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We work over an algebraically closed field {{formula:d53c28b1-408c-4224-9fe4-ed9e7767bc1f}} of arbitrary characteristic. All the Hopf algebras and fusion category notations follow the monograph {{cite:f4f20cc212e60ea14cce519b79dec684f209a191}}.
| i | ba7411d6a7d7035125cd59795b1dd791 |
where {{formula:df01381f-aa42-4fa2-bb08-87ba8fa773c8}} is a random binary mask, {{formula:3c87661f-4338-46b9-bb02-f37bac3a9106}} is the pixel index and {{formula:17243eef-5ed2-4bc2-933b-690a6131adfb}} is the probability of the pixel {{formula:abd3bfe6-f13c-405b-a8b0-423889e2444f}} being 1. In this case, {{formula:426ee3dd-37e3-4e0b-87e9-00bb5a7f566a}} and {{formula:3fe5df56-4e12-4713-b596-7169df03a724}} . Hence, {{formula:20369de4-4750-458a-adaf-f20f2c0c4047}} can only contain as much pixel information as the pixels from {{formula:a9f0c8d6-904a-4151-a53a-c720fc7758ef}} , but cannot recover any of the pixels already lost, and hence is farther from the manifold. With this intuition, we attempt to learn a mapping from {{formula:7bc8dbcb-932b-4147-b1ba-fa3681cdd827}} to {{formula:30b6df94-67de-4456-833c-70f0147cd802}} , where {{formula:6d0802e1-b8db-4c3a-b110-47d1af2bacd5}} are formed from a random degradation of the already corrupted image {{formula:cf7b7409-6947-4edb-9485-31e1bb2f2213}} . we attempt to learn this mapping using a Fully Convolutional Network {{cite:ab38cb2fc10025a81d7b724e3660f59d4205b96d}}, which was used for semantic segmentation and later became popular in literature for image to image mapping tasks. Learning this mapping encourages the network to invert the degradation model by making use of the context around it. To enable using the context, we choose FCN architectures with sufficiently large receptive fields so that the network can utilize as much information as possible. This leads to a training scheme where no clean examples are ever seen by the network. During inference, we feed-forward the images {{formula:a5ac9a67-8cf0-4454-94fc-21218f18c474}} into the network and obtain approximations of the clean image {{formula:5bef753e-0b5c-4c78-93b2-cfa3b820528a}} . There are 2 methods for performing this inference, as mentioned in later sections.
| m | 26b95413a8b2ae57f882363bada3e24f |
where {{formula:c1a6b736-c79e-41ad-b3b1-0299d8843678}} is the distance between adjacent samples and {{formula:b3f702e2-f5ea-4940-8548-beca28b1d91d}} . This expression is fully differentiable, and reduces to the traditional alpha compositing with alpha values. NeRF {{cite:7d16163749bbb8c6b8303df3813185b21e915b03}} adopts a 2 stage approach, a coarse and a fine network, with the fine network using importance sampling based on the values of {{formula:95c768ab-5c79-41fa-83e1-0b4a56f9910c}} from the coarse network to sample closer to the surface.
| m | 1fd5da2d4a6ca1dad7f9b4b6b4059ddb |
Given the work that has been done on extending the classical double copy on maximally symmetric backgrounds {{cite:438aa073f29f19868c789d726400f85ba6ed65e3}}, {{cite:492651bb4d94c9b805037f9763181bc514d85c53}}, it could also be interesting to consider maximally symmetric extensions of the twistorial formulation of the Newman-Penrose map. Since (A)dS shares the same twistor space as flat spacetime {{cite:ff9d3c5f90bc6b1783cf848539a4b48205b836bc}}, and since the property of being an SNGC is conformally invariant, it seems reasonable to expect that much of the formalism we have developed here can be adapted to the maximally symmetric case. It would also be interesting to extend this formalism to arbitrary asymptotically flat spacetimes using the generalized Kerr Theorem of {{cite:fd525841d3f1e52c43b3cff8c66842d59f26262b}}.
| d | 933b1a904efc819e47f3184bfb463200 |
The term message denotes the unit of exchange between two IPs in the SoC. Though complex in nature, the message flows could be represented as finite state machines (FSM)s. The SoC architectural simulator gem5 {{cite:b1591a78c2f4e19a3c44d48f2d5138499d5b488f}} includes such FSMs to describe its CHI ruby protocol {{cite:bcb9b5be97941d9f02e1cfbdd512f74d651a56c9}}.
{{figure:60930afc-3172-41bb-88ce-b36e263edfdd}} | i | 4863d4ba42d44eb2a23507bbc5c7bea7 |
The last metric used in active learning is the variation ratio {{cite:bd04a41193c9a139b985be2ccfe67683ce0b5700}} which measures the dispersion of a nominal variable, and is calculated as the proportion of predicted class labels that are not the modal class prediction. It is defined by: {{formula:e4e69bb9-ecfa-41b4-a1bd-7d2d523fd0e9}} , where {{formula:04da6695-2543-4a35-b1cd-ba4072960dcd}} is the
number of predictions falling into the modal class category.
| d | 7ad7dc001febb095e615678d08ff7096 |
Comparison with attribute-based ZSL. We also compare our result with
the state-of-the-art results of attribute-based ZSL methods, including Lampert
et al.'s DAP and IAP {{cite:ed7d17b3de6e1f4a30cbecf53b827807f74c4d63}} and Akata et
al.'s
label-embedding method {{cite:c198f1600d39080a36daa84ebe9b1cd54fa12bdf}}, on the AwA
dataset.We list the results of average multi-class classification accuracy in
Table REF . Overall, compared to the
state-of-the-art attribute-based ZSL, our proposed method achieves better or
comparable performance, especially compared to DAP and IAP. It should be
noted that all the attribute-based ZSL methods are based on the well-defined
visual attribute and the category-attribute relationship. In contrast, our
method does not depend on manually defined visual attributes; instead we only
exploit `free' semantic word space learned from linguistic knowledge bases
without the need for any manual annotation for the AwA classes. This is thus a
very encouraging result. If we apply the given visual attributes on AwA to do
the similarity computation, we can get 49.5% performance, which is much
higher than the existing attribute-based methods.
{{table:5916ed8c-0a12-4c50-a133-469b4b9efa7d}} | r | 21894ec83522548c15d4f97ccf363eb9 |
The performance of the proposed BPSO method will be compared to that of the BB algorithm, that will be also jointly applied with GP. BB was first introduced by A. H. Land and A. G. Doig in 1960 {{cite:b7e18a3e009002f84eb1ce0e3d833512aafb228c}}. It is an optimal algorithm for solving combinatorial problems but it requires a much higher computational complexity compared to BPSO. Its complexity is not exactly measured but evaluated as exponential time complexity in the worst-case scenario and shown to be less than the optimal exhaustive search method ({{formula:c8248619-2e39-443c-8ca7-fbde59da9985}} ) {{cite:9e03561f11ee62909f202e787946aab1c1820fa7}}, {{cite:e327f0ac1318f6b0b0ad07a52a153cb40578a539}}.At each iteration of the BB, Algorithm REF is executed to find the corresponding solution using GP. The BB is a search tree-based algorithm that iteratively solves the optimization problems given in (REF ) and (REF ) using their relaxed forms. In other words, the problems are solved for continuous solutions of {{formula:f05efd10-4156-41a4-918b-e2f71d3eb505}} in {{formula:6c42732d-f12a-4253-afc7-b6626cbf92aa}} where the GP is executed to determine the optimum solution with non-binary values of {{formula:4a6b9e21-314d-417e-abe5-75e66cfcfb37}} . We denote the optimum continuous solution and the corresponding utility by {{formula:8d99b0b1-ba54-4e01-9f73-51cec8265ee0}} and {{formula:7f8b6d79-11d7-4b2e-a15f-094f85f2c458}} , respectively. If the obtained solution satisfies the binary constraints for all elements of {{formula:e2efb656-44d7-4d68-a351-6c2de19092d7}} then, the optimal solution is reached. Otherwise, further steps are needed. The algorithm solves the problem assuming that the first element of {{formula:4a63fe58-ff23-4507-90cb-ecd185a01529}} is fixed to 0 or 1. Hence, the problem is split into two subproblems named the children nodes of the original problem called the parent node. If the solutions of these subproblems do not satisfy the binary constraints, they will be also split into two more subproblems. This process is called branching and will be executed until the optimal solution is obtained. In order to reduce the complexity compared to the exhaustive search method where all the possibilities are tested, the BB can stop searching in one of the directions of the tree if at any node, the cost function value is greater than a previously defined upper-bound solution. More details about the BB algorithm can be found in {{cite:005417f40446f94bed818b038f1881211004e121}}.
| m | 2e70ecb95b100f93918f3cd8741f4c2e |
Another alternative for initialization is the tensor power method, which has recently gained popularity in the context of learning latent-variable models {{cite:801d48d65a85ec588953737884d12b079b442bb9}}, {{cite:b2fd9be09ddfacf7b594bda60998154a08d69297}}. Nevertheless, the TPM (with random initialization) suffers from the same high-volatility issue as randomly initialized GD. The argument for this would be nearly identical to the one presented above, and is hence omitted. Instead, we invoke a perturbation analysis result in {{cite:801d48d65a85ec588953737884d12b079b442bb9}} to illustrate the insufficiency of the TPM.
| m | efdce9f38c570203f7a7abb45411cabe |
The second approach that we study is the upscattering of DM by gas atoms in a hot thermal source. DM that is thermalized near the Earth's surface has kinetic energies near {{formula:f09d98ac-a803-4ed3-aa7d-3585ccb7d422}} , well below the threshold of any near-future direct detection experiment. However, in the presence of a thermal source containing gas with temperature {{formula:060ed1ac-1969-4960-8418-889f8b14fc0f}} ,Recent examples of this technology include incandescent light bulbs. DM near the Earth's surface can be upscattered to kinetic energies around a {{formula:da86afc9-eb40-4e76-a35c-95c19f328b11}} , potentially within reach of planned detectors. While this presents a challenging signal, it is not outside the realm of possibility, with existing experiments already probing electron recoils with {{formula:0142b59c-dd3c-43e6-a804-ac4c1dee599c}} {{cite:aa9622d2831d783fd1ac049a41c800749acf3db1}}, {{cite:7edf5d53cdc31c8f1d49c93b74f522f8f15e3919}}, {{cite:549eb51d7fcbcaecf93a8d8f7f3e1ad0899f82ee}} and future proposals extending down to energy depositions below {{formula:124869b4-9c0a-4e0c-97f6-6cd68f0d63c0}} {{cite:6ec71430cd4899fe0bd473ddc48ec91775388e5f}}, {{cite:30f49deb7debc07571b5875ac9275403713b46d3}}, {{cite:2d337f74841777714b8fd05d39f698fef9c7445e}}, {{cite:1976609752470ee5c8ccb01ff1885b841d47f40e}}, {{cite:04d05973c59a6c98c630bdf212e3b9f70b80a646}}. This technique could also be further improved by optimizing the thermal sources.
| i | 8f607fa044a6b479549d822dc8ce2dbc |
This section presents numerical results of
well-known test problems for benchmarking the modified SF-PIF
methods' capabilities. We mainly compare the results
from the third-order and the fourth-order temporal methods of SSP-RK and
SF-PIF. We used the well-known three-stages, third-order
SSP-RK method {{cite:fe398cc7aca3fd3928c705e0ce05e75d19b79b99}} and
the five-stages, fourth-order SSP-RK method {{cite:0a94a4ccb2f0c0415047c6fcf5bda8b04c00c932}}
(RK3 and RK4 hereafter)
for the comparisons of the third-order and fourth-order SF-PIF methods
(SF-PIF3 and SF-PIF4 hereafter),
respectively.
| r | d89c3bbd91fbd35727ef4a40ba0a7020 |
Our numerical experiments include comparisons with a variety of models and methods.
Total-variation Regularized Least Squares (TV) is an important baseline that does not use any training data but rather leverages geometric models of image structure {{cite:198a3c71077f2b2da71996be4082d764f9096c7e}}, {{cite:08c7bf6473fb544160c5655fe24c1d4afcf2cd86}}, {{cite:a1826a6b53fcf61e98484b68def2f6b667d903ae}}. The PnP and RED methods are described in sec:pnp; we consider both the original ADMM variant of {{cite:34bffc68c31d2926108681dc0a16ce571bdee44f}} PnP-ADMM and a proximal gradient PnP-Prox method as described in {{cite:48e077c98568720eda3fec459061d958a60c0460}}. We utilize the ADMM formulation of RED.
Deep Unrolled methods (DU) are described in sec:DU; we consider DU using gradient descent, proximal gradient, and ADMM.
The preconditioned Neumann network {{cite:427a6a89f6a938f15364794548b6453142fd2ba8}} does not have simple Deep Equilibrium or Plug-and-Play analogues, and is included as an alternative deep unrolled method.
| m | f14478b148914bfe7ce061c12de77a2c |
Seq2seq {{cite:ea8b978dd9f23c5430d9e00855504610a93fa232}}, breaking through the traditional fixed-size input problem framework, converts an input sequence of indefinite length into an output sequence of indefinite length. It also incorporates a Global Attention mechanism {{cite:8ad6c14548f78e8a2b436367021958818a302800}}{{cite:2531be1038709a8a76024c1e51e78be366c5bd01}} to notice more textual information;
| m | 380ab5e7e3e52e46d24833ac3da1dfb1 |
For nearly a century, small molecules, or organic compounds with small molecular weight, have been the major weapon of the pharmaceutical industry. They take effect by ligating (binding) to their target, usually a protein, to alter the molecular pathways of diseases.
The structure of the protein-ligand interface holds the key to understanding the potency, mechanisms and potential side-effects of small molecule drugs.
Despite huge efforts made for protein-ligand complex structure determination, there are by far only some {{formula:1bd0fd9d-53ca-4452-8862-8ab5f5fa5fe8}} protein-ligand complex structures available in the protein data bank (PDB) {{cite:b3bfe8ec04b39cbe29694155271c3ceeb268991e}}, which dwarfs in front of the enormous combinatorial space of possible complexes between {{formula:0d78d830-382e-4cde-9ee4-167135ae0e01}} drug-like molecules {{cite:0b975ef2ab83f1a54f9ef2dc879268d92634c3e0}}, {{cite:6481f8c71f0375042e438c4f65993963b7ce18d4}} and at least 20,000 human proteins {{cite:fa6311293deb99f75ab8ac79517d022239918f68}}, {{cite:cadab546b22f04dba36e96e07f407abddbb12ed3}}, highlighting the urgent need for in silico protein-ligand docking methods.
Furthermore, a fast and accurate docking tool enables binding pose prediction for molecules that have yet to be synthesized, empowering mass-scale virtual screening {{cite:499a0c178c8ab5e69403feab013a425102f7f187}}, which is a vital step in modern structure-based drug discovery {{cite:5528fb07401b4f7d90001c9f91ca5f2cdaecccc7}}.
Compared with models that only output a scalar score (e.g. binding affinity) for each protein-ligand pair, docking software provides pharmaceutical scientists with an interpretable, information-rich result.
| i | 8166a16cdb451dfa13ce84e73201e856 |
where {{formula:f00bd447-9ec8-44e7-9038-f605c1e7e129}} is the viscosity of the fluid and {{formula:0c3d5a25-3e3f-4dbd-8572-e564f46f9be1}} is the force per unit length exerted by the filament on the fluid. {{formula:f9d8686c-05eb-4e5e-a90e-4c9e29487172}} is the operator for SBT {{cite:161bc5798ed767b1f6fb8d346c4c18d5a9e01e36}}, {{cite:7872e5f6387bbb1a7c76160685bb3f5de9a333fb}} which can be written as
{{formula:c360b8dd-7890-414f-aaaf-7932e3534420}}
| m | cce8272136000e5e670a44b054a051cf |
A partial covering scenario can also explain why Mrk 335 only shows a mild trend of softer-when-brighter (Fig. REF ) because a partial coverer would preserve the spectral shape as it leaks different fractions of the same
intrinsic continuum when the covering factor changes. The softer-when-fainter pattern at the very lowest
count rates is likely due to a soft X-ray component in the form of multiple emission lines
{{cite:9acd19f901accc6958c811c1bbebd805308b895d}}, {{cite:20e204c9bc79492bb94353d961155d83ec7d824f}} and a (distant) reflection component {{cite:d5834ffa43e9071eda61e1465dedce116ebdef95}} which become increasingly apparent as the primary continuum diminishes. While the X-ray covering factor obtained from the current and
previous (intermediate to low state) observations of Mrk 335 is high ({{formula:1a90d1ac-e2c1-4d04-8299-221771a0abc0}} 80-95%), a partial covering scenario
for Mrk 335 is independently favored by previous UV observations that revealed variable absorption lines, including
Ly{{formula:61d21d17-95f0-41b2-bb99-31d95ba51501}} at 20–30%
covering fraction of the UV-emitting site {{cite:9acd19f901accc6958c811c1bbebd805308b895d}}, {{cite:20e204c9bc79492bb94353d961155d83ec7d824f}}.
| d | bf04132484b986647d20d783f28456f9 |
Given a batch of ground truth trajectories and corresponding measurements, how should we learn observations models? One approach would be to learn a direct mapping from measurement to state, for example as a regression or classification problem {{cite:4d5c92648bd8fb99b29c1e365947fda4136ad47d}}, {{cite:c0cd99327f2453b99a12cafe0b10ba33f3beef59}}, {{cite:118caed4a69458a3ffcedff5eecc474f659e74c5}}, {{cite:26c6f4aaf6152a8679a2c06d61e6ba381f5fe481}}. However, while easy to optimize given a direct supervised loss, this only minimizes a surrogate loss independent of the graph optimizer and is not guaranteed to minimize the final tracking errors that we care about. The other option would be to directly minimize final tracking errors between optimized and ground truth trajectories {{cite:6926f69b4a17ad1710f4d589a2dd3349e2af30d3}}, {{cite:95729368c349ef980304e7e6e507728ac66ae690}}. However, many state-of-the-art factor graph optimizers, e.g. iSAM2 {{cite:2c9efbb6eb781f11115c8e48cbbc28c1d384f47c}}, are not natively differentiable due to operations such as dynamic re-linearizations. In such cases, we are limited to black-box search for learning parameters which is very sample inefficient {{cite:6e2deaa67a73143bf4044b90e74d8ecc10b8f874}}, {{cite:84b4fb8694d3c5c9107ad6cd7ca62f1a107d019a}}, {{cite:05093143c1abd569d276a17834d2d48cfd83080f}}.
