelihood and (2) learning the likelihood matters, should be generally relevant for all state-of-the-art methods.
| d | 99d5287111e505576dd9403712336498 |
Beginning in the early 2000's, a few authors addressing general methods for machine learning and artificial intelligence included the CVM in their comprehensive reviews of methods. For example, Pelizzola broadened his earlier (1994) {{cite:55d6231e39c6c91c61051a0705bc53330e0fd4c7}} work to include the CVM in a more general treatment of probabilistic graph models (2005) {{cite:405e4ee03a6f78187e95edc558143da27f22208c}}. Similarly, Yedidia et al. described the role of the CVM as one method for belief propagation (2002) {{cite:a98154c944ded192594bdc65a98d7578ac7b8df5}}. Wainwright and Jordan included the CVM in their extensive monograph on graphical models, exponential families, and variational inference (2008) {{cite:dd817651d741e73780b597a3764d36fe3564d340}}. However, in all of these treatments, the CVM approach was included largely for completeness, and not as a primary method.
| m | ce3c49854ee7fc2144bc798ca4f0c8b2 |
We consider that our theory can be experimentally verified.
In particular, the dynamics of isolated non-integrable many-body systems have been investigated using artificial quantum systems such as cold atoms {{cite:4f422907e7033f6e71e46ea311bfbbe2160a47d7}}, {{cite:af3238f50cdead58b0358871c6bab8c09fc5a407}}, {{cite:4e20e234254d13eb2e6f68f1dc79f69010fe6410}}, {{cite:8973b015116b12edec44eda910b252668cd066e2}}, {{cite:55f3326695f2f805537b58f967ffb203f9d30626}}, {{cite:d729be7d43e09f09a7b3a58f03c041b0615158ad}}, trapped ions {{cite:fbabd4fc433ae3dbb6e518d44974b37279f25cf7}}, and superconducting qubits {{cite:3f813c5221e6e041c6231e785fccaffd0715d074}}.
Not only local physical quantities but also informational entropy are experimentally measurable {{cite:af3238f50cdead58b0358871c6bab8c09fc5a407}}, {{cite:3f813c5221e6e041c6231e785fccaffd0715d074}}.
Because our numerical calculation is performed with a small bath size of 15 sites using numerically exact diagonalization, we cannot observe the separation between the two time scales, the Lieb-Robinson time {{formula:07bc49d0-f5c0-40bf-abda-9444da2de014}} and the relaxation time {{formula:22c39954-5730-443d-a9fe-1b4ec03e4554}} , as mentioned in Sec. .
However, experiments with around 100 to 400 sites are currently accessible {{cite:8973b015116b12edec44eda910b252668cd066e2}}, {{cite:55f3326695f2f805537b58f967ffb203f9d30626}}, {{cite:d729be7d43e09f09a7b3a58f03c041b0615158ad}}.
Therefore, the separation of the above time scales would be experimentally observable.
It is an interesting future issue to directly verify the theory of the long and short-time regimes by such real experiments, which would open up the experimental investigation of the emergence of thermodynamics from quantum mechanics.
| d | 1e848cbc557b7d4fdc188d5d1197f620 |
SPARF View-Generalization benchmark.
In Table REF , we report the average PSNR results on the validation set of SPARF for different methods on unseen shapes during training on all 13 different object classes and on out-of-distribution views. It shows that our SuRFNet can generalize to out-of-distribution views on unseen shapes during test time, surpassing state-of-the-art PixelNeRF {{cite:ca8c2b09a953ddd7ec5631c32f2512d76bb70989}} and VisionNerf {{cite:5547110892ee15b1650d99322c6c16dcd14413c2}}. Visual comparisons can be found in Figure REF . As can be seen from those results, the learned 3D prior results in multi-view consistency, especially when rendering from out-of-distribution views. More results can be found in supplementary material.
{{figure:5d65741e-be9e-40ef-97f6-7be447b84bfa}}{{figure:c2efd599-cebe-4c99-b683-94ef4a2abe45}} | r | c7ba77c3080e56dde34ec72df180505a |
In this paper, we introduce a quantile estimator which is computed by directly pooling the detailed simulation outputs from various replications to obtain a sample quantile estimator,
called pooled sample quantile estimator. By pooling the dependent (within each replication) and independent (cross different replications) simulation outputs, the resulted sample quantile is introduced to estimate the quantile.
The pooled quantile estimator has been investigated under independent and identically distributed observations, such as {{cite:30fedaa43d5a1ead35cf51096da21046eecdd139}}, {{cite:dd5028e449124d6ea3ea6baa3e9c976523e82e5b}}, and recently been used to construct the confidence interval of quantile estimators in {{cite:fda673b81842286904190130505f7a6b336059ad}}.
In this paper, we develop the asymptotic results of the pooled quantile estimator based on the framework in {{cite:7193028a667fffdfad064549dc4d2f555c27a6cd}}. Our asymptotic results show that the proposed estimator has better performance especially under the situations with multiple processors and urgent time deadlines, i.e., the job request is too urgent to produce sufficiently longer sample paths. We highlight our contribution
as follows.
| i | f374077090ae7b8726b5ed39a70c778a |
In the following, we will give an example of the inconsistencies and inaccuracies introduced by the time-correlated noise using the case of TTVs. TTVs may be caused by a perturbing object in the system such as a stellar mass companion of the host or another planet{{cite:74723366c66c994c1df338fbf4715bd8a14bcbaf}}, {{cite:d4c0311171824c2186a704fb083dfc242d055107}}, {{cite:130c77c87ba9da117e624cdf12d697bb774f08c6}}, by exomoons {{cite:f11ab42099c89e83141f9d5d50c8800ef8ac7f12}}, stellar activity (see e.g. {{cite:a1f7da2eae7d53c9165ede1eef59c8155dc759c9}}) or other, non-dynamical phenomena {{cite:bfb1278f5fcc0f8ae8354cf68f3cf22f4ac38d3d}}. As TTVs have a wide range of origin, their analysis may be applied of many different phenomena in a given exoplanetary system. We argue, however, that correlated noise may cause phenomena that mimic TTVs, making proper noise handling essential as underestimating the uncertainties may result in false TTV detection; while overestimating them may hide real phenomena.
| i | ce0e5486f84748b8361c8a1a450c5d4a |
In this section, we describe our approach to learning fair and accurate models and highlight the connection to MTL {{cite:43f0cddaa1410bd7aa6a02376a8c90d550d19b5f}}.
