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A number of choices in the algorithm are taken to aid computational efficiency.
We allow for intra-limb coordination of multiple joints encapsulating multiple actuated joints within a graph node, which reduces the number of message passing steps compared to related work {{cite:be755a458e07df024074f1484ddde5fd8974d158}}, {{cite:e109b0afc1d87f16977d198cfeac2956765e3d12}}, {{cite:5a93d9a5a0070332bf40360aeb51d063bdd399fa}} in which each node controls, or approximates the dynamics of, one joint.
We use smaller capacity models than {{cite:be755a458e07df024074f1484ddde5fd8974d158}} to learn the dynamics, but find that these are still effective when used within trajectory optimization, especially when combined with the multi-step loss function introduced by {{cite:5d53c1f4db5d45d88394d51c8e71bd8e8ba6156d}}.
We also showed that the additional inductive bias introduced by shared weights between limbs of the same type helps prevent over-fitting in the low-data regime, resulting in sample efficient training.
With these choices, in addition to some strategic curriculum learning as described throughout Sec. , we were able to conduct training on a single computer without cloud compute resources.
We believe this to be an important feature in making deep learning accessible and reproducible.
| d | d2e8ef3902102cf0d224915cf780053e |
For both the HBOS and the iForest implementations the data was preprocessed by a standardisation step, which sets all the features means to 0 and their standard deviation to unity, followed by a principal component rotation, where we retained the full dimensionality of the feature space. The purpose of this rotation is to remove linear correlations between the features, an assumption that is required by these methods. The preprocessing steps were implemented with Scikit-Learn {{cite:261b183fba0a841e52a11256b68b60ff6230a2df}}.
| m | 89ffb75709450c2e116e89b056841c15 |
In the foliage-gleaning bird case study, we explored the sensitivity of model run time and parameter estimates to the number of neighbors chosen for the NNGP spatial MSOM. We found a fairly linear increase in run time as the number of neighbors increased (Figure REF A), with parameter estimates being relatively consistent across the number of neighbors used in the approximation, especially with five or more neighbors (Figure REF B). However, we note that this data set is comparatively small (373 locations) and has a limited extent, and hence incorporation of spatial random effects did not improve out-of-sample prediction (Table REF ). Parameter estimates, model fit, and out-of-sample predictive performance will likely be more sensitive to the number of neighbors for large data sets {{cite:13c6e158713e7226254247aed184951793ac5998}} and data sets where spatial dependence is prominent. When fitting a spatial occupancy model using an NNGP, we suggest following the recommendations of {{cite:13c6e158713e7226254247aed184951793ac5998}} and initially fitting the model with 15 neighbors. If the data set is moderate in size or the initial model fit suggests spatial autocorrelation is modest, additional decreases in run time may be obtained by decreasing the number of neighbors. WAIC and k-fold cross-validation can subsequently be used to determine if this decrease in neighbors has any impact on model fit and predictive performance.
| d | bb178b44dca9323a07423d4885c29b25 |
In recent years, although the identification of scalar mesons is difficult experimentally, some experimental efforts have been devoted to measuring {{formula:770cc7ac-d313-4833-970e-5ff37320348e}} decay modes. For instance, the light scalar {{formula:2eeaf5ea-3d26-4a71-90ef-6d350111972a}} was first observed in the {{formula:38b24a16-fe28-4e0d-822a-91775a22a9b3}} decay by the Belle {{cite:93e9d5768d3cd94ec782102d63877d2c187a8436}} and BABAR {{cite:e9aba2876ca217fa0b107ff41db21583080acd22}} collaborations in 2002 and 2004, respectively. Since then, more and more {{formula:42c24408-26db-4e1b-93d0-2232d413a1b5}} decay modes have been observed by Belle {{cite:636076e7cf1ee142c5b571e9400cca10f7502257}}, {{cite:a8493dd4b3e42c658c2d2eb464245f0d92e47b43}}, {{cite:c14b534f68fa13681fbdf86dd31ae4a9b587d6b4}}, {{cite:8324aec52321b5baaab46b0da6e0b351efc232fd}}, BABAR {{cite:f9d1b16d4b067277ff06e42e0bf65c10b0789f45}}, {{cite:9b40ee4c28c0f6cf19393f633760a9ba6dbd16e9}}, {{cite:5c3b1785e43a4cc3ddd08dcec76dcceb5fd4d759}}, {{cite:88f5b654f9feb179b600efbcf6b2365838d57141}}, {{cite:f9d37b8fe22a4ba4ca4aa9d202a9d08a544c1d6d}}, {{cite:580a2f56ac1cf950ac3ce05cb07c9cfd83b8dd30}}, {{cite:0b2775160e6701d935212d24ee1ec31192989e2b}}, {{cite:bbbeb33a0da33a04e99ded684196200bb0b65af6}}, {{cite:e03a37ad54e07ce55b2221fbe0ba873a3b3744d1}} and LHCb {{cite:2adce825636da69f618daf44f50641e9a1903adc}}, {{cite:b86d5d553f4451ac060eb0ace942e4eea040396f}} collaborations. Motivated by the rapid development of experiment, some theoretical studies on these decays are made within some QCD inspired approaches, such as the generalized factorization approach {{cite:593be79f67bb6acfc3838a22014731d256e9fd2b}}, QCD factorization (QCDF) {{cite:4d266a835a3c7c454b92050bd54bceef1f3d5615}}, {{cite:02f08273a0ad705705124d492b3b45957cc25c49}}, {{cite:3b2aa86ca7a30b17960bf66ed75249c38fe48385}}, {{cite:4b6fb526f164e556ca8a72df4921c67e0191c36f}}, {{cite:33aa3eed4f411beae924bf9b273faf97fa459b29}}, {{cite:164b9dad30cf9b94b68518ed10c46511da27865d}}, {{cite:74bd5a165325665f50a5fec671d0d62a92fd2fa7}}, {{cite:abdce88390a290f6cbea407b30bdc0c2f486b759}}, {{cite:deb34a20e12589e60c9b6e8cc38aab64806e4054}}, {{cite:6ac002756ab01e01192db78fcb1e3eda4af166e3}}, {{cite:a85721e62f0213c402a67e88c2eeca3f210d0405}}, perturbative QCD approach (PQCD) {{cite:6d029020c9dd5b3c1222462b2867c79b024890c4}}, {{cite:662f4670d905e9457b1aed69cbaf0b1c02bf7819}}, {{cite:24cb8b7311873b41dd9debf587e52723eefd7a52}}, {{cite:ecb836f5a22ff956c44f769c046fa2744b947c36}}, {{cite:481f6c12c67517cd282400ee96a44019d9bb07d8}}, {{cite:e89a8177fae74ab5785c03a4f8b5728d130b32c7}}, {{cite:4661beb0aa856f4e05e614c6e294047ba2a10e19}}, {{cite:3636cfce59385cd3c9a48556c8f58e61af998945}}, {{cite:595b9c7a3c9d67238e56e67c7fc90ea97cf4381d}}, {{cite:3d82b58f5c3afe0936351703f4dea07da9263760}}, {{cite:4ef3ad533760928a5a3cd39f823cdfbceadc191b}}, {{cite:14c860446006cae213551ab51c8609b1dc610a3a}}, {{cite:481f6c12c67517cd282400ee96a44019d9bb07d8}}, {{cite:2ee20ae35875cac3a9100d6acde6488046304ff1}}, {{cite:ecb836f5a22ff956c44f769c046fa2744b947c36}}, {{cite:8f6a89ed0620724931d01baef4fc03e8571b00ab}}, {{cite:47ffb73b9571cb2de804c0f8271d0530ab9f778e}}, {{cite:ce4a930631ba7dfcfdd723cfbda76119ab5f6e6f}}, {{cite:2386a5c8e4824ec999cdaee964d8eea6b7d606f5}}, {{cite:9016398f5ef33bcd0fb3706606448f20531d585d}} and other methods {{cite:9e9c4ee0020d500ef12a79cb70e2ff146af51ee0}}, {{cite:4d78298c5689aaac85f03f879a59670fd8e282c7}}, {{cite:c40599f50488bfeb68c3848c8514f51f5383eb4a}}, {{cite:2ca548c2f023df4eb8e794a2185768d13e50dac8}}, {{cite:48f989ada08f32abf34befaa83c620c52d4e05c3}}, {{cite:2d378c73bfefc37ad5db300baabf88da84674cc2}}, {{cite:93c1866fe2df50adbb3cad4d9bf50b4fc27d6a2b}}, {{cite:10fbdeb5433ee12c09a501f4f09ec393fdfb4050}}, {{cite:96c163fdb77e659dc492acec69334994cf2752bd}}, {{cite:b40a4a7fb0acafdd958d98f47ff8dbbac8129d69}}, {{cite:bd7bc9d8138c104b68f4432378ef1026e8db1956}}, {{cite:022c023c8cec536a18fb705ab3f8f146316f21d3}}. Most of these previous works mainly focus on the {{formula:2fd36e14-6f5a-4a8d-b67c-3a56a83a4563}} decay modes, but the {{formula:0b03c3f2-3db4-4bd9-a8d6-eae670ae7cf3}} decays have not been fully studied theoretically because most of the {{formula:2d14528b-e7bb-40d5-805b-457bd024d644}} decay modes have not been observed.
| i | 46702e870a9bb1feca22747c534c775c |
For {{formula:c2b87ebd-0d94-45d7-a05b-964052bf7e8b}} , a pre-trained ResNet architecture {{cite:cb0ffec4fbbeeb493bb50c528eb80bfa597843b8}} was used (the classification layer was removed) and the image feature size {{formula:51e89ef1-7570-4d16-947c-bb0e501dcbd7}} is 512. For {{formula:8b9290ae-ca59-407a-8cc6-b7cdec46447a}} , a pre-trained BERT {{cite:57a39af12424f4e102cc5f8758be78bcb31c1e5e}} language model was used and the text feature size {{formula:1fa22b18-f250-492e-905c-a167d17303e7}} is 768 (which was obtained by summing the last four hidden states of each token). For the noise discriminator {{formula:e217933f-5bde-4beb-a719-9e513396db96}} , we used a 5-layer fully-connected network, which was trained only during the meta-learning stage.
Hashing networks {{formula:f8dbcb27-76ba-4c24-944f-56ab69424dbe}} and {{formula:35c112d1-1741-462c-af56-d82af8f70e58}} are fully connected 3-layer networks and a batch normalization layer after the second layer was included.
The quantization loss hyperparameter {{formula:9dcfc787-f6ea-428e-98d1-31a1af180e04}} was set to {{formula:397671f7-fc12-457e-a9d1-7a3763a63764}} . Both intra-modal weights {{formula:82d24ef3-da57-4592-ae34-7e1fc010d6ec}} and {{formula:fdda61bf-e4cc-4bab-807b-126ea544325c}} from (REF ) were set to 1. The total number of training epochs was set to 150 (75 for meta-training and 75 for main training epochs).
| r | 90540836eb43527c351b1b58af88edac |
In this work, we directly use the playback signal as an additional input to the network, allowing the model to implicitly learn to perform AEC. We propose an encoder-masking-decoder architecture to achieve this in a computationally efficient manner capable of running continuously on edge devices.
We evaluate this technique on two resource-constrained tasks: multi-KWS on a dataset derived from GSCv2 {{cite:232fbf0967fc3b34c26447d41e412da0760b4fb4}} and DDD on a dataset collected from Alexa devices.
| i | 33e0b5175f6f7227623ac881ff4c6f1a |
Finally, remarkable results have been obtained exploiting time-dependent signals. An entirely complementary field of electron quantum optics {{cite:392df3e8525204a37cd945fbe237f8a6692c6b0e}}, {{cite:254f4b36df83ab5818826e3fbff48e5c08f4d426}}, {{cite:eab0aa721023ea7492cef03c30dbefb1ad130f6f}}, {{cite:33b0c7f4c47a996d327da053dc070836fdf59ab5}}, {{cite:43ba5963323349f3bbf2a67fc1df76f5ddab12d8}} has been developed in parallel to the standard interferometry. These platforms allow to exploit two-particle interference like the Hanbury-Brown-Twiss {{cite:6bb1a05b06c28409ff933d3a7fd244a5b569340a}}, {{cite:f3ee9981b4f6bfe1f0cace304eae75310dbda048}}, {{cite:5204e1d9c2139be470f7f2752a57237331276074}}, {{cite:8d7a142656deb768b364f09ed872216644e9c3be}}, {{cite:c84218214f78ebaeeab59e1c4ed642ffffdf660f}}, {{cite:cdbe0dee7bda34ddfc620188a0fed6cdd95265a1}}, {{cite:f62259427563c4d4fb004f8dd62f1f82eb78697d}} and Hong-Ou-Mandel {{cite:cb3aae595060756ec221a30eefd7eae57cabfb0c}}, {{cite:447b39e4b4bb1c1fcd8b0d855cd2af2ec4e49e9c}} schemes, that are directly sensitive to two-particle statistics and paved the way to the recent success of the anyon collider experiments {{cite:b5ead59d5256633eaf9167da31555917fcbd2b07}}, {{cite:5724e40b1025a1ba24920ee7a1568a9587b3cdfd}}. Furthermore, anyon colliders and interferometric setups could be merged and joined together, offering the opportunity to exploit complementarities and reciprocal advantages, and develop novel platforms for topological quantum computing.
| d | 9b3d1df32ceb05b0b69cc19691f8ae82 |
For example, the framework can be applied to eigenvalue problems related
to physical systems. For instance, the general conjugation formula Eq. REF
has been previously invoked {{cite:9c34acd3ea05e1117a33313c20ae1632f3dfb910}} in the context of particular
parameterized quantum circuits for the electronic structure problem of quantum chemistry.
This problem involves minimizing the expectation value of
the electronic Hamiltonian, which
is not diagonal in the computational basis. Circuit ansätze for this problem often utilize
fermionic creation and annihilation operators and simple reference (e.g., Hartree-Fock) initial
states. These operators then have interpretations in terms of transitions between occupied orbitals, analogous to the operator-function correspondence of
Sec. REF , suggesting a route to apply and extend our framework and results to this setting.
| d | 072313d20ec8546aeac740c7c95b5019 |
Estimation of residual dual norm is straightforward for affine problems
(cf. {{cite:e58f82591b5bf07f61fa8250c3c8c06af51aa997}}); furthermore, for certain classes of linear and nonlinear PDEs, the successive constraint method (SCM, {{cite:eb727f96601fd8fed9e093c269c5a6e831df74c0}}, {{cite:62e5760cd16b16a734aa9e007e7830e597d91166}}, {{cite:6493d1860eb5d359927be1328ef2352384c10fba}}) can be applied to obtain a rigorous error bound for the prediction error. In addition, the strategy in {{cite:6562a0b53e9b5b7e7a6c9fd69ec9667f6a966706}} can later be applied to significantly sharpen the error bound.
For a class of parametrically-affine PDEs, exact estimates can be derived to bound the error with respect to the exact solution
({{cite:c8c46164ace9549c03f27c4a630889398af1f490}}, {{cite:d1da67a6ca1a7ffede3c227a1be2f248c83daef9}}): this class of bounds is extremely important to devise spatio-parameter adaptive strategies for parametric problems, {{cite:f4dcd0fcb98a7480369606aeaeca3994a96dfac4}}.
| m | a10e9f79d30e6a388773ea2b13e45524 |
Fig.REF shows the result of linear regression between ImageNet (IN) {{cite:fdf1290f23c64d3952b2b377d9fb96ab2d10c189}} test accuracy of a pre-trained model and its performance in a target task with distribution shift. For self-supervised models, we use the linear probing result as the IN accuracy as reported in their paper {{cite:778d4ede1c6c2fb385d405a1c53f271d20014be9}}, {{cite:3c6d80d8a4348738a673278433c413f72946f552}}, {{cite:372042dc8d1dab927a3b26b82c73c5f093135056}}. Fig.REF shows all the regression analyses of learning algorithms and datasets. For Waterbirds, the correlation between IN accuracy and downstream performance is statistically significant for GroupMix and CORAL. On iWildCam and DomainNet, the correlation is more obvious than on Waterbirds. However, on FMoW and Camelyon, there is no significant correlation between the two performances. This phenemenon further validates our hypothesis that for object recognition task, increasing the performance on the standard dataset (IN) is helpful for downstream tasks under distribution shift. But the benefit of IN performance is no longer valid if the downstream task has quite different visual features such as dense images in FMoW and Camelyon.
| r | d0f494b70b5787b40cd9414ad3c9d88c |
c. Repository meta vector generation:
We map
the metadata in a repository to an {{formula:5da5b2bb-7464-4d81-b51b-e14f4d4ab50a}} -dimensional distributed vector, {{formula:46fdd33f-1f4e-4177-93df-d683f8a5c2ce}} in this step. Following the basic principles of doc2vec {{cite:ce392d0cca61007e86ec60a80a269dfa20ba0317}} approach, we adapt it to our needs and constraints here. Specifically, as metadata in a repository often consists of unstructured text and is small in size, we employ PV-DBOW, discussed in Section , because it performs better for small text dataset.