{{figure:699bbac5-ce65-45b3-b35d-66e7e6b232d7}} | i | e28727925ceeb33c21ac6cac3e06f029 |
Over the last decades, numerous algorithms for point cloud registration have been proposed, which can be divided into two categories: coarse registration and fine registration. The coarse registration algorithm can generally be divided into three steps: 1) extract the structural features of points; 2) search the correspondences; 3) calculate the optimal transformation matrix. Among them, structural features extracting is vital for this type of method. Generally speaking, feature descriptors map neighboring points' features into histograms according to the number of neighboring points {{cite:650999055aa89fbe73c6212bbdd612140254a438}}, Euclidean distance {{cite:b1a968842fe54f9723a672f70f35ac32a1cf9f9a}}, the difference of normal {{cite:56d6deb8d3af18df8c3c02753c73c67618b8c515}}, surface curvature {{cite:d8d65bc34a5cf0266bae4627ff30aba1ed1d49ed}}, etc.
| m | 7e196e679798dd783b5aea10af65bbf6 |
Formally, {{formula:a0fc930d-b1c7-4d3a-b41d-b85812824389}} Majorana fermions act as matter fields and {{formula:60313881-c230-4344-8f56-e15af4762c71}} Majorana fermions act as gauge fields. The {{formula:51990023-348d-4094-95c5-20846d655185}} and {{formula:868dd98e-c74e-4afe-9e0d-b114e44ec0fa}} Majorana fermions are coupled in a gauge invariant way, thus the interacting Majorana fermion model can be viewed as lattice gauge theory nevertheless purely composed of Majorana fermions. The matter fields can have spontaneous global symmetry breaking that lead to local order parameters. However the gauge symmetry of gauge fields can never be broken due to Elitzur theorem{{cite:2dfb89dbb40b871ac4ed0beac606022730f72fb3}}, {{cite:b46bca01325b2729428708771b4efd96d330a9b0}}, but gauge fields can host topological order. The interacting Majorana fermion theory can unify these two frameworks in a single formalism.
| d | eb309eaa5a6916ff62835bd28f024759 |
Relaxed LDP. Some recent works {{cite:0859b2d255b352afe1b770e6e94aabf85eaeec62}}, {{cite:8db2efdc0c7a4e0b98712ddd40b4d96b0baf2302}}, {{cite:46de8ac521e942fd4fda7dbc74757056e4bff46c}} relaxed the LDP by considering the input variants. For instance, ID-LDP {{cite:0859b2d255b352afe1b770e6e94aabf85eaeec62}} relaxes the LDP with different {{formula:22865139-e450-4d23-be5d-52333c41798a}} for different inputs;
geo-indistinguishability (GI) makes every pair of locations indistinguishable, but the “level" of indistinguishability depends on their distance (locations that are far apart are more distinguishable than locations that are close together); CLDP {{cite:8db2efdc0c7a4e0b98712ddd40b4d96b0baf2302}} provides distance discriminative privacy, and relaxes the protection for different pairs of inputs. Different from L-SRR, all of them cannot strictly satisfy {{formula:bea0f9f7-37de-4dd5-8d2a-ffb61d605d42}} -LDP.
To validate their limitations on rigorous LDP guarantee, we present some numeric analysis with the same setting (by converting them to {{formula:81707e8d-d1e6-4acc-8d59-fcb8e8db0942}} -LDP). PLDP {{cite:1475ff66a9832d34a851f885af1ce094d6a62fc4}} is experimentally compared in Section since it focuses on LBS.
| d | 22760c88a65d6db2ce8837ea3b6fee6c |
PTs liberating large amounts of energy stand out as the most promising candidates to produce detectable GW signals. If this energy originates from the vacuum energy of the meta-stable minimum, the PT is accompanied by a period of supercooling. This occurs when the meta-stable vacuum energy begins to dominate the energy density of the Universe, resulting in an additional period of inflation.
It has long been understood that supercooled first order PTs are expected in theories with an approximate scale invariance at weak {{cite:4e3104bf1100799eb3aed57901274c68faa93bb6}}, {{cite:c5af7417935c3d0534c0a5591c348f1230b957c1}}, {{cite:c05d81c9e16f61a1d81c050e009f91b0ca80ae44}}, {{cite:0f60ec3775836da18299939a4c97e7e6700b8abc}}, {{cite:641232a61115613c19bd01a5e2ce34c23ad12199}}, {{cite:85fe0a9610effe23efee12a922e0ad94cb053b91}} and strong coupling {{cite:90d8b90304d929cc46337bbce9032011502a3077}}, {{cite:1c43d95e9447ec2c99d80dca232fe18bb17a811d}}, {{cite:07dbe5bb3533f47e9335b4c730e8a856c9e6bfe2}}, where the dilaton dynamics determines the vacuum tunneling rate.
| i | bf93dfa87b9515b610b995d52b085908 |
We also evaluate kNN on an alternative neural network architecture, EfficientNet-B0 {{cite:01f595cf61e52367b4e23ec2a015c0d903deddb0}}. In Table REF , we report averaged evaluation metrics across datasets mentioned in Table REF and follow same experimental setting. We see that non-parametric kNN is largely effective and outperforms existing techniques. Further, as we can see in Table REF , the proposed kNN-based method outperforms all the other traditional non-parametric techniques in terms of both AUROC and FPR95 by a significant margin, while using same embeddings used for training of these other classical models.
{{table:2df4cfff-bef3-4d29-bf8b-b87f500bf685}} | r | 39445966b2d61ced4daedc26f15f13c6 |
Figure REF shows our results for multiple regression. The adjusted {{formula:6d7ac9d9-4351-45d5-b251-450186a61427}} of the model for English is {{formula:eb200e49-9629-4e7e-97b3-bed71a9d0b48}} , with {{formula:b8c368a7-a1c1-4eab-a635-304eb731dbef}} , {{formula:6de44af8-8746-4d86-8150-4eb43b99d2c9}} ; mean regression coefficients for prototypicality ({{formula:202f2555-6e8a-4393-add6-1a43881eae33}} , {{formula:9053217d-ab2c-4f3f-9388-4e03df24c954}} ) and frequency ({{formula:d1399991-af0a-4be4-931a-a4daed8424fb}} , {{formula:93504a7f-ce43-4d35-b38a-1d431cd55171}} ) are significant, but for valence ({{formula:59b2a09a-643a-4c0b-8479-2f49c079933b}} , {{formula:92f58dc3-0b11-4ba4-b6ef-a91a3cfa7290}} ) it is insignificant. For French, the adjusted {{formula:bf5f3cf4-c3e2-4b5b-9194-62cefded2878}} of the model is {{formula:d19451ac-35a9-48a5-90a8-ebd9dd57ecc0}} , with {{formula:ce9062db-48f0-4921-a876-ba60dfa7d358}} , {{formula:35149790-ba1b-4eda-b114-8521019a2eaa}} ; mean regression coefficients for prototypicality ({{formula:27c8fbdc-fbc2-4d70-af57-482d79daa303}} , {{formula:adcb7021-2b34-4a7e-a7cd-4ee3e346f2ca}} ) and frequency ({{formula:bcd01f0c-8be9-4cc2-bb99-4d62e1755a08}} , {{formula:535ec0f5-439f-46ae-9d47-d25ec034a6ec}} ) are significant, but for valence ({{formula:d0f647de-4ccf-4d3f-8fac-ecc1f6bdd3c2}} , {{formula:69d7da5c-5998-4119-88be-cb53d6fa6bfd}} ) it is insignificant. These results show that frequency predicts semantic stability, which confirms the previous findings {{cite:94a43ff64c78125a38d6571b24cfcb8f5960f7ed}}, {{cite:b35cad89d401c365461ddb3afe28e62152aeaebf}}. Beyond frequency, we find that prototypicality plays an important role in predicting semantic stability of emotion words, manifested in its significant and negative effect. This provides evidence for our hypothesis that prototypical emotion words tend to be semantically stable over time.
{{figure:5e3cf7f7-3f3f-4146-8e61-e5b1998ea8ec}} | r | e13d7f41a943ccc0204b43090ba9fa3b |
The Lie symmetry method is the most sophisticated to solve the NPDEs because it is based on the concrete mathematical framework and also it is the one of the powerful method to find symmetries of partial differential equations. Lie symmetry method was developed by Sophus Lie (1842–1899) in the latter half of the nineteenth century. For details of the technique, one can study the popular literature available in the Ref. {{cite:228935ef1de785f0325ab0f29215b5936546b8be}}, {{cite:99900a9911e0c4f74cd43880c06e8b5656300514}}, {{cite:34a8dfba026fe02c9e4cb34a22632e55354cfdc2}}, {{cite:f517f34a539ece9ff1bf02a4304970b1bdfda275}}
| i | 2e724818126c7073865dd2e00fb18cd8 |
Defense.
Several countermeasures to model stealing attacks have been discussed in previous literature {{cite:4da69f7a2b1946f1cde2711fc20925e044593c17}}, {{cite:49eed56809a5401bc6ed8cded99bd358f9b5b223}}.
One straightforward countermeasure is injecting perturbations to the predicted posterior probability reported by the classifier, i.e., perturb the probability while retaining the top-1 label {{cite:4da69f7a2b1946f1cde2711fc20925e044593c17}}, {{cite:6877c2cb55852fb34ebdcab35c0f2bbfc1b155f5}}.
To cope with different types of query responses, we consider adding random noise to the response regardless of the corresponding label, i.e. the distribution of the random noise is independent of the node class label.
Concretely, we add random Gaussian noise into node embedding and t-SNE projection returned by all three target models and use GraphSAGE as the surrogate model to understand the effectiveness of such countermeasure. According to the defined threat model, the accuracy of the surrogate model measures the attack performances.
A higher accuracy of the surrogate model indicates a more successful attack.
We use the ACM dataset as an example and the results are shown in fig:defensenoise.
We observe that the random Gaussian noise slightly affects the accuracy performance of the surrogate model.
For instance, in fig:acmtsnenoise, when {{formula:7293fef6-9d48-4b33-9d42-9c7b7ff0fc17}} (i.e., the standard deviation of the added noise) is greater than 7, we can observe the accuracy performance of the surrogate model starts to decrease for different target models. In contrast, if the query response from the target model is the node embedding vector, we can only observe much fewer fluctuations of the surrogate model's accuracy with increasingly stronger random Gaussian noise injected to the embedding (see fig:acmembeddingnoise).
To summarize, our preliminary experiment does not establish concrete evidence that adding random noise would counter our attacks.
We leave designing effective defense mechanisms for model stealing attacks against GNNs as our future work.
| d | 0d826d39249ee76031c44aef0dbdf4c0 |
In addition to a non-linear or even non-convex function {{formula:e3364611-07e4-4c83-9df1-e5114ff0ef7b}} in the above practical applications, another common feature is that there often exist additional constraints in the decision-making process such as hard-constraint like safety or soft-constraint like cost. To this end, there have been exciting recent advances in the theoretical analysis of constrained kernelized bandits. In particular, {{cite:5e2920b16aba8ae842b74119c30262dd6a51b323}}, {{cite:a641cdd458fb33059f261aa121458f75d8d3f501}}, {{cite:b1443526dcc0c0bd3dd5e5d40b41252cf7f48aac}} propose algorithms with convergence guarantees, while {{cite:47593759974a13cba922e683cc36da70d764f61b}}, to the best our knowledge, is the first work that establishes regret bounds for their developed algorithm, although under the Bayesian-typeIn the Bayesian-type KB, {{formula:ed2ac7cc-d5f4-45f1-869d-f4c19f9a0f12}} is assumed to be a sample from a Gaussian process and the observation noise is Gaussian. In contrast, in our considered frequentist-type KB, {{formula:c99448b8-470b-4a71-8750-f6f2f8fb9415}} is a fixed function in an RKHS and the noise can be any sub-Gaussian. In general, a better regret bound can be achieved in the easier Bayesian-type KB setting {{cite:831e56484a230e8ac6e7bf0a828b6aafdcf87112}}. setting.
These algorithms mainly focus on KB with a hard constraint such as safety, i.e., the selected action in each round needs to satisfy the constraint with a high probability. As a result, compared to the unconstrained case, additional computation is often required to construct a safe action set in each round, which not only incurs additional complexity burdens, but often leads to conservative performance.
| i | d1b60475b30c350b07376437cf76d25c |
Last, from a more general standpoint on s, our general approach may seem close to the design of {{formula:0ccd62c4-8189-4c06-abd7-453b2fd34d7d}} -exponential families and even deformed exponential families – the knowledgeable reader will notice that our s technically look similar to escort distributions in the way we design them through (REF ), despite a normalization which belongs to the divisive normalisation of distribution rather than the subtractive normalisation of {{formula:4cab3496-7cb2-45af-bac9-b15875a7cc8b}} -exponential families and deformed exponential families {{cite:2f79dd2c4cad72ea5430566289fabd3871fe691b}} (alternatively, we rely on a {{formula:609e32cd-9bcf-4516-a751-602a5886fc81}} -subtractive normalisation, using the arithmetic of {{cite:a8a5537ab0b6d56bce93c39e402eb55b41c2b34f}}). Classical escort distributions, however, appear independently of the {{formula:eab19de5-5ad4-4add-8d48-d352a409e89b}} -exponential families or deformed exponential families: they do not belong to their axiomatization. In our case, they do, and the fact that we chose to somehow “mix” and in the axiomatisation of the , by constraining the normalization of the , seems to yield technical conveniences not known for {{formula:48e1ec03-639a-4dd7-bbc3-fbf8c054b338}} -exponential families or even deformed exponential families, the first of which is the elegant closed form of the cumulant in (REF ). Beyond such technical conveniences appear some concrete advantages for clustering. Given the ubiquity of exponential families and Bregman divergences in ML, many interesting questions arise on other potential advantages for other uses and applications. One promising direction is the investigation of the Riemannian geometry of the parameter space {{cite:7ff03a0e05b99d5ecff0ab7a85efee9d945d45d0}}, {{cite:abe7733458dee82328872ec6298d7bf322a0b0d0}}.
| d | 84680ffac085c58f62e70abdf1fd699e |
We compare the proposed approach with other various state-of-the-art methods. These methods include Gate Convolution (GC) {{cite:89ab6b02104df906f67cc72a0f1ca337b648def9}}, Edge Connect (EC) {{cite:7715216d648bfa334d702877cb192cf099188a27}}, Contextual Residual Aggregation (HiFill) {{cite:29d733185f13b3ed737cc9b2e2189f83c866e7ed}}, Multi-Task Structural learning (MTS) {{cite:3699e2de85056b92f828d54dfe9249291a57257d}}, Co-Modulation GAN (Co-Mod) {{cite:db41a8eb9761ee11ef5bfaf3e8bd01d3cc466070}}, and WaveFill {{cite:d93d80b8a2e244e070664b3ab7c125ae90bbb71e}}.
For these relatively early methods (GC, EC, HiFill, MTS), we retrain them with our data splits and training settings. For Co-Mod and WaveFill, we use the officially released model weights for face and scene images.
All inpainted results are combined with the unmasked regions of the original images and resized into {{formula:206ec4c9-3c27-4b84-8031-2cb47c2019f9}} .
| m | 97350cb24aee95616b931292b49c0b12 |
First, it has the proper analytical structure with the right cuts. In particular unitarity on the RC produces a
second Riemann sheet. Poles in this so-called unphysical sheet have a natural interpretation as dynamically generated
resonances. However poles in the first or physical sheet (ghosts) are not allowed and they must be understood
as artifacts of the model if they appear.
The IAM partial waves are obtained entirely from the one-loop or NLO approximation. Thus the results depend only on
the renormalized chiral couplings and are UV and IR finite and renormalization scale independent.