We consider the following functional form
f(x,s) =
w(x,s), (x,s) X S,
where {{formula:b2da4d80-2ff3-487e-82de-8da5e54d4855}} is the inner product between two vectors in a Hilbert
spaceFor all intents and purposes, one may also assume throughout that {{formula:79cb6d01-05f9-49d8-811a-e2f7cf04beeb}} , the standard {{formula:5110f8c9-ba3a-41d5-b076-10d1bd88e242}} -dimensional vector space,
for some positive integer {{formula:d6d1d386-9dd1-4a22-aa9d-cc65219f5f7d}} . {{formula:fd575c08-973b-4f1c-9586-470cecace25a}} , {{formula:f2084a6c-7c27-4d8a-89d8-aaf264729279}} is a vector of parameters,
and {{formula:d13bf506-65db-493b-93f8-9a022faaedc5}} is a prescribed feature mappingIn practice, a bias term (threshold) can be added to {{formula:1a30fc3b-1868-46dc-ad9a-e074c1aaa935}} (which may depend on {{formula:40ca153e-7917-48aa-9e24-6bb561534099}} ) but to ease our presentation we do not include it if not necessary..
| m | 81abadcd6b7a3d244fd783b6a0760c1f |
Model Uncertainty:
The Dice Loss {{cite:0a8f4731ff40e2cb33cad6bdaf700c23037afa4f}} between prediction logits {{formula:a824c5d2-ce9e-4e48-8f90-adc57c83b25a}} of the DOINN model {{formula:792d22f9-2a53-491f-bfc3-0a08381465fd}} captures the model uncertainty:
{{formula:39ecfacd-ae3b-4486-aad0-46d7d7f24962}}
| m | b507c272f6d3449dca769e92641e784c |
Sum-Product Networks (SPNs) {{cite:b0133db938d84ad1e9ecf9298ad5c28e644d0b54}} are deep probabilistic models that permit exact and efficient inference.
SPNs model probability distributions as a computation graph that consists of sum nodes (representing mixtures) and product nodes (representing independent factors). Specifically, time complexity of marginal and MAP inference in SPNs is linear in the network size.
| i | a7f00e1e730136e2a1c306e27b995574 |
C. Binggeli would like to thank A. Gavel, A. Lavail and M. Sahlén for helpful discussions. M. C. Toribio would like to thank A. M. S. Richards, E. Fomalont and L. T. Maud for useful discussions. A. K. Inoue and K. Mawatari acknowledge the support from the Japan Society for the Promotion of Science (JSPS) KAKENHI Grant Numbers 26287034 and 17H01114. A. K. Inoue and T. Hashimoto acknowledge support from the National Astronomical Observatory of Japan (NAOJ) ALMA Grant 2016-01A. T. Okamoto acknowledges the support from JSPS KAKENHI Grant Number 19H01931. Y. Tamura acknowledges support from NAOJ ALMA Scientific Research Grant Number 2018-09B and JSPS KAKENHI Grant Number 17H06130. This publication has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 730562 [RadioNet]. This publication makes use of the following ALMA data: ADS/JAO.ALMA#2017.1.00190.S, ADS/JAO.ALMA#2015.1.00821.S. ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC (Canada), NSC and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and NAOJ. The authors acknowledges support from the Nordic ALMA Regional Centre (ARC) node based at Onsala Space Observatory. The Nordic ARC node is funded through Swedish Research Council grant No 2017-00648. This research has made use of the VizieR catalogue access tool, CDS, Strasbourg, France {{cite:4ee4c400eae20c26c38d9a3b448fa27d582fb4ad}}, Astropy, http://www.astropy.org a community-developed core Python package for Astronomy {{cite:b3a1ac13e6c338e3e4bc08cd5a755187c8c9a07c}}, {{cite:05c9471bc772357b75ed95a228241fb513987d9e}}, APLpy, an open-source plotting package for Python {{cite:16d21c98b12b804c0cdf65a8bf2ca344f84d5b6c}} and NASA’s Astrophysics Data System (ADS).
| d | f76cd6041d51d6c56890733e462407bc |
On the other hand, we have not tackled the most important questions: do asymptotic observables exist in expanding spacetimes? If so, what are they, and how are they computed? Can census takers in an eternally inflating universe be used to define a measure on the string Landscape, and if so, what is it? It is very possible that these questions will ultimately lead us in directions orthogonal to the the ones we have pursued in this paper: as discussed, even a decelerating cosmology suffers from asymptotic warmness, and in light of this it is not clear that even the Strong dSC is sufficient to guarantee the existence of well-defined observables. Another possibility is that our semiclassical description of expanding cosmologies must be modified significantly in the full quantum gravity, so that distant regions of space contain little new information, and asymptotic coldness is restored. This possibility is worth exploring further, especially in light of the recent realization of black hole complementarity in terms of islands {{cite:576152c27fcbc17abc665dc4f4defd00db10e364}}, {{cite:2dd74e977330ff5fcb3c610b503c0cf2ad829d2e}}, {{cite:c1d982c6bb1f903f8082638bff4c4cc95ce93beb}}. Ultimately, our current cartoon picture of de Sitter and/or eternal inflation may be subject to serious revision.
| d | 8057a49387077fc1ad9c119609790f36 |
Several methods on properly constraining a weight matrix of a simple RNN without gating mechanism are proposed to alleviate the gradient vanishing problem {{cite:672cdb0b15ab9079f5eae3a796bf1ef24844b66f}}, {{cite:cf28c4331d803b4ecd7b9632e16c83c92764908d}}, {{cite:8c615af154a10c7c5cd062dfc425adc9de392b36}}, {{cite:9c1067cf80acbc7798c2f95cbb6af23fff42ec13}}.
These methods limits expressivity of models due to parameter constraint {{cite:c95cdbfd117761ff985d6d1ae551cdc7267ec5c1}} and thus are not usually used for practical tasks.
Our method takes a different approach for learning long-term dependencies through time scales of models and does not limit the model expressivity.
| d | a7352d3a9e2c5f4dbbc70f9bf35b02e9 |
A cognitive theory is a general postulation of mechanisms and processes that are globally applicable to families of tasks and types of activities rather than being dependent on a particular task. Cognitive models are very specific representations of part or of all aspects of a cognitive theory that apply to a particular task or activity {{cite:14993d55564f3a3c0b5478b2bd9b88a6c1e2d3fb}}. Specifically, normative and descriptive theories of choice often rely on utility theory {{cite:9f4867cee2dbfa3c84391b242455265ad844dd2d}}, {{cite:a99a54d7d0c843abcabb8cf8d9299d0bdbd1a284}} or aim at describing the psychological impact of perceptions of probability and value on choice {{cite:fc210d4fb82417b88a90bbc8645dcdbbfc0e4eb8}}, {{cite:7506cc6bbcf45542086fc3552e654b2a93c3c7a2}}. In contrast, models of decisions from experience (DfE) are often dynamic computational representations of sequential choices that are distributed over time and space and that are made under uncertainty {{cite:756f8f37abe32b888e15a500b232a8bc8977e066}}.
| i | f03830e4fb69289268706f37a138ce36 |
[leftmargin=*,label={{formula:88588987-a56c-49ac-9c62-7928db1853a6}} ,topsep=2pt]
ViP-CNN {{cite:9062b03919aae372fa054b1833f690405517ce54}} predicts predicates using visual features from three bounding boxes, including the two object bounding boxes and a tight bounding boxes covering the union of the two objects.