{{figure:b151788b-0100-4f29-9c49-4c1493d9eed0}} | m | 49a731734526196399043259cb7f1507 |
In contrast with the same behaviour of the elimination and deletion problems with respect to the inclusion in {{formula:017e1093-7b57-476e-94eb-353b44f07356}} , we would like to point that they behave differently with respect to kernelization (we refer to the books {{cite:fdcb4defe39009e7c51941a1712cee62dc9f2cae}}, {{cite:9197a9ea2555b4f0a2ec0046a87b131b1ef1cebd}} for the definition of the notion). It was shown in {{cite:d721d7a47ade62f82dbf26376a27dfc49320d81b}} that Deletion to {{formula:4599993f-de29-457f-9649-f53ac2c20651}} admits a polynomial kernel for {{formula:e4817349-785f-40ae-9e69-affb86e59ddf}} (in fact, Deletion to {{formula:f7deaacf-2aec-4f20-9476-542712419db7}} is polynomial for {{formula:60ce2385-ea93-48ee-a7c8-d93c3283684d}} ) and there are formulas {{formula:7e5da2bb-eab5-4e82-a21e-cdf340a127b6}} and {{formula:547a9058-9a9d-4bb1-9646-fd6a0ff25508}} such that Deletion to {{formula:1123db06-0d60-4f8e-92f0-8526169baf5f}} has no polynomial kernel unless {{formula:d3a4d63d-9d2b-4517-bde2-12b1a741524c}} .
For the elimination problems, we can show the following lower bound.
| d | 54205d7c6b5b71d7ea008fb4fd4853a8 |
A strong correlation between {{formula:45f5ab23-c021-48a5-bed8-3ebd5e6f1a23}} and {{formula:aa075cbf-4178-4033-ba19-c3834e6c8cab}} has already been observed in a number of X-ray binaries, for example 4U 1608{{formula:53544afd-e1e6-444a-88ba-2636e3dd289e}} 52 and 4U 0614{{formula:fe563499-c854-4e90-a8f8-f64f25f7d61f}} 091 {{cite:9693ead9f07062d1bafc41896efa879e4e600f66}}, XTE J1550{{formula:f9055e85-c120-4593-9c76-05ccad8a871d}} 564 and GRO J1655{{formula:048e5750-0764-49ea-b8db-e8e9b93a33bb}} 40 {{cite:32e13c58ec5e830e1b4797973b58c2152d98062a}}, Cyg X-1 {{cite:abbee0d199dd38992241bb0488216568df67e638}} and Cyg X-2 {{cite:75f61cf6097727b1a80c8811d7ab4ba5308132be}}. {{cite:32e13c58ec5e830e1b4797973b58c2152d98062a}} observed a positive correlation for XTE J1550{{formula:62e4ed18-9ae0-417d-b9ad-b26f8dd2907a}} 564 and a negative correlation for GRO J1655{{formula:29eaada5-c2ef-4bab-ae09-ff6283ac8bd7}} 40. The authors explained that an increase in the mass accretion rate increases the QPO frequency, and the contribution from the power-law should be more than 20 % for QPOs to be present. {{cite:32e13c58ec5e830e1b4797973b58c2152d98062a}} have also suggested that the opposite correlation in XTE J1550{{formula:789acb5b-2aa8-4e1e-9169-04c5ff9fcee2}} 564 and GRO J1655{{formula:dc3326f4-98fc-4357-b915-2f912c1326dc}} 40 could be due to different regions of QPO generation in the two sources. To explain the correlations, {{cite:b4adce8ed4b8cdbb0a9d86d4b8487d84afbf3a31}} proposed the transition layer (TL) model. According to this model, a compact bounded coronal region is formed as a natural consequence of the adjustment of the Keplerian disk flow to the innermost sub-Keplerian boundary conditions near the central region. It ultimately ends up forming a TL between the adjustment radius and the innermost boundary. However, this mechanism is unable to produce the inclination-dependent QPOs obtained by {{cite:e297a5b07ec32bfafb5f461b3ac0c81fba934200}}.
| d | 5eca51c37231d6881defbeaa77302d29 |
where {{formula:f05ff7c6-7403-4ff9-8379-42129734c988}} is the learning rate. Here we use the Adam optimizer {{cite:917389d6e291f243b78ab6e4440087bd3fcb0a08}}, a highly successful version of the SGD method.
From the derivation of the DNN formulation, one can see that the proposed method automatically deals with the
phase boundary (or discontinuity in the gradient of the solution) without knowing the locations of the discontinuity a priori.
{{figure:87783fd3-8700-42c9-a4f0-1079d711eab6}} | m | fe17b27850a5dd5fcc2c5a9f273ea738 |
The usages of large sets of images has been a common practice for computer vision research. The usage of art datasets has been less common, but paintings have nevertheless been used in various ways. Models that learn to convert photographs into
painting-like or sketch-like images have been studied extensively for their
application as a tool for digital artists {{cite:1d8cb593f6450152eb902ccfd5904e54bd9fceff}}. Recent work has
shown that such neural style transfer algorithms can also produce images that
are useful for training robust neural networks {{cite:55b53bac99bf3e03bb250cfe65f8a2d60d071395}}. In a related paper, we more explicitly discuss specific applications of the MIP dataset for computer vision {{cite:28facf34c85e029edfac1fce4ada2d69cb10b52b}}.
Similarly, other
domains of computer vision research might benefit from painterly depictions.
The finding of our perception-based recipe for the stereotypical depiction of highlights on glasses
could be useful for the generation of images. Current image generation algorithms
are capable of generating novel images, based on learned
statistics from a dataset {{cite:0b0f45e1574b2b776d862b4037c5912f764d7eaf}}, {{cite:388aae8961a34c133570adcf6240ae9d946d0332}}.
While a specific category of generated images, e.g., faces,
{{cite:6c73a6434f7e14f2aed8af4f481a9efa25607e85}} is rapidly becoming indistinguishable
from reality, a larger set of categories is still proving difficult to generate
due to the lack of sufficient training data. Moreover, it would be interesting
to see if applying explicit painterly techniques, e.g., perceptual
shortcuts, or stereotypical depictions could be leveraged in image generation.
Perceptual shortcuts do not mimic the statistics of the real world, but instead capture image cues in a stylized depiction that explicitly trigger convincing human perceptions. Image generation algorithms that learn to use perceptual shortcuts might more efficiently capture image features that trigger perceptions.
| d | 1bfb3496ac9cdfd215944fef42ebf1fe |
In this work we adapt three GAN generator architectures to the 3D lung CT patch modelling problem: the widely investigated DCGAN {{cite:ac98c5aca09ee1cae70ec0a11a7084c058eea331}} representing a baseline approach, and styleGAN {{cite:4590b8afa7b07e4d1676886959dc657f9ef33743}} and bigGAN {{cite:a3b165307a9ced66dccccf490a2cd3ebc53e9266}} approaches which are more representative of the state-of-the-art in generator architectures. It is important to emphasise that these methods could not be used `out-of-the-box' and modification was required to allow 3D patch output. Therefore, we denote the methods investigated in this study as DCGAN3D, styleGAN3D, and bigGAN3D respectively.
| m | e1a6e0ad42cfe79a8059273d12d59cf0 |
However, deterministic neural networks assume that the mapping learned by the network is accurate, which is not always the case, and produce only the learned output for a given input. On the other hand, uncertainty quantification (UQ) not only describes predictive distributions over outputs for given inputs, but also indicates whether the model is confident about the prediction. The uncertainty can be divided into two categories based on its sources: epistemic (model) and aleatoric (data) uncertainty {{cite:449b3983fe7483a6193410f12dfe749b1df0101d}}. Epistemic uncertainty is produced by the neural network itself: its architecture, training procedures, the number of samples, etc. It can be mitigated by collecting more representative training data, which helps improve testing performance {{cite:a9dd1e6a89411cab5eed0fc2ed5eed4ca74ece0c}}. Data uncertainty describes the variance of the conditional distribution of a prediction for given input features. In contrast to epistemic uncertainty, data uncertainty cannot be reduced by modifying model architecture, training algorithms, or collecting more data under the same experimental conditions because the noise distribution in seismic data cannot be considered constant.
| i | 3724af045a5593ab4f625068e6b9f831 |
The available data described in Sec. is split in a 7:2:1 ratio into training:testing:validation sets.
Using the training and testing data the networks were trained with the Adam stochastic optimizer {{cite:64227464026d7454bf4a08be849d729b2385fbe3}} with learning rate 0.001 until there were 100 epochs of non-improvement in the mean squared error loss on the test data (up to 1000 epochs).
A batch size of 32 was employed and all input data was normalized to {{formula:d9a2a666-cf94-4de2-b537-ab0b49cb7af2}} prior to training.
All reported (root mean squared) errors and correlations are computed with the held-out validation data.
| r | 6dc27bd63bd999b7eb19527bcb47035c |
Lastly, a disadvantage of applying resubstitution with upper bound correction to analyse DL models is that the final classifier should be linear, as the computation of the upper bound becomes more complex in other circumstances. The large number of connections in the net and aspects to be considered such as activation functions or dropout make the application of the VC dimension in deep learning architectures too complex to generate upper bounds {{cite:886ae433555f2288bc8a94f71789e8ab4520871b}}.
| d | 81e26763615fe8813fc4df884d984617 |
We make a direct comparison to the square lattice CNN model described in Choo et al. {{cite:01205bf2ae5289151fa69e456a3c875740c15c69}} who use a translationally equivariant CNN symmetry-averaged over {{formula:9771a2ee-a45b-4688-aecd-a65127758327}} , while we use a model that is equivariant over the full space group {{formula:ec6900e3-58eb-4afa-a78e-b823581bfaac}} .
As explained in section REF of the appendix, their model can be mapped to a G-CNN over {{formula:a7246f58-e5ae-48e6-84cc-c586fea83ea8}} with masked off-diagonal rotational filters. Our model uses slightly more memory, while their model has more layers and
uses an improved optimizer. We see that the G-CNN model
nevertheless has better ground state energy accuracy on the difficult-to-simulate spin-liquid state.
Neither CNN architecture is competetive with the architecture detailed by Nomura et al. {{cite:b0ac2584f939509e75329ad4afc9b0afe3456b7b}}, who combine a restricted Boltzmann machine with a pair product state (RBM+PP). Theirs is a shallower model that uses far more memory.
For the ordered state, both CNN based methods are very accurate, and the discrepancy may be due to convergence issues {{cite:7f7edcd856237acffc6c9bb8cf9c49ab8d1846a9}} with the adaptive moment (Adam)
parameter optimizer {{cite:0d7d31505fd870def1ba1b410fcee4e1e238cc30}}.
| r | 89fc17878b667f5e2a40480f15334666 |
By definition, it is easy to check that (REF ) is L.S.C. and () is continuous. Moreover, (REF ) and () is coercive (see {{cite:e76b2b0c36af55844a6eba10d268dcb839faa466}}), that is,
{{formula:088f9e3e-9f45-4fac-b094-1bcd760682af}}
| m | e3c1f9fab5b65702bcacef9f43678553 |
Spoken speech refers to the natural speech that we use in the everyday life {{cite:5ee102ad6c48afcd5b775b76f3bd68f0cabc7dcf}}. It is known that imagined speech brain signals resemble the features of spoken speech brain signals in some portion, therefore, holds potential to utilize spoken speech data to improve or enhance the imagined speech decoding performance. Unlike imagined speech, spoken speech data is relatively easy to be acquired, and are able to check whether the user performed the speech correctly, therefore, may be better to train the decoding model. Although spoken speech holds strength in data collection, decoding imagined speech is still the most crucial point in the field of BCI, since the first aim for BCI systems are to help patients who cannot move or talk {{cite:54a4d243b93fd07516d1b1811c6660951da5765f}}.
| i | c530eaf70678df097b20ef8a49b28861 |
{{cite:2de6bb383923677b70e23a6b523666abfb6eacdc}}, {{cite:4cc86e01b4ce1f7a508e100b22e659d9b49d30df}} formalize the divergence between two domains as the {{formula:d685bb92-110e-4f6b-8519-32a884e97d0a}} -Divergence, which they approximate as the difficulty for a discriminator to differentiate between the two.The approximation is also referred to as Proxy {{formula:8344514c-ec46-4d06-b2ab-418bd6ea7faf}} -Distance (PAD) from {{cite:4935caa8fb63c372b67fc90fac7920860ea2acb6}}
Discriminative Active Learning (DAL) applies this concept to the active learning setting {{cite:6442c101b2bb31fd5639570846aac87b4a00f62a}}.
| m | d1e12d3b33cab8b418371c6a9efcdd27 |
Evolutionary simulations: In order to simulate the evolutionary dynamics of this system we consider a population evolving under a “copying process” {{cite:1676c132a6ebee86b167f705a23704ec1205fe0c}} in which individuals are able to observe the utility of other individuals and compare it to their own. The dynamics of the model are as follows: An individual {{formula:77da94b6-2c10-41e0-a427-053fbb495fca}} is chosen at random from a population of fixed size {{formula:5ba641ea-5af5-4835-ab55-84b6268b7bd5}} . A second individual {{formula:f79e3db2-7ca5-4660-9792-ddfce9985ff8}} is then chosen at random for her to “observe”. If {{formula:c9be1e83-5e33-4d6f-821b-da5133cbb6e7}} has utility {{formula:fbccb759-cbbe-4789-b93a-52c41dbe5a48}} and {{formula:2454a0db-bb66-4844-b62d-f6f36baee7b6}} has utility {{formula:6eb3d675-70e0-4b05-b51e-6090b1369b8f}} then {{formula:de461701-5133-4878-9be8-aa4924604467}} chooses to copy the strategy of {{formula:7ab2109a-b98d-4553-b1bb-2bfaa8f8f722}} with probability {{formula:73f20caf-650a-49bf-864c-39e5ad68d0e4}} , where {{formula:dce63346-fee4-422e-9076-2ba06222ef9a}} scales the “strength of selection” of the evolutionary process. Note that if {{formula:dc58fe5a-8742-4ede-8907-bddb26af0d85}} the probability of {{formula:f8adc57f-e2df-42bb-9b94-82e64e2b3e4c}} copying the behavior of {{formula:24e000e5-26c3-4a3b-a4d5-5b318e878c98}} is close to 1, whereas if {{formula:67857ca2-7c77-457a-b12b-29c06dfcb3be}} the probability is close to 0.
| m | b47206f3f9e528e958f4fcae09a58f87 |
We include four existing methods for comparison in this work, DrBoost {{cite:ff1bc6f62e2ff6a544d31769b0f24045efe9d3a2}}, DPR {{cite:42d4a21722e3295a083657fc6939d903cdfe9636}}, SPAR {{cite:870f5ca895ce6f660606e16a76df6714977e1a42}} and a heavy hybrid model BM25 + DPR {{cite:42d4a21722e3295a083657fc6939d903cdfe9636}}.
SPAR is an ensemble model that involves two encoders, which
achieves the state-of-the-art (SOTA) performance on the NQ dataset.
We refer readers to the details of SPAR in the original paper.