They satisfy exact elastic unitarity on the RC,
{{formula:dd1084c0-dbfe-48f2-9317-e082bd5c69d6}}
When expanded at low energy, they match the NLO amplitude
{{formula:9d8f3b43-69a7-4aa1-8d40-70c94750d10b}}
Finally, the IAM method can be extended to the coupled channel case too
{{cite:62aeded932e8e53236b879aeede12d87278128a4}} particularly if the particles appearing in the different channels are all of them massless to
avoid overlapping left and right cuts. This is the case here since we are considering the NGB and the {{formula:f3f94497-ae1a-47a9-8468-6291fa128f7f}} particle as
massless. From the perturbative expansion
{{formula:45846425-b392-447e-8f94-8da5ee5d7462}}
a natural generalization of the IAM method gives
{{formula:2a893960-1f73-48ac-82c9-22563f0481a6}}
which satisfies exact multichannel elastic unitarity on the RC
{{formula:0831f772-6244-452f-ab0d-5effcbf8e126}}
In addition the matrix elements of {{formula:08f5e0a2-5d94-4130-9095-b09f642c056a}} enjoy all the already mentioned desirable properties of the elastic IAM.
This coupled-channel IAM is particularly useful in the isoscalar channels where the {{formula:34c617b6-eec4-46f2-b968-50dcfd0db3fc}} and {{formula:8da8e316-e4d2-4bc2-893a-7d3da5ae6c50}} pairs can
be strongly coupled.
| m | f889953f46a71eed20031089d6403ba6 |
Given trained tasks followed by a series of new classes, the ultimate goal is to maximize the performance of captioning on the whole coming and previous tasks. The ContCap framework is presented in Fig. REF . At any time point {{formula:02db155b-07cb-4f22-adad-f1f711ecf007}} , the framework has performed a sequence of tasks ({{formula:0ea34f6b-d2a0-441a-b388-702c2cedf2ba}} , {{formula:e98a0500-e233-4708-b073-4cacc71c30f8}} , ...), and samples from dataset of task {{formula:93137fd2-eb21-4556-a166-7e0d81f7c95b}} are previously unseen. In learning task {{formula:4821818c-38c3-46a1-a501-41806f45e1ea}} , continual learning techniques are applied to information from Knowledge Base (KB) with an expectation to describe well on both the task {{formula:464ad31a-e430-4458-b01f-c6df9fec763d}} and the previous ones. KB contains the acquired knowledge and the knowledge accumulated from learning the old tasks {{cite:4b6c5af6a51b2e99093f675cc6994a379bce9f03}}.
| m | 2ec15408acf3f504c10d5fefd980dd5c |
We conclude this paper by emphasizing that thermal and hydrodynamic processes, with or without viscosity, are multiscale phenomena where hierarchical energy transfers play a critical role {{cite:49a88b6437db91b60ddfbb3b78a95fd78c9cb480}}, {{cite:ceca1e892178d2632c5dbfda72b39c03dfd69bc5}}. Recently, {{cite:e2144436b74d1e1d89904734234d6807332b339f}}, {{cite:567b4bc755858b4c9c94a432bf8f544893cb1509}} attributed irreversibility in a turbulent flow to the asymmetric energy transfers (e.g., forward cascade in 3D Navier-Stokes equation), which is a hydrodynamic property. Following a similar approach, in this paper, we propose hydrodynamic entropy that successfully captures the evolution of 2D Euler turbulence from disorder to order.
| d | 546d9e7ee12d33dac899d5a28e03e1bd |
Recently, intelligent reflecting surfaces (IRSs), also termed reconfigurable intelligent surfaces (RISs), have attracted significant attention from both academia and industry {{cite:80bb3828ea412d8d237aadc78347803aa6c19ac1}}, {{cite:2058f085c88de5dd56c0d92dfc19bfa310c7d826}}, {{cite:dc84b567047213fc25ae6884f6e2e130c6674220}}. IRSs are composed of large numbers of reflecting elements (e.g., low-cost printed dipoles) {{cite:b2904251a69ff96cd6988d7945f737b6e5b8f746}}. The elements of an IRS are based on metamaterials with subwavelength structure and are able to adjust the incident signal's amplitude, phase, frequency, and polarization, thus being able to collaboratively
change the reflected signal's propagation {{cite:05df4364f65eafd8804cf1882fa91fe54be6f123}}. Different from traditional reflecting surfaces, where the phase shift is fixed after fabrication, the phase shifters of IRSs can be dynamically adjusted between 0 and {{formula:e802fced-631b-43f3-a0d0-ea8d1195677e}} to adapt to varying wireless channel conditions {{cite:238b7d140e0c8edff0930ad32b56c7098ec79813}}. In addition, different from current base stations (BSs)/active relays, which require power-hungry and high-cost radio frequency (RF) chains, IRSs are much greener and more cost-effective due to their simple integrated passive components, such as varactor diodes, positive-intrinsic-negative (PIN) diodes, micro-electro-mechanical system
(MEMS) switches, and field-effect transistors (FETs){{cite:2058f085c88de5dd56c0d92dfc19bfa310c7d826}}. Furthermore,
IRSs can be fabricated as artificial thin films and readily attached to existing infrastructures, such as the facades of buildings, indoor ceilings, and even smart t-shirts {{cite:80bb3828ea412d8d237aadc78347803aa6c19ac1}}, thus making them promising for implementation in practice. Due to the above appealing benefits, IRSs have been recognized as a key solution for improving both the spectral and energy efficiency in future sixth-generation (6G) cellular wireless networks.
| i | 147f55f8e44bdb6b705b34c351db6595 |
For the first time in the literature, we analysed light curves of the system. The inclination ({{formula:dc190f3b-706f-4af2-abb6-1246aaba03d1}} ) of the system was found to be 69{{formula:f4ea4fb2-f9a8-460f-a508-7abf58a189df}} .71{{formula:a944b274-a3af-447b-ad08-fd8d90f46302}} 0{{formula:3875e726-abee-45fd-b075-69f3e0dbfcf2}} .16, while the temperature of the secondary component was found to be 5352{{formula:17215461-2605-4b54-b174-6a2a77da89f5}} 15 K from the analysis. The fractional radii were found to be {{formula:2eefac3b-81f0-4bad-9804-926f450306c6}} for the primary component and {{formula:31a127ea-0def-4744-a8b2-d4675746ad4d}} for the secondary one. In this case, the sum of fractional radii was computed as {{formula:abf57eea-dfa9-4812-a874-007e6df41ab5}} . Thus, HH Boo seems to be in agreement with {{cite:7a0060c6a2b72c2b797832d91f92c00bfc0da1bd}}'s criteria for overcontact systems. The {{formula:b4deddb3-8c6c-463c-8e0c-80351d9c33ad}} analysis indicates that the orbital period as {{formula:8f4981bf-fd82-40b7-a938-3aaebea7d7e0}} . In addition, the temperature of the primary component is 5699 K, while the secondary one is 5352 K. Although some W UMa type binaries have components with some different surface temperature, they generally have the same surface temperature. Here, the primary component of HH Boo is a little bit hotter than the secondary one. The {{formula:25c1b819-f169-428e-abce-a43886cad429}} analysis indicates possible mass transfer from the second component to the primary. This case should be the reason of the hotter primary component. Considering some characteristics of the system such as the short orbital period, small mass ratio, hotter primary component and ect., HH Boo seems to be in agreement with the members of the A-type subclass of W UMa binaries {{cite:909f9cc8a458f0a4fd965b4505c270f8242dd82d}}, {{cite:a084c66fb906d9e2d4b4bbbe00fc0a8b101f4be8}}.
| d | 4148a01c1aca876da13ebc89c962285d |
Theorem REF and Theorem REF show that local statistics near the edge {{formula:fd5df55b-7850-4b40-b6d4-1b5f02216aaa}} only depends on the number of blocks relative to the eigenvalue {{formula:05c324a5-ae44-406b-b919-30fc3f8f6f33}} of the added perturbation matrix {{formula:71013f2b-3152-47ab-b749-0d2d1db1d3e1}} . Together with fluctuations of outlier eigenvalues due to Benaych-Georges & Rochet {{cite:fc35844c8cf7a8f5084acf4369a37f12689860e4}} and Bordenave & Capitaine {{cite:89a6d13de40d3fb70a9456a52f0f59706756512f}} in the complex case, this thus completes a phase transition for complex eigenvalues in the deformed complex Ginibre ensemble. It can be regarded as a non-Hermitian analogue of the BBP phase transition at the soft edge of the spectrum
in Hermitian Random Matrix Theory (RMT for short), first observed by Baik, Ben Arous and Péché for non-null complex sample covariance matrices {{cite:0aadbea933d4325b12f5269905aeb6c9f843a1a1}}.
More precisely, extreme eigenvalues display distinct universal patterns in three spectral regimes created by the perturbation: (I) In the subcritical regime where all eigenvalues of {{formula:ed560c23-dbdd-435c-93a7-facb0e4699ff}} lie in the open unit disk, local statistics is governed by the Ginibre edge statistics; (II) In the critical regime where some eigenvalues are on the unit circle and all others lie inside the open unit disk, local statistics is
completely characterized by an infinite sequence of new kernels; (III) In the supercritical regime where some eigenvalues stay away from the unit disk, outlier eigenvalues converge to roots of the eigenvalues of certain finite random matrices, see {{cite:fc35844c8cf7a8f5084acf4369a37f12689860e4}} and {{cite:89a6d13de40d3fb70a9456a52f0f59706756512f}} for a more detailed description.
| r | 0118ec108dc6af679f88104f45ffe772 |
Although, p-dispersion is mentioned to have relevant applications for MOO {{cite:a1888428b3af83f5736c30d198c0900e486f6e8b}}, {{cite:829a97418375d160749e6641dc62c33b9efe0ab0}}, no specific studies concerned the p-dispersion in a PF to the best of our knowledge.
We note that an affine 2d PF is a line in {{formula:e94ee63c-9605-4cff-8f06-28b49a7da5c7}} , such case is equivalent to the 1d case.
Hence, Max-Min and Max-Sum p-dispersion problems are solvable in {{formula:55230868-2b93-4282-a8a7-9c4271b79cbf}} time thanks to {{cite:829a97418375d160749e6641dc62c33b9efe0ab0}}, {{cite:5af52523b80770e3178fc884eec69d09a15580c9}}.
General planar cases of p-dispersion problems can also be seen as specific cases of three-dimensional (3d) PF, affine 3d PF.
Having a NP-hard complexity proven for the planar cases of Max-Min p-dispersion,
it implies that the Max-Min p-dispersion problem is also NP-hard for 3d PF.
| r | a5dd77cdf4dd441c952bc0e83282a941 |
We generate the flat-fading channel using the SOS method with {{formula:61b043b3-afa6-46c8-b8cb-b65a27fa8317}} . The sampling period {{formula:d9a9f9d5-01b5-4aa1-af3a-4af9b52a86d7}} is set blackto 1 ms with a maximum Doppler spread {{formula:1948fc70-5048-4433-92be-3809cff86cca}} of 100 Hz. The ML-based predictors are trained using the Adam optimization algorithm black{{cite:a94ee7b766846d568674e0a4d58ca96806eaebe2}} with a learning rate of 0.01, a hyperbolic tangent activation function, and the MSE as the loss function. Dropout regularization is added to reduce overfitting. We also use early stopping black{{cite:57247ea593a4ab47a2bbf080ac67c41811dc4a4e}}, where the training process is halted if the loss function does not improve beyond a certain threshold. For simplicity and to save computation time, we limit our models to predict only one channel sample, as opposed to a sequence of samples. The reported results were obtained by averaging 100 independent MC trials.
| r | 80bdf619d6830f0286dd4597e30160a4 |
Automatic landmark localization is an important step in many medical image analysis methods, such image as segmentation {{cite:1d8980f589b0dc12c21e3bf8bd6232bd3c04c7cc}} and image registration {{cite:7bc66a51b37950e450fc2537d1c9a24832d07123}}, {{cite:21b0eeb23b3e8cb4780b432f5d669cde4cb35b09}}. An erroneous landmark prediction at an early stage of analysis will flow downstream and compromise the validity of final conclusions. Therefore, the ability to quantify the uncertainty of a prediction is a vital requirement in a clinical setting where explainability is crucial {{cite:49049793cd617ff2ee86808f5ca7f8264bdf07ef}} and there is a human in-the-loop to correct highly uncertain predictions {{cite:45a6a68b0246900aa77fa8f3fc95eac553c4e28f}}.
| i | 37529d05547f3f8799373d9bfb2a8e75 |
In this section, the results are computed using the proposed method and compared with the state-of-the-art eye blood vessel segmentation methods both quantitatively and qualitatively. Table REF shows a quantitative comparison between the proposed method and the state-of-the art segmentation methods: FCN{{cite:38d344cf2f6b2e8cc3aa509f084825da227830c9}}, UNet{{cite:85162656c686094b94e128268e5ba8a72001eea8}}, cGAN{{cite:ebb887edef3c5c3f8c238df365a72c3fb46269aa}}, Hu et al. {{cite:15e7b92168e235dfe170387a053dec50e08f6fc2}}, Jiang et al. {{cite:cfeb127a9a887cb704bab9d2c53f5b2cd79b38b8}} and Soomro et al. {{cite:af7fceed38257bb9b0f7039ba30517a0ef7615b4}} using both DRIVE and STARE dataset for retinal blood vessel segmentation. For the comparison, different similarity metrics are used such as area under the curve (AUC), F1-score, sensitivity, specificity and accuracy. It shows that for the DRIVE dataset, the proposed method yields the best values for all the metrics except specificity. It yields AUC, F1-score, specificity and accuracy of 0.9890, 0.8003, 0.7851 and 0.9659, respectively. Where the AUC is approx {{formula:91c93665-bf72-458f-a3ff-7ca1553910f3}} more than of the second best Jiang et al. method, F1-score {{formula:88c44dde-0339-4f9c-a943-1a7271a534e7}} more than of the second best cGAN, sensitivity approx {{formula:90d749ac-6629-4256-876e-2af81b25e510}} more than of the second best Hu et al. method and the accuracy is only {{formula:e3251fda-fb6a-4eea-bfa7-52e594322ef3}} more than of the second best Jiang et al. method. In turn, the proposed method yields a specificity of 0.9834, which is approx. {{formula:7eb00297-7d4b-4867-810f-d7ed71c0e100}} less than of the FCN.
| r | 379dec146b6221bc05f7959515e452bb |
Current cosmological acceleration is an overwhelming characteristic of
our universe, driving the expansion rate and shutting down the growth of
large scale structure. Yet in seeking its origin, physics explanations
almost invariably sweep under the rug the elephant in the room: the
original cosmological constant problem that a much higher energy scale
vacuum energy should have dominated the history of the universe, calling
into question our understanding of how gravity reacts to vacuum energy
{{cite:4539be67a62410ca31074be4c2c18f3510819bcd}}, {{cite:399ce7bd55f6a3c6c5f3944df7b3dfce825ff399}}, {{cite:49521f1f00674a3065dd6a52bb93c7c50c432a24}}, {{cite:5c9b0e9a728c3e7b919e4a61e759e8379a1e8196}}, {{cite:7a0e9b05c1ea9740c6eb162c77cfa94ea83b842f}}. Exploring a low energy cosmic acceleration by
traversing a physics terrain where there is an elephant under the rug
is an uncomfortable position.
| i | 7911ef3ef0453d22d34de53d10931643 |
Given that the spread of stations is non-uniform, traditional convolutional methods do not work. As a result, this paper employs graph convolution to add context {{cite:0b508f4aa4c7797a00c6ac3620f5f1f4e7688f8f}}.
Specifically, this paper employs a form of graph convolutional networks similar to GraphSage.
Specifically, we define a graph {{formula:41cb7aa8-3656-433f-bc7b-247af756ab57}} over the state space.
Specifically, we let the set of vertices {{formula:219a359b-82e8-45c5-b1a3-37ccfc502220}} to be the set of stations and add edges between two nodes if the corresponding stations are within distance {{formula:913a686a-dcaf-491d-b20f-6cfafc74ab33}} from each other.
Letting {{formula:3f0ffdad-0082-4809-bbe0-66ee57a87d7f}} be the distance between stations {{formula:96726e16-22d1-4647-915e-b38c0bc038d5}} and {{formula:88b18723-0ce5-41a0-a4bf-f083691f9358}} , the corresponding weight is defined as {{formula:64f55e0d-4911-45e2-a07c-8b1d6d76f985}} , where {{formula:1c20ceb1-d467-4be1-a326-04ea1b1aa0b9}} is a hyperparameter.
| m | 247508c07487de49f5cd4dbdac3a1cdf |
t-SNE.
t-distributed stochastic neighbour embedding is a nonlinear dimensionality reduction method for visualisation that maps similar high-dimensional objects onto nearby points in a 2D projection space, whilst mapping dissimilar objects to distant points in this space with high probability {{cite:048459a095e58c2740d66963c50aa7dc4c0d6f5f}}, {{cite:19f4b2a0d61a6447b515fd4aa76985ddc04e2d5b}}.
The t-SNE is able to visually cluster data based on its local structure, and to disentangle complex data with several manifolds.