PPR-FCN {{cite:51fd3b317c817e47baebf5bae68d0f9b9796852b}} is similar to ViP-CNN but adopts a different architecture to combine the information.
DRNet {{cite:804bbbb256d236203eb73ed6830bdb2332d90bbc}} takes as input the appearance feature, location, and word vector embedding of two objects. The model architecture is designed by unrolling a conditional random field model.
VTransE {{cite:9d42b843728b5827ca17d5862eb6daa1040cdba2}} predicts predicates from the feature vector difference between two objets,
where the features involve appearance, location, and word vector embedding.
| m | fb0ed2fd23a2250c3f8b594f12ddb834 |
The experiments of Relativistic Heavy Ion Collisions (RHIC) have
produced a strongly-coupled quark{{formula:6f8c8a6f-1454-4376-a1b6-d25ef71da859}} gluon plasma
(QGP){{cite:3478c6f0245df8678c33938912225f2953775fe9}}. There are no known quantitative methods
to study strong coupling phenomena in QCD which are not visible in
perturbation theory (except by lattice simulation). A new method for
studying different aspects of QGP is the {{formula:e780b58f-503d-4bc7-8b74-39b0b6525009}} correspondence
{{cite:d0bfd848ad4edab293122975fb2259820a66248b}}, {{cite:1814c801c4491e57a40c49c251e5c35376d41128}}, {{cite:8916c60a388bf2847df891a5dc555b9522ded837}}, {{cite:a38899931dd46f82b636db8522e743838ecd985e}}.
This method has yielded many important insights into the dynamics of
strongly-coupled gauge theories. It has been used to investigate
hydrodynamical transport quantities in various interesting
strongly-coupled gauge theories where perturbation theory is not
applicable {{cite:8316913a4fd8de42a4103547ba90c8b76c5d7901}}. Methods based on
{{formula:1497038c-0498-4220-9f94-7459a562ee1e}} relate gravity in {{formula:e0a43cf1-5727-44d3-a1c1-2cd545510581}} space to the conformal field
theory on the four-dimensional boundary. It was shown that an {{formula:f0ae22c2-9516-4de1-af43-7af308c25e2f}}
space with a black brane is dual to a conformal field theory at
finite temperature.
| i | a00fb5f787a204f514b8066116c9f270 |
Diversity in a small world.
A network has the “small-world” property, if it is possible to go from one vertex to other vertices by passing through a very small number of intermediate vertices. More precisely, the small-world property refers to networks in which the average distance between vertices scales logarithmically (or more slowly) with the number of vertices. First popularized by the celebrated Milgram experiment {{cite:8d02870afbe256987a9ef6f0f7aa6a0981372063}}, the small-world property has been identified as a common feature in a wide array of population structures {{cite:a9410b2c2fdaba6d5ce8beae69c3e871063c06c8}}. Therefore, understanding its implications for diversity is crucial.
| r | 1c35f4c7fb1dcf1518140db450866d33 |
We report simulation
results in R with synthetic data demonstrating excellent agreement between our theoretical
predictions (Theorems REF -REF ) and the behavior in practice. The code can be accessed in https://github.com/philipthomp/Outlier-robust-regression. For robust sparse linear regression and trace-regression problems, we simulate a design with i.i.d.
{{formula:0e5381a3-6f17-45bd-85d4-79dd82fcbd8c}} entries and {{formula:7347c7fb-9046-42f9-af20-f00d130dac88}} noise. For noisy robust matrix completion, the sampling design is uniformly distributed over {{formula:41135dfa-885c-4587-9599-210f80bcb98b}} and the noise is {{formula:7e8c5559-c9e9-4871-9fa2-0d6fd4c86638}} . For numerical reasons, we solve (REF ) with the scaled design {{formula:02045236-a892-4f74-8e20-c3edbc77e0bf}} . We solve (REF ), (REF ) and (REF ) implementing a batch version of a proximal gradient method on the separable variables
{{formula:eb17a935-93d0-4259-9857-791a6df51bd1}} using a stepsize equal to {{formula:6ed321cf-626e-4832-8f24-3c1124ac4a38}} . The proximal map of the Slope or {{formula:e037d216-4a49-4264-9328-3f98dbfec452}} norms are computed with the function prox_sorted_L1() of the glmSLOPE package {{cite:4822b263904bc119ef0ffa6997223aef565b4e35}}. The ({{formula:daf66aa8-4166-4563-86b2-fa7719eefceb}} -constrained) proximal map of the nuclear norm is computed via ({{formula:37ead775-8c3d-4a20-8fd1-42cb2b6e5bb0}} -constrained) soft-thresholding of the singular value decomposition.
| r | dabe85263b6ba0b610a3c3502c81eb4f |
In LQG, the dynamical equations are often too involved to be solved explicitly, making the identification of physically relevant subsystems and the calculations therein so far impossible.
It is therefore judicious to test many concepts and techniques of LQG in symmetry reduced systems, where this issue can be overcome.
The application of LQG-inspired techniques to the cosmological setting, from which the field of Loop Quantum Cosmology (LQC) emerged, has produced promising results, among which is the resolution of the big bang singularity {{cite:3a3fdcd19b5c8307c60f042c2e7c766606a2366c}}, {{cite:8c7cb2bef8572f031c3cc79001883918cc02cde1}}.
It has been shown that such modifications of quantum origin can be captured in the so-called effective models, which are classical models with a modified dynamics that reproduce the semi-classical limit of the quantum theory{{cite:94582b996b6273e86a2e0152ba182cb360cb4c07}}, {{cite:0413fa36fa8c34643cd3ead44340ffacff92425c}}, {{cite:42051bf9d7531a9ac7b6fe0056fb7f05e24f9124}}, {{cite:cc088829e024b922256394e316d12557de71283a}}, {{cite:4cd7b0aa3af05f8808f17795e28424df8f0deee8}}, {{cite:61efdd2eef5f7190a32b83bd9be05c5028a53e17}}, {{cite:1e27c7dd6963db6cd47f4d31034d963710932f84}}, {{cite:a4e04f7c23437faa6acffbf39a0c13f59bbf336e}}, {{cite:9d93ae7d2853893e047c21d0092831416f67a08a}}, {{cite:4a787a5d0cf609a8a8454196274c8b1473178ae6}}.