In Table REF , the performance of DrBoost (using 5 or 6 weaker learners) is from the original paper and the performance of the other three methods are from {{cite:870f5ca895ce6f660606e16a76df6714977e1a42}}.
| m | 6fde0d9a328de7a9230239bf73ee3760 |
There exist several variants of edge length optimization problems in linear arrangements {{cite:bd2275a1e1e931e59dcea3d898eb35b893137103}}; two of them are the planar and the projective variants. In the planar variant (minLA/MaxLA under the planarity constraint), the placement of the vertices of a free tree is constrained so that there are no edge crossings. Such arrangements are known as planar arrangements {{cite:cd9554a5fd9ab3d0bad8f2afa2b481b105b4161c}}, and also one-page book embeddings {{cite:3670cf9694305e985f4ef5a3ece42a8c3e434537}}. Two undirected edges of a graph {{formula:9d25b269-b7ed-4610-ba80-ebd631476dc3}} cross in {{formula:0047848e-4eb4-4e6e-9f05-a6de7fef1a3b}} if {{formula:f5e224f1-0a7a-441b-8ef4-23c4890697ee}} when, without loss of generality (w.l.o.g.), {{formula:5c2365cf-0e21-4ce8-88bd-d27825f5d141}} , {{formula:bfdc68d9-12e5-4878-9fc0-f5b7e8ef109c}} and {{formula:74237462-201d-489a-8df4-3ce5b772d46e}} . There are several {{formula:f2a2537c-d0d2-405a-af6f-7820aa0cd5dc}} -time algorithms to solve planar minLA {{cite:585941b42b4c1a61879d8abc5fab098b8ecba96c}}, {{cite:de6c0721a42e3cf3319833e645e9850470ffdc3a}}, {{cite:bd2275a1e1e931e59dcea3d898eb35b893137103}}. The solution to planar minLA of a free tree {{formula:5cef927a-510c-4de9-b63f-7821bfaf3557}} is denoted as {{formula:b29d4e58-7d52-4f3f-afd0-d2351106b8e0}} , where `{{formula:570fc389-7e96-4ab5-9c2e-34211c3aee49}} ' stands for `planar'. In the projective variant (minLA/MaxLA under the projectivity constraint), a rooted tree is arranged so that there are no edge crossings (i.e., the arrangement is planar) and the root is not covered. A vertex {{formula:9f83f3da-e38e-47d4-9674-e6542d3fa88e}} is covered by an edge {{formula:f875ee38-56c6-446e-826d-a17d926f9a52}} if {{formula:29ce83a1-7865-4d03-b147-d303ca14206a}} when, w.l.o.g., {{formula:d25c257f-7886-442e-9b24-0408f3bcdc36}} . Such arrangements are known as projective {{cite:cd9554a5fd9ab3d0bad8f2afa2b481b105b4161c}}, {{cite:8486a2ae8a0d961c381df748f42eec74e5c36e78}}. There are several {{formula:cd3a94bd-9e38-4581-974b-049229f56aed}} -time algorithms to solve projective minLA {{cite:de6c0721a42e3cf3319833e645e9850470ffdc3a}}, {{cite:3aa88b48cf72057b87eaec4b9d652ccd8c13dfdb}}, {{cite:bd2275a1e1e931e59dcea3d898eb35b893137103}}. The solution to projective minLA for a rooted tree {{formula:0d445cb3-e57c-4c2c-a571-c56f2ad6c880}} is denoted as {{formula:b552e669-11fc-4c94-928e-15e93706a4af}} , where `{{formula:fb4b81c7-7a3c-4be7-97f3-1c5d9df4607d}} ' stands for `projective'.
| i | b0bdbd7bb90b446633d8cd5e27036d27 |
Due to its stability, an entanglement source based on the Sagnac configuration has been installed on the first quantum-communication satellite (Micius) {{cite:bba81b13e5bf8f35ac72e19358a8143b80da0a66}} and used to demonstrate satellite-to-ground quantum key distribution {{cite:3b660c4592036074c67363585f30bd2e906cd201}}, entanglement distribution over 1200 km {{cite:1fee51aa47625e31d6185745118a8ccc93187c71}} and ground-to-satellite quantum teleportation {{cite:a5a8f9319e66af7c76ff4dcd3376667a86922ac8}}.
| i | d3c9e80b860cca273f186d0117c233c2 |
On the downside,
direct ST suffers from the lack of large ST training corpora.
This problem has been addressed by researchers through transfer learning from the high-resource sub-tasks {{cite:811c09737c6724cb83cebdec171a2642e83adda1}}, {{cite:109737002c6d4929d75d79eee4df04a14f5e049c}}, {{cite:e31b52c2eed853de6274e89eb95ca66bedbc1b18}},
multi-task trainings {{cite:db1ea5395e3cf7180e28b5c84ff18abe210bd6b6}}, {{cite:889e1684f83ab614d6248d78d9790e97ba2c98c8}}, {{cite:e11fbce9cdaf56027e40e6edc6c920570f9c8d25}},
and the proposal of data augmentation techniques {{cite:fa53509143fca2eab0182d428238b429cf563faa}}, {{cite:e7c921f7561f03cde4b999cad39c9810d05e2fcc}}, {{cite:c6444002dd8b9db7ad87fa4a0faa022b13d4ccde}}.
In this work, we focus on the transfer learning from MT.
The classic approach consists in pre-training the decoder with that of an MT model.
Its benefit,
however, is controversial: indeed, {{cite:e11fbce9cdaf56027e40e6edc6c920570f9c8d25}} showed that it is effective only with the addition of an adapter
layer, but this has not been confirmed in {{cite:21426ae8cfe700cb1cf9086e30e829fe6216028d}}, while in {{cite:b2d8fd3b78c826e797a5d6b088a5aa77eba6aab7}} it always brought improvements. Another, more promising possibility consists in distilling knowledge from an MT model.
| i | c276c63dea33c3e4b67621a3d69564b3 |
blueLaplace’s (1799) calculations and conclusions have been confirmed, prominently by {{cite:b807bbd0bc8ba1e1e8cff0457342d57e3c4fd02e}}. Based on these equations, a link between the rotations and the torques exerted by the planets of our solar system is expected. Indeed, we have shown elsewhere the influence of Jovian planets on the Sun (sunspots, cf. {{cite:b3f83dee8523e56ac1d296a23adcf047409c0cfb}}), and Earth ({{cite:969d838b66f4fd0156367a13c7d99790a1e7397a}}, Figure 11). In the latter paper, we show the similarity between the envelope of the Chandler oscillation and the ephemerids of Neptune. Figure 03 of {{cite:969d838b66f4fd0156367a13c7d99790a1e7397a}}, reproduced here as blueFig.REF , shows the remarkable agreement between the sum of forces exerted by the four Jovian planets and the {{formula:94623231-5f0d-4812-abd1-d1bacbd3fd0c}} component of polar motion.
| d | b89455b20fd8f29e3b29cbfcf263f639 |
The above formula written in a schematic way allows to easily explain our idea and differences with other methods. Indeed we have written the above expression with {{formula:c01f6041-2703-4241-8b01-80207b347391}} as {{formula:43d02b73-ac12-4f6b-a11d-53ea20336ab8}} hadrons are ultra relativistic. In our actual analysis, we use simulated data from MadGraph5{{cite:b7f495a3270c81788ac5e925bcffa3103eca8f71}} and Pythia8{{cite:270ec26bb2f8c7fe6e22d9bcba8ef608b0aaecc1}} throughout, hence we use fully realistic data and templates predictions without simplifying assumption, e.g. the actual velocity of hadrons is always considered.
| m | bed0af3899daae50a5dcfb12b2e76390 |
The transverse momentum dependence of the strange baryon to meson /ratio provides a unique way to study the properties of the hot and dense, color-deconfined QCD matter called quark-gluon plasma (QGP) created at the Relativistic Heavy Ion collider (RHIC) and the Large Hadron Collider (LHC). It is observed that a pronouncing enhancement of the strange baryon to meson ratio at intermediate exists in nucleus-nucleus () collisions compared to proton-proton () collisions {{cite:4c7efdee1d98e5dec0cfa20a2dc446d2673732cf}}. It is believed that this anomaly strange baryon enhancement and the shift of the /peaks towards higher can be described by the introduction of the parton recombination mechanism to the hadronization process and the hydrodynamic parton radial flow induced due to the formation of the QGP phase. However, the enhanced strange baryon to meson ratio at intermediate , together with many other QGP like phenomena {{cite:a920d94f9f7f1308cd4022abd2580a165cb28ceb}}, {{cite:e90bd553684002202930e9dfcd4f98e432e5b1a3}}, {{cite:31f76ff38a4b7ff4173b8882fb2cedd0f4b83ca5}}, {{cite:28693c83c7ecbc36e73195872599e505fef978e8}}, has also been observed in high multiplicity and collisions {{cite:c0582a16a3ce8902b95d05cce68fac3a0ebd71b6}}, {{cite:a920d94f9f7f1308cd4022abd2580a165cb28ceb}}, {{cite:71d7051a14d0079df985e6b301486249c36a2885}}, {{cite:632939f457ea4254012c8b149bd8ccef695de3cf}}.
| i | 4dddca19fe84e5b4ddbb3566e5fd030c |
A term of this form remains because the gravitational Lagrangian, built from the Ricci scalar, contains second-order derivatives of the field variables.
The established procedure, given by {{cite:b0da939cebdf09580ac06afc44f43e892a54f5e6}}, is to just extend the EH action with the negative of this term.
Thus, this final boundary term vanishes by construction.
The York term is often omitted from the action when working classically, as it is non-dynamical.
| d | a7e9a09cf902983e5c6d228d270aa311 |
Results and Analysis. We report results using the same evaluation metrics as in {{cite:11066c6bb9090ef60c42551622151c8f1852e6f5}}; Table REF and Table REF shows evaluations at the segment and event levels, respectively. Audio, Visual and AV refers separately to audio, visual, and audio-visual events. As the name suggests, segment-level F-scores are evaluated at the level of segments, while the event-level F-scores are computed by concatenating positive consecutive snippets in the same event categories and then computing an event-level F-score based on mIoU = 0.5 as the threshold. We also compute two aggregated metrics, Type@AV (Macro F1) and Event@AV (Micro F1) which are averaged audio, visual, and audio-visual event evaluation results and the F-scores considering all events for each sample, respectively.
{{table:23191c5d-fcaf-40f6-a677-ddd8a560f6e4}}{{table:b9f880fd-aab3-4dfa-8b15-c1baffcb7e16}} | r | b93af1eb31965558ea166c8413fe9967 |
MOT17 Table REF shows quantitative results of PatchTrack along with other recent MOT systems on MOT17 {{cite:b61da861df65d5c82470b40e509bd17167e026fc}} test set in private protocol. Compared to Non-Transformer-based methods, PatchTrack reports best numbers in MT and ML, and shows superior ability in trajectory prediction. On the other hand, PatchTrack performs comparably well with other Transformer-based methods, achieving second-to-best results in most metrics. Compared to TransTrack {{cite:a3f7d9780de47e5125bb6ba6261d3bd1f394e48c}}, which has state-of-the-art results in MOTA, MT, ML, and FN, our system is able to produce less than 50% of FP. We provide additional visualizations of PatchTrack and TransTrack in Figure REF . While PatchTrack is able to perform on par with TransTrack, our system is able to avoid tracking one object multiple times or causing ID switches when a previously fully occluded object re-appears.
| r | b09c4ea1a592d400472d785e7929c048 |
A classical approach to perform model discovery is by sparse regression and consists in finding {{formula:0c6c330e-ce82-4992-b426-df4d0342ae7b}} such that, {{formula:135f24ba-19be-49da-ab0e-5d0c59b8a931}} , where {{formula:32feb897-f5a7-4dc5-b8e0-439f4284651d}} is the time derivative of the field {{formula:b95f5a6b-750e-4dc3-82bc-0a4b96eed737}} . Each column of {{formula:a32b2acb-dc7e-4fd5-b94a-136dba8149b7}} is a candidate term of the underlying PDE, typically a combination of polynomial and spatial derivative functions (e.g. {{formula:4bb74608-1f47-41a1-97cf-01b24fa31be4}} , {{formula:da0bc20b-bd01-4d06-a0d5-d450272e5c55}} , {{formula:f3fe3708-5943-4ee7-8af0-927d866c6256}} ). Usually, {{formula:36ec3f01-18d2-42ce-8d45-5741e9bb3a92}} is identified based on a single experiment consisting of {{formula:8e53816d-272f-42f2-b4dd-ebbd0f439541}} samples of the field {{formula:7caff0bf-1901-4974-a265-3a090b0d8157}} , see {{cite:baac35a93d0e2a9f93452bd15b4d9f4a7e9e45b4}}, {{cite:0a544182e0029638d87ad21eb03315ae7ede878c}}, {{cite:d289b0123998bdcb1d35cc71c2d1b168921c6c59}}, {{cite:64d65128778fe532c97ee09fb5ac378f627d3df8}}, {{cite:9f6022f6a698277b663dab2901faab1c07162419}}, {{cite:61551ef9d61b5af0592c9fe01dc92dd334cc7fd7}}. However, in practice observations of the same experiment might lead to some measurement differences. For instance, it might not be possible: (1) to fix identically the initial and/or boundary conditions of several experiments, (2) some of the parameters might not be controllable and will vary. As a result, there will be experimental results which exhibit natural variability. Let us denote {{formula:0fce2017-471b-40d0-a171-c7acf4dcf709}} the number of experiments at hand from which we would like to find the underlying partial differential equations. If we perform {{formula:2a5e04eb-c034-45f4-ae98-c1ebed358ac9}} individual model discoveries as described earlier, the data across experiments will not be leveraged, loosing an opportunity for learning. To leverage the data across experiments, the {{formula:b7f419f0-6b5f-4e7e-8304-54dee1233ded}} libraries could be stacked {{formula:3f56cddf-b422-4954-b9f3-9dafa5fa79c7}} and then a single sparse regression could reveal {{formula:b5bd68fa-6cfd-4d77-b8f0-6ef4c205c6bc}} , see {{cite:0a544182e0029638d87ad21eb03315ae7ede878c}}, {{cite:779ee3588b55da78c4e8647b0813c82074630cf7}}. However, this approach is not adapted if the coefficients of the underlying PDEs vary from an experiment to another.
In this paper, a more general approach to this is proposed: by promoting sparsity group-wise we leverage the data across experiments and are able to handle varying coefficients across datasets. In {{cite:9db8a1c92da9300a9625f748a25b2dd9ae24ab7c}}, a group sequentially thresholded ridge regression was proposed to infer parametric PDEs from a single dataset. In {{cite:eeb75669be6fc068372246640e3e8d08a1eab0f7}} a group Iterative Hard Thresholding algorithm is used to enforce conservation laws and impose symmetries. In {{cite:a3ed4868296014beed497a9a7808bde96d5801a4}} a group Lasso is used it to try to infer the law of gravitation from experimental ball drops.
| i | 9aa094a4b1782c949d589fa6831331b3 |
To investigate the stability of our system, we show the boxplot of the RMSE values of ATE over 5 runs for all the 5 sequences in Figure REF . We can observe that, on V101 and V102, our system not only achieves lower the RMSE ATE than ORB-SLAM3, but is also more stable with smaller variance. On V103 and V201, our system is on par with ORB-SLAM3 in terms of performance stability. However, our system demonstrates larger variance on V202. We conjecture that this is due to much more violent motions in V202 which cause difficulties in self-supervised depth and uncertainty prediction {{cite:4f6e8c8720ba81a5ec8c9226a1eb76e422693d73}}.
{{figure:32e9880a-1b72-4421-afc8-39509034ec1d}} | r | b6d5403892c136424bd30eee9f9d29a6 |
[RQ3] Performance of PerDoor against state-of-the-art Defenses:
We evaluate the effectiveness of PerDoor against two existing state-of-the-art defenses, Krum and FoolsGold. Figure REF shows {{formula:017f42b8-5b13-416d-821d-212eb93a0805}} for 5000 successive rounds considering both these defenses and unprotected FedAvg. We consider that the adversary injects backdoors at the stable point. We can observe that while FoolsGold performs almost identical to unprotected FedAvg in terms of {{formula:fbec5df1-2904-46ba-882f-0b7cfa8b15a9}} , the main task accuracy of Krum drops below 80% (i.e., almost a drop of 10%). It may be noted that the accuracy drop is not because of backdoor injection but due to the internal anomaly detection mechanism of Krum consistently producing global models representing data from the majority of clients. The result also aligns with the observations discussed in {{cite:93cb7bbb7eda869712cd56d969abbd39186a07de}}, {{cite:9e446f59db4b6286f28c396921a7f26e2e19a76e}}. Figure REF shows {{formula:f2c02522-e111-413c-8f79-3621d9b90c5e}} over successive FL rounds after the backdoor injection considering all three aggregation methods. We can observe that PerDoor can efficiently inject impactful backdoors into the global model even in the presence of defense methods.