The algorithm is stochastic, i.e. it will output a different projection of the data for the same choice of hyperparameters if different random seeds are used.
We use this to our advantage in the annotation tool, as users can rerun the algorithm to get new visualisations of the data.
{{figure:8de916a3-d819-48a9-93f7-4bc820f796d0}} | m | 201056c91dc310346933823afcadc7e4 |
Spectral methods are known for their excellent convergence properties
{{cite:9ce6d61b5f062f019527b5c4a4c64922b88f3844}}. If the solution of the problem is analytic,
the error decreases faster than any negative power of the discretization size.
However, in their most straightforward implementation, spectral methods suffer
from a fast increase of the condition number, leading to slow convergence and
numerical instabilities. For high-order differential operators, or if high
accuracy is desired, this quickly becomes prohibitive. The combination of these
properties makes spectral methods ideal candidates for FOP.
| m | 837828d30d26e4431f270cecfe999536 |
Methods used for comparisons. We compare GPR-GNN with 6 baseline models: MLP, GCN {{cite:0a302a79d9ec94031971b90fcaec47c4b22a3b72}}, GAT {{cite:e30a553b9f18a83102dd40eda6372b598a154804}}, JK-Net {{cite:8e97451d1aea8632fb21bc8047ed476ffccd115c}}, GCN-Cheby {{cite:147689c2611386df46dc58b7f7f5b5738441852c}}, APPNP {{cite:54460d3995662d9da118a49be44af5791b7887c2}}, SGC {{cite:cd5a6d9369c0437c1f8863560b1131bdd8e2c48e}}, SAGE {{cite:eed15e07c9b7757770668d83d75d73107e954dad}} and Geom-GCN {{cite:1eed75ac04cab0225ec4ee153e583f30b227d07b}}. For all these architectures, we use the corresponding Pytorch Geometric library implementations {{cite:811925a82b36233bae534130df0d69a83dd043dc}}. For Geom-GCN, we directly use the code provided by the authorshttps://github.com/graphdml-uiuc-jlu/geom-gcn. We could not test Geom-GCN on cSBM and other datasets not originally tested in the paper due to a preprocessing subroutine that is not publicly available {{cite:1eed75ac04cab0225ec4ee153e583f30b227d07b}}.
| r | 753493cdaf44255bea4e723c45262390 |
The ContrastiveCNN-JL outperforms both the baseline and the ContrastiveCNN in every trial. This implies that the information gained by combining the traditional loss term with the contrastive loss helps learning a more meaningful latent space representation.
Latent space analysis
T-SNE plots
T-SNE visualizations of the latent space are presented for the baseline PCConvNet, ContrastiveCNN, and ContrastiveCNN-JL in fig:latent. As a example, we only present results for Note Accuracy on the Middle School dataset. The effect of the contrastive loss can be easily noticed, although the embedding spaces are not ordered perfectly in either case. The two models based on contrastive loss display a more defined distinction between low classes (0, 1) and higher classes (3, 4). Small same-class clusters can also be identified.
Class Distance Surface plots
fig:surf shows the distances between the centroids of each class cluster within the latent space of the models trained on the Middle School dataset for Note Accuracy. While the contrastive-based models appear to have trouble properly ordering the middle range of ratings between classes 2 and 3, the distances appear to scale more smoothly than the distances within the baseline PCConvNet, indicating better ordering within the latent space.
{{figure:4dbe4b46-6afb-4b1e-b64e-87cc26a3c553}}
Davies-Bouldin Index
fig:mid-db shows the Davies-Bouldin indices of each model on the Middle School regression set. Each contrastive-based model has a considerably lower index than the baseline, which indicates that the latent space clustering is improved. Within this set, the lower the Davies-Bouldin index, the better the regression performance, implying that better clustered latent spaces do correlate with better regression.
Conclusion
This paper presented an approach to representation learning to improve the accuracy of a system for music performance assessment. We introduced a weighted contrastive loss suitable for regression tasks and showed how this latent space regularization improves results on a large real-world dataset for music performance assessment.
In future work,
we plan to incorporate score information into the models, as this has been shown to improve performance {{cite:3b3b146ff1f5b506f41f950ac4733b12b27e2b28}}. More analysis should be done within contrastive learning methods to assess the effect of margin size, and number of classes on the performance of the model and the goodness of its clustering.
Another approach to ensure that the learned representations contain relevant information is multi-task learning. It is worth investigating what related tasks might help increase the performance of music performance assessment. Moreover, supervised latent space regularization methods such as AR-VAE {{cite:aba66b85f51f5773e83f80a4dcbe3236ba81883e}} and I-VAE {{cite:a9ff85763f02534c2c418bd2ec0ba9c3caeb3364}} might be incorporated to force specific dimensions to specific performance characteristics.
{{figure:42b02a85-d630-45a8-840f-15929cc07185}}
Acknowledgments
We would like to thank the Florida Bandmasters Association for providing the dataset used in this study.
We also gratefully acknowledge NVIDIA Corporation (Santa
Clara, CA, United States) who supported this research via the NVIDIA GPU Grant
program.
| r | baabf0328cde635ec320163a289f4c32 |
We introduce the SuMe dataset, the first dataset towards summarizing biomedical mechanisms and the underlying relations between entities. The dataset contains 22K mechanism summarization instances collected semi-automatically, an evaluation partition of 125 instances that were corrected by domain experts. We also create a conclusion generation task from the larger set of 611K abstracts which we use as a pretraining task for mechanism generation models.
We benchmark several state-of-the-art language models for the task of generating the underlying biochemical relations and the
corresponding mechanism sentences. We train general domain LMs (GPT2 {{cite:97d126cdd82da5b219f628c0fe34ec1a7140200e}}, T5 {{cite:a06fe4bbc0eff373a15812b900caa7a9e59c9576}}, BART {{cite:5b2be2e563bbd303dc61cbbcacd0c1617eb0e311}}), as well as science domain adapted versions(scientific GPT2 {{cite:1ff33f0f320bdde3f7245cf908093d3d6125fc0f}}, and SciFive {{cite:69e86118c1b851a0acdd907cd179dced0f4cad56}}) and benchmark their performance through both automatic evaluation and manual evaluation on curated evaluation samples.
The evaluation by domain experts suggests that this is a high quality dataset coupled with a challenging task, which deserves further investigation.
To encourage reproducibility and further research, we release the dataset and the code used during its creation. Both are available at SuMe webpage.
| i | a1ab92ff9abce64cb5686011e5505b20 |
All parametric inputs are taken from PDG {{cite:50dba2fc14cdd4f49aebc6da4120984b9988fba9}}. In
particular, as input for the top-quark mass we use the
{{formula:be4d1546-ad79-4bed-b145-d08e8ba3d60f}} mass {{formula:5aeabe07-00d5-4e11-9c71-4126ebc5e544}} GeV, obtained by
converting the pole mass {{formula:cc9b2e52-5178-4763-9739-aa6ab0117ac9}} GeV {{cite:50dba2fc14cdd4f49aebc6da4120984b9988fba9}}
to {{formula:4cf864a4-8ef7-41bd-8c7f-d53547ea96a9}} at three-loop accuracy using
RUNDEC {{cite:cbbd6dc0184abbbc84c648ee21f9f860aaf2ae9b}}.
| d | 56143b11c4b948b264695416e58575e8 |
The water wave problem refers to the motion of a free surface over a body of water of finite of infinite depth.
Its classical formulation usually assumes that the fluid is inviscid and irrotational. It is well known since the seminal work of {{cite:cb1b0fe463a71f74bd82ba72a62ca2d2e12c5825}}
that, in this setting, the water wave equations can be written as a Hamiltonian system with a standard Darboux symplectic structure
whose Hamiltonian is the total energy. The canonical conjugate variables are given by {{formula:3365ee4a-6ac8-4444-8351-d9e972a25eac}} ,
where {{formula:34329717-b3e3-47fd-a6bf-38443ce3fc6a}} is the surface elevation and {{formula:a2908b25-d0cb-4883-b8e4-d6adcf345ab2}} denotes the boundary values of the velocity potential on the free surface.
With introduction of the Dirichlet–Neumann operator {{formula:d1e4ec17-ac20-4105-9402-cd73d083c19d}} that maps the Dirichlet boundary condition for a harmonic function
in the fluid domain to its Neumann boundary condition, this Hamiltonian takes an explicit lower-dimensional form
{{formula:81cda5e1-7ce8-4fa4-8513-5e9f27337ea9}}
| i | f6f2ef4b5a4c5586e30737d871f6601e |
The expression of relativistic
Bernoulli parameter ({{formula:9c7d0433-4038-4b52-850f-95f07537c7ac}} ) for adiabatic and isentropic flow is not conserved along the streamline of a radiatively driven flow or across the shock, but {{formula:5b815dfa-2af6-4a5b-9cf1-949c6ab9d780}} is a constant of motion. This gives us a great tool to find various classes of solutions. One must not
confuse {{formula:d6f6086d-cf85-48b9-b0b9-9e8b5ed0c07a}} with the generalized relativistic Bernoulli parameter obtained for accretion discs {{cite:ccf6831fc67e2b39c62d152bb219ca0a60758d84}}, {{cite:d6f19a304250fffe03c7382f15c4e33e49cf0454}}.
Since the streamline and various dissipative processes in an accretion disc are different from the jet
(compare {{formula:3f1b136d-9bac-4817-a931-5f79ef5ba3a9}} of Eq. (REF ) and Eq. (18) of Chattopadhyay & Kumar 2016),
the values of generalized Bernoulli parameters will not be the same for both jet and accretion disc,
even if the jet is launched with the local accretion disc variables on the foot points of the jet.
| d | 9cab7785c44f6c39bc059509ce54c272 |
Alternatively, we can take a different Monte Carlo approach to
Equation REF and sample from {{formula:5ec9daff-6cfc-4769-b001-ec8fb4799e0f}} by simulating datasets.
For each posterior sample of the parameter values (conditional on all the data
under study) we can simply simulate a new dataset based on those parameter
values.
We can then compare the observed data ({{formula:5ca034cb-4a12-4c95-8834-edb3d13692c3}} ) to the sample of simulated
datasets ({{formula:a32b7c56-1c25-4d87-889b-82eac84d2b9d}} {{formula:7598062e-2f7f-4e25-8e06-e32da4fff682}} ) from the posterior predictive distribution.
In all but the most trivial phylogenetic datasets, it is not practical to
compare the counts of site patterns directly, because there are too many
possible patterns (e.g., four raised to the power of the number of tips for DNA
data).
Thus, we have to tolerate some loss of information by summarizing the data in
some way to reduce the dimensionality.
Once a summary statistic is chosen, perhaps the simplest way to evaluate the
fit of the model is to approximate the posterior predictive p-value by finding
the percentile of the statistic from the observed data out of the values of the
statistic calculated from the simulated datasets {{cite:187ac9d217bbd379e29204f53623106988056ffb}}, {{cite:6760ff99031b28d88a85576aa6984128e57fccfc}}.
{{cite:8323592c4f050a3d87f0b6bfcc746c9073fc13bf}} explored this approach for phylogenetic models using
simulated data,
and found that a simple JC69 model {{cite:2233faaebfb48dc4e1a6ae43b982811e94ebef20}} was often rejected for data
simulated under more complex K2P {{cite:1390e7f003ec2556ccc40bb106b86faceabd3811}} and GTR {{cite:12f87fd6323bf3868e03bcd34d3f7d476ce3522d}} models.
{{cite:90e84dd22bf0bea41dfd96e59e5f983747b64d6e}} also used this approach to corroborate their findings
based on marginal likelihoods {{cite:13e111b37a21560fc24704ddbe6cd2d24da603e8}} and cross validation that
allowing among-site variation in amino acid composition (i.e., the CAT model)
leads to a better fit.
| m | f16129b974cea6902032752e9beb9e8d |
In this work, we have only considered three subpopulations: the galactic field
and cluster binaries, as well as high-redshift Pop III binaries. As mentioned above, many other channels have been proposed and can plausibly contribute a seizable fraction of the total rate.
Our analysis can be trivially extended to include these and other subpopulations, at the price of increasing computational cost, correlations, and potentially degrading the measurement of some of the parameters.
On the other hand, most of these different channels predict distinctive features in the BBHs they produce, beside their redshift distribution, for example masses, spins and eccentricity {{cite:5ac72e807afd033df0f0d9333804ac020aee8ccd}}, {{cite:030af85be2a6bc4ee7a311f45d55b1768d7bd2bc}}, {{cite:776d59f4402c1b59e2f6c1625bcb8c0a929f79b3}}, {{cite:dfab4010021701dace07b1fee88f75bcce87c771}}, {{cite:5ce32132987a81224762e43ae8395262c58884fd}}, {{cite:c6a6f16f427e1b604236f56fa607679e2c008738}}, {{cite:4cd4f298f2de9d73f430f28215522881cd942e8f}}, {{cite:a8e746f093f9deb8d52d4b1ba4e051365f879484}}, {{cite:e136faa77e9ceeb4eccf1f5aafb84cb18fcba8c0}}, {{cite:df8f8b479a9bdc5315ede8b454ebccf9f9bc3550}}, {{cite:29c24a030186e2a49b4fb08d0e80186a1cb92d39}}, {{cite:e315e8d45d9e71340ebf8850ad181613b51ea432}}, {{cite:7930b0ad2be3dd38d67f0963c95a0f200d13fdb0}}, {{cite:3bcbb119e4dee8d381e103115e9f18ea1b426895}}, {{cite:0adb3583efc3a8bcad174d0a22df4da830127c00}}, {{cite:8d95eee273d013c0fc93b0c07dd7366af982a419}}, {{cite:23dcdb60fe16048d343ca3bcdfdcb36f9cac590b}}, {{cite:a2ad52291619e0ad84394eb310ae93e41f41c907}}, {{cite:8d9d6acb1ef53e39890fe04d086655e4c6248279}}, {{cite:a2e0b67c282923244fb50be7a6ce6f6e3923718e}}, {{cite:40da406bb920c87adfabed2df4de38679c0694c9}}, {{cite:66fdcc573db436257de6ee8bbaf2f60223e93683}}, {{cite:6f933914782f98cc51b94786afa90c3cb6959875}}, {{cite:acc7aec604337f4a0987ce9046e2145b9e23a2c5}}, {{cite:db9dd74303179f3018d3225bfe78cbd0bd7ee279}}, {{cite:b4e3f834428b81528c921aa1ed9a298497d207f7}}. Including these features can enhance the precision of multi-population inference, help fighting correlations, and improve the understanding of each formation channel.
We leave this extension of multi-dimensional BBH parameters in the 3G era as a future work.
| d | 5c9bf7b8e291bd993d4cd55c51250375 |
Pretraining models on massive datasets followed by finetuning towards specific downstream tasks is commonplace in natural language processing and computer vision approaches. The uptake of similar approaches for chemistry is lagging due to the limited number of large datasets and long training times involved. Training atomistic property prediction models from massive scientific datasets is a compute-intensive task, and much of the focus in recent literature has been on transformer-based models {{cite:eb00ec124ea415fd1158ce0f7e739af3b2e224ed}}, {{cite:a1e179a975b37710716b94f98409990cb24bbd7b}}. The reduction of atomic positions to character strings via the SMILES notation has aided the generation of large datasets. For example, Wang et al. trained the BERT architecture on 18.7M SMILES strings from the ZINC database {{cite:eb00ec124ea415fd1158ce0f7e739af3b2e224ed}}, while Chithrananda et al. trained a network based on the RoBERTa architecture, called ChemBERTa, on 77M SMILES strings obtained from PubChem {{cite:a1e179a975b37710716b94f98409990cb24bbd7b}}. ChemBERTa was later shown to perform well on downstream property prediction tasks {{cite:7fc6d5d6d6cfabfbd060ba53f857a3a6570b5e5c}}. RNN-based generative models have been trained on a 1M-molecule subset of GDB-13 {{cite:08a992a6c49a5d9e18970a71aa867ab53b1537c5}} and a 1.6M-molecule subset of ZINC {{cite:d16653f1616e25d9ad1c06076c3a864f207f7f20}}. More recently, Ross et al. developed a transformer-based encoder that uses linear attention, called Molformer, to efficiently train on {{formula:ecc61c6d-59c2-416e-905e-dfefa560b8c8}} 1000M SMILES strings, outperforming several graph- and geometry-based baselines on regression and classification tasks from benchmark datasets {{cite:d4bec3fc73cd883b3db7c1a48d74c07bbe417a6b}}. Subsequent work has explicitly incorporated spatial properties into Molformer for training on comparatively smaller datasets {{cite:2c829049556e8510090b002464f3ccf8caaeaaae}}.
| i | a4dc830cd6dfae1c8a9b1663894d8edf |
Contrastive-based method {{cite:d5af882473d4f47cf68c0018114627801e04c508}}: As our closest work, this approach acquires discriminative representation from unlabeled images via two global and local contrastive learning.
Global contrastive learning pre-trains the encoder of the segmentation network to distinguish the global context information such as the anatomical similarities between two slices,
while local contrastive learning focuses on dense embeddings and enforces pixels undergoing different transformations to be close and pixels at different spatial locations to be pushed away.