The efforts were also extended to the context of black holes, and several LQG-inspired models for the black hole have been introduced, often concluding that the singularity at the center of the black hole can indeed be resolved by applying LQG techniques {{cite:f700feb721c813b786148a1c40eedd355d44dc29}}, {{cite:0fc0cfa30a8f5f4de67f38a9a55aa7beafbee777}}, {{cite:9acfc97fcafab981ac72b8390314efdcd3efa283}}, {{cite:0f145a896d3346cf6f1ba849fc8193069f879e7e}}, {{cite:e5fa12d92853a72090f31df479783d5ab04c3aaf}}, {{cite:7069cc8c11239f270ea16d8aa85bb4da45541be7}}, {{cite:8a091ee6d8289a5a2a441531790b728b7705879b}}, {{cite:38583a8a57b3f993324c41c23ce40e3192d18760}}.
As a complete quantum description of the black hole interior has not yet been achieved, black hole effective models have attracted a lot of interest.
| i | cdbe3f2951c1b13dcdb953d7e294a196 |
Formulating the environment as a player {{cite:3277c7430062c0bca8f30339946c7fc0216ceb68}} in an agent vs environment game is an interesting way of ensuring the distribution of tasks (strategies available to the environment player) does not bias the ratings of the agents training on those tasks. In Sections REF and REF we examined environment vs agent vs agent games demonstrating that these ideas can be extended to multiagent learning. Indeed a multiagent inspired path to developing increasingly intelligent agents has been proposed {{cite:788e2c8dcfb752f66f5423597e670362ea23050c}}, {{cite:195bf3ce26ffded9f6dd18443b4ed4cfd6425121}} based on the richness of such dynamics.
| d | dcd67a80c652d9f30a672a15a117db4c |
Then the equation has a groundstate solution {{formula:8609bfe5-4e75-4285-8bf0-b1d082a0682e}} if {{formula:99b40d3e-0194-42d5-a3cf-0fc54aaae624}} satisfies strictly the inequality in (REF ) (see {{cite:643cc33ade5f36eecfe31801998e96aa336c0c63}}, {{cite:5c9be038a66fa4b9fb472364aff0b82ed71db4a2}}, {{cite:d943f0e9801e590f930224ce2082d10ecd6dfb56}} and in particular {{cite:529a1d8b880ac630fc74fa43ce90e5345e100796}} which is a survey for the Choquard type equations, the related problems and the related references therein).
| i | 31e430cc99ed27982e32fb40b9dd58b2 |
The dCME can be approximated using the Fokker-Planck equation (FPE)
and the chemical Langevin equation (CLE). These approximations are
not applicable when copy numbers are small {{cite:502fbbd0e80487bb404ecfe92ddd41b77b3d2828}},
as relatively large copy numbers of molecules are required for
accurate
approximation {{cite:e0960a03fe664885f40bca0c181fa70d95da1b04}}, {{cite:502fbbd0e80487bb404ecfe92ddd41b77b3d2828}}, {{cite:bf57920726c6df0411e8312b68f92c46814522c2}}, {{cite:87dc47d61f7f77aced744ba8f5e9ab1a3a3ea96d}}, {{cite:d0c04b8147c703be5ee804e4c61baabdba9e455b}}.
Recent studies provided assessment of errors in these approximations
for several reaction
networks {{cite:82323a74b61e76a223689142cfe542d1bc5a6df9}}, {{cite:8c57d1d72e1208d499d89133cd16f2ea860ab919}}, as well as
numerical demonstration in which the CLE of a 13-node lysogeny-lysis
decision network of phage-lambda was found to fail to converge to the
correct steady state probability landscape (see appendix of
ref {{cite:07d8d168e6f2bb45986104bbf0e188b85dbd8852}}). However, consequences of such approximations
involving many molecular species and with complex reaction schemes
are generally not known.
| i | cdf1cf7c7a09050d65298910914b3dab |
In this section, we report the results of three different types of features for the three training methods on the two datasets: (i) Maximum Response (MR) filter and texton maps of {{cite:b1f12233296825dd6baa656a68ea912c223ccdec}} as baseline handcrafted features. We used a publicly available implementation of this method; (ii) CNN features extracted from a VGG16 network pretrained on ImageNet dataset {{cite:d3339de235661326189cb58d1b1c0607b875d9c2}}; (iii) Our proposed DRFs extracted from a pretrained ResNet-50.
| r | c8eea91206f4a70e527d687d0e9e6fcc |
The effectiveness of adjusting time-constant parameters to the task may also have implications for neuroscience: though effective time-constants of real spiking neurons are variable and dynamic {{cite:daf97a2dd92f83b326086ed2aea1b5e3194c935d}}, the benefit of training these parameters in SRNNs suggests these neural properties may be subject to learning processes in biology.
| d | 2fdc11a28173aaa99c8dfe7911f0333b |
Multifractal analysis is a useful method to quantify properties of complex system, and it has been applied in many different fields, e.g.{{cite:3841f60980ef32c147c8403d1a50be109b3c1cec}}, {{cite:542a581c515874c4ddc2e175c247729a1062d168}}, {{cite:37f9c7046cfbd3d6ed025bc1452f391d22e9d056}}, {{cite:336469178236693b62ca41d89354d2669f02b49e}}, {{cite:04bb669502791b882a59828c3f624bc7a76928b6}}.
Multifractal analysis is also popular in studies of financial markets and multifractal properties have been intensively studied{{cite:04bb669502791b882a59828c3f624bc7a76928b6}}.
To investigate the multifractal properties of the Bitcoin market, we apply the MF-DFA method{{cite:c5c1b95bef15f3e9d6bbd25fe0f594fc13798763}}.
The MF-DFA method is described by the following steps.
| m | a8adbb37af8fab204e79f798cd4491f4 |
We have upper bounds for Euclidean {{formula:1bcd67b8-590a-4583-b1e4-d49dc066ca0d}} -distance sets with several conditions, which are counterparts of that of {{formula:327a1259-f580-43d2-9499-472207461319}} -inetersecting families. Let {{formula:0d47fa7b-51cf-4d59-a760-ecdac2e52b00}} be an {{formula:6f524cbd-e83c-4dcf-add1-ba8e24d8dea6}} -distance set in the Euclidean space {{formula:fed008d1-2505-4f32-a6a8-19ae6209e4e4}} .
For {{formula:cb72ed3f-6a1d-4fc8-a47c-a7d38d2f15ae}} in the unit sphere {{formula:95512fc7-8058-4532-b7f9-441aa16f053c}} , which corresponds to the condition of {{formula:2fa2509b-18bf-4331-956d-ca93cbc1a20b}} -uniform, Delsarte, Goethals, and Seidel {{cite:7acefa299140e149c5ab766ac140c7bd2e1da9e3}} proved that {{formula:ac85d641-7ca3-4ac1-9f38-6e5e59be4574}} .
With no assumption, Bannai, Bannai, and Stanton {{cite:2cb7a6b327a6ae980e7eb80b7dda93fbca40b5c3}} proved that {{formula:83ab2ee3-579e-4c3b-bea4-c1f35c6ab4ae}} .