{{figure:ba3aa204-52ad-4aee-ba76-d6e68fef7213}} | r | 938fb02f0075cc5135082dc774725b06 |
For likelihood problems, it is common to use Bayesian inference and deploy the MCMC toolkit. Unlike frequentist estimation, Bayesian analyses rely on sampling from a posterior distribution rather than optimization. Well known samplers include Gibbs and Metropolis-Hastings. Because they can be slow to converge, gradient-based samplers are increasingly popular with Metropolis-adjusted Langevin dynamics (MALA), Hamiltonian Monte-Carlo (HMC), or stochastic gradient Langevin dynamics (SGLD) algorithms. A comparison between rnr, rqn, and MALA is given in Section . Unlike Bayesian inference, this paper does not require the information matrix equality for valid inference. Convergence diagnostics used for MCMC algorithms such as trace plots or formal tests {{cite:696f8051c54d310c233b3695305497529596cf7c}}, {{cite:5dd1b5356d2e040f7131db492d4e605a198663cc}}, {{cite:1db18faa6e5c84c552d0eff9436426bc98a6751a}} can also be used to monitor convergence of rnr and rqn. Lastly, while the detailed balance condition guarantees the posterior is a stationary solution of a Metropolis-Hastings algorithm, convergence rate results typically assume a (nearly) concave log-posterior – similar to the convexity assumption in this paper.Recall that the detailed balance condition ensures that the random walk Metropolis-Hastings algorithm is ergodic but deriving the rate of convergence is more difficult. See e.g. {{cite:afc6af3c8eda0a8bc107aa964731d99516c0ee93}}, {{cite:e2b968f8ddbd50ba5e65904232722295671e5f58}}, {{cite:9bb948265e6d51ff0e0d7f5dd1e92dd270654837}}. {{cite:7ac463774a5162849f1792dbd04736df74471180}} show how optimization can be used to sample from a Bayesian posterior with an intractable likelihood. Here, optimization is used for resampling.
| m | f080c6653f1974afbccee3f92fc9b59f |
In the dispersive regime of cQED {{cite:443a9d66fbf7db7a9329e57d896e94fc887e9a67}}, after applying the rotating wave approximation, the bare system Hamiltonian in the driving frame (at frequency {{formula:1e34bdef-3fb7-4f5a-96ec-012db634e155}} ) reads
{{formula:0290df87-34ff-438d-b0d6-e52a9de23f54}}
| m | b99d4edde31080fd8a8fc9aace4033f8 |
First, let {{formula:3dd7e315-3445-4e70-b608-1b381fff85ff}} be a simple group of Lie type, then using {{cite:db1cc7f3c0d215c094d8207433f5cdfea3ea4fa1}} the Steinberg character of {{formula:d00aa4df-1036-443a-9776-cc778d4ae532}} is not a {{formula:b36480a8-8515-4b69-a366-f66b396f7f29}} character and it is extendable to {{formula:a7ef59c9-bc07-46d9-9e63-a4fa97511671}} (see for example {{cite:2bcb70f45cc6f436778b1e8c6637e2fd1c337eda}}), except for the cases {{formula:185ed58c-97ac-4c20-a128-2dc8d757d315}} , {{formula:55e11481-04a4-45db-94f6-84b4d7361bc0}} or {{formula:328ab81a-2d15-4a67-bfa8-53844f3868c3}} . One can check that in those remaining cases {{formula:5b52d1d3-cf00-4316-9af9-16724ee459c5}} has an irreducible character of degree 4, 6 and {{formula:e89c701f-a20f-4aec-87f0-dee5ed32dd58}} , respectively, which is not a {{formula:071e81c1-0013-419a-a606-e27a8c113490}} character and it is extendable to {{formula:d353ddaa-64a9-4544-9849-b83bc1bca3db}} (see {{cite:51b0cf8afb6cf787d79ca0e0511be7176fe6ceb2}}), as wanted.
Next, let {{formula:e4e76a66-aeaa-4e69-989f-4b710f054145}} be an alternating group of degree {{formula:612579c3-173f-4272-a17a-eabf527c34ec}} . By the proof of {{cite:db1cc7f3c0d215c094d8207433f5cdfea3ea4fa1}}, we see that {{formula:4cb8d86a-0d1e-4f79-bf6a-fb99558cc1bb}} has an irreducible character {{formula:b8f87381-b46c-48e2-a54c-2c08a54db139}} of degree {{formula:89745063-fce4-4b90-8735-0e0048405382}} which is extendable to {{formula:1789072b-1525-4b4a-818f-4fbd98c67a00}} and it is not a {{formula:2aacbbef-c707-40ec-8407-fc0f131a6cb3}} character.
At last, let {{formula:b6b54b6c-7d25-4177-92ad-2ca9c310dd75}} be a sporadic simple group or the Tits group. Then according to the the proof of {{cite:db1cc7f3c0d215c094d8207433f5cdfea3ea4fa1}} if for each {{formula:906593f8-0774-426d-9c21-c8da53080c4f}} listed in the first column of Table 2 of {{cite:db1cc7f3c0d215c094d8207433f5cdfea3ea4fa1}} we take {{formula:f10c817e-bc9e-49c7-8025-a2bb98cafa25}} to be the character in the third column of Table 2 of {{cite:db1cc7f3c0d215c094d8207433f5cdfea3ea4fa1}}, then {{formula:c284076a-7399-40c0-a2ce-89152031873a}} satisfies the hypothesis of the Lemma.
| r | f12d2147862c356db16f42af69371750 |
In this paper we have shown that HTLs arise from classical limits of off-shell currents. The classical nature of hard-thermal loop amplitudes was made manifest by relating the momenta of the
soft particles to wavenumbers. The classical limit is then obtained following the KMOC algorithm. In this way, the
high temperature limit is formally equivalent to an expansion in powers of {{formula:dcc296e4-e197-450f-be0b-0ffe6d1a4dc3}} thus allowing a map
between HTL amplitudes and classical limits of off-shell currents. The off-shell currents encode the information of permutation
of comb diagrams and can be easily computed from Feynman diagrams or Berends-Giele recursions. Since our off-shell currents in the classical
limit are gauge invariant and satisfy Ward identities their “on-shell” properties would be interesting to study, in particular the Britto-Cachazo-Feng-Witten
{{cite:ea6375fb5f1bf12e1fb24473c947aaeb095f1206}} recursion, the colour-kinematics duality and the double copy{{cite:f9ecff23850ec045d4fe2588867b45d4e34cbe27}}, {{cite:0f55e8a180d416ff24bf7e252d7a5e354df0bec3}}, {{cite:e9f916573fa1f6d4fdff8c1832ae4b5794326875}}. For general off-shell currents
these properties are generally more difficult to make manifest than for amplitudes {{cite:4806834c1ccd7b899929d27223cca7e27df2956c}}, {{cite:a4e46c6e629778653a65003ab52f6a5dcb4054db}}, {{cite:40ebf2b834c9e7609dc8dc9181ae81e5e40bf65e}}. At the classical level the double copy
is much more flexible but the idea of a formal replacement between colour and kinematics is preserved {{cite:02459b57193ab0c7e50203c5b18ed5fe013f79e8}}. This classical double copy
is the appropriate to relate gravity and QCD in the high temperature limit.
| d | 6cb56d4ee1a6ae38aaf496a105ef0bc0 |
In order to build language-invariant models, it is critical to consider the two perspectives: (i) avoiding catastrophic forgetting and (ii) learning language-invariant features.
Catastrophic forgetting {{cite:0f88d165fd0f9ff69e6c5bc8672589f274cd0992}} is the phenomenon that a model forgets knowledge of previously trained tasks (languages) by incorporating knowledge of the current task (language).
Language-invariant features are the features that are common and unchanged in different languages.
Taking these two perspectives into account, we present the following two methods.
| m | f06bd37af802118cdca35ae02d258c25 |
Principal Components Regression (PCR):
Principal components are the linear combinations of predictor variables
such that the transformation makes the new variables uncorrelated. In
addition, the variation of the original dataset captured by the new
variables is sorted in descending order. In other words, each successive
component captures maximum variation left by the preceding components in
predictor variables {{cite:f5f8897a73b2861fa0c8d64e59a07031bc3538fc}}. Principal components
regression uses these principal components as a new predictor to explain
the variation in the response.
Partial Least Squares (PLS):
Two variants of PLS: PLS1 and PLS2 are used for comparison. The first
one considers individual response variables separately, i.e. each
response is predicted with a single response model, while the latter
considers all response variables together. In PLS regression, the
components are determined so as to maximize a covariance between
response and predictors {{cite:60a75913c4d9b31f46436ffcf01300c62240a906}}. R-package pls
{{cite:f4ab2ad462d2d00fb6a943ddb5e45b7bd5702f30}} is used for both PCR and PLS methods.
Envelopes:
The envelope, introduced by {{cite:c31d55b8bb6f5bf70fe2431977bf380954df31b1}}, was first used to define
response envelope {{cite:804db5985a506875930e1cc5959dfdd387931a2c}} as the smallest subspace in
the response space so that the span of regression coefficients lies in
that space. Since a multivariate linear regression model contains
relevant (material) and irrelevant (immaterial) variation in both
response and predictor, the relevant part provides information, while
the irrelevant part increases the estimative variation. The concept of
the envelope uses the relevant part for estimation while excluding the
irrelevant part consequently increasing the efficiency of the model
{{cite:cc97344bcb9fc06eaab3dc29158b40c883aa3a71}}.
The concept was later extended to the predictor space, where the
predictor envelope was defined {{cite:69916a1ee786dbf1591a012f019686023ade6c24}}. Further
{{cite:d2ad39c2b93a5ce855ce2a49726c6d2ee6e40af9}} used envelopes for joint reduction of the
responses and predictors and argued that this produced efficiency gains
that were greater than those derived by using individual envelopes for
either the responses or the predictors separately. All the variants of
envelope estimations are based on maximum likelihood estimation. Here we
have used predictor envelope (Xenv) and simultaneous envelope (Senv) for
the comparison. R-package Renvlp {{cite:6a1a9e131cedf7ffbbff2dbfbf49a174730afb8c}} is used for
both Xenv and Senv methods.
| m | 9b68ef926254d56281557d55b6bdef52 |
tocsectionReferences
Appendix
Asymptotic Variance
To state the asymptotic properties of {{formula:d8403b54-0f21-49cd-b8b1-3f413bc0ea3c}} , let
{{formula:b27132ea-39cb-4651-954b-ebdfedf1fe88}} be the individual's contribution to the estimating equations for {{formula:37eff4f5-66cb-482c-8827-658ec6bd84f3}} ,
{{formula:e1d8a3d2-2bf7-4a74-af2b-c525f2f5c199}} be the individual's contribution to the estimating equations for {{formula:208d0674-4604-4cc3-af89-242af4176637}} , and
{{formula:24add143-7b5e-4b39-8b77-85bd65aba56b}} be the individual's contribution to the estimating equations for {{formula:fbbd803a-09a9-45d3-a0a4-19c935132d77}} .
Define
{{formula:191c682a-1a25-4d32-90ce-4dfa2d06fdd0}} ,
{{formula:3ab10027-eb72-4001-a222-53bb8d350891}} ,
{{formula:0d6930c2-a1e9-472e-98a6-ebab28e576ad}} , {{formula:6da218ec-e816-4312-91e1-c17f325967c0}} ,
{{formula:80823dc0-83a5-42e7-94d6-b7164644a529}} , and
{{formula:07fffcf0-6971-4829-94e9-e8a822894cb8}} .
Theorem 1 If either the missing data model or the covariate model is correctly specified, then
{{formula:f2871c26-a278-443d-836c-04d5ef96c8b7}}
where {{formula:85fbcdbc-e5e2-4563-b422-038e4a3d108f}} is the true value of {{formula:9c3f509d-3754-4f89-94d8-542df3f693f5}} , {{formula:fa438de8-840f-4843-85ff-5d64430836b7}} and {{formula:45e3e053-8b35-4284-914e-937aa8349bda}} are the probability limits of {{formula:80f3d2cb-bb9d-4188-a0dd-bb9d45abf000}} and {{formula:123e0b64-b386-4288-8a6d-df046b17c300}} , and
{{formula:510396a6-7884-4c7d-8d2d-160344c8b370}} .
Inferences for {{formula:d506b244-5938-49da-a44a-deac09082b6c}} follows by replacing the unknown quantities in (REF ) by its consistent estimators. We make use of “generalized information equality” {{cite:5f9618c322568d32fcfd06482d12dbe5005229c0}} that
{{formula:d93efdcc-2841-4c1e-ac62-6de430521f69}} , and
{{formula:121f9023-339a-4611-9bfd-37b83cabb63f}} . Similarly {{cite:1e4eb8c11c1d5e1ac66ec8bee5767c303ec7f032}},
{{formula:40257b75-8f14-44d1-af87-90a6cef47f90}} , and
{{formula:b1f1158d-6e53-4cb8-9687-8ab4adb9a7a7}} .
The matrix {{formula:64a605f1-c496-4304-b32a-c403368bd92b}} is replaced by {{formula:8bbdbb47-1db7-4498-9dc9-9605f957e103}} , and
{{formula:0133d6e9-1a6a-4c9b-b1ea-219dc1b9554a}} by {{formula:27da8b70-6650-4666-9827-9e2df5ebdd45}} ,
{{formula:bf47ca0a-b49b-4346-aba4-e1344b9b361d}} ,
{{formula:5a0669d2-c261-4a57-8af2-5bf70f8e1f79}} ,
{{formula:88ea10ab-5eca-4b65-9d56-52819c682ff4}} ,
{{formula:dabdad40-cdd8-4d28-b914-e9298886f912}} ,
{{formula:b6902158-a9fa-400c-8f9c-b13641ea0e72}} .
The proof is similar to {{cite:707b701aec9b90ed439ba8e880e7f1bd559d9019}} and is omitted here.
| d | 040da478a1bffc60ed7e36b8c43e375e |
The RWA model reformulates the attention mechanism into a stand-alone model that can be optimized using gradient descent based methods. Given that the attention mechanism has been shown to work well on a wide range of problems, the robust performance of the RWA model on the five classification tasks in this study is not surprising {{cite:5a3e58c1c4a2af45714cba7e643fdf8c5ca78d43}}, {{cite:015f47790a3a336e17b09d375fda78053d417844}}, {{cite:1c1bfb9111332526e8b63fba36e02fbdbf165e66}}, {{cite:7f71b0269c8ef5438ef472ae297610d9bb2ebf40}}, {{cite:8438918f38efb27c3e672bb85a24d0a58692264b}}, {{cite:dc1e6496a653cfffe445cf9ce47c778c9c84c372}}. Moreover, the RWA model did not require a hyperparameter search to tailor the model to each task. The same configuration successfully generalized to unseen data on every task. Clearly, the RWA model can form long-range dependencies across the sequences in each task and does not suffer from the vanishing or exploding gradient problem that affects other RNN models {{cite:f98749f628b3875df9d3e92211b83dccddaf51f8}}, {{cite:0434654936a9fb0464f39964454cc57ba3c88780}}.
| d | fae3014be641210756f7dbef9c57a994 |
In this section, we breakdown the quantitative analysis of Tab. 1 in the main paper into a per-scene analysis. Tab. REF shows the per-scene quantitative evaluation of our method in comparison with iMAP{{formula:c7ba57c0-f9b7-4759-aa94-c7a7de4d230b}} {{cite:d8c7f5d01724b76ef8a9f940f847fc022019042b}} and NICE-SLAM {{cite:5e2f89e47d4aecbd076404f293522a5eb23484cc}} on the Replica dataset {{cite:1c72d015a922220c6e9b607f20bc4ce2ebbaab95}}. As it is shown in Tab. REF , our method outperforms previous approaches in all scenes of Replica {{cite:1c72d015a922220c6e9b607f20bc4ce2ebbaab95}}. Also, lower variances in our experiments are an indication that our method is more stable from run to run.