We refer Contrast (Enc) as our PyTorch re-implementation of the variant using only global contrastive objective, Contrast (Dec) as the variant employing only local contrastive learning, and Contrast (Enc+Dec) as the full implementation using both contrastive objectives. For Contrast (Enc) variants, we pre-train the encoder of the segmentation network to distinguish whether two slices comes from similar slice position by assuming the volumetric scans are coarsely aligned. Towards this goal, we manually split an ACDC scans into three partitions, while we fixed the partition numbers for Promise12 as 5, similar to {{cite:0e12d6b76b81c6c904072c7744113499760145f1}}. A nonlinear projector is used to convert the global representation to representation vector, comprised of an average pooling layer, 2-layer MLP with LeakyReLU as the activation, and a normalization layer. For the variants using local contrastive learning, we take the dense embeddings from the layer before last {{formula:976710d9-2866-4843-9600-b39fab99f18c}} convolutions. These dense embeddings are then projected to pxiel-wise vectors by a dense projector, consisting of an adaptive average pooling of size {{formula:72a52c4a-5ca8-42a6-ba51-bc533af2a66b}} to reduce the spatial size, 2-layer MLP with {{formula:2c02b078-cb73-455e-81d1-a673238f986c}} convolutions with LeakyReLU as the activation, and a normalization layer. Positive and negative pairs are then defined on these {{formula:ad54f6d0-a694-4c2d-808d-c616c4e2846c}} grid, similar to {{cite:d5af882473d4f47cf68c0018114627801e04c508}}.
It is worthy to point out that we only optimize the parameters for the encoder in the pre-train stage only when global contrastive loss is used, while the whole network except last {{formula:11bc8f4c-5dd9-4562-853f-483f16a59a66}} convolution is optimized when local contrastive loss is employed.
We employ two stage strategy: pre-train and fine-tune to evaluate the quality of the learned representation.
| m | 63b2e8c72d5577fbfdcfeea60897ef77 |
Our mathematical characterization of the Rawls classifier shows that it uniformly applies a threshold to a certain ideal score of features, whose description requires the underlying data distribution explicitly. We give a description of the Rawls classifier as a threshold on an ideal score function given by a convex combination of signed unveil functions, which quantify the likelihood of an individual belonging to a sensitive sub-population given only the unprotected attributes. Computing these unveil functions from a finite sample drawn randomly from an arbitrary underlying distribution is intractable, a familiar obstacle encountered for exact implementation of the accuracy maximizing Bayes classifier and the optimal group-fair classifier characterized in previous work {{cite:25175218941e6548232b53a5d3bac7c5b3391d86}}, {{cite:7e773efece957185a9a96b94c5c3e1e6955e8592}}.
| r | 817db02f80f5676bccf595fe4129a589 |
Table REF shows the results on ImageNet, including top-1 and top-5 classification errors on the test set, number of weight parameters (millions), and search costs (GPU days). Following {{cite:bdb5d383ec26f07b16460fedd41a27d401e9fe9d}}, we take the architecture searched by LeaSE-R18-DARTS-2nd on CIFAR-10 and evaluate it on ImageNet. As can be seen, applying our LeaSE method to DARTS-2nd, the top-1 error considerably reduces from 26.7% to 24.7% . This further demonstrates the effectiveness of our method.
| r | 5646e8724a97beeff9100f6eebbf054f |
PGExplainer. In contrast to GNNExplainer, PGExplainer {{cite:9a031cf3aec1a70b40a6f9c68d0154f5b8f8e4fa}} generates explanation only on the graph structure. The direct optimization of the mutual information framework in Eqn. REF is intractable {{cite:afdd322e3bd64eeb718fa2c42c8723f26bb8b155}}, {{cite:9a031cf3aec1a70b40a6f9c68d0154f5b8f8e4fa}}. Thus, PGExplainer consider a relaxation by assuming that the explanatory graph {{formula:f3783681-574b-4de7-81a1-3ea37db2dced}} is a Gilbert random graph, where selections of edges from the input graph {{formula:ce7131bf-86ef-48f0-aa5d-e6d8015b873e}} are conditionally independent to each other. Due to the discrete nature of {{formula:8b85973a-2905-47ec-8019-21ed9d2fd7b8}} , PGExplainer employs the reparameterization trick where they relax the edge weights from binary to continuous variables in the range {{formula:1e2919aa-4e82-4556-873a-496c03c14b9a}} and then optimize the objective function using gradient-based methods. It approximates the sampling process of {{formula:6c6262a3-6905-4570-b221-3a107f6d80fa}} with a determinant function of parameters {{formula:2f8ad94a-3a65-41d0-95b5-68fcfc5b9a2d}} , temperature {{formula:ac840fc2-7d68-4d19-ace7-eea329914130}} , and an independent random variable {{formula:3ce307ad-4e2b-4dac-a051-4f8b93d07011}} . Specifically, the weight for each edge {{formula:cc89a777-c535-4423-b1d1-5825155524f2}} is calculated by:
{{formula:a1b96749-8ebd-443c-bd5d-d7b9b7db66d8}}
| m | cd09b0e5764fc7c5d524e2550c156a46 |
There have been numerous attempts to solve the Hubble tension, focusing on both expansion epochs in question {{cite:482f36b3deddd1b1062dec6f61c9202332972d22}}. Possible late-time resolutions include a vacuum phase transition {{cite:f640925f2214ee3f0b310b69eac2049b4948222c}}, {{cite:a62bcb1967b2bbac1aee06dbbe1e9eef0db834d4}}, {{cite:e5e47cdba940d8397bd10ca797a2010451c7124c}}, {{cite:195dfdd7f31992d8c2eb8b9de0f2082ab88a1c8f}}, {{cite:c52b1b987f35ff0900fa9fa57e74f8ca70de4632}}, modified gravity
{{cite:7dedcd3e82cc8ae20272d5d707555d48389d70a5}}, {{cite:c517bb8347d5bcf2e711dad137f72ffd47ef1b03}}, {{cite:28f64c35fabdf9b46b69351a76e4dd8db5a35b0a}}, {{cite:6cbdf2e07396aad9037dca41b4030d6c92c32a3e}}, {{cite:b03caa2f1238326c8687eb16bb9c422e14cc1673}}, {{cite:b3e4448c96fc4d7bf41bb469718667e23e1a6036}}, {{cite:1ccfbc79e974b3515e58c1e085f0260bea1c9380}}, {{cite:5d3a323d9a0702334374eb0d605d68b98f5e69ec}}, phantom dark energy {{cite:329f31773fb569f5b6e51d91ce8e958234b112df}}, {{cite:45889548eb533a1fe587ab9cc1506c5436fc8aba}}, {{cite:9808a499ea4340116890ad6ba3b014195a0b3faf}}, or interacting dark energy {{cite:df32b776fdfd0ca1e1965590b234904eea9fae76}}, {{cite:ac16bd5c0db9880c87d2d3f925a9f5fb90bc8884}}. Model independent parameterizations of the late-time expansion history also have some success at relieving the tension {{cite:7408894586c17caebdbf4eaaa5a1ad642a8804a9}}, {{cite:1cf383073bf0c0195d3ed443bace0d3b7512c7ae}}, {{cite:9717c8186045e8ead86405185e789ca4f731442e}}, {{cite:9a1c623c84c85ee7964c2487779bdfde9ba190a2}}, {{cite:404ac18b41e8a926b39eadb2a4b172fd4fb9862c}}. However, all these late-time resolutions are challenged by tight constraints from late-time observables {{cite:d6bced37d5d3e270d7d72dc96a3c929ad4e413b3}}, {{cite:45889548eb533a1fe587ab9cc1506c5436fc8aba}}, {{cite:ac16bd5c0db9880c87d2d3f925a9f5fb90bc8884}}, {{cite:7d6d0defdfdfc07a8a961b1319f083b4c80d3d2c}}, particularly BAO {{cite:607dcf0d257a8f15c4effd583dec6894afa03dad}}, {{cite:ab6a09d4ec4e740c1298465be4e0251e1eeec546}}, {{cite:ca5e94ed3b96ee06788b9d70999177389ff88756}}. Early time resolutions which modify pre-recombination physics are suggested to be the most likely solutions to the tension {{cite:a615172e351ae5a11c50047d3d4d36e536bbc7bb}}. Many such resolutions have been proposed, including interacting or decaying dark matter {{cite:5221d5443267f072e0d15949761e7f8219d091be}}, {{cite:df6e662c9749b933ae7793a95a9eabab170422ce}}, {{cite:83befd540946f093722d2947ebd28f89ff9d0c9b}}, {{cite:fcd59e9bb15384a961ba986432cee345f9642d76}}, {{cite:d138503dda3ee1c3dfc7fa33814d1555e293afd4}}, {{cite:2a5b132e37547c02098d97bd794ee87b21fe2844}}, {{cite:4083d6dae1b80f55a9fafde84638e3a9cec106ca}}, {{cite:13b2f70a8844a89255ab00326860f0d13232f25f}}, early modified gravity {{cite:1f4ce33cd9e22eeee763ca51468bee17dcab17d4}}, {{cite:0c124f2e8e2450b8e70512a6a737a19c0d98b472}}, {{cite:a30d784688a18d58a73fc406b8c795dfdf92c46f}}, {{cite:8b223af0250c7dfe760b6bbd3e25b13d9050826a}}, modified neutrino physics {{cite:5a63c208def6f5a544eb60c558e7eb9f95881431}}, {{cite:1ce6c4175033fd973e438674cb04dfa369ac07a9}}, {{cite:b15d3db5bd3af2d512fe51b19e9c97bf5591888d}}, {{cite:d30bc4bb658aa5d7874a3abf6bb34741c27807ea}}, {{cite:acbd24506f1e775e7d8b101e43f2917231f9c4ea}}, and early dark energy (EDE) {{cite:d531db67d39872edac6b607e0980068772c35998}}, {{cite:f18c053c28cca2bdabecf9e2e817e82848f2084a}}, {{cite:acca2ca01224aded17a2cebdede25263bcf97154}}, {{cite:ce7a447534ab4fa2a748c523397e58cea2856069}}, {{cite:5d49010e0596889b7d498de92b12d100c9b24bf1}}, {{cite:63b1a454996a472b574bd2522943abc7218992b1}}, {{cite:cc519138605fcc3a1e56a87ba6d3fb060f558f3f}}, {{cite:65565cf5f57a62737463a73b693b30e9f440aa90}}, {{cite:8f433c1d46d7fb8fe562553efd70cfcb6b832cce}}, {{cite:048b10de212c5d0f28c8778caa97b46e08ea9d02}}, {{cite:8d957b59705a9fba0ed1c4f6764ca45ba10695f6}}, {{cite:02c73bb5d9197c412e421fb01e5b786ff241b384}}, {{cite:44550ce911292722d2fdcffbb99d7d0261c4d365}}, {{cite:03af34bcc2da51fb6f4acb4c07047cd6a35e2cb3}}, {{cite:cdd5f51bb1573b1b97dac3692b956d7df998cd39}}.
| i | 374ce30b826cd79bf8b22e9ae3030414 |
Our detailed evaluation in Table III, IV and V summarizes the state-of-the-art in object detection for autonomous driving in adverse weather conditions. From our results we conclude that the detectors which perform good on the KITTI benchmark {{cite:f6e8bb8579bfb82daf1c7cb7277f23a5094d4786}}, can fail in such adverse weather conditions. The main reason for this is that this benchmark does not cover such extreme weather scenarios. Consequently, it is necessary to improve benchmarking datasets to cover such cases.
| d | 095b9ef2fceae42a55c385ea55d28690 |
Our technique is also applicable to observables on separate quantum systems, e.g., {{formula:b6e06e6a-b407-4b3a-831d-21f770135521}} is measured on a first particle and {{formula:a346c87d-94ef-4470-8f88-bf73dea44c45}} is measured on a second particle. The standard procedure for weak measurement would couple {{formula:eb980d1d-f618-47d2-918d-3a46823b850c}} to a single pointer using {{formula:f4eb14e0-70bb-429c-82e5-1599a6205315}} , which is Hermitian now. This, however, requires a three-particle interaction which is challenging. Our method uses a two-particle interaction on each system while still only using a single pointer. One would first use the standard von Neumann interaction Eq. REF , to couple the pointer to {{formula:a85b5b19-5e0b-4631-a633-1693c05f5a10}} , then couple the same pointer to {{formula:089d776a-c6e4-46cc-b3d8-2587ac580bbc}} . This double coupling can be challenging to implement. Particularly, in photons one would need an optical nonlinear effect at the single-photon level. As our technique largely preserves the initial quantum state, potential applications include demonstrating contextuality {{cite:388c91e18b1133ee4063be7ed3e7c24a14f27c8b}}, {{cite:76546426063c7bcf842ea34652c77835d2d44eee}}, {{cite:e54254f3a2409c4c3e5d8667752dd8f702cec23b}}, {{cite:7e35045d3608fa9505c5335cc493d8395a8f7b27}}, and tests of Leggett-Garg inequalities {{cite:1576ae2592bd4e334aa32dd52445a242f8a4d8ab}}, {{cite:d1d5b7218f82e2e6afa7a253212bb57f0fcfe76d}}, {{cite:e1c365964dd06bbccb9614e3099dc6511c93bb45}}, {{cite:fcc4e778cef121c6af5ded708005367be34322e3}}, {{cite:69672e098b79a29f61fde15cc536bf5eae53a78a}}, {{cite:81666e14ba1964c7f72c334ce3a4d7458c10b97a}}, {{cite:249cb5801b6e81c15efd42465374d2114d242703}}. Motivated by the direct measurement of entangled systems {{cite:bf1a256c6ffe02e4d5c3b33d29e55554a0ee2dba}}, {{cite:a136b3fd36ee97d0e954644a658e2a35c7957657}} and entanglement witnesses {{cite:6703378d19af836f5b15807d79145603e873a092}}, {{cite:48cc1533c90c7e3c02912ceda0c97031828b831e}}, a potential future research direction is the use of this technique for characterizing entanglement.
| d | c9e55ac8b47e85b1d78252d5a1861479 |
Finally, see {{cite:656d5e570499d1afe825c0e729c91ef06520ac69}}, {{cite:c46e9e525a537307f5172108f696eb4a66d80e7b}}, {{cite:562fc13d408fa6590c681e8f69741280f6054630}} for a replica exchange MCMC technique that considers two {{formula:06924f82-3d80-448c-8125-b9959580481a}} particles that follow Langevin dynamics with two different temperatures.
Specifically, the sampler swaps between the two particle chains with a certain ratio and at each step samples from the current chain.
Concurrently with the present work, the replica-exchange MCMC technique has been employed in conjunction with DeepONet for operator learning {{cite:d4d6ddb4d644e283f41a8c4d317050acc2ede6dd}}.
Additional UQ methods based on MCMC can be found, indicatively, in {{cite:a5ec4056b57f786f03d966fb3dd15031e9be9b2c}}, {{cite:35ec22df347bc4288e20b37e00d15fb910c95248}}, {{cite:1aa5f1e1f8967e7d1635f6ff565e569ce0887051}}, {{cite:c08e5f24ce05d141dedafcc4f1737473b282bef1}}, {{cite:1d3ea395000052fb73d900808011b530130780a6}}.
| m | b0ba0cba8e1f40634d350e7910fd7936 |
The EM strategy based on symmetry projection works as follows. If a quantum state {{formula:a61a36be-58af-4377-9a59-8d1e4ccd1bc0}}
(ground or response state) resides in a subspace with spatial or spin symmetry, a projector {{formula:de39925d-0a69-4eb6-acb0-92c2625a0173}}
can be associated with this subspace such that {{formula:ce0349df-7941-4e92-9178-b94db632cdc8}} .
In the presence of noises in experiments, the quantum system needs to be described a density matrix{{cite:f24f1a9098b22effdf3761763afecb2ae3632614}} {{formula:f598c09d-d03a-40a7-b9e2-edb13e4e1e21}}
instead of {{formula:e8258f4d-3cff-4087-be32-825a4682ea41}} , which can have undesirable components
outside the correct subspace. To get a better estimation of the
expectation value {{formula:3cc34676-6b02-400b-a0b5-ed9af9c9a8d7}} for
an operator {{formula:1d411adb-2d7f-4266-93b6-cc3f1a7bb576}} that commutes with {{formula:4fe89ed6-e968-4c68-a8a4-546a459050c3}} (e.g., {{formula:3ad1b79b-f273-4ff8-8a71-93f8204a89e9}} ,
{{formula:4d64e561-2ea6-4205-a247-3911a34e559e}} , {{formula:6efc4bee-b0b5-407b-8091-107dfcd995c9}} , and {{formula:42d84af9-2280-4136-b41b-c21e74e6dbfc}} ),
we can use {{formula:aa743da5-c1a2-4281-b706-8c0c78cfd2be}} with {{formula:2b1e4e30-ae8b-442a-9b80-8da7441769d5}}
being the projected density matrix. This EM strategy may require
a small amount of additional measurements for computing the expectation values of
{{formula:16f50d45-e546-4f1b-a5d8-3ca4fd7e5f44}} and {{formula:03128f1f-560b-4d4e-8635-a25ebe552039}} . The choice of {{formula:11456086-2807-4855-86b4-00a709ccdfac}}
for different problems is presented below.
| m | c8f277ae9f60feb658b888c1d80fddff |
The benefit of preserving pretrained features.