For {{formula:705b4800-c918-41e3-bdd3-0f09b3259437}} in {{formula:0aae18fc-53c5-4ed1-a7e7-b9451c7acb5d}} concentric spheres, which corresponds to the condition of {{formula:73768bbd-d248-4c48-9bf7-c2adaab92181}} different sizes, Bannai, Kawasaki, Nitamizu, and Sato {{cite:df43205b526f81601c57fb013cb35b53cc5169ac}}
obtained that {{formula:19a43db5-18c2-49ea-b764-74596da4012a}} .
Recently simple alternative proofs of these upper bounds are given in {{cite:80b4277b7658899cf520d4a05a657105c2ee0026}}, {{cite:b6b94aa45c3c2d368dd48dd1bda7bfc9497724cd}}.
| i | 86bd533d117aedbf5033d19a067a3ebf |
Utilizing the feature extraction capability of deep neural networks, Simonyan et al., {{cite:d9830ed514c8f8ce0dc7cac0604d316108feaafc}}, uses a 2D CNN to create a holistic representation of each input frame of the video and then uses those representations for recognition. Temporal dynamics of a video can be modelled by sequence modelling using recurrent neural networks. The works {{cite:a95f65c1815a476282df195817084db2f3270b67}}, {{cite:4f3d95ae9b7851f5f5cc6501bf52cb20fb5fbc11}}, use Long Short-Term Memory (LSTMs) to model the temporal dynamics of the features extracted through CNNs. In {{cite:cc83493ab5d837badd9c2485e9f0f4b2e4be13d3}}, a 2D CNN-LSTM architecture, where, in parallel with the LSTMs, it also uses a weakly supervised gloss-detection regularization network, consisting of stacked temporal 1D convolutions. A simpler variant of LSTMs, Gated-recurrent Units (GRU) {{cite:7b18d99613392d3704a7154d70c4cfe2697986ec}}, which consist of only two gates (update and reset gates), and have the internal state (output state) fully exposed, have also been used for temporal modelling {{cite:7b19818f83da8fd9dd29260358df56205839cd17}}.
| m | d968614c9a0960be9c529497e5b55f3b |
For the first statement, use that {{formula:ac45c697-8b0c-4283-934c-cd79ea9f50d9}} to write
{{formula:275c2034-6607-41ae-ad4d-e589567289dd}}
for all {{formula:9361423a-eca3-4cf2-8895-9007c33749f7}} , {{formula:3b148264-7aef-4938-9ea3-5b31c0b2e18a}} and {{formula:6306116b-ccee-429d-9651-bb23a4d2d7dd}} , where the final inequality uses that {{formula:7e6bc0d3-5103-42c3-9d11-c690fd13a993}} for {{formula:2ccbf798-2fca-4383-a137-d17e6fcd741b}} , and that the sequence {{formula:d69976ae-2320-4231-9bd9-417a2cf7a593}} is uniformly bounded in {{formula:237d2a65-4782-4cff-adfd-7c91c2e0f110}} .
The remaining two statements follow from Fourier multiplier theory. Indeed, by cutting off the frequencies of {{formula:4c996952-fa94-4beb-94a2-bc82bf06024d}} , for both (REF ) and (REF ) it suffices to show that
{{formula:acb4cf40-a996-414a-bc50-3804c4608961}}
for an implicit constant independent of {{formula:fef10927-62c7-4915-b30f-8db818b5cdd2}} , {{formula:827df7c1-f894-43eb-a2e5-36ad9f0d01cd}} and {{formula:fbdcad83-24dd-40a3-8b88-0b4ff6df4337}} . To this end, let {{formula:735b95f0-03ed-4168-b6f1-941a9c91b5cc}} be such that {{formula:4f58d919-410f-475d-896d-e42fdc83c014}} on {{formula:4349c956-bcde-4af8-b1a3-1fbc200f58cd}} , and {{formula:89c07578-823b-4dac-9ae3-4340f1d8bf32}} if {{formula:557be898-222d-43e5-ab53-d80f33f68d4f}} . Set {{formula:54d69f9c-54b7-46a6-accf-8b1746344254}} for {{formula:d2352758-2aea-4f7a-90c6-38411ba5e9ac}} and {{formula:4b7a89d9-25fd-4e27-a400-5e97fb1988cd}} . Then
{{formula:5721c197-b2ac-4e4a-aba5-106c326f0bb5}}
Now, for each {{formula:d5aff510-96d6-48c2-8253-384bf8a14199}} there exist {{formula:c4f98281-3df2-4848-9291-43113eb2e7d7}} such that, for all {{formula:3b4a45a2-6fa4-4990-a4aa-725b9691fff0}} with {{formula:44745c7e-08e2-4679-8067-83f4fe70fb90}} , and all {{formula:1e9ec3f7-07b6-4244-a2d8-f90b5082d945}} and {{formula:5e7cb916-0a90-4510-afd7-f507402dc7e3}} , one has
{{formula:a9b5f19d-43d8-4773-9239-fe1ef4933e7f}}
Hence the Mikhlin multiplier theorem on the Besov space {{formula:0929a062-654c-4447-b4f6-7eae131e6f48}} (see {{cite:a6a65fd34761a6550fd7c266121d38266ec01b92}}) shows that the collection {{formula:c0ab207e-253c-4801-ab6b-1446f1cef4c7}} is uniformly bounded in {{formula:2141f287-b4ff-43cb-af2d-be7e25417705}} . Thus we can use (REF ) to write
{{formula:83b8635f-6a91-4931-a8d9-75731de36c89}}
for implicit constants independent of {{formula:1a1a5f75-e162-4882-b70f-6c321297e8dd}} , {{formula:2fbd1839-34e9-4b4e-9cf7-9cf761a15401}} and {{formula:ff2ac0fd-88a7-4ee5-947e-642cc2caa00b}} .
| r | 0be793f1b35dbb31b3ed8679c1ebb03f |
Empirical studies. Coincidentally, shortly after a preliminary version of the present paper was submitted, NeurIPS 2021 required all authors to “rank their papers in terms of their own perception of the papers' scientific contributions to the NeurIPS community.” Using this dataset, an empirical study may be used to analyze what would be the outcome if this mechanism were used in NeurIPS 2021, or at least were used as a reference for the decision making. On the flip side, peer review involves much sophistication that has not been considered in the development of the Isotonic Mechanism, and therefore more efforts are needed toward the employment of this mechanism (see Section 4 of {{cite:cdc9ee317873676a7c9d668500452daffad1f437}}). Perhaps a more realistic starting point is to integrate the Isotonic Mechanism or its relaxations with the long line of research that aims to incentivize reviewers to provide more accurate review scores {{cite:7a56a2ab705126f199ae84d64f6548adf2578086}}, {{cite:c8a6e9a1cc0d0652c0cf2b58fcc092c7c05e8ed0}}, {{cite:becd715d90a249cfa6f6e1828072def6f3d2e192}}.
| d | 641c63e30093570c9b5c4859646a40f4 |
In this study, we aim to design a paradigm that distinguishes the causation edges from spuriously-correlated edges and obtains the faithful DAG.