{{figure:cd87873f-aeb8-41af-93d6-a237bbcd80c7}}{{table:6a1d4f72-9972-446c-a6a5-12a16f00708b}} | r | 9519b39121f9dc5b7bb78967ad435a08 |
FEM eliminates the need to calculate the gradients from the output neuron and provides a faster and simpler method to get an importance score of the input pixels based only on the features that have been extracted by the network. It does not examine the classification part of the network but uses only the feature extraction part of the CNN to explain the important input pixels that have been extracted by the network to produce the decision.
The method is applicable both for 2D and 3D images or video, considered as a 2D +t volume. We will now illustrate it in the problem of image classification from ImageNet database performed with the VGG16{{cite:889a5d8fb9127767408d49b849edb80f8f23e9c4}}. We propose the reader to visually compare the heat maps presented in Fig. REF obtained by using different LRP rules{{cite:d588cc2cb865a882ad36cf0532d777a880154055}} and FEM.
| m | 64094db3126d40eccc4e8920fdd1b9f7 |
To compute the probability of this event it is convenient to rely on the {{formula:fca42275-7d1c-4d9c-aae2-8b9884cf6d55}} -dimensional generalized spherical transformation of {{formula:93536408-a432-4fd5-b469-743e9bf297f0}} {{cite:f6c4e76dfdd602d3092b45254a016e0979678e2a}} given by
{{formula:84e7e6c4-5b42-48ef-9560-7594121be7b8}}
| r | 7e8c1b031b6acdd459e1651ddfa65762 |
After freeze out, the only mechanism by which polarization of a DM medium can be achieved is via irreversible processes like those discussed above. But this can only happen if the spin-flip rate aligning the anapole moment with the background current is much greater than the universe's expansion rate. When DM decouples, the universe is in a radiation dominated era, and the Hubble parameter is given by {{cite:ea5307a43ac93d428aba19f44c5a46affea7bd78}}
{{formula:ccec53bf-6355-4489-a865-df60a76c9033}}
| d | a6ee01823ef46bc518ac0f5b85808d2b |
Datasets. Currently, we perform experiments on the Something-Something {{cite:fd3395f6ccf956c65fe8d6362d455bdd6d795b19}} (V2) and the Something-Else {{cite:168f047c3d011db51c08138441279eb55e3b71c8}} (compositional setup) datasets. Something-Something is an egocentric video dataset of people performing actions with their hands, with 174 unique object agnostic actions, e.g., “pushing [something] left”. Nevertheless, the objects the people interact with might overlap between training and testing, indicating that RGB frames based models might pick up undesireable biases by overfitting on the objects' appearance to discriminate between the actions. Therefore, Something-Else proposes a compositional generalization data split, on which the performance of standard video models deteriorates. Here, the objects at training and testing time do not overlap, and hence, the models encounter strictly novel objects during testing (the number of actions remains the same, i.e., 174 unique actions). In future work we would also validate the performance improvements on a few-shot version of Something-Else, as well as the Epic-Kitchens 55/100 {{cite:b4fc366d011da1c27fd0ef7fa3ae6503cd01dd94}}, {{cite:98f829413e2fbd2a032f7b24d2ce5ef106dd95ca}} datasets – including long-tail actions and kitchen environments unseen during training.
| d | 1dea831c29e766c9b974a905fc1d5418 |
The presence of a permanent EDM in an elementary particle implies Charge-Parity
(CP) symmetry violation. Even though the phase of the CKM matrix of the Standard
Model of particle physics (SM) provides a large CP violating phase it results in
tiny electric dipole moments of elementary particles, too small to measure any
time soon.
However, many SM extensions permit large CP violating phases, which also
result in large electric dipole moments {{cite:7b5f307acb3dfd69a781ff9f79f02d5c59e7d664}}, {{cite:29e9daddd2708d957d4706c2322dad172090e6c7}}.
Recently, the muon electric dipole moment has become a topic of particular
interest due to the tensions between the measured muon anomalous
magnetic moment and the SM expectation {{cite:86a51668eb592fa55584ee4cb7932fdbdaaee134}} and hints of lepton-flavor
universality violation in B-meson decays {{cite:7d5d2073d3d8be1896ee91f59a76edc142bb31a1}}, {{cite:4dcf8369cc3531d45cbc983136e769da7f4af91e}}.
| i | 4649253fa238cf88869be05309151882 |
We assess the performance of HLR and HLR++ on these four datasets, for the top-{{formula:f42c0ad5-b80b-4caa-b493-6a38a122eb8a}} recommendation task introduced in Section REF , with {{formula:3f8d3a51-ab15-4352-8cea-2d0602c06659}} . We closely follow the evaluation protocol proposed by Sun et al. {{cite:4c7f257d99b1c5cdd0d5b4aed479022be2f235ce}}. Specifically, datasets are splitted as follows: 80% of user interactions are used for training, 10% for validation and the last 10% for test. Models must correctly recommend an ordered list of {{formula:a71952a7-70ee-4bb1-8d2e-cae9e5966c51}} items for which each user should interact with positively, in the validation or test set.
We report five standard evaluation metrics: the Precision and the Recall, for prediction accuracy, as well as the NDCG, MAP and MRR scores as measures of ranking quality. Last, as collaborative filtering is known to be prone to popularity biases {{cite:a0d251e7c28b53477d247f79b806ced7da267e48}}, consisting in recommending more popular content, we furthermore report the median popularity of recommended items. The popularity of an item is defined as the number of users who interacted with it.
| m | 0891a4b6c93a5e184a41a92becdcfdfc |
The success of the conventional theory of superconductivity {{cite:0099a3c2117cd27113249f4716016c1e7c6e9c8c}}, {{cite:07d375dcd35661448375d486acfe8ad8d4000145}} in the description of numerous phenomena observed in superconductors prompts us to consider the validity of the almost universal belief in the law of entropy increase. The history and the basis of this belief will be considered in the next section. In the third section, reader's attention will be drawn to the change of the sense of the law of entropy increase after the victory of the atomistic-kinetic worldview over the thermodynamic-energy worldview. The assumption of molecular disorder needed for the validity of the law of entropy increase and examples of its violation in quantum systems will be considered in the fourth section.
| i | 313e382db445963594c707f2961c4931 |
Autonomous mobile robots have recently started walking around us in shops, exhibitions, controlled closed areas around universities and innovative companies. However, human motion is unpredictable by nature, a mind state determining similarly to decision-making and inner motivation processes.
Still, recent data-driven approaches have made a great breakthrough on predicting human trajectories {{cite:3bc6add7320db4607c4090b36385730915693ca0}}, {{cite:230bd1ce29179f6e7cc149a91eb7e630cf84f21e}}, {{cite:6ca6ecb460745dfe9b27b49518db40f0e84d69b6}}, {{cite:acb09fdb975fd5dbf43a76f9f9e25077ce42b713}}, {{cite:ead94ed33b96f988efaefb400dd68bd4bb7186b7}}, {{cite:dc718b0ed79632acde772cb79615215ad221a234}} and allow researchers to focus on the most important aspects that might condition such predictions: environment, surrounding agents, past history, or how to interconnect all these components, a task unreachable for past model-based algorithms {{cite:adf3c90df5ea399ff917c00a05d4147ade12a2e6}}, {{cite:d9a68f427e6d00a6fb1e84a22cc8c5626f070a05}}.
| i | 1df77ab8fd530f2fb26fdca9d0b9de54 |
The delta method {{cite:441340b9e59d4adfa8675c63e2dd4c5d2b6adc2d}} is a classic approach that is widely used
with small models with an analytic Fisher information matrix
(, linear regression)
and, more recently, auto-differentiation unlocks
the delta method for a larger class of models {{cite:d68e816e17066b1b2743bb23f4df07cfffea7d35}}.
The bottleneck is the need to calculate then
invert the Fisher information matrix,
for which there are various approximations {{cite:8e2063a95a30efa42c09763f87cdaea494fe1545}}, {{cite:a90116f616420965f817734801379a7b31f3d5e2}}.
The delta method applies to a wide range of (differentiable) estimators subject to
regularity conditions that ensure asymptotic normality of the parameter estimates
and this constraint carries over to the implicit delta method.
The functional delta method extends the delta method to evaluations of infinite-dimensional parameters (see Ch. 12 {{cite:dec15c0ab442ee6f65ba5eaf35ee165a2b285df7}}) but is usually restricted to analytically deriving influence functions in theory by differentiating the population estimand with respect to distributions and then approximating the influence function by plugging in estimates of unknown nuisances {{cite:1a039790ebe6184b956dc7c536a31bee1ceeb65a}}, {{cite:ceaef2f7fbdf7dfff818c776ed27f51bbde41e8d}}.
| m | 69d2bdd1f9af85f213e60498dbca031b |
There is always a trade-off between privacy protection and other quality of models, such as model effectiveness or efficiency. It is well-known that cryptographic-based approaches require high computational overhead, and perturbation-based approaches could damage the model's accuracy.
Recently {{cite:2ae71a8427918aac13cda2ce7baa968daed70d58}} shows that applying differential privacy can potentially improve the robustness of anomaly detection when the training set contains noises. The intuition is that deep learning models with millions of parameters are capable of remembering all the training samples including the noises. In the unsupervised anomaly detection scenario, the model would consider rare samples, such as backdoor samples, in the training set as normal ones due to potential overfitting to rare samples. However, DP makes the model underfit rare samples by injecting random noise during the training so that the overall performance can be improved.
It is worth studying in what circumstances privacy-preserving approaches can also improve performance and robustness.
| d | 7ab55f5bd2878df874ac8a2f0f24c55e |
The original BERT paper {{cite:421e35fb99a1cfacfa2d68f8aca2a3ff76d26f58}} reports a perplexity of 3.23 for the 24 layer model with 1024 token input. The BERT Base model, trained on the same corpora has a perplexity of at least {{formula:1b2c4d5e-b387-4d1c-98f2-daf2379efb50}} both for English and Russian language. This can be explained by the significant variation in topics, and even languages, covered by those models. Since online social network (OSN) texts are a subset of the entire text array, training only on OSN reduces perplexity to {{formula:7ecf4031-ad58-414e-97bf-90946ac937df}} for the multilanguage BERT Base model (RuBert OSN). Further improvement is possible through the use of additional information regarding social vectors, allowing the evaluation measure to be reduced to {{formula:77d5645d-dce3-4f92-a6fe-2f267685ff81}} , as shown in Table REF .
{{table:1c41d240-9ebf-4d24-8f4e-2750c19350b9}} | r | 79aaaf8022a2160342e48e124926f4b4 |
The two findings directly lead to the proposed change in computational procedure as shown in Fig. REF , which reduces the computational complexity and accelerates the inference of the GCNs.
Here, the proposed techniques are applied to four representative GCNs {{cite:4b6093a02872ebbc0be126142680f0fdcf3eb436}}, {{cite:4f6cfceb2a3803abce5081abb82d3d930a1addf9}}, {{cite:c1db3b9b5efd393e0c492dff5fb2bbca27327a39}}, {{cite:441379820c2ba63444b7d60d0cd468c204641893}}.
It is shown that they can improve the efficiency of existing GCNs significantly, indeed.
For example, for ModelNet40 point cloud classification with 2048 points, compared with the original DGCNN, the accelerated version is about {{formula:29b84b55-200e-4ca4-8373-8863e327f9de}} times faster, reduces GPU memory by 57.1% and computation by 86.7% without loss of accuracy. More results are shown in Sec. .
Thus, the contributions of this paper can be summarized as follows.
| i | 7eb388b2cc650ff947ec0242de05957d |
This is equivalent to applying the nullspace
method {{cite:2e87c1a3419b4797792f7e71617cedd760b6e9ba}} to the saddle-point system sadsys.
| m | 0605869d0f584b3bc2c0d1d41e061e19 |
In this paper, we attempt to explore a knowledge distillation framework for learning to segment multiple organs combining a set of single-organ datasets.
In particular, we employ teacher-student models {{cite:7ac20dfb5f01a9ec1ec73e63ddd9129edcc3fc1a}}, widely used for knowledge distillation for image classification {{cite:d639411df7850151dbbc78e820734da126240eb6}} and segmentation {{cite:7ece8a2f0d0b499cb96eaf99f8978924f39ca1da}} tasks, which utilizes the soft pseudo labels or intermediate features from the teacher model {{cite:7708f2a816ce4810011248b6f72544015e3895fc}}, {{cite:102f13bfdc309da83073dc00556e679fb55948dd}} to train the student model.
In our case, we have multiple teacher models, each of which is a single-organ segmentation model. It should be noted that the above setting is different from a typical teacher-student model not only in the number of teachers, but also in that each of the teacher networks is for a different single organ segmentation task and they jointly teach the student to segment multiple organs (Fig REF ).
The classical consistency learning used by teacher-student framework thus can not be directly applied.
| i | 6059954c5142798843f6c8760979f473 |
Remark 2 Note that all the four schemes considered do not directly estimate the cascaded BS-IRS-user channels for all users, but leverage the previously estimated BS-IRS-anchor/anchor-IRS-anchor/BS-IRS-BS channels or reference user's cascaded channel, which thus makes their NMSE performance affected by the accuracy of the previously estimated channels. Based on the observations in Fig. REF , it is shown that by exploiting the anchor-assisted training, the proposed two schemes outperform the benchmark schemes. The main reasons can be summarized as follows: (1) as compared to the real-time estimation of the reference user's channel (in {{cite:2e13a9037001af6e7f5943b8bf4c8af2721e5f93}}), the off-line estimation of BS-IRS-anchor and anchor-IRS-anchor channels (in our proposed schemes) can achieve higher accuracy because more transmit power is available at the anchors than that at the users; and (2) as compared to estimating the BS-IRS-BS channel for resolving the BS-IRS channel (in {{cite:529f41eb7b8a3b1902791b549a5876ebfc054be9}}), estimating the BS-IRS-anchor and anchor-IRS-anchor channels (in our proposed two schemes) is more practically favorable, since the BS-IRS-anchor and anchor-IRS-anchor channels are much stronger than the BS-IRS-BS channel (due to the much shorter IRS-anchor distances). Moreover, it is also revealed that Scheme 1 benefits from increasing {{formula:ed901c14-1071-4fdd-a563-01d600656b50}} for not only the training overhead reduction, but also the NMSE performance improvement by exploiting the BS multi-antenna gains. Due to this reason, Scheme 1 can even achieve lower NMSE than Scheme 2 if {{formula:fbf1f87b-6e37-4f8e-b37b-4005c65d4619}} is sufficiently large (e.g., massive MIMO BS).
| r | 0200dcd6aa5b150b69b4c26860dc03ce |
VGG-f.
Since VGG-f {{cite:8e96cd364ace78aa6987f659bb2023ed4c6f3728}} is pre-trained on a distantly-related task, object class recognition, we do not consider it as a viable model to be included in our combination. However, the fine-tuned VGG-f model reaches respectable accuracy rates (see Table REF ), even surpassing the fine-tuned VGG-face model on FER+. We also note that our VGG-f model trained on AffectNet using down-sampling attains an accuracy of {{formula:7ef9da5d-19e0-4b04-a1e1-89cd9f074286}} , surpassing the AlexNet model of Mollahosseini et al. {{cite:ac246590a99df455bdc0bb237f688104a9fa2304}} trained using down-sampling, which attains an accuracy of {{formula:8e5719d9-e5ee-4cde-b503-adc03b95fc74}} . Although the two networks, VGG-f and AlexNet, have fairly similar architectures, we believe that the significant performance difference between these models is due to the DSD training procedure, which we applied for training all our CNN models, including VGG-f.
| r | 1ff6acd94c39e47046b6b02f88491d12 |
The whole flowchart of the neural networks based synthetic speech detection models is illustrated in Fig. REF .
Firstly, acoustic features are extracted from the speech signal. Then, several different designed convolution blocks are stacked to extract contextual representations of the input acoustic feature. Finally, the fully connected layers map the deep features on the label space of speech and the probability of being synthetic speech is calculated by a softmax layer.
In recent years, many acoustic features have been proposed for synthetic speech detection, while Mel-frequency cepstral coefficient (MFCC) {{cite:3cc714e5e900df3be799c59bd00189f5bd1b02fc}} and constant-Q cepstral coefficient (CQCC) {{cite:de7db23040246cfd8a42e4a2983a2a7169401704}} are two of the most used acoustic features.