Our work adds to growing evidence that lightweight fine-tuning, where only a small part of a pretrained model are updated, performs better under distribution shifts—and we give a theoretical grounding to why this might be the case.
Zero-shot language prompting in vision {{cite:85d0d574e462ac8aa34898f42811db9e4cf09f25}} and other lightweight fine-tuning approaches in NLP {{cite:abdabca71ce338629b1b3a78b5942d92078b47cf}}, {{cite:98b7c036997ef21f1510b77804901e404fb09881}}, {{cite:0c44c12cfc6b41b3bbc0c45f67c1c2af0aeb3d33}}, {{cite:63206ef8af52a91321e598ea0044b2ad4cd583b4}}, {{cite:8bb9eb9ac1d6ccfaaf1b916180114ff15aa2f372}}, {{cite:b3f0d7312f1770292501a53fb65b8ba601a312ea}} have been shown to improve OOD performance.
In independent and concurrent work, {{cite:a6dc4a0fe28a5a6044ec3ba61e4579100fbcb69e}} observe that through the course of fine-tuning, ID accuracy continues to increase but OOD accuracy plateaus.
Our work shows something stronger: at no point in the fine-tuning process does FT outperform LP.
| d | f90dd334661a968e58ebebcb38e8e7ab |
To confirm the effectiveness of our method across different data sizes,
we experimented on 10 language directions, including IWSLT14 En{{formula:a0851472-f6e5-4e17-b33f-9bbcfb5da95e}} De, WMT16 En{{formula:c84d3175-a96b-4775-9317-a5888aab9ccb}} Ro, IWSLT21 En{{formula:f8bd4612-cae2-4f2e-b5bc-3cdd04bf46a0}} Sw, WMT14 En{{formula:292eeee2-a2ec-4487-9a42-0c6b8fe86bce}} De and WMT19 En{{formula:e9a5bf22-a1d9-40be-8d48-5bb0fb030fc0}} De. The smallest one merely contains 160K sentences, while the largest direction includes 38M sentence pairs. Table REF reports the results, we show that BiT achieves significant improvements over strong baseline Transformer in 7 out of 10 directions under the significance test {{formula:6c4efd35-da76-4596-a142-b45553076941}} , and the rest of 3 directions also show promising performance under the significance test {{formula:9190ec59-6d50-4538-9339-3a81a3abb96a}} , demonstrating the effectiveness and universality of our proposed bidirectional pretraining strategy.
Notably, one advantage of BiT is it saves 1/3 of the training time for the reverse direction. For example, the pretrained BiT checkpoint for En{{formula:b1756765-6c9c-4ba8-a5d2-b1a62ac870ef}} De can be used to tune the reverse direction De{{formula:7e5442f1-ad52-420b-90fb-72fa2c1b4dac}} En. This advantage shows BiT could be an efficient training strategy for multilinguality, e.g. multi-lingual pretraining {{cite:55d5b97e598b84447c74ddd56fa3290ce1a3571e}} and translation {{cite:4ba769211714a6678df00f9b7c11cd2962a862a1}}.
| r | fac5f76051b9c1c07ac92cbf9d0fe93d |
Synthetic molecular machines are one of the frontiers of nanotechnology {{cite:b16336c337462cc69bda574d496ab0b455cedd59}}, {{cite:64401bb9a5596653f81de9f6583a5fb2e6d5da20}}, {{cite:e765dd11d1a253fb232096836eef9ebfb452fc1f}}, {{cite:8f84d6b732f64ee0cbf98b3a59b63166d8b5b161}}. Enabled by the idea of a quantum robot we can envision extensions of the molecular machinery toolbox where the quantum states of the nanomachines play a fundamental role in their dynamics.
These devices would combine resources from the environment, stochasticity and non-equilibrium to execute coupled quantum motion and processing of quantum information entering the realm of quantum nanomechanics. For example, in the entanglement qubot one could set the correction sites to perform the operation {{formula:651f65ed-d9c0-47ef-ae1d-2f4043af8d5e}} , and initiate the spins in the state {{formula:af8c36ed-b019-4e00-af4a-e4c95afde0de}} . This would cause a periodic spin-driven motion of the atom. It would be interesting to investigate the possibility of building quantum time crystals {{cite:ab7288cab9804eb976339d8a740cf089fc2f6b5c}}, {{cite:512f77d9da5a7de46a4104de567d170bbb41c88d}}, {{cite:645ac98202c06d065c4aef4ef5a0d41e64dac861}} using this scheme.
| d | 6c9af284606af0db1726ab2092e4d3b9 |
We now discuss the relation between our work and the existing literature. We start with a brief survey of the physics literature. The first indication that a space symmetry can enrich the topological landscape of a material appeared in {{cite:adca86a83dafd34fc76d5bb7112ad4422e422555}}. The first indication that a space symmetry alone can stabilize topological phases in a material came from Refs. {{cite:21b3aa4ea04921b26473678add165920095fba06}}, {{cite:16961e6f543353c5ec3150a71f00d8d87119be0f}}. Prior to these works, a topological phase was synonymous with a non-trivial bulk-boundary correspondence. However, these two works put forward a broader definition, which says that a band insulator is in a topological phase if it cannot be continuously and adiabatically deformed to its atomic limit. This concept evolved in what is today known as topological quantum chemistry {{cite:bb1f660fae21af0b08d99f5b6df8b0cc55f5e252}}, {{cite:223f652a268da07588bd92902401d20d58b2ce05}}, {{cite:c6c4bfd131cfb064bf93159e12fc8de91f0f9bc0}}, {{cite:c0e495f46d6a097f47f8233d8b8f9a2dff01d6c8}}, which perhaps can be defined as the science of identifying topological bands in stoichiometric condensed substances. It comes with fine tools that have been combined with first-principle computer simulations of quantum solids to assess the topology of the energy bands in large classes of stoichiometric materials {{cite:2999036f1f5e3542ba623bffd3ec574eeb79e790}}, {{cite:2dee75dc04d35c309107bada753f83d4e82a19f1}}, {{cite:69a9f977e660bb727e44630e2064d622aeea614f}}, {{cite:53f382dd602ca9481ce2759c4db83297d8345591}}, {{cite:d537b46f14425c04b6dbbb8fbe5462c54a909cff}}. The topological criterium in these works is the pure homotopy equivalence of the bands, while ours is stable homotopy. The latter allows new degrees of freedom to participate in the deformation processes of the models and, as a result, our predictions hold even when the physical systems interact with external structures. Furthermore, we do not identify atomic limits or place labels like topological and trivial and, instead, we simply calculate the equivalence classes w.r.t. the stable homotopy of the spectral projections generated from the algebra of dynamical matrices. K-theory then supplies the complete invariants of these classes, hence enabling us to see if two spectral projections can or can not be stably deformed into each other. Lastly, we are seeking to implement a bottom-up approach, where we design meta-materials that deliver the topological bands, as opposed to the top-bottom approach in {{cite:2999036f1f5e3542ba623bffd3ec574eeb79e790}}, {{cite:2dee75dc04d35c309107bada753f83d4e82a19f1}}, {{cite:69a9f977e660bb727e44630e2064d622aeea614f}}, {{cite:53f382dd602ca9481ce2759c4db83297d8345591}}, {{cite:d537b46f14425c04b6dbbb8fbe5462c54a909cff}}, where large libraries of existing materials were scrutinized for topological bands. Of course, the latter still represent an extremely valuable source of information for meta-material scientists.
| i | ee068a83586fddc8b607286c1ff27c6f |
Traditional outlier filtering strategies can be broadly classified into two categories, namely the individual-based and group-based {{cite:05de854a1575b38fea32caffaee397572f01de2f}}. The individual-based approaches, such as ratio test {{cite:dcc025dbd3cbe4b996f0256f2e056933ea4bd5d8}} and reciprocal check {{cite:9504a41eafc1e4356b445d23c0206c3eaee7e883}}, identify inlier correspondences solely based on the descriptor similarity, without considering their spatial coherence. In contrast, the group-based methods usually leverage the underlying 2D or 3D scene geometry and identify
inlier correspondences through the analysis of spatial consistency. Specifically, in 2D domain, the spatial consistency only provides a weak relation between points and epipolar lines
{{cite:fe1060c028087e872f77aaf59d2a66c5f59e6f99}}, {{cite:eda58ae817822eda5cd931d60a0d5f3de896f8a1}}, {{cite:f5160b6f49e656a2b1016759a92c0421e951c938}}.
Instead, in 3D domain, spatial consistency is rigorously defined between every pair of points by rigid transformations, serving as one of the most important geometric properties that inlier correspondences should follow. In this paper, we focus on leveraging the
spatial consistency in outlier rejection for robust 3D point cloud registration.
{{figure:4362f951-1d0f-4eee-9b77-22c0a6d5b129}} | i | b8138b247d3455a9490878094cad430b |
In this section we present evidence that in the case of {{formula:75e76d62-6b36-40ee-9697-a57dd3cafc83}} discussed in the previous section and for a single-site operator which we introduce below, K-complexity indeed saturates at values below {{formula:78dfd49a-cf14-4170-8ae9-c38ea81743b9}} , which is the expected saturation value for chaotic systems such as SYK{{formula:e7d4ca6b-bd12-4398-b440-a6eba10d80b0}} studied previously in {{cite:1d648730370638a4a68ee438df69f00d103a73fa}}, where the Lanczos sequences featured less disorder as illustrated in Figure REF .
| r | 11ba38a9e618a76179ef8e95c274e5f1 |
All simulations are performed using an intertwined application of Metropolis {{cite:e590532c955925a1badbd0505b42c3f75fb2918f}}, {{cite:4bfcfc21cd7850d26a25229e10bcbc243a61a97f}}, {{cite:2e22e4bc00f82027f6796659e539da1305f5be05}} and over-relaxation steps {{cite:0ef67b4297d808fa363401f503a31596d173e374}}, {{cite:123012d3f5e1f1d1e79aa53f96271c5d4418bce3}}, {{cite:d5cfea156534903cf3ec1f3e3a12ab25b4ccbb16}}, {{cite:da94ca988d6379301ba1e41d8d7c1295afb3a96a}}, {{cite:cf668951ed1ccc266d35eaad6e6421029fa43db1}}. These are two independent update steps coming in pairs: one for updating the link variables and another to update face variables. We now describe both in more details.
| m | f8ed70e7331e557b585f61a14b05ad95 |
On the contrary in the AFM phase, due to the simultaneous presence of an odd number of spins, periodic boundary conditions, and antiferromagnetic interactions, the system presents a topological frustration in which, due to the absence of an energy gap, the quasi-adiabatic continuation cannot be straightforwardly used.
However, as shown by previous works {{cite:9b2cc792a8818cfec48995666ffa01b13ab7275c}}, {{cite:4da1d12d457942039dcaa2a85946ed8bdee27adc}}, in several respects the ground state can still be seen as a global state with multiparty entanglement on which, through a local deformation, an entanglement of a local nature has been generated.
However, unlike the FM phase, the global state is no more represented by a GHZ state but by a W state, that is, in physical terms, a linear superposition of kink states {{cite:4da1d12d457942039dcaa2a85946ed8bdee27adc}}.
This fact is crucial since, differently from the first kind of states, part of the entanglement of the W states is local, since they are the family of states with multipartite entanglement that maximize the amount of bipartite entanglement after local measurement on one of its part {{cite:c1cbb1c172f217fb49886702126c9872ffc604dd}}, {{cite:21d95a6ce6c18cd655eb237199e0cc91546ed323}}.
The presence of such bipartite entanglement, absent in the states coming from the FM phase, provides a path along which the entanglement cooling algorithm can act, reducing, but not removing, the amount of entanglement in the system.
Moreover, for every single pair of spin, the amount of the bipartite entanglement in a {{formula:bc24fca7-5fdb-4ca0-ad5f-75e199eb7d82}} state reduces with the size of the system, hence explaining the fact that the difference between the values of the two initial and final plateaus in the dynamics of the {{formula:3faa5e6a-77d9-4f16-a041-7ad3adb89ad6}} state reduces as {{formula:70539047-4605-43d5-8ec1-82222392c237}} increases.
{{figure:9fb74656-aa88-4ecb-82d3-01838dcd0c88}}{{figure:9b280883-b987-479a-87a7-92c3b6cb6326}} | r | 565a3c4b6d9b36f094089eee98ca00e2 |
where {{formula:73a772b6-02f8-4788-bbb2-527086fe3e8e}} is the dimensionality of the Hilbert spaces of the component systems. We use the shorthand notation of {{formula:a06a7292-5343-4f44-8cb9-6f4898f3c8d6}} . The effect of {{formula:61df7136-867c-4aa8-8feb-7a97d2190e09}} on a product state is {{formula:ce6b1a6f-e7d0-4cee-a0d7-39d9f5d384af}} . The swap operator depends on the choice of local bases, states in the component spaces are regarded the same if their vector components are the same in the bases chosen. Therefore, the symmetric and the antisymmetric subspaces also depend on this choice. For example, any pure antisymmetric state becomes symmetric in the bases corresponding to its Schmidt decomposition. However, the symmetricity or antisymmetricity of states are preserved if both parties perform the same local transformation {{cite:683c73bb51b676a57e211e13cad55ab8d0911e0d}}. In Ref. {{cite:43d0162340092dce230ee136744fc36349eea399}} the authors consider only identical systems, where the choice of the bases is not completely arbitrary, but their methods are more general. As {{formula:cd5f8588-d81e-4d6e-b6dc-e3c42615bc19}} , the full space is the direct sum of the symmetric and antisymmetric subspaces. It is easy to check that the symmetric and the antisymmetric subspaces have dimensions {{formula:423e3f96-aa75-4757-915a-14d0581585db}} and {{formula:aa3ccf40-7976-4583-973b-8da6925fc473}} , respectively.
| m | d2b8b8aaff0c7ba62957582b42eb7297 |
FBNetV2 {{cite:955ab40e115d1dab24fca944144737d639213f01}}: As shown in the paper, the authors searched the FBNetV2-L1 model ({{formula:7f686369-6bf0-43dc-ae5a-7b04d705641d}} M FLOPs) with total {{formula:dba46d93-8530-434e-adab-ee83792e1353}} k GPU hours. We linearly expand the number by FLOPs and obtain {{formula:c61c3539-9708-4235-bb56-639e62a859a6}} GPU hours, i.e., {{formula:8435c9e3-98a4-475a-83ea-df3ba4f48983}} GPU days.
| m | 575d76f2e28b6a0aa6fd83049a24237a |
The field of artificial intelligence (AI) advanced significantly in the previous decade due to developments in deep learning {{cite:d6d663b64710262e89cad60fdfd1d0e0b9f55011}}. In the early years, deep learning methods showed stellar performance for supervised learning where each data sample is coupled with ground truth (labelled data) e.g., each image is associated with a category. Unfortunately generating labelled data sets is time consuming, expensive and there may not exist enough experts for labelling the data at hand (e.g. medical images). The straightforward solution is to use clustering for large-scale problems.
| i | 23a95edcea706fb4479cc7583b77d521 |
for all {{formula:fe281752-9afb-46d4-b6c4-8191d712c92e}} {{cite:637f5cf1ae1ff66969c75f46e651d5496cd9758c}}. This means that Algorithm REF achieves an {{formula:005eeeb6-b5b9-44a2-b638-575abc3973db}} rate of convergence in function values to the optimal value.
| m | f9fc6522b6f9eb70c43f329a76697832 |
correspond to the identical meaning as earlier. The increment of the
resonant widths is due to the broadening of the energy levels of the
wire including the ring, where the contribution comes from the imaginary
parts of the two self-energies {{cite:dc8a7e57bf126a495c5275b1ac00c11dfdb4aa62}}.
| r | 402d8a5f4666d28d6cd4dbf5df1cd461 |
Finally, it is shown that the basic formulation from {{cite:713af0d6cfe912f59e2c3371bcd85b79beefdc98}} can lead to asymptotically inconsistent calibration {{cite:2459d0b1d3d9e5bdc56fc14bd7b116f53c1490b4}}. To improve the Bayesian calibration, we could follow in the future the {{formula:2a7ef035-a5d7-4e8e-8c37-9e916dd716ef}} calibration in our setting {{cite:785a034222a2f0e6e55adac463ee4c209fc5b4ab}}. The benefit would be to yield a better overall match compared to the likelihood distance. This might improve the quality of the calibration further.