Although learning causal structure from observational data is challenging, we draw inspiration from invariant learning {{cite:c7f91af3b68c6f4479821d94c5b72b19942e12e9}}, {{cite:c38f96e9bce31b8f133ac9c5176bf476c6dc70ca}}, {{cite:6cbe70a8291a33db56c75e4bb387147af3ff9383}} and approximate the task by searching the edges with invariant structural equations in multi-environment settings.
Across different environments, only factual causation edges remain invariant, while spurious edges or edges with wrong causal directions hardly remain stable, according to the assumptions in invariant learning {{cite:c7f91af3b68c6f4479821d94c5b72b19942e12e9}}.
Though reminiscent of past ideas - e.g., causal structure learning in multi-domain, from heterogeneous/nonstationary data {{cite:9012fcee81aac4577905cc8f8b448e803b39c775}}, {{cite:513b3a398e6fbaf1e4aa764afc712661f1f1c391}}, {{cite:8bc69c51028ecc99a059e55ee310b81ab0a30940}}, {{cite:aa9290d78ef278673155965d345a984f961b125d}}, {{cite:0e3808276b594841eb5ac0c4bc4754463ded5d04}}, {{cite:f56afeebda0153eab4ae7c577f7f9e66f3bd2f07}}, {{cite:549ae382db1e23aa99ef73e3d1c9600f91ab5022}} - these methods are only applicable in a linear system or restricted to conditional independence tests, which suffer from high computation complexity as the number of variables increases.
To achieve effective differentiable causal discovery in both linear and nonlinear scenarios,
we reconsider Table REF and additionally exhibit the multi-environment information, which impacts the distributions of additive noises.
Applying ERM on these environments separately results in different functions when there exist spurious correlations in the causal graph. This inspires us to exclude such unstable edges towards a robust DAG across environments.
| i | fd0d542b1a2f532e1f490860a86a4a53 |
Here we adopt an algorithmic information theory {{cite:62168e958ed257d79d44e281adee08f73aa810c5}}, {{cite:d4ddeed1f7864009565062cf220ea22c180a90b0}}, {{cite:b26772f4ce5cb8078f87dfff58fa46d361e3b95d}} approach, and argue that if the objective function to be optimised is `simple' (in a technical sense, discusses below) and the set of geometries over which the the objective function is evaluated is also `simple', then:
| i | 3b254cd87ac64f037163ed8e94a0d47b |
Answer these interesting and vital questions about particles is the starting motivation of the current work. In the Standard Model (SM), we describe the excitations of relativistic quantum fields that are characterized by fixed quantum numbers including mass, spin, and various charges {{cite:a2eef95e79be04222b8aa40214896f46bdb0d47d}}. So far all the information we know about SM is obtained by detecting the quantum numbers of the fundamental fields. Quantum numbers and their structure determine what we can talk about the knowledge of physical particles. Our basic idea is that particles are nothing but a set of quantum numbers that can be measured by certain apparatus of finite resolution. The strong coupling described by quantum measurement will lead to the dynamical quantum Zeno effect (QZE) that gives rise to the low-energy/slow-oscillating effective models. As a popular and amazing effect arising from quantum mechanics, QZE {{cite:53b410465a25c43a0a4eb4b1cf8b7ef547ee03b8}}, {{cite:20fb870e260b48d4938af13c3b79a5a94f31039f}}, {{cite:ae00e9d88cce0c6611f8c1810242d92b974c86ee}}, {{cite:8cfe5ec20e86cf0ee64adef6ded2ae27c5899302}}, {{cite:fe0efe579b985ff714dd7fa3602875195e59ff02}}, {{cite:c14298a6b3db0a84862cf8de7dd447c952294ed2}}, {{cite:2ea12853995d4674327570a2c6f8885038063c97}}, {{cite:3e88bc3b993d86ecd9e68f1ee6aa7509cd5cdd65}}, {{cite:955d552c2295ab6c8a90cffbca4a1360398cf920}}, {{cite:4224d1f66928a4650dbf827d4db7677a58c576be}} means that a system's unitary time evolution from an eigenstate of the measured observable into a superposition will be inhibited in a subspace by the measurement-induced projection of the system. To put it another way, the fast oscillating components induced by the interactions among “more fundamental” particles are treated as classical variables that have to be smeared over short, finite periods of time determined by the measuring apparatus, then one obtains the effective particles and their structures for the quantum mechanical systems.
| i | 018f0eb7c8df28fe32f696a7dcd88786 |
where {{formula:4d332d0d-e0f2-478d-8555-7052bfe54562}} are transforms that aim to maximise the correlation of the vectors. {{formula:db1cab6b-a7e8-4078-a66b-6ebe6fda4931}} increases where neural representations have encoded more similar information. Further details regarding SVCCA analysis can be found in {{cite:08bb181d3880c43c7c45fef4a1c20f5e495b121f}}.
| m | 4771aa6b1bf60bba7e82badd9c9ad64f |
The investigation of all possible adatom species in rows two through five of the periodic table was completed using JDFTx {{cite:9c6e33c12f1e589193898611f87ef232055c406e}} to take advantage of GPU functionality. These calculations were carried out with ONCV pseudopotentials {{cite:d86805e37a5237f0e6c4b94eb956a3765239a2c1}}, {{cite:76ab6e7a1d050af3ab031c33b68799ada3c2af06}} using the Perdew-Burke-Enzerhof (PBE) {{cite:7c974034e3f45975ab2b4eb19719e1b325eceb8f}} exchange-correlation functional, a 1090 eV plane-wave energy cutoff, a 15x15x1 {{formula:1e372b0c-0937-4f3a-9d98-3629a673734f}} -centered k-mesh, and Methfessel-Paxton smearing of {{formula:71a77179-6792-474a-9cec-10d18f408d23}} eV.