In addition, light convolutional neural network (LCNN) {{cite:09d19d46c88bfaf1445d0a1557b75deaca28d6bd}} and residual convolutional neural network (ResNet) {{cite:81ef9281a1fb080f9624fa09c0c02874f67ca413}} are the popular neural network architectures used as deep representation learning and classification for synthetic speech detection.
Nowadays, several end-to-end synthetic speech detection models based on neural networks with mere the raw speech waveform have been proposed {{cite:f81b2b44cd802be2c636e1175ea76bfb4427c896}}, {{cite:a50c0b0fca23ab6ec5282155439dd1fa40fc5367}}, which could achieve satisfactory performance.
| m | 7419ff99be83400d2a9e56c521f164d4 |
Once equations of motion were found, we asked whether these equations match the ones already known in the literature. For TNC we showed that the equations in the present work match the ones obtained from world-sheet beta functions {{cite:705e775e9676685a38f93c7c2096943157c8863a}} when {{formula:58fcdb61-126c-4f88-8469-33559627c8b0}} , that is, contraction of the electric field with the field strength of the Kalb Ramond vector, in (REF ) vanishes. In its presence the difference between the two sets of equations turns out to be merely a factor of 2. The origin of this discrepancy is not clear to us, see section REF for a more detailed discussion. On the other hand, we showed that the SNC equations of motion obtained from DFT match precisely the ones obtained in {{cite:45790f6731675537646afba0182b75f8583207d5}}, {{cite:ee524d4aea41d3def7b5adbb99fd8a9d24bfe739}} from the world-sheet beta functions when the foliation constraint is imposed. As already mentioned, the generalized SNC metric reduces to the TNC one in a particular limit, which implies that the equations of motion will also reduce to the TNC ones. Recalling that the foliation constraint reduces to the torsionless limit on the TNC side we conclude that the SNC beta functions {{cite:45790f6731675537646afba0182b75f8583207d5}}, {{cite:ee524d4aea41d3def7b5adbb99fd8a9d24bfe739}} reduce to the TNC ones {{cite:705e775e9676685a38f93c7c2096943157c8863a}}, which is consistent with what we found by embedding both theories in the DFT framework. It is worth stressing that the discrepancy between the TNC equations and beta functions disappears in the absence of {{formula:2cfe11f6-cb67-41de-87b1-304dfb6086a7}} , which is also implied by the foliation constraint on the SNC side. The full (non-linearized) SNC beta functions with {{formula:51602e16-213f-4dd4-ad9b-c30b7afe000b}} are not known, therefore we are unable to tell if the discrepancy we find in TNC theory will also appear for SNC.
| d | 7ac8b82fedb0f2570061d764ec32c5a6 |
Synthesis and crystal structure.
Polycrystalline sample of NdTa{{formula:a3bf8965-8f77-4d3f-b2f2-14d6771cbf77}} O{{formula:9022a939-d023-4cd9-ae81-bdc186346360}} was prepared by conventional solid state synthesis method from high purity Nd{{formula:a84605ac-5e6b-4864-b301-0cb007ef78ad}} O{{formula:1d236f84-18ab-41c7-b9df-99a7d6acb443}} (Alfa Aesar, 99.994%) and Ta{{formula:e4a5e61f-f9fa-4c76-9f5a-635f604334e9}} O{{formula:680aeda1-1dcd-40f8-b589-7dd4469fa1fb}} (Alfa Aesar, 99.993%) {{cite:30991e4514e220a70a1bb1600269483d8689f223}}.
Prior to use, Nd{{formula:54a00fef-ca86-4366-85e4-648279bf2deb}} O{{formula:4f9d45d1-3eab-4aff-b3d9-05fe17d2d6e7}} was preheated at 900{{formula:e13bf789-0eab-4874-8e62-b339e57fce2d}} C for 12 h.
Stoichiometric amounts of each material were mixed and pelletized.
Single phase NdTa{{formula:35a5d232-05eb-4b0d-9da6-45205a0bee6f}} O{{formula:547c4307-5641-4027-8980-db6ef3cda24d}} sample was obtained after heat treatment of the reactants for several days at 950{{formula:efec8efc-f7de-4f4a-9db5-f10ef0f675c8}} C, 1000{{formula:eb49819f-4580-4eea-94c9-0425bace79cf}} C, 1050{{formula:d4667e61-0a79-40ab-9ae2-72418fcba721}} C, 1100{{formula:e9c383b9-8817-45b9-ad5c-58b9706d49eb}} C, 1150{{formula:e84c52cd-7c67-4686-b02f-fac6d99f9f48}} C, and 1200{{formula:fbc19c27-7b9e-492a-a80d-17d91668b2dd}} C with intermediate grindings.
Its phase purity was checked with Rigaku X-Ray diffractometer at room
temperature using Cu {{formula:a1fd1ca9-d361-49a9-89c3-f392f2b0caf5}} radiation.
The Rietveld refinement was carried out within the space group {{formula:d72370fe-ac89-417e-aed1-f11498f758d6}} using fullprof suite {{cite:c30ba44aecd14c4e52f7618c6684a96a72241a29}}.
The results are shown in Supplementary Fig. 1 and the parameters are summarized in Supplementary Table I.
No anti-site disorder was detected in this compound.
| m | 476616723c78eb537026d40cf6b4687e |
CNNs have served as the defacto architecture for medical image segmentation for the past decade including UNet {{cite:9d01c24079d035fc5162170c0fd23a01a4095897}} which follows an encoder-decoder based architecture utilizing skip-connections to retain multi-scale features. Since then, extensive research has been done to leverage this design and propose mechanisms which can capture global context. Recent advent of vision transformers has released a wave of methodologies which has further pushed the envelope of performance on computer vision tasks {{cite:9c0d4f62af52bc699ff1255148a6e9e2d756dbbc}}. Medical image segmentation has also seen an influx of transformer based methods which leverage global context achieved by the self-attention mechanism {{cite:fa16a8f51d67a23bb8cc029cef811a28cb4433fb}}, {{cite:c785180ed4ec3516d952b21bb3f645a898db0290}}. Such methods have recently achieved SOTA performances on array of medical imaging tasks including the segmentation of multi-organs{{cite:0021e8a7462fa63cb3ca2e5f6336156ced054c81}}, cardiac {{cite:319a8e5c41d8a15b9d5850b71526efa91318b579}}, and polyp {{cite:8132418c693b91717a8216f81cbe699626ba5912}}.
| i | 7f3cd9b25ca43acf81bb9852780e0ea4 |
DistgSSR {{cite:727fa83b3cf80097c0e725c3838ac02a03bb0224}} and LFT {{cite:f1a0b52c2520f130e9b58a20fa587e135ab0e8d5}}: two top-performing LF image SR methods developed on the bicubic downsampling degradation;
SRMD {{cite:ade05958ec695a6cb2b11e55a7691ae05957c782}}: a popular non-blind single image SR method developed on isotropic Gaussian blur and Gaussian noise degradation;
DASR {{cite:640d5ac02d8c19100b5095665ec976d1f1311224}}: a state-of-the-art blind single image SR method developed on anisotropic Gaussian blur and Gaussian noise degradation;
BSRGAN {{cite:dc653cf0291c59915b5633a1a3363db7ae0ccb5c}} and Real-ESRGAN {{cite:47ed98398f9d3c1e5d465d24f86cba59b9fcfc3f}}: two recent real-world single image SR methods developed on the complex synthetic degradations.
| m | 3188cf4854792427d8788eb25b54879b |
Pulsars are rotating neutron stars that emit broadband radiation received as pulsed signals
by the observers. The pulsar radiation reaches the observer after propagating through the
ionised interstellar medium (IISM), which disperses the pulsed signal, thereby delaying the
times of arrival (ToAs) of pulses as a function of the observing frequency
{{cite:556bcf6c45f95b1b75cf01e338c3b33e6c6e7efc}}. This dispersion delay is directly proportional to the
integrated column density of free electrons in the IISM, usually referred to as the dispersion
measure (DM), and inversely proportional to the square of the observing frequency ({{formula:4da18a64-eb51-4e50-bf8b-a8fefff90951}} ).
Precise measurements of the DM can therefore be made by measuring the pulse ToAs simultaneously
at different observing frequencies {{cite:5656902d76c5d78717642ab6c0f6f7f3163eb4d4}}, {{cite:32a4ca5a164ed2a3a71ee6529f5bb12cc301db08}}, {{cite:2ea3f79f55b1af0b2473afa2e5d6f70d3139a4b7}}.
| i | ea8499941e38637642b34e8c279fe8cb |
Following {{cite:ee48ac3ac00ee48491afd81c42a84f2ce21148eb}}, we applied the procedure proposed in {{cite:de09ce5133f2cb1362cc2efda9e3dd20615cae55}} to calculate the tracer sidereal rotation rate
{{formula:afda7827-0c35-4c5d-8d9f-7c9180050a1c}}
| m | 11d7c42907c61329d4618a65d9e3bcae |
Ensemble methods belong to a family of architectures with a long pedigree in artificial intelligence that begins with Selfridge’s pandemonium architecture {{cite:37d22c7a03185e779a7edade358bb492fcd927f7}} and includes Minsky’s “society of mind’’ {{cite:90c27c420ace2b52a5d97ecb2fe16d2b7a682eb7}}, the blackboard systems of the 1980s {{cite:9e01076871b55ed74aee66ddb316641aa3340b15}}, mixture of experts models {{cite:664f9502f993cda8b565a7fccc43aa2c2a5cd87e}}, and global workspace architecture {{cite:30135e3c7417c4b1a3b6455b79dd7a6292e1d1bb}}. All of these architectures feature sets of parallel, independent modules or processes that compete and / or co-operate with each other to collectively determine a system's behaviour. The profound benefits of such architectures – which are manifest in the biological brain as well as in engineered systems – can be summarised in three maxims. 1) Competition: selection from a pool of processes or modules encourages specialisation for different contexts, and the right specialist in the right context will out-perform a generalist (“jack of all trades, master of none’’). 2) Co-operation: when independent processes or modules specialise in different aspects of a situation, their expertise can be combined in a compositional fashion, which aids generalisation (“divide and rule’’). 3) Collectivity: the aggregated contributions of a diverse set of separate processes or modules yields better performance than any single monolithic process can (“the wisdom of the crowd’’). In this respect, the choice of an ensemble method to deal with catastrophic forgetting is not ad hoc, but is part of a larger picture wherein modular architectures are used to address some of the deepest problems in building AI that approaches human-level intelligence.
| d | ca791e008b08e51fd15401c6d9493246 |
To interpret the performance differences for depression detection between our DMSN architecture and DMSN-A, DMSN-B, DMSN-C models as well as P3D, we present the class activation maps (CAMs) employing the Grad-CAM method {{cite:bb9dcf74bdb09fddb6530c8e7b16543449caac8a}}. In the visualizations of Fig. REF , lighter colors represent those regions that are most relevant for a model's predictions. Considering the most activated regions, the models appear to explore the eyes and mouth regions. In fact, these regions convey important information about depressive states. As we can see, our approach is more effective in exploring such areas than
P3D. In comparison with DMSN-A, DMSN-B, and DMSN-C, DMSN seems to be more successful in capturing face expression variations from these areas. We understand that this capacity of DMSN is a decisive factor for the good performance in depression detection.
| r | ed7616ad67525e85a88690ccf1f90a47 |
The gas expulsion process can also significantly affect the dynamics of the star cluster during the gas embedded phase {{cite:83f3999c19d0059e5a0ed545c3dd0f4da9b8fa0c}}, {{cite:34e3b37866059218acfdce2e87b9abb1bc294a15}}, {{cite:9537536f0b467397b32f877ed9954dece1c603c8}} and the formation of tidal streams {{cite:68fcace2ac63347d4554da59827ddb631f7afad1}}, {{cite:7077ff499af31bc2d8b2da8622a75b29c604fea5}}.
The UV radiation, stellar winds and supernovae from OB stars all can drive the gas expulsion.
Thus, the gas expulsion is also sensitive to the stochastic nature of {{formula:53396b29-cd4d-4b4d-a7ad-6dfbc206baa1}} .
A stronger feedback because of more OB stars may quench the star formation earlier, and thus, the star formation efficiency becomes lower.
As a result, the damage to the stellar system is also stronger and a larger number of escapers is expected to appear during the first few Myr.
By considering gas expulsion, we expect an even larger scatter of the evolution tracks due to the variation of {{formula:59acfb86-4f1e-4ba5-abca-716dcb740645}} .
| d | 6c673d090cae5d1c19edea42640db40d |
Here we discuss several exciting future research avenues that can address current limitations of our method. While the disparity estimation network outputs dense disparity maps for each view, we do not explicitly utilize the estimated disparities for 3D object detection. We rather use the disparity estimation network as an intermediate medium that allows the image backbone network to extract 3D aware image features for overlapping regions as shown in Fig. REF . Although we have shown that such indirect guidance already adds performance improvement to the object detection head, explicit utilization of the estimated disparity maps or depth maps would give us better performance. As a future work, we would like to improve the performance of the stereo matching network and integrate the network with the object detection head for better utilization of the estimated disparities.
As mentioned, instead of a dense depth map, we use a stereo disparity map obtained from the overlap region to utilize 3D information of the multi-view scenes for 3D detection network. This significantly improves the accuracy of the 3D detection pipeline.
Therefore, there is plenty of room for performance improvement if the dataset contains the dense depth map to inform dense 3D geometric and uses the dense depth map to replace stereo disparity map estimation with dense map estimation on the overlap region. In terms of training computation complexity, many 3D object detection methods rely on CBGS {{cite:98cd64c90f53b17069e852eea9a8c78a3880ba71}} to improve the performance, regardless of increasing computation complexity approximately four times. However, our proposed method achieves state-of-the-art results without using CBGS method.
| d | 651a47d17577af7306c46eb15a49112f |
For the {{formula:de980749-e310-4c63-adee-4068349dc75c}} matrix multiplication in neural models,
we refer to {{formula:de0bae7f-8ac1-410b-bf77-3efa20c8202f}} as weights, and {{formula:fcb4e550-b675-42ea-814a-b325453e1244}} as features.
Weight-based methods {{cite:af3c3f19617540572227012ebd4dbac3443ef330}}, {{cite:eafb01723280a8bcdf72f9b3005fb2b973432636}} prune networks based on values of {{formula:9e6bb71c-9d28-462b-bc16-e84d0f12ab94}} , removing features with smaller weights,
which are comparable to {{formula:f8c3e28a-7bd0-4114-82a3-5b853ca2b4da}} or
{{formula:7bbbe4ef-7bf4-4a7e-afe9-ce6b076dff98}} regularizers for feature selection {{cite:673c4308cddb18c9d4d8aecda8fd19a5a151ce34}}, {{cite:f7596f76638948ef404ed8792e8b1be44301508f}}.
MI-based pruning method is comparable to MI based feature selection, which
attaches attentions to the features by measuring
feature-label
correlations {{cite:0e052f99997c4ff36d2a1e5296471f5720e6b481}}, {{cite:97f60d61d4ef77c89e68465b88e8f882ededa8ce}}.
| d | 7e8a4f8db8e52cc8bfb843ace2b06941 |
In summary, by leveraging insights from neuroscience, we designed an original brain-inspired deep learning architecture and thus add to a growing body of literature exploring the cross-pollination of neuroscience and AI. On the one hand, the current study demonstrates that we can effectively use neuroscience principles to design artificial computer vision models, and probe them using classical stimuli and illusions from neuroscience and cognitive science. On the other hand, we also illustrate how modern deep learning techniques can be used as powerful tools in examining our theories of brain function {{cite:7cc3c9827b01af46f8002fab97fb14389c08b951}}, {{cite:15aae7049a12f57894d4f31c9c1452aa62b8ce74}}, {{cite:bfa6a02ac50019ffc34409a8c46a0d2f715cb035}}, {{cite:347de5917822911859cff986f8a97ec0f9e66724}}. By building and testing a brain-inspired model, the current study highlights the essential roles of feedback connections {{cite:f8efd95357c33a70e572d9569ab1ac4f2a0b209a}}, {{cite:b95a2660a4e47e2832de29dc567b01ad8f6da7b2}}, predictive coding computation {{cite:d36ce3a6d5bfc62cd44b310772c53df79be071b7}}, {{cite:19e5ef524c29769acef8219b37e75d7468767e4a}}, {{cite:86c9b3396cd5b569d1eef8df7aa0c4c38e6c5df5}}, {{cite:72eaa46c957d52e4403122dda824a68dcd5a0e8e}}, and prior experience of natural environments {{cite:284fee265b65a1d033c6b91671ecbde87d1393bd}} for the perception of visual illusions. Future work could use the same kind of predictive coding model to test other aspects of the predictive coding theory in neuroscience, such as its tendency to produce oscillatory dynamics {{cite:32206a84acca3279f07c7f26ea98e26284d49b18}}, or other phenomena observed in human vision, such as ambiguous stimuli and multi-stable perception, or the Gestalt rules of perceptual organization.
| d | 2cc12cfab70e441b5e999a3602224745 |
To extract visual features, GoogLeNet {{cite:fcfdbe0bc2140f7d6b5e26215cf84196a91e2914}} or
Inception-V3 {{cite:9202b93b16f7bf4d9e6e23624799f54219aa1de2}}
were applied
as base models.