| d | bc4e076e2a0b851f27c5ba7e11757e36 |
Only Q2 has been resolved till now in the positive {{cite:adae0b94bd28df0514bc181b6fe9a8945e2a1c53}} as can be observed from Table REF . At its core, Q1 asks if a query oracle can step up, i.e., if it can estimate a structure that is of a higher order than what the oracle was designed for. The framing of Q1 seems that Beame et al. expected a polylogarithmic query complexity for estimation of the number of cliques using BIS. Pertinent to these questions, we also want to bring to focus a work {{cite:6d2365b7e6d186293794e36e3a54b6928d6a0490}} where the authors mention that it seems to them that estimation of higher order structures will require higher order queries (see the discussion after Proposition 23 of {{cite:6d2365b7e6d186293794e36e3a54b6928d6a0490}}). They showed that {{formula:692a98be-6b34-4c95-9b58-5d05892e3ff6}} many BIS queries are required to separate triangle free graph instances from graph instances having at least one triangle. This lower bound follows directly from the communication complexity of triangle freeness testing {{cite:38d2f80440bacbee5a1acf51464497f74126b733}}. However, the full complexity of triangle estimation when emptiness queries like BIS are available remains elusive. It seems to us that the observations in {{cite:fde23a33e926d03fa16fab810eb34376c3587b26}}, {{cite:985e2055538269a66f27a7c1f1a3e6ece3b2b7b2}} and {{cite:6d2365b7e6d186293794e36e3a54b6928d6a0490}} about the power of BIS in estimating higher order structures stand in contrast. In this backdrop, we place our results by answering Q1 in the negative with a lower bound involving BIS in this paper. BIS has an inherent asymmetry in its structure in the following sense – when BIS says that there exists no edge between two disjoint sets, then BIS stands as a witness to the existence of two sets of vertices having no interdependence, while a yes answer implies that there can be any number of edges, varying from one to the product of the cardinality of the two sets, going across the two sets. We feel that this property of BIS gives it its power, but on the other hand, also makes it difficult to analyze. That is probably the reason why works related to upper bound for BIS and its generalizations exist, whereas works on lower bound were not forthcoming. Though not on BIS, the work of Chen et al. using IS queries was the first to discuss a lower bound on independent set based oracles. Our work goes one step further in being the first one to prove a lower bound for the BIS oracle. We resolve the open question by showing a requisite lower bound involving BIS for estimating triangles. Our result even goes further – if we want to estimate the number of triangles using a polylogarithmic number of queries, then even a stronger query than BIS (named as Edge Emptiness (see Definition REF )) is hopeless (see Theorem REF )!
| d | abfa58f58a346c38fe1c4697f2e1ab1a |
Recently, successful analysis of the correlation functions of EMT
operators in lattice numerical simulations has become possible
thanks to the small-flow time expansion (SF{{formula:00747541-cb39-4ee7-b73b-38fbec32b6b9}} X) method {{cite:a1d1444edee0502ac66f7c964aaeb35c12dffcc8}}, {{cite:c0b68f7282a34b8a1fc4c0ed699db163d1b2ee8f}}
based on the gradient flow {{cite:d0828cf722be81b2e497bd40dd96b57fe62213e4}}, {{cite:15f93802c76ab118e2b86bddc1d49b208356d970}}, {{cite:29eb1ee2684cb9d64d15d4cd65821e9cf0deeac2}}.
Its application to the analysis of thermodynamics in SU(3) YM
theory {{cite:b456420723375f86afe1ef9c29e441557dfd10de}}, {{cite:24b55044918b5fdc4abea72fa8d7154a911be2a7}}, {{cite:0d3d45f3789e72a1ddbbe09e751e0bb6d84b4f82}}
and QCD with fermions {{cite:96fa7bccc4385fc45e13481b329f72c0406f3cc3}}, {{cite:55da048e50cec64065c6b16c9baa4bbe613ba96b}}
shows that this method defines the EMT operator properly and
is effective in suppressing statistical errors in numerical simulations.
The EMT operator defined in this method has been applied for the analysis
of various systems {{cite:978e23f9c57af9bd717e67e756c760d287277cd5}}, {{cite:45c8d806671468749519ed253c83d0cf9fec1141}}, {{cite:91d6c8bbdf41d49abd9553ee48a073491f35b318}}, {{cite:8210556492c12b2cc03974ccd6c5a369ce691f07}}.
We use this method for the measurement of {{formula:eb960ecd-e34a-41ca-9de8-5d2d17524a41}} in this study.
| i | 4adadae8e639ef883de050670eb95621 |
Non-Hermiticity has been successfully engineered into several optical lattices, acoustic systems and topoelectrical circuits {{cite:b50b892742436ca55337cc1b81db1aa51dfe655c}}, {{cite:67dda9de639cd46f8f3ed32123fb3119ede95c46}}, {{cite:718a89de628f8e4eb49ebe73c3dfd38d7e7250ad}}, {{cite:33332cc7de5f5c6a50f29e7c79e0a7a232ca1d82}}. In particular, the inclusion of non-Hermiticity in the three-site Lieb lattice using coupled optical waveguides {{cite:f173ac62b126d0be09448bbe87059e137b66b1ea}} can be feasibly extended to our lattice system. It has been established that optical lattices fabricated using femtosecond-direct-laser-writing can adduce non-Hermitian gain and loss through periodic `breaks' in the waveguides, which lead to loss of radiation modes. This loss can be tuned using the length of the breaks.{{cite:1c997aa165ea821d402382707759f333a9bb990e}}. This method of engineering gain and loss has also been successfully realized in a graphene-like honeycomb lattice {{cite:8f9c5db4af08ec933e78b07cc02fb64457ad7efb}}. Further, it has been proposed that atomic loss in ultracold atomic gas systems can be generated using a resonant optical beam to kick the weakly trapped atoms or by using a radio frequency to excite the atom to an irrelevant state, thereby simulating loss{{cite:565b55011f1edce4ab67b9facea861916baad0a4}}.
On-site gain and loss can be effectively mapped onto a non-Hermiticity-controlled coupling between neighbouring atoms. A synthetic imaginary gauge field engineered strategically can make these couplings asymmetric {{cite:dc7552591f4bbbb5d93a8bfcd93016a3cd107668}}. Such complex gauge potentials causing non-reciprocal hopping can be implemented using a non-Hermitian anti-resonance ring {{cite:a038ef42971ac5fbdd52aeefaf7a154e33ea9d0c}}. Due to the directional coupling, the photons become attenuated or amplified depending on their direction of travel.
Furthermore, two-dimensional non-Hermitian systems with gain and loss or non-reciprocity have been proposed in classical topoelectrical circuits {{cite:718a89de628f8e4eb49ebe73c3dfd38d7e7250ad}}, {{cite:33332cc7de5f5c6a50f29e7c79e0a7a232ca1d82}}, where the non-Hermiticity can be ingeniously engineered using combinations of resistances and LC-tanks. Information about the eigenenergies can be extracted from the electrical response, admittance and impedance resonances {{cite:b098b826d6bab34d0fb348320157edc22a800e05}}. In light of the above rapid experimental advances, we believe our theoretical findings can be experimentally tested in the near future.
| d | e934e9ce41bf89d0bd7ae142ddd6317e |
Occlusion {{cite:d8bfa62231bcd831e04c92f634c448500809efda}} is a perturbation-based method that involves replacing portions of an image with a block of a given baseline value (e.g. 0), and computing the difference in output. A heatmap is formed using the difference between the output probability attributed to the original volume and the probability computed for the occluded volume, for different positions of the occlusion block across the input image.
| m | f2f5fcb790b7adf9ffc8f168976c8517 |
Figure REF shows the variation of sheet resistance (R{{formula:254077a9-cf4f-4613-bbea-901a7e32ebb9}} ) with temperature for PS (S1, S2) thin films in various magnetic fields perpendicular to the film. We observe non-metallic behaviour for our PS thin films which is in contrast to the metallic behavior reported for the bulk materials.{{cite:2ac6a7a497cba5389932db90caa5d57ffe2f10c5}} We speculate that this non-metallic behavior is a result of the quasi-low-dimensionality of the films. This is supported by the fact that the resistance of the thinner film S2 (10 nm) is more than an order of magnitude larger than S1 (18 nm) as seen in Fig. REF . A change from metallic to insulating behaviour on reducing the thickness of various topological materials from bulk to quasi-two-dimensional has been reported previously.{{cite:79a91c2203f05e7040796f8956dcab98c796462d}}, {{cite:63299d44791b2a8a0b3d204720440d1ed67fd6f6}}, {{cite:886f5f8e813e579f65bfaac4f9728b2869e6faef}} Below 20 K, there is a pronounced upturn in the sheet resistance. This is highlighted in the inset of Fig. REF . This enhanced upturn may either be due to electron-electron interaction in the two-dimensional limit or disorder-induced weak localization (WL).{{cite:9b9dbf687a11765254a22002d2fdc0177b8a71a2}}, {{cite:49e676a746741ed3aed4bd939f9395fa2b8e3719}}, {{cite:69adde324c6d8f54b516a0ea8d7dc81026543bef}} We will return to discuss this low temperature upturn in detail later.
{{figure:3c055579-bb8b-45ea-9956-6c3f4316a15b}}{{figure:f3da1cd2-1e9d-4014-9f0a-d40d56d1f63e}}{{figure:90f86c7a-a0f0-4659-9fb6-ccd7e42bda9a}} | r | 6396e44b8a0a0c64ae2cfd85e319fba8 |
where the expectation is over the set {{formula:02898d85-219d-4310-9e85-d8a6f42ca6b4}} of configurations of points (that is, for us {{formula:9d406bd6-db05-46a9-aa06-d1fac4bc4eee}} ) and {{formula:7aa41cc5-0e5c-426c-819f-183e0166d94e}} should be viewed as a parameter of the model and, in general, {{formula:3c1882df-7f7e-4d63-88d4-6103bf0714b4}} becomes the spectral variable of this transformation, and the matching {{formula:9fccbe68-2817-48d9-b431-56668dd9fe09}} motivates the distinguished role of {{formula:7144dc94-d5b0-4819-a344-c4e82292c4f1}} in (). In the context of random particle systems, this particular multiplicative statistics is associated to the notion of a {{formula:0659ff9e-3cc9-4c9a-885e-72033463a32f}} -Laplace transform {{cite:79e3cebe62ef7f9071b3285b194de8acf9c3fa7b}}, {{cite:14eddd592416d9efba5b4d560fcad57e5bad6155}}, {{cite:62807f499daaf578722cabea4c46231e70c589a9}}, {{cite:2cb55c708bd8f1c383f3d79383bc65c04cdcb8ba}} that we already mentioned in the Introduction, and it has been one of the key quantities in several outstanding recent progresses in asymptotics for random particle systems {{cite:cc2db01cb71b900e7b027de0a2755752e8e24270}}, {{cite:2e4869af8e48f220a89c81738033f09ce09ed7cb}}, {{cite:1822d40262f8274481d356654012d14bc4cf144e}}.
| r | dae3e0e5fed8e193afc3384a2bb750de |
We assume a flat {{formula:71c63f90-b126-4c36-975b-2764a4caa7bb}} CDM model, based on general relativity and perturbed up to second order, in which the matter is pressure-free and irrotational on perturbative scales. Generalisations to allow dynamical dark energy and relativistic modified gravity are straightforward, but are not included. For numerical calculations, we use the Planck 2018 best-fit parameters {{cite:421e8dc3609b2523f675f7ed88a9575a8ce805f7}}.
Perturbed quantities are expanded as
{{formula:23adb01f-3e84-40af-8667-c5f346a4a599}} , and may be split as {{formula:90d2d025-b391-4881-83c4-4ca2406f22ff}} ,
and similarly at second order, where N denotes the Newtonian approximation, GR denotes the relativistic correction and nG denotes the local PNG contribution. GR corrections are highlighted in magenta.
| i | c60cbef6fb183299055e68aab05aac7a |
Let us review the matrix result of the RTLS, which was first derived by Golub, Hessen and O'Leary in 1999.
{{cite:176d7cc00ea1bb184a3c29157f0f04e9da841c73}}
For the RTLS problem, if the constraint is active, the solution {{formula:a7aa93ff-b2d2-428f-9961-9b1280d9be60}} satisfies
{{formula:5d0d8884-bd00-49f1-877b-ed432727d130}}
| m | ed27815bc06d53ea4d9ab5049c3ca551 |
We managed to solve exactly both equations (REF ) and (REF ). One observes from obtained analytical expressions of the eigenvalues of these second-order differential equations, the behavior of both of them is drastically different. First of all, the energy spectrum (REF ) corresponding to the model with only one infinitely high wall is equidistant. However, the energy spectrum (REF ) corresponding to the model located within two infinitely high walls exhibits non-equidistant behavior. Also, despite that the first model is confined to the positive region of position {{formula:a1462749-1d0c-41ac-9844-a71452f31aed}} , its energy spectrum (REF ) is almost similar to the well-known non-relativistic quantum harmonic oscillator with the constant mass {{cite:e8a529401c95220e52f259003cf86c51fff34a26}}, {{cite:8f67ff4c16a93a8edde1dd6a20bb07d1214f4fdc}}, {{cite:d59acc0555e482dce780902ddcd6bf975fbfef8c}}. Its first term completely overlaps with the known oscillator energy spectrum. The only difference in energy spectrum (REF ) is the existence of its additional second term that depends on the so-called confinement parameter {{formula:ebfa9419-7b7e-4388-ab89-ea045871e906}} . It seems that if letting to {{formula:be9d9add-517d-40f8-bc86-c9ccd99eea37}} , then the non-relativistic quantum harmonic oscillator model will be directly recovered through simple mathematical computations. However, it is a misassumption. Therefore, one needs to analyze some details of the energy spectrum (REF ), too. It consists of three terms. The first term does not overlap but is similar to the known oscillator energy spectrum. The second term adds non-equidistant behavior and the third term is simply some constant that does not contribute anything to the general non-equidistant behavior of the energy spectrum (REF ). In general, all three terms depend on parameters {{formula:ed221da0-cd37-49fc-977c-cc1048c498f0}} and {{formula:ea51759c-650b-4335-9dec-5e00ae6b22ce}} . Then, the case {{formula:08cbbc64-6f43-497a-be7f-04f74e62dce2}} violates its such a general behavior through the second term. Parameter {{formula:7f5ecd83-8d4e-448d-b568-01cbda41553f}} is in its denominator. Therefore, this term goes to infinity. From a physics viewpoint, masses of both models changing by position simply become zero if {{formula:8ebff6ff-6d2a-4459-95ae-7a24218e27e6}} . Therefore, both models restricted within the positive region have a number of singularities, which never allow them to recover the well-known non-relativistic quantum harmonic oscillator model with the wavefunctions expressed through the Hermite polynomials.
{{figure:f670e62e-f773-4aab-8c69-769359d10cee}} | d | f9780b787dd1c941d643f040e9884088 |
In contrast to forward GVFs defined based on predictive knowledge, the backward GVF represents retrospective knowledge, which captures the accumulation of signals from the past to the present time {{cite:74b88c018435e3e8e16f909a79114a63091e2379}}. Although the concept of the backward GVF has not been formally proposed until very recently {{cite:74b88c018435e3e8e16f909a79114a63091e2379}}, it is rooted in a number of important RL applications such as anomaly detection {{cite:74b88c018435e3e8e16f909a79114a63091e2379}}, emphatic weight learning {{cite:333e88c0fa84dedad1f146f529c5ecaf0e0a8e12}}, {{cite:74b88c018435e3e8e16f909a79114a63091e2379}} and evaluation of gradient of logarithmic stationary distribution {{cite:7cbc5f15b21be1e6b95778c76b16fe5844961281}}, {{cite:1d40872650ae952849a8a3318b2242d2bf22e53b}}, {{cite:7d23eb233dbdf87f2b9a15b934e0a2f92828cacb}}. Differently from the forward GVF, for which the Bellman operator can be defined independently from the sampling distribution {{cite:26b5ee8b1247f6d51a2dbf4bda2fa2b18a3b34f5}}, {{cite:190ed8f76b40379618db9acb6df322d2e6e44ced}}, {{cite:51ca56cbbec3cfbfae9a77011613747e5e6b7eef}}, the Bellman operator of the backward GVF is only valid if the sampling exactly follows the on-policy stationary distribution {{cite:74b88c018435e3e8e16f909a79114a63091e2379}}. Due to such a reason, off-policy evaluation of the backward GVF is much more challenging than that of the forward GVF.
| i | 6ffbb3e4e0a9943a3c79e114b9c356bc |
As pointed most of definitions of fractional derivative use the integral form. In contrast, R. Khalil introduced a limit based definition of fraction derivative {{cite:c502e6f3bf3f08a835e2d3f6a236cc99f086f24d}} in {{formula:bbab90fb-b02b-42c8-a1da-b61e5db6c708}} , calling it as conformable fraction derivative in analogy to that of standard one. However his definition lacks to include zero and negative numbers. We hereby define a new derivative, referred to as deformable derivative, which is much simpler than that of Khalil's one and overcomes not only this shortcoming but ranges over a wider class of functions.
| i | b7c6e016d434332f9e2065ce6d39dba7 |
Quantum field theory can be used to restrict the possible creation and annihilation operators to those that satisfy commutation or anti-commutation relations for particles with integer or half-integer spin respectively; see, for example, {{cite:26d22b363f1f5d383405bafe44af6a990246ac0b}}. According to the spin-statistics theorem, there are only two possible statistics, those of bosons and fermions, associated to the commutation or anti-commutation relations of creation and annihilation operators.
| i | 8ac0d6749074f12a406d42ae409a2b41 |
Other interesting aspects which we have not experimented with at this point, but which are in our plans for follow-up work include (a) to confirm the current results or their variability on different network architectures, but more importantly in relation to the capacity of the network, e.g. with lottery ticket {{cite:c3f981f6cf664569bb493867b2c839d009576e5c}} and distilled {{cite:12d3a554176bf395b45e2b92080b4ac2028f4897}} type of networks; (b) the potential effects of other activation functions than ReLU in the effectiveness of the Delta Activation Layer, (c) using an advance quantization scheme along with the sparsity loss to reduce the accuracy drop and (d) the effect of lateral inhibition and winner-take-all strategies in promoting temporal sparsity {{cite:6195bfaaaad7cdbbff1e9d1b885d34b1df74cfe7}}.
| d | 2f7245ba8829f48723711581490ea2da |
To fill this gap, several lightweight crowd counting models were proposed in recent years {{cite:743206b131997c877a56389e4e83690dcfd08cf8}}, {{cite:ac1b37d4aeeff1469fb1147a434ff5b76080e2c8}}, {{cite:e5af98155b2650427f59c39e535ab0318dc6c56a}}, {{cite:17a8c44d50589e63961bb2352eab75eeaecc2805}}, {{cite:9225b1e37f88fae623d50104fd81893e8f561d2f}}. Although the computational cost is significantly reduced, the performance of these lightweight models also degrades much, as compared to those heavy models in {{cite:27c2686566afc917094fb028406cfb6e2b2cd4e1}}, {{cite:743206b131997c877a56389e4e83690dcfd08cf8}}, {{cite:a1f06c664b75b9d2579aa2a822b53ac175c212e4}}, {{cite:774c54a499dfe79359fd75ba0cf3efd309676587}}, {{cite:dfbfd5b03c6c67b43dda43a5b23880de06d6bd65}}, {{cite:c0a1cb33c96e5ee747d01fa0b96a56092a3c3050}}, {{cite:609d1e88e499b3a682a40971e3e7db1af4501417}}, {{cite:2fc5ae7070fc15b55ebed49005b77e2537edc53d}}, {{cite:c684aa08abc3040476fe342844aafba39daf4d80}}.