| m | 4280984e38b5a09ba91e37a2baf16e95 |
The first-principles calculations were carried out based on the density-functional theory (DFT) as implemented in the Vienna ab initio simulation package (VASP) {{cite:9561e43a1abd7caa9b28d147d81e09d1a7ac40a0}}, {{cite:76591b7139dbbf32bc9bf09594bbdaf45c322455}}, using the projector augmented wave method {{cite:cddb492c2ef4c397f9fc9bfaddac46105029b49b}}. The generalized gradient approximation (GGA) with Perdew-Burke-Ernzerhof (PBE) {{cite:a2be6b08501e2bb4550a8bcdac74e94367dd5118}} realization was adopted for the exchange-correlation potential. The plane-wave cutoff energy was set to 500 eV. The Monkhorst-Pack {{formula:afcaf00d-1550-4063-a7be-5258d7e382f8}} -point mesh {{cite:5dca4da731e8c31e54cf84c50e51fa4a4a9d7e24}} of size {{formula:73c574e2-7797-4e95-83f0-36e8815ad163}} was used for the BZ sampling in bulk calculations. The crystal structure was optimized until the forces on the ions are less than 0.01 eV/Å. From the DFT results, the maximally localized Wannier functions (MLWF) for C-{{formula:d8727b0c-a5b2-47f9-b877-3101d4e9aa5d}} and C-{{formula:f0dd567c-76ac-4e93-81a7-f846a72acf7d}} orbitals were constructed, based on which the ab-initio tight-binding models for the semi-infinite systems were developed to study the surface and hinge spectra {{cite:d041bc453367fa8deecd5f4d8ebb13aec038fc31}}, {{cite:b6bf5989083932f42ad423a7ce104c5e405fa4b2}}, {{cite:10c1fee3c62d39307d6f533d74d78f7e263c1339}}, {{cite:523469aacf6f5d09ca6f68cdd87a796cbbd36e35}}, {{cite:1c9a2a563ab6a55009ed6ec0b786f1c4c8d53cc1}}.
{{figure:bb48d194-da31-4915-8c36-07ce9f3fda8a}} | m | 66d1a21b978bac4865b2274ad4ef0840 |
With the very recent release of the third GW transient catalog {{cite:55ba8594c12b404a7138d4de616d17b411e8972f}}, the total number of reported coalescences increased to 90.
Some of the more remarkable events detected to date include:
| i | a95740b2fa6e5ecac5ff0a03fd67f123 |
We did not provide an effective analog of the global Clifford unitary transformation-based method in {{cite:4c87b4ea76068ca56d561ca73600c810cf56b122}}. There has been work which provides description of global alternatives using stabilizer states {{cite:ea10f3f9052959210098c94f3025969366df19f8}}. Whether there can be a scheme based on such states that is competitive with the classical shadows method {{cite:4c87b4ea76068ca56d561ca73600c810cf56b122}} remains to be seen.
| d | f62fc7318410548a9fcd4eef76503c52 |
NVM devices present an attractive option for implementing synaptic storage due to their demonstrated potential for low-power multilevel operations and high integration densities {{cite:d424466734a5ffe1cfdaa22c315ead62f26d7099}}, {{cite:4019e5b04097ed8074b26cc6c3bda0dce4482cb4}}, {{cite:6f6c9232ee56c652127b0d43706af1f2903444f6}}, {{cite:eb5f676f3a4d3c827d89385d4a04b94e6349a40b}}.
Recently, several NVMs are being explored for neuromorphic computing: Oxide-based Resistive Random Access Memory (ReRAM) {{cite:856a6a123cba0a8540457da9a75f98317da29150}}, Phase Change Memory (PCM) {{cite:c8a7f9f30c8e535ed8f5e9f0f2b6405d667236b8}}, Ferroelectric RAM {{cite:6b77804674822b34ef8d5e88b221d0ecfe5c2ef6}}, and Spin-Transfer Torque Magnetic or Spin-Orbit-Torque RAM (STT- and SoT-MRAM) {{cite:85241199e64931b75ca3cf697e7994b098c246eb}}. Table REF shows some recent neuromorphic hardware demonstrations integrating NVMs.Beside neuromorphic computing, NVMs are also used as main memory for conventional computing {{cite:7be298334fa985e6ac678a749c383c59b509ed9f}}, {{cite:4556887748a347b95ce083d25be8a7b6976ccf7e}}, {{cite:85019f9b9aec931b40ad3b8b00f65c81f8e17d26}}, {{cite:ca887c161e7684573543909fb33222e5e9679ec8}}, {{cite:ed90364832c581324e004055e235f04ce14493d6}}, {{cite:fea8727d4d26cea28f482a7963f5e1d84d8730db}}, {{cite:42e0fe758cb41f506b2fb0abd306f4a3c2b0b82a}}, {{cite:abbba42aaf7e204610c3b045e002004effff11a9}}.
{{table:4f0a6645-57a5-4acf-aee4-38f283b8da66}} | i | 41b068c7071cfcca8d7421f19b3cd80c |
In conclusion, we have shown using quite a general treatment that Single Field Inflationary Models can indeed be compatible with the Swampland De Sitter and Distance Conjectures in a wide class of cosmologies where the Scalar Field follows the usual Klein Gordon Form. We began by discussing in brief about the Swampland Conjectures and their implications on Inflationary Cosmology, after which we briefly discussed the Exact Solution Approach to Inflation. Then using that approach , we showed systematically how Single Field Inflation in Modified Cosmological Scenarios can bypass the problems it faces in GR Based Cosmology. We showed how the {{formula:4b12072a-7f1f-4b63-9a09-428aa6e7b338}} parameter for Inflation can still appropriately small for Inflation to occur and how the e-fold number can still be to the scales required by the latest observational data {{cite:04335e7e5f38fee62bf61fd70e0051d871e615ca}}. We then showed that both the observational data for Inflation and String Theoretic Definitions of the c and {{formula:afad2041-6a6a-4aeb-b60c-d59c19c5deab}} parameters of the De Sitter Conjectures and it's refinement , respectively, can agree for Single Field Inflation in Modified Cosmological Scenarios. Hence, in essence, we have shown that Single Field Inflation is still very much compatible with the Swampland Conjectures in a wide Class of Modified Cosmological Scenarios. One crucial point which we would like to elaborate here is that in obtaining the equation of the inflaton field we have assumed that the matter, specified by the inflaton
scalar field, enters into the action Lagrangian in such a way that its variation in a Friedmann-Robertson-Walker-Lemaitre background metric leads to the Klein-Gordon equation, expressed by (11). Therefore our method is only applicable to theories where the background metric alongside the perturbations, are not modified.This means that Horava-Lifshitz theories of gravity {{cite:1065c3fbf202157723c2aa397579804095935dfc}} or theories of similar plight are beyond the scope of our approach. Hence, we cannot comment on the compatibility of Inflationary Regimes in such theories with the Swampland Conjectures.
| d | 5a8452177338f74f9fc836462eeeb4d3 |
In the following sections, we describe our modification to LaserNet {{cite:3b227734be7097b807ad1903f0a8a561a7cefb8c}} to fuse RGB image data, and to jointly perform semantic segmentation of the 3D point cloud in addition to 3D object detection.