GoogLeNet {{cite:fcfdbe0bc2140f7d6b5e26215cf84196a91e2914}} is a 22 layer deep
CNN and was the winner of ILSVRC 2014 with
a top 5 error rate of 6.7 %.
Depth and width of the network was increased but not
simply following the general method of stacking
the layers on each other. A new
level of organization was introduced
codenamed Inception module (see Figure REF ).
In GoogLeNet {{cite:fcfdbe0bc2140f7d6b5e26215cf84196a91e2914}} not
everything happens sequentially like in previous
CNN models, pieces of the network work in parallel.
Inspired by a neuroscience model in {{cite:74c99ebe3d5a6fe973b51317c21ccd942af9207b}}
where for handling multiple scales a series of Gabor
filters were used with a two layer deep model.
But contrary to the beforementioned model all
layers are learned and not fixed.
In GoogLeNet {{cite:fcfdbe0bc2140f7d6b5e26215cf84196a91e2914}} architecture Inception
layers are introduced and repeated many times.
Subsequent improvements of GoogLeNet {{cite:fcfdbe0bc2140f7d6b5e26215cf84196a91e2914}} have been called
Inception-v{{formula:a0fdb9db-0adc-4128-a1cf-8247c8b3071b}} where {{formula:c42bd954-b07d-4e8d-b298-aaaad0ea7513}} refers to the version number put out by Google.
Inception-V2 {{cite:9202b93b16f7bf4d9e6e23624799f54219aa1de2}}
was refined by the introduction of
batch normalization {{cite:4c876a13a718e9520839c52326e7da8c05c23b8d}}.
Inception-V3 {{cite:9202b93b16f7bf4d9e6e23624799f54219aa1de2}} was improved by
factorization ideas. Factorization into smaller
convolutions means for example replacing a {{formula:96e61ba4-538f-4c5e-bc8c-d12af6d86d6e}} convolution by
a multi-layer network
with fewer parameters but with the same input size and output depth.
| m | 8380104c8c23119cc260022abe060358 |
and shown in Table REF . It can be seen that the obtained soft photon's energy for each FSRQ is about a few keV. For FSRQs, the number density of the soft photons at the keV band from the dissipation region inside is very low and cannot absorb {{formula:b09f9e04-54e9-411a-8bc7-0a6d9ba93da1}} -ray. Therefore, if {{formula:bf6ef87a-c6e8-42aa-b80a-648579d2a2db}} -ray is indeed absorbed, the soft photons must come from the external photon field. In AGN environment, the hot corona surrounding the accretion disk could emit X-ray photons from 0.1 to 100 keV {{cite:8f1ac24ca00619e6ea730209303bafbd9bf1a11f}}, {{cite:eb3cbc80e8888b2443d7bcfd635ba9928549fd9d}}. If the X-ray photons emitted by hot corona are boosted in the dissipation region, the dissipation region need to form in the corona region. Therefore, we assume that the dissipation region is near the jet base with a distance {{formula:4cf21bcb-a669-4326-88c8-b6e6d12e78b0}} that comparable to a few times larger than the Schwarzschild radius of the central SMBH. If {{formula:2cc9cc33-4325-4c1d-9e82-22f997b9a75e}} , the required minimum flux of soft photons to absorb {{formula:3a46b1c3-b1a5-4f80-99cb-21f43c46d21d}} -ray can be given by {{cite:3f2c9a513549c993a78c109e1122e2dc14ef4c30}}
{{formula:9c0e9fde-5ca4-4a9b-aead-9fa0c96ab5b7}}
| d | 58e17df75bdf27c8fc517ff9038674ce |
In general, it would be interesting to see what is a maximal local closed sub-sector of the holographic dual of Chern–Simons Matter Theories. We expect that Chiral Theory covers all of it. In this sense, the relation between our results and particular vertices of {{cite:9f5d42fab7978d19641fab83a0ad834b8bba55cb}}, {{cite:ea56aa923bb7d801ba62049c4e792d4e0ccb2998}}, {{cite:ccc260d5e64a51791bc989a469c159fdd564ac75}}, {{cite:492c1670c4e89ca72bcd9d67f0c0e8a74dc1761c}} is not clear beyond the lowest orders.Cubic vertices decompose into chiral and anti-chiral parts {{cite:fa96d6d693d7c561c87f6c576537e87fc96e4ef0}}, and hence, different truncations – holomorphic/chiral/self-dual – mean essentially the same at this order. Note that the usual cubic vertices from the Lagrangian vantage point appear in {{formula:76d83cb7-b6f1-42fd-8944-325e7b4b3e32}} , {{formula:36d6a696-d221-4872-8c97-8778d58058a0}} and {{formula:90924df5-fcd9-4210-8e0a-485b83e8f0f6}} . There is an infinite-parameter ambiguity at higher orders {{cite:0ffd26b54e741865fb94cc3e7e16734a2cf139d6}}, {{cite:f7269b6b8faac3ba48dfd8fec7fcc872d221c4c5}}, but this analysis does not take locality into account, which may eliminate some parameters as well as to introduce new ones. It may well be that there are well-defined, in the sense of being local, holomorphic subsectors of {{cite:0ffd26b54e741865fb94cc3e7e16734a2cf139d6}} and the question is whether they are smaller/larger than Chiral Theory. One way or another, Chiral Theory in {{formula:f662a46e-e4f2-4ea6-9045-1a5992841bc8}} is directly constructed as a smooth and local deformation of its flat space cousin {{cite:a431a918b545c5a47cc42a86dc65f3fef60c6674}}.If Chiral Theory in {{formula:eea2e749-1f76-4bbf-9b97-2b56df38fc46}} corresponds to the local form (not yet available) of the holomorphic vertices of {{cite:0ffd26b54e741865fb94cc3e7e16734a2cf139d6}}, our paper gives a `one-line solution' in all orders that provides an alternative completion to the low order analysis of {{cite:9f5d42fab7978d19641fab83a0ad834b8bba55cb}}, {{cite:ea56aa923bb7d801ba62049c4e792d4e0ccb2998}}, {{cite:ccc260d5e64a51791bc989a469c159fdd564ac75}}, {{cite:492c1670c4e89ca72bcd9d67f0c0e8a74dc1761c}}.
| d | 1f47deb6747ebc690358177cfe5d6415 |
For estimating the variance of parameter estimates in the outcome model, we compared a resampling approach and a novel analytic approach for a logistic regression model that accounts for uncertainty arising from the propensity weight estimation. In empirical studies, we found the proposed analytic estimates performed better than the bootstrap estimate. Surprisingly, the bootstrap estimate tends to overestimate the uncertainty even though we replicated the estimation method within each bootstrap sample. Perhaps there was more variability in estimated weights within bootstrap samples than within the full simulated data set. Previous work on implementing entropy balancing weights ({{cite:f77db7c5d701138df01ec6bca7cf6f59344472e3}}) and exact matching using the propensity score ({{cite:09383d8d6ee9c7b0a975593acf52354b205e8aba}}) also reported conservative bootstrap variance estimates, but the stratified double bootstrap where units are resampled from the survey sample and convenience sample used by {{cite:3dbda4eee3688ed26077db33108a199f52c15681}} provides similar variance estimates to a design-based approach. The proposed analytic variance for model-based propensity weight estimation methods accounts for uncertainty in the estimated weights. The design based standard errors, however, perform well even though they fail to account for the propensity weight estimation process. We suggest using the proposed variance estimator with a model based propensity weight estimation procedure because it may perform better than the design based estimate, but the design based approach should perform well if needed. In our context, the two methods did not diverge substantially, but they could if there is high variability in the propensity weights. It is possible to derive an analytic variance estimator that accounts for the weight estimation for the CBPS model. However, it is made difficult because the CBPS model is overspecified and fit using generalized method of moments ({{cite:5a6a3de02c5988d25e23a1b8f764bd01013de0dd}}, {{cite:d831c2c613cc745ad2ac9a56c4f6ab19f7c935da}}). One might be able to incorporate the final scientific model into the CBPS model as an additional balancing constraint for a simultaneous estimation approach. This may be an interesting area of research to pursue.
| d | 26e986bf269059e61734de0c756d91aa |
where {{formula:86768945-5c76-47b7-bab3-d9bcec4cf2b7}} stands for the t-product {{cite:50777014646301d8b7c6bd2dfe992fa6257e043f}}, {{formula:23282805-33a2-4469-b561-435a25954890}} and {{formula:bd597eda-2940-42a0-94fe-166694a5b09c}} are some sampled lateral and horizontal slices of the original tensor {{formula:45585be9-b9e4-4962-9db7-a969613c2b17}} respectively and the middle tensor {{formula:cdcc2790-a149-4e0d-ab01-c9c585a95b4f}} is computed in such a way that the approximation (REF ) should be as small as possible. For the brevity of the presentation, we have provided the details of different tensor CUR approaches in Appendix II.
| m | 2493380588c06daae5bbb8b89e4e2a17 |
However, the basic model for MPMAB in most prior works assumes that players have full access to all {{formula:de5cb91b-e5e9-41bf-bbbe-f01933719221}} arms in each time. This neglects several important factors of systems for many real-world applications, where each player can only access a subset of arms that dynamically changes over time (i.e., an arm could sometimes be “walking” and not accessible to the player).
For example, consider the problem of content placement in next-generation wireless networks (e.g., 5G/6G) {{cite:6c4494d2cbd7af703f8481b427b77bf66c3c04b0}} where {{formula:4adabcfc-1389-4b16-8a10-77ba637c5fd7}} cache-enabled base stations (players) serve a region where mobile users request for {{formula:05541220-6e15-4938-9d0d-1c51f9110d36}} contents (arms), e.g., movies, videos, etc. Users receive a large reward (e.g., a short latency) if the requested content is stored in the nearest base station, otherwise they are served by farther base stations with a small reward (e.g., a larger latency). The base stations initially have no information about users' content requests and contents' global popularity since each base station only have access to a subset of contents due to its constrained cache size. In reality, users' content requests are highly dynamic and hence each base station needs to repeatedly determine the subset of contents to be cached so as to maximize the total reward of serving users. Another application is mobile edge computing {{cite:7c8232df0a55d241cabeef6f847a5d0c33013680}}, {{cite:de1928760ebd9d11cbde4b6f535030b92fbd385f}}, where edge clouds (arms) with computing resources form a shared resource pool, which can be allocated among user requests (players) that only have access to some edge clouds within the same geographical region. Additional real-world applications where players only have access to a subset of arms are presented in supplementary materials.
| i | 7fe10b0bd65f7b10060d54a5da51bbc1 |
We consider only trees, but similar results should hold for standard generalizations of the model with more edges (e.g., {{formula:3785f0cd-5000-4459-b518-4410aa9e40a2}} edges are drawn at each step, {{formula:155b84a6-b737-415c-8af4-a6173dc57b58}} could be random). Such generalizations are of interest because their graph properties are more natural. For example, commonly, the diameter of the model is close to the diameter of a real network for {{formula:a8579f42-0e00-4ac1-a19d-e98dc308f06c}} (see, e.g., {{cite:cb848fc19db6002a24aace1fa0022b28fecdf7d5}}, {{cite:c9333d94e4fa777bd8840329df94b0d28e492321}}). To achieve such an effect in our model, one could consider models in which the choice is made with respect to some other criteria. For example, coin toss among vertices with the same degree could be replaced with a choice that minimizes a distance between the new vertex and the vertex with the highest degree.
| d | a34a2a55d7a5720131e7f36423a4192d |
In previous work TlNi{{formula:c477e7c2-0867-45b0-a9b1-e4007fee6839}} Se{{formula:ce67ffb5-cbbf-4ea9-a845-baf1d3a9ffdb}} showed some evidence of potentially being a d-wave superconductor {{cite:8ad11be6a46739c7796aba9963c05234533feae9}}. Generally speaking d-wave superconductivity can be identified in SANS studies by a change of the VL structure with field or angle {{cite:c1a46e86a7b0ae1f088e74e5d6e851d0597ae25e}}. In this investigation we have seen no such rearrangement. This does not preclude the existence of d-wave pairing entirely, but it is far less likely. Anisotropy is small in the VL with field and angle variation but has a consistent relationship with field variation and reflects a possible shift of flux lines attempting to align with the fourfold crystal structure. Previous photoemission and Raman spectroscopy measurements by Xu et al demonstrate van Hove singularities (VHS) with fourfold symmetry about the Z point in the FS {{cite:b5b390115fabbafbba00f682cc04d2d44d90d6f0}} (these VHS are held as the explanation for the observed heavy-fermion behaviour). We also see that by rotation of the crystal, the anisotropy can be minimised.
| d | 5a881671053d7330a77835432aa81507 |
Farhi et al. first proposed QAOA {{cite:56d243582ee60e75b5c9bbf55589010765d3135b}}, and studied it in the context of finding a maximum cut in a graph, known as the Max-Cut problem. For 3-regular graphs, they showed that a {{formula:7ba6cb4e-d0b9-46c8-9109-c5848c92cd33}} QAOA achieves an approximation ratio better than random guessing, but lower than the best known classical algorithm {{cite:3f01408b685223dfd79c0fe66a46d45d01b7058e}}. They also argued that the expectation value of the cut produced by the algorithm is a non-decreasing function of {{formula:e85de9a0-4a53-46ac-b16b-5638c175a895}} . Therefore, QAOA is expected to be a potential candidate for quantum advantage using near-term devices. Many researchers, since then, have studied QAOA in the context of the Max-Cut problem {{cite:2c59971e08e2e52d52b74aac7ee0c05701cc34fd}}, {{cite:b269fa72723a932dc92efaf1189a57c639c2a376}}, {{cite:adf093bf5ca4fbbbef261038045ff588d1b3c79b}}, {{cite:fd4505e664b5f09241d5b75b1087a5d477de6b64}}, {{cite:1d44ca0b4b8d0ca9ff63910b97cb001698cb7a5e}}, {{cite:6ea4c91bd598305c2b21dffd6b05770311fe2dcc}}.
| i | 88ff5a31af3ff40dbdec7a350b017f57 |
Image-level adaptation, such as {{cite:bbad1d1083103cb3d42c916dcb2f2c65e717a5bc}}, {{cite:e4022e9cc120c3ec92147e7caf88c51d3941a3ad}}, uses a generative adversarial network (GAN) {{cite:7f44bee48fbe399cd2d2d032ceb30a173100846a}} to transfer the image styles of the source domain to a target domain. Feature-level method like {{cite:db2dad382aba94afc7d726f1e5e6ce5ac7a55a3e}} investigates underlying feature invariance. However, the performances of these approaches are still unsatisfactory when compared to their fully-supervised counterparts. Recently, several clustering based methods, such as {{cite:0a370b599ff22b21f716125935e37d934d14eb53}}, {{cite:2fc5417269cf3bad4ffcf2276c848c07055cc181}}, {{cite:ac31108286c4f2c2814c36892c0e07786999ade1}}, {{cite:231731f3aa8ca7fbb3c11fe94b911942fa449548}}, have been proposed, which employ clustering algorithms to group unannotated target images to generate pseudo-labels for training. Although they achieve state-of-the-art performance in various UDA tasks, their abilities are hindered by noisy pseudo-labels caused by the imperfect clustering algorithms and the limited feature transferability.
| i | 464ce36aff490450394c9fc150d4d9cd |
The problem that Byzantine-tolerant training algorithms cannot solve is the backdoor problem {{cite:862920be737e7b97c86f2e87fe379f15f5edd351}}.