Along this line, an efficient lightweight crowd counting model called the structured knowledge transfer (SKT) was recently suggested in the literature {{cite:da8d466fe0a436f39c13bf25594bb726c20a0c73}}, based on the framework of knowledge distillation (KD) {{cite:bf2bc0e9633329a05f971d2d58838c35f30dc657}}. In the framework of KD, a lightweight student network is trained to acquire the knowledge of a well-trained heavy teacher network. To fully distill the knowledge of the teacher network, two complementary modules, i.e., an Intra-Layer Pattern Transfer (Intra-PT) and an Inter-Layer Relation Pattern (Inter-RT) were introduced in {{cite:da8d466fe0a436f39c13bf25594bb726c20a0c73}} to exploit the structured knowledge of the teacher network.
| i | 21789263134d65b296b0764616438edc |
Tongue image encoder.
The task of the tongue image encoder is to produce features which are close to the target 3D features {{formula:707306f4-d5bf-4e71-b31d-6eaaa8c98fed}} of the AE. To make the encoder robust to various camera angles or illuminations, we employ a rendering framework where we utilize the textured raw scans (TongueDB in Section REF ). We render our 1,8K textured meshes with a pre-computed radiance transfer technique using spherical harmonics which efficiently represent global light scattering. Additionally, we use more than 15 different indoor scenes coupled with random light positions and mesh orientations around all 3D axes, resulting in approximately 100K images. As an encoder we used a ResNet-50 {{cite:62f11c8ab2032f122c2131952f65aeaaa90d640a}} model pre-trained on ImageNet {{cite:61e5d140009665f79157496d11cdce07ac02a1ef}} and fine-tuned it on our dataset. In particular, we modified the last layer of the network to output a vector {{formula:15305f00-0577-4374-9014-4a31099bbc7a}} similar to the dimension of the ground truth vector {{formula:ebaa7631-31a6-4fc5-b39c-2fda45019fae}} .
| m | 3e63fc2944b8d9f83eb25360d5574395 |
[leftmargin=1.5em]
metapath2vec {{cite:6462b6182f4d8d48410d08df1ce009035abcdb26}}: A heterogeneous graph embedding method that performs a random walk on meta-paths and utilizes skip-gram to generate embedding. This model relies on a single user-specified meta-path, so we test all meta-paths separately and report the best results.
GCN {{cite:5d9230df7e6aa65c750a933e92368826439b62c5}}: A homogeneous graph convolutional network (GCN) performs on the meta-path connected homogeneous graphs generated by different meta-paths. We test GCN on different meta-paths and report the results from the best meta-path.
GAT {{cite:0ece1b1884bce736b8d1ad18e955f84fa9160269}}: A homogeneous GNN, which utilizes the masked attention mechanism on the homogeneous graphs. Similarly, we test GAT on meta-path based homogeneous graphs and report the results from the best meta-path.
HetGNN {{cite:d64f68623ea6555047453783029d6b35bb806248}}: A heterogeneous GNN, which jointly considers heterogeneous node contents encoding, type-based neighbors aggregation, and heterogeneous types combination.
HAN {{cite:9cd2bf951ccc8ed9c39480ac93b4d49fbfacbd17}}: A heterogeneous GNN that learns meta-path specific node embeddings from different meta-paths first and then leverages the attention mechanism to combine them into one vector representation for each node.
MAGNN {{cite:3342622b9bd5f21ae5ced34999892474e9970bf8}}: A heterogeneous GNN that boosts the graph embedding performance by encapsulating input node attributes, incorporating intermediate semantic nodes, and combining messages from multiple meta-paths.
MAGNN-AC {{cite:0d57418dcd4829206319b3020c77fc34a691dbbb}}: A state-of-the-art heterogeneous GNN, which uses topological relationship between nodes as guidance to complete attributes for no-attribute nodes via attention mechanism. It can solve missing attributes problem in heterogeneous graphs.
| m | acf7e095698af34590e0fd5c9f57e6f1 |
Intriguingly, in spite of the small coupling, it may be possible to test such a scenario with direct detection experiments, provided the mediator (the so-called dark photon) is sufficiently light, such that scattering cross sections are enhanced {{cite:18ce0fa497ec2a4b3c3ccb3f3bdcdf606e7b801c}}, {{cite:a50e3d6b2dccdae74b9c4590a6d39ec90836ba5f}}, {{cite:e767b102337a39c209772b90444acebf352fc160}}, {{cite:f39703be2d08b4f2f31b3573f572af6bcfeb5c82}}. Indeed, much of the literature has focused on the case that the mediator is either exactly massless or that its mass can be neglected in all calculations. In this case, there is a one-to-one correspondence between the relic density requirement and direct detection signatures.
| i | 2c2e1e7adbbf2d9c0a66de15400594fb |
Currently, there tends to be an all or nothing approach to transfer
learning. Either transferring all layers improves performance or it
doesn't and possibly decreases performance (negative transfer). The
same approach is often taken to freezing layers, either layers are
frozen or they are fine-tuned at the same learning rate as the rest
of the model, and weight regularization, either all transferred weights
are decayed towards their pretrained values (L2SP or other recent regularization techniques) or towards zero
(or sometimes not at all). We advocate that the all or nothing approach
should be discarded and instead all decisions made about how to perform
transfer learning should be thought of as a sliding scale. Transferring
all layers, freezing layers and decaying all weights towards pretrained
values is at one extreme of the scale and is likely to only be optimal
for source and target datasets that are extremely similar. Training
from scratch is at the other end of the scale and is likely to only
be optimal if the source and target domain have no similarities. This
lines up with the observations in {{cite:a54f03e431d0fa7b0097ff0735fa29d6197ed801}}
that “first-layer features appear not to be specific
to a particular dataset or task, but general in that they are applicable
to many datasets and tasks”. Recent work by Abnar et al. has shown the potential for improvements in transfer learning by taking into account the similarities of the source and target task {{cite:5d8823a44296ed3acfb291d140048ed9bec6caba}}. More work is needed
to show how to perform transfer learning optimally for a given source and
target dataset relationship and target dataset size, rather than showing
whether transfer learning is effective at all.
| d | 746438069a12fb496908f513093291a2 |
This can be verified from {{cite:b9ba1932579289bfea66275e50e095c6aaeb71db}}.
{{formula:68cdc88e-d325-4ea7-978c-ff483040fcf5}}
Lemma 4.6
Let {{formula:3139ea72-f169-47cb-9dc9-8fb778634b80}} be a positive integer. Then
{{formula:c0ed2dd7-3690-4e2d-a6c6-d28281d7fcc5}}
provided {{formula:85d3fb74-7888-42d0-8978-7c5a2da369aa}}
| r | fc4b6f238673afd272dc996d50444597 |
If the ALP has flavor universal couplings or if the strength of ALP couplings to fermions is at least comparable across several flavors including electrons, then the red giants {{cite:0ed37bda388019aa5c81e5442e2adc37c1fea6ae}}, {{cite:54ab7bbc7aa8867e67c1abea9d9d8aa51d1c2c24}} and XENON1T {{cite:d7d681ef524cfad87b39ccfe0992d90e187d5654}} limits, shown on fig:photophobic, are applicable since they constrain the ALP-electron coupling. The latter is clearly more stringent and relevant for larger span of ALP masses,
excluding {{formula:724b87d5-4adb-491f-a671-50b734e382db}} . Clearly, the XENON1T line is chiefly below the green band in the region {{formula:5d328581-ea0b-471c-9550-368d08577227}} keV, disfavoring the flavor universal ALP coupling scenario for such parameter choice.
| r | ad01ef046cff416d7c3ac9c5cdcab755 |
Recently, there have been a few works {{cite:e885ab681536ce3eb71257ee5c28368a3756728a}}, {{cite:05c4773489bb7be15605e43b61d7aba6ae255257}}, {{cite:27abe1b60a3a14ebb02b7d8f8ad55bc5337970a3}}, {{cite:97d7ff362a93f5699190059e05ded745db00724b}}, {{cite:d991daa1e59e6c7b32e8f8f6b8ba52549897472f}}, {{cite:ea41eefded575ab623ea6d06d64b77e8e200fa3e}} trying to reduce the dependence of image captioning models on paired data.
Specifically, {{cite:e885ab681536ce3eb71257ee5c28368a3756728a}} proposed a method to generate captions in a central language (Chinese) and then translate them into a target language (English), without requirement for image-caption pairs for the target language. However, a paired image captioning corpus for the source language and a paired corpus for translation are still indispensable.
{{cite:05c4773489bb7be15605e43b61d7aba6ae255257}} connected the visual and the textual modalities with visual objects (e.g., dog, mirror) and an adversarial manner. It achieved unsupervised image captioning without any image-caption pairs. Nevertheless, their method relied on the recognized visual objects to decide whether the generated captions are image-related, which necessitated complex models and schemes to obtain higher-quality image captions, e.g. image reconstruction {{cite:05c4773489bb7be15605e43b61d7aba6ae255257}}, sentence reconstruction {{cite:9e988fa39ea34f40f8e746ea94a3baf9baee954d}} and adversarial learning {{cite:315eabe834e70356da221299b1211acc04477d51}}. Moreover, the visual object based approach does not consider attributive words (e.g. attributes (small), relations (standing) and color (white)), which could help improve the image representation.
{{cite:27abe1b60a3a14ebb02b7d8f8ad55bc5337970a3}} used the scene graph to bridge the gap between the visual and the textual modalities. Since the scene graph constructed a series of semantic relationship information, the model achieved good results. However, in order to construct the semantic relationships, they needed to use Faster-RCNN {{cite:6b3c2d2a2b4649e47c9c163cfc66dae57fe08686}} as the object detector, MOTIFS {{cite:4c433f7cac39d6aa44f2f40e165c31db50757a2c}} as the relationship detector, and an additional classifier for attribute identification {{cite:b1f489cc1927bbf3acf137d6134f327f33252b00}} for generating the image scene graph.
In all, although existing methods for unsupervised image captioning have made appreciable progress, they are hard to implement and still far from real world applications.
| i | 415f5b42ece3fca72da65e7e2f6a10d7 |
The {{formula:7daf5519-de0d-40a4-81a9-481671387d43}} is expanded to order {{formula:9aaa2c99-d3db-4734-9c34-98f21551a264}} or order {{formula:54639ca9-be77-47e7-86d3-be808b0f8c74}} with {{formula:835195fc-e35d-47e8-824c-9be293ae3878}} {{cite:67fdabf0fff55610251991cb7de1275d6446e8e7}}.
The {{formula:9b04e594-b54e-4a4d-89f5-7867c86082ff}} is expanded to order {{formula:0c3a08c3-a7e7-48eb-9880-bbee29b72663}} or order {{formula:251cba1c-f4bb-48bc-881c-5f4565d51cea}} with {{formula:8629db5c-e79b-4bba-a27c-9c6a45fec469}} .
The {{formula:f3281783-f8a4-402f-86a3-d30804fa37d1}} is expanded to order {{formula:0383a026-b80b-4eeb-bca3-d2ad211faa66}} or order {{formula:8020541d-801d-45c0-9487-a34c9f2e1709}} with {{formula:aaca41f2-2656-49dc-a914-a12e7b2d0d85}} and {{formula:c053cbaf-0614-4faa-b3ab-bc20a41fdb16}} given by the following intrinsic relations imposed by the unbound nature of pure neutron matter (PNM) {{cite:b31722af2510a015660f863852c6ee8e11e28f0b}},
{{formula:2965a1cf-213a-4a17-8f4b-bc2dc5f643af}}
| r | d9a508e6cea19453e48646d9c47323e3 |
The separation between generated OOD examples and IND examples is visible in t-SNE {{cite:d1f3f81d5177beb1cb83de7e5e32d9771f2401fd}} visualization as well. Figure REF shows the t-SNE visualization of IND and generated OOD data.
We can notice that generated data create recognizable clusters close to IND data but do not mix with it. Finally, we list OOD examples generated by OodGAN in table REF .
{{figure:2844f398-f21b-4b4f-82ba-0defec5b49c8}}{{table:aae9a666-18a8-4e45-bb81-bfc935549120}} | r | 6194146b4b2b827c6348c1dd4eb7f1db |
While SABR can be instantiated with any certified training method, we chose Box propagation (DiffAI {{cite:7d4b6bb422b32694553f07e2dce4115afde30bfa}} or IBP {{cite:458e1407ddfa42ef533c01f72a8043f470e1a680}}) to obtain well-behaved optimization problems {{cite:3264ca9433f7b23b4444e9b2a4ee44a703584857}}.
| m | c6b002ebfdd85b41077f9aa7dcb0f236 |
We now perform a Monte Carlo Markov Chain (MCMC) analyses, confronting these two DCDM models with recent cosmological observations.
To do so, we make use of the MontePython-v3 code {{cite:1f2424485c4ff4dc515c9911aaa2f5ed3ed5b4dc}} interfaced with our modified CLASS version.
We perform various analyses from a combination of the following data sets:
| m | bc1a964a6fb8fde1e670186f14d37046 |
Recovering 3D structures based on geometric constraints is an optional method to estimate depth information.
This kind of methods relies on consecutive frames taken by one camera or stereo matching based on binocular camera.
For the former, structure from motion (SfM) {{cite:3be7da85c963197dc55c69905fd120cca218e863}} is a representative method by matching features of different frames and estimating the camera motion, but the performance heavily relies on the quality of image sequences {{cite:73e186f4f2275297ccfe6c515f6e58539bbb4bf1}}.
To alleviate this problem, a variety of sfM strategies has been proposed to deal with uncalibrated or unordered images {{cite:c094a76379e9ac5a68ef6f2fd665f02f0e6a717a}}.
For example, incremental sfM approaches {{cite:6e2362dfeeb15f1dc24f40e55f7a3bd35950bcbe}}, {{cite:dfa8851f0c149387870d3fc46595ba657d3f2a09}} add on one image at a time to grow the reconstruction, global methods {{cite:96c1af1c0840a7e14f2d514127234c4e5218726d}} consider the entire view graph at the same time, and hierarchical methods {{cite:2f4173f386ac3352c36c30d84fad295a26b8a547}} divides the images into multiple clusters, reconstructs each cluster separately and merges partial models into a complete model. However, they still suffer from monocular scale ambiguity and high computational complexity {{cite:73e186f4f2275297ccfe6c515f6e58539bbb4bf1}}.
As for the latter, it calculates the disparity maps {{cite:4789002d4d895e706645514ced16bb6b160bff11}} of images through a cost function, and its bottleneck is the accuracy of matching the pixels of different images {{cite:de7b5f68f3993e7e31a37a6e7c79558e79f67987}}. Different from sfM, the scale information is included in depth estimation since the cameras is calibrated in advance in this case {{cite:9bad9e0cb4982ce85a354433845403fdf260fd21}}.
However, in addition to the high consumption of computing and memory, calibration drift is also an issue {{cite:a95fd56af257984f31109c01610627aa8b97b2ac}}.
| m | 3db7fe2e2c4b8b87c43d3707ea6de044 |
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