An overview of our proposed method can be seen in Figure REF .
| m | 1509d21c2e91df4716b85efd0cb0aaf8 |
Since the discovery of the {{formula:643c2654-2c51-4dd1-b4d2-0d52d6ca9fd3}} state {{cite:caec8dd44fef58371e137465c77c817937203446}}, over thirty
exotic hadrons have been observed by several experiments (see
Refs. {{cite:d74b0eac473bef38260afd8e9d4c6b78745299d4}}, {{cite:6f4159110838e2beff82d556c2700169e58c9add}}, {{cite:a0cc0fe86dae9c845533768a8ee9d605d247f2d4}}, {{cite:9d705a2ede71151012de533092fb2c46d63fe227}}, {{cite:35f038ee0934549fdc4e666269291addba313271}}, {{cite:eef06c72d57444e667fdd63da293c8ef9a694f02}}
for recent reviews). Most progress has been seen in
the charmonium sector, where tetraquark (pentaquark) candidates
with masses around 4{{formula:5145bca8-959a-4113-bd7f-880582113812}} have been found decaying to final states containing
charmonia and are believed to have a
minimal quark content of {{formula:f1cdbaba-4927-458e-825a-40bd72e06028}} , where {{formula:7883847c-40e3-4555-b76f-d0275a01847a}}
refers to a light quark {{formula:bed993a0-fa9a-4d1c-9af2-d36605a34183}} . Two tetraquark states have also been seen in
the bottomonium sector, via their decay to {{formula:5dec84cf-89bb-4402-9919-6c6b932d5f3f}}
final states {{cite:a5c85162314db91d7a2fc97b015ee67c4e74d8e9}}.
| i | b94a2d9c0f1f0a973026937c84036efa |
where, in our case, the acceleration {{formula:6bc288db-5479-42e3-8864-d0e9c22cac6e}} on each particle is evaluated self-consistently by direct sum over all other particles, {{formula:10aa9d06-2606-45a9-af4e-e930208d01ee}} is the dynamical friction [{{cite:ae88db193d429c2eecfe02abea061208c07dd11b}}, {{cite:13a2159eaeb680f388aeef5e9cd30c715ab849ae}}] coefficient, and {{formula:92886ecc-0647-496a-9d66-82ee62137362}} a fluctuating force (per unit mass).
| m | 44914e08e00337825b75ad4b37c84e72 |
As for the Coulomb gauge, the instantaneous potential has too large
linear part, which gives an upper bound on the static potential
{{cite:0bf7af14e083d9c175c8d8ca1f249847e3beb6d0}}. It has been suggested by Greensite et al. that
the energy of the overconfining state is lowered by inserting
dynamical gluons between (anti-)quarks,
which is called “gluon-chain picture”.
This gluon-chain state is considered as the ground state
in the Coulomb gauge {{cite:81ef576ae5ca4a359c4d0077bdf6f3eacf6c4c11}}, {{cite:15e32917a5ffc3b939e6d74d9a8e73f84bbc7f8c}}.
Therefore, dynamical gluon degrees of freedom must be
also important to describe hadron states in the Coulomb gauge.
| d | 7d399357c64451a31f919504cf67796f |
It also seems plausible that factors beyond stochastic optimization drive human development. There is, for example, evidence suggesting that children gain access to additional computational resources during their development, allowing them to apply more complex strategies {{cite:78365a6dcb325e2a7c78cc1094fc78db46136f8b}}. This idea of development as complexity increase could be readily incorporated in our framework by replacing the evidence lower bound from Equation REF with a {{formula:2c9835b2-398f-47b0-9a69-82b1fbe2d821}} -VAE objective {{cite:2f45f919349e2dca5ee2d19157d631b598956c5a}}, {{cite:f957c551fe6ffa0ec429380e2d71533ef7756055}}.
| d | cc93d5ee03c2170d3e53523eff0b1049 |
Effectiveness of Disparity Map Quality.
To quantitatively compare the reconstruction results of Stereo2Voxel and Stereo2Points with different disparities, we replace DispNet-B with SGBM {{cite:ccb8c002b9f357314d5cc9f1c92800d3b00dead9}}, DispNet, and GA-Net.
As shown in Table REF , the reconstruction results with disparities estimated by DispNet and GA-Net are slightly better than with disparities estimated by DispNet-B, while SGBM degenerates the reconstruction results.
The experimental results indicate that better disparities lead to better reconstruction results.
| d | 34cbf799904e6d6d972d5f0869e19b25 |
However, most of those previous work can only handle regular data, i.e., they need to assume either the underlying data distribution is bounded or sub-Gaussian, or the loss function is {{formula:a16f056c-106b-4d97-9164-a84448151340}} -Lipschitz for all the data. This is particularly true for those output perturbation based {{cite:4a90e38dec5b6cef5b001230315f61a1f3c32b48}} and objective or gradient perturbation based
{{cite:cadbfa5df4ca1e1c436567c7f9f19de7f2b1cbef}} DP methods.
However, such assumptions may not always hold when dealing with real-world datasets, especially those from biomedicine and finance, which are often heavy-tailed {{cite:6fdf882714f034a67c4d3a004228699e30488f48}}, {{cite:b2719267730831833a276d3b6bd9e1a7d07b0600}}, {{cite:9fd02dcf12d4a45abbcd21201d38814da0f1ee5b}}, implying that existing algorithms may fail to guarantee the DP property. Compared with bounded data,
heavy-tailed data could lead to unbounded gradient and thus violate the Lipschitz condition.
For example, consider the linear squared loss {{formula:511edb7b-da99-4e04-b651-3972c85cb84a}} . When {{formula:e4108a51-9446-4a0b-9e0b-45e7df863301}} is heavy-tailed, the gradient of {{formula:889b0466-f98a-4166-af66-b9fa42d6156d}} becomes unbounded. To address the issue, one potential approach is to truncating or trimming the gradient, such as in {{cite:5814f348c2cb4ef00881b6e42d1091af9a8a1e83}}. However, there is no existing convergence result based on their algorithm. Thus, new private and robust estimation methods for heavy-tailed data are needed.
| i | f19fe577b9656cd1d5d3c6a5b06df356 |
We provide a first overview of the method in Fig. REF . As for the MOEA, we use Non-Dominated Sorting Genetic Algorithm-II (NSGA-II) {{cite:dbefdddef46395cc3ae4ee8ece4785112c57557f}}, which has shown good results on this problem in prior work {{cite:e5115fbd1ff44cf9b4b8a0f146467c4b317b27ba}}, {{cite:9dfcd87eca93cc78a37b888832e2e58f3d9045d9}}, {{cite:4b3a7fd5d11bf4a591a29971547175daa8f74100}}, but whose runtime made it prohibitive on large networks. This computationally heavy method is marked in Fig. REF on the left with a heavy red arrow. Instead of attempting to further improve the algorithm (with likely minor gains in efficiency), here we design an alternative which fundamentally changes the way we treat the problem input.
{{figure:21673ae6-0f87-4d21-a2a3-f8ebf3afdb6a}} | m | 3c879392ce8cba62950c32c1106a8c7d |
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