The backdoor attack is a hybrid of training-stage attack and inference-stage attack, which is very different from pure training-stage attacks such as the convergence-preventing attacks, or pure inference-stage attacks such as adversarial examples {{cite:a30037daa8894af9b253f68b59ec4a9f1ec1f5be}}.
On one hand, backdoor attacks preserve the model's normal functionality on benign data so that the backdoor is hidden.
On the other hand, a set of attacker-specified triggers (a.k.a. backdoor triggers), such as small patches with particular pixel patterns, can control the model's behavior when those triggers appear in the model's input.
Injecting a backdoor can be viewed as a multitask learning, where the main task is the correct classification on benign data, and a side task is the attacker-controlled behavior on data with backdoor triggers.
Even if Byzantine-tolerant training algorithms can guarantee the convergence, learning of the side task cannot be prevented.
Attacks that successfully bypass Byzantine defenses are shown in various literature {{cite:bf96e1269573845c320217eb6da7b75880fd45f5}}, {{cite:3dc7ac7356587484c51404534aee3a6e1d1f5687}}.
{{figure:e675e5ab-102a-4a61-9375-e6049c90763c}} | i | 17ca0729dd40768333a066a2b5af8634 |
However, the partial decay width of the {{formula:7219bff5-6952-48cb-8c9c-1785f26314b2}} is much smaller than that of the {{formula:bc99b30b-8737-45ac-aa3c-1e5723e65ee1}} three-body decay.
Detailed numerical results are listed in Tab. REF . We find that the {{formula:f38d1e78-ca54-4212-a70f-f8c364f013bf}} three-body decay width is estimated to be 125.79
MeV at {{formula:e8c9201e-f927-4fb5-b8f7-eb27ce931ca9}} GeV, which is approximately five times bigger than that of the {{formula:68e09959-2309-4ea4-a007-9cbdd6448000}} . It is because that the
{{formula:ece96263-a408-4d30-afd0-9d31a7e81557}} assignment for {{formula:eb38063c-020e-4551-8b05-dce34a5e0788}} can decay to the final state {{formula:a3181344-e965-45d6-8025-a00b6e7b3022}} by occurring at the tree level, rather than via the
triangle diagrams for the {{formula:82ed2343-df49-4d97-af61-92b0a2b44d49}} decay. And the two-body or three-body decay modes of the multi-quark states through the tree
diagram are usually the dominant ones. We also find that the partial decay widths of {{formula:4d705c34-6401-4c5b-be77-d37af14647e9}} and {{formula:032ab31f-3ddf-41e6-bdcb-a41ed3b59953}} channels are
smaller than that of {{formula:dcaca6ab-1d30-464c-9741-d484644e81f3}} channel due to the relatively small space phase. The more important reason for this is that {{formula:ff900772-3e14-4ddf-8b9d-2deb9f14da98}}
has the largest {{formula:23098400-eed1-47e8-8944-9e54df58aa5e}} decay branching ratio, while the decay widths of {{formula:831f1ec2-c34d-4f31-97fd-f51fc500fe83}} and {{formula:ec85f363-594a-4489-bdb5-48e0e0017ffd}} are quite small,
about {{formula:b939e02a-bfed-4cc3-ae2e-3a4bef2a6c16}} and {{formula:a2913f8d-891f-4188-9cbd-cbc13d21934a}} of {{formula:e1f9b3da-2515-498e-996c-85285936b426}} experiment width, respectively {{cite:e841ab5c620ecb912f4ba772f197f72640bc5bab}}.
{{table:526bfcb2-610f-4d59-a68c-2cd8ed9dbf7b}} | r | eef1cbc1b84ae76799b45937327b85c5 |
Local contrastive
In dense predictions tasks, we desire a fine-grained pixel wise prediction rather than a global one.
As such, we further investigate the difference between global contrastive MoCo v2 {{cite:6ffb9e54a6782c912e8a10af2d965de684acf726}}, and its variant DenseCL {{cite:e0e5b6e9030ffed0bed76e1affd75eb9df08f4ce}}, that includes an additional contrastive loss acting on local representations.
{{table:4338bce5-ca2e-4930-b130-05c45d4392be}}{{figure:bb7e9189-0f0d-4e5e-9101-e2ade55dd2ea}} | m | 6cec8b0ef30980595738d0d12f503dc9 |
Our virtual patient is modeled through two ordinary differential equations presented by {{cite:89ac4f2602aa5e667438523fdb2f5ba5f46f4f9c}}. This system is trivially flat with obvious flat outputs. The design of suitable reference trajectories with the corresponding open-loop controls becomes straightforward. A major source of uncertainty, according to {{cite:214dac9d03374b160f226029cb48b83989be5318}}, is the unknown fluctuation of the drug delivery to the tumor, which should be related to actuators faults, i.e., to a classic topic in fault-tolerant control (see, e.g., {{cite:8e7e5cfeb3f3ea2d835dcde791b3b0db5891b8c2}}). It has been already noticed that model-free control is well-suited for dealing with actuators faults: see {{cite:baf53a2fc2a5e55da995cca254439c029c9c5cfe}} for an academic example and {{cite:644d09300e80cb286c80580ae083d82294133765}} for a concrete case-study. The loop is therefore closed via model-free control. Let us emphasize the following points:
| i | 472ec010a6ca8f02bea3a3379af71850 |
In {{cite:47bfa7974486cbce3554ac2e72f3e5ce51345bd1}}, the first part of the series, we focused on characterizing the topology of Gaussian random fields via homology, quantified by the Betti numbers. Simultaneously, we presented a study on the geometric and topological characteristics of Gaussian fields, exploring the differences and complementary nature of the topological and geometric measures. We focused on the investigation of the geometrical properties in terms of the Minkowski functionals, a program introduced in the cosmological context by Buchert and collaborators {{cite:9aae2136e6d4e581ebb64ceb49dc2eb00fda0cb0}}. In the process, we introduced a theoretical exposition on the Gaussian Kinematic Formula (GKF) in the cosmological context {{cite:056261171df45d8981d5f8d8ea454907ea030124}}, {{cite:47bfa7974486cbce3554ac2e72f3e5ce51345bd1}}. Further, we established that homology and Betti numbers provide a more detailed topological description than the Euler characteristic, propelled by the observation that the shape of the Betti number curves depends on the spectral index, as opposed to the shape of the Minkowski functional curves that show no dependence on the choice of the power spectrum. This is an observation {{cite:5cb22b7a475d12333c6ec80e55d338a332b931c4}} had already established in the context of comparing Euler characteristic with Betti numbers.
| d | c19dde14faacd3283e731640f85dbb3e |
The technological advances in WET to power wireless devices efficiently open up the potential to build a fully wireless powered communication network (WPCN) without battery replacement. This would significantly reduce the maintenance cost and the frequency of energy outage events due to battery depletion. Another interesting application of WET is to jointly transmit energy and information using the same waveform. Such a design paradigm is commonly referred to as simultaneous wireless information and power transfer (SWIPT), which is proved to be more efficient in spectrum usage than transmitting information and energy in orthogonal time or frequency channels {{cite:6b1eaff1d5eb98877272a56dca73f02654aab834}}, {{cite:6ee642183584d8569a1fbe1577deaff175ffbffe}}.
| i | 030f834680849d62430849d45fcfdb89 |
where {{formula:12cbb61f-9fff-41b0-9012-08620920576b}} is the hydrodynamic force in submerged conditions and {{formula:9ea77e28-871e-457b-97eb-a5f80e481428}} is the particle velocity. In granular flows, the Reynolds number is usually very low, hence the hydrodynamic force can be assumed as the Stokes force {{formula:f9f054b4-c184-418d-a734-900ff16c9b2b}} . During the settling process of a single particle, the particle velocity increases until the hydrodynamic force is equal to the driving force, and the particle reaches the terminal velocity {{formula:84c2d8a8-842c-4153-9d3b-5b562f2705ff}} . In previous works {{cite:0ccc0af360545b1a48b76412930e25e41a44fb7c}}, {{cite:977792b84101cb9763c5e8018be1df0a122dd2e8}}, in the inertial regime (or dry granular flows), the drag force is neglected, which assumes that particles travel with a constant acceleration {{formula:04cb0545-122f-435a-8323-553d4ec9fd7d}} , with a deduced settling time {{formula:294886f5-0346-4b78-9bcc-8a136a5a37b5}} and a time scale ratio {{formula:041baa03-b4d5-4909-9cee-5636f8e24613}} . The constant factor {{formula:5ba321a3-b6c4-47f0-b56c-0c03cee02090}} is usually ignored. In the viscous regime, we assume that the particle travels with the maximum velocity {{formula:37dd2e67-21c4-42e0-b901-05fcdf043af7}} for the characteristic length {{formula:842157ee-487a-478f-926a-db76e8338539}} , the settling time is {{formula:709d001e-f4e5-484c-a20a-5970ebe40830}} , and the time scale ratio {{formula:7e65961b-4cc0-4a23-a29a-bc9f184c781d}} . However, when the particles flow in the fluid where the inertial force is comparable to the hydrodynamic force, also known as the viscous-inertial regime, we can describe their rheology by neither the inertial number {{formula:2f3c57ff-5c5a-488f-a982-81ecaa533e2f}} nor the viscous number {{formula:02df7cd3-312d-4bf0-82d4-ead485deb399}} individually.
{{figure:b0fe31e1-2153-4155-a61d-30581e6f1417}} | r | 0017657036069a24e1998f63141d6c80 |
Fig. REF shows the UAV optimal hovering path for the proposed Algorithm REF and compares with {{cite:11ec2c70865a5c26b79e673c58cca8839238b02e}}.
For Algorithm REF , the UAV flies between the BS and user.
During the entire flight, the UAV keeps a safe distance from the adversaries though the UAV does have the perfect location knowledge of the adversaries.
The optimal hovering path is narrower and more directive compared to {{cite:11ec2c70865a5c26b79e673c58cca8839238b02e}}.
Though the UAV serves as an aerial BS in {{cite:11ec2c70865a5c26b79e673c58cca8839238b02e}}, their proposed algorithm shows a wider optimal path.
As a result, the UAV consumes more energy compared to Algorithm REF .
Moreover, Algorithm REF shows a better optimal path, which can save UAV PEC, while the UAV is working as a relay.
{{figure:6baed18a-fdfc-49c6-b8da-bd66e2218a50}} | r | 48e5b2facfdf50212c2cb1301ec9397f |
We also highlight the evolution of {{formula:29cfc0f1-1b5a-4076-8a8e-087a26b18ea4}} in F3, which shows clear oscillation with 180 s period that is sustained over time and does not show any observable damping (Fig. REF ). There is no consistent phase shift between the oscillatory behaviour at the loop apex and in the loop legs, suggesting the oscillation is standing. This is further supported by the fact that the location of the maximum velocity amplitude lies close to the loop apex. This oscillation pattern is very similar to the commonly observed regime of decayless oscillations {{cite:df3771fbb1cc6152f2ddc766ac354ee40176ffb6}}, {{cite:6708b37af9ae28bb08dbc110da2b0fb6b4dbc99d}}, {{cite:64e880147ca0546d68e4a744aabbebcf177bf129}}.
Conversely, an example of the damped impulsively generated (or "decaying") oscillation regime is observable in F2 following an event associated with impulsive temperature increase in the loop (Fig. REF ). The oscillation velocity amplitude is largest at the apex and the evolution of the longitudinal {{formula:a0312623-d4ab-4ddd-aaec-333dfd6e5f8f}} profile matches fundamental harmonic of a standing transverse oscillation. This suggests it is a natural response of the loop to a perturbation accompanied by an impulsive energy release. We also note that for several cases of oscillations in loops F1, F4 and F5, the classification into "decaying" and "decayless" is not as clear (due to lack of clear steady damping pattern such as shown in Fig. REF ). F3 is the only loop that shows persistent undamped oscillation present for the whole duration of simulation.
| d | ddd2fe14418b17a51c6c2077ae100458 |
We used four different machine learning classifiers (with default parameters except for increasing the number of iterations) to predict the degree of warmth for the individual twins: Logistic Regression (LR), Linear Support Vector Classifier (Lin-SVC), Random Forest (RF), and K-Nearest Neighbours (KNN). We used the Scikit-learn {{cite:77a0702129473350530dec30f7fa4c4392386043}} library in Python to train the classifiers. To evaluate the performance of the classifiers, we ran classification tasks five times using stratified 5-fold cross-validation with shuffling. The final metric was the average of the {{formula:beb8be68-4bff-4fab-b8f0-d2af97f16f2e}} -score of the classifiers over the runs.
| r | 6110f36eb1640356e22c301be7db5fe0 |
Since the triplet and fiveplet include charged scalars, we consider
{{formula:d2709f20-5ef8-4a82-a629-38bce8492b64}} as a lower bound on {{formula:ff6182a8-e2a2-4b9d-8572-4ef12860aa10}} {{cite:eca89b6e1414a663fb937e09f42ef3b16b1de112}}.
In order to check whether there exist wrong vacuua that are deeper
than the EW one {{formula:fd17b769-23fa-4fc3-b259-6b6b6af5e232}} ,
we show in Fig. REF some observables with (left) and without
(right) the condition (REF ). In our parameter space (REF ),
we considered the case of negative {{formula:2b8fea69-800f-4bce-9e0b-6a1c5fff172b}} ({{formula:6bcbc24a-7af4-4c0f-9612-652d414dc56c}} )
since there is no reason to consider only positive values.
{{figure:ebcd6f29-333f-4d95-9ac3-4974639eb7b9}} | d | e9969135e1fc14ef538c8045e91039c5 |
Based on our error analysis, we see opportunities for further work in the development of tailored loss functions or post-processing methods. The prediction of speed should be disentangled from the prediction of volume to avoid the bias to predict low speed. Also, the underlying city map should be utilised to adjust the predictions based on available metadata. Other research directions could further explore how to better deal with the temporal dimension of the data. While LSTMs have not outperformed U-Net architectures in previous attempts, Temporal Convolutional Networks {{cite:4d4e306d95545821dccec42c22cfb5dfbe1dd82f}} or temporal graph networks {{cite:ebe3c858245500e082edc7d7481747d8c134a74d}}, {{cite:59b35740c7e70a2828bc34a2da1265865d65f1de}} might be a promising research direction.
| d | ea581728659d91f02451e16f3e7efb80 |
The SORT {{cite:dfea57e3fd4f5ed865569085da3b996fc5b14a4a}} algorithm obtains the least IDF1 score and the highest number of identity switches. This is due to the linear motion model assumption and simple IOU score for re-identification. Deep SORT {{cite:ab14512a1604c57fff96fa00f3f186f3a0b46ea6}}, on the other hand uses features obtained from deep network for re-identification resulting in better IDF1 score and lower identity switches. For JDT based networks, performing detection and re-identification with a single network using a multi-task loss performs better than having separate networks for detection and re-id tasks, evident by better performance of FairMOT {{cite:bcfc15687cd00d4e07bf04e66fd3a961aba9909d}} compared to Tracktor {{cite:19213406cdddfc1d81c2c07033df01469c326afe}}. JDT tracking algorithms, however, {{cite:bcfc15687cd00d4e07bf04e66fd3a961aba9909d}}, {{cite:19213406cdddfc1d81c2c07033df01469c326afe}} do not not show any significant improvement over deep SORT evident by lower identity switches of deep SORT in comparison. The MOT Neural Solver method achieves the highest IDF1 score of {{formula:2edb91cb-765b-4d39-a2a0-3a67ce124621}} and significantly lower identity switches than the other methods. This is because the other trackers use a linear motion model assumption which does not perform well with the motion of hockey players. Sharp changes in player motion often leads to identity switches. The MOT Neural Solver model, in contrast, has no such assumptions since it poses tracking as a graph edge classification problem.
{{table:28b7263b-72c0-4a6a-b853-3040c5a01156}} | d | 84ada5be688c66b682007cdbcab5e9d9 |
For {{formula:959670ab-ad52-4006-8604-6e3b5c9460af}} GeV/{{formula:8bd25c95-6a47-494d-9437-6f0f1c5051db}} , a suppression of similar magnitude is observed for both mesons within uncertainties.
The suppression is described by NLO calculations using EPPS16 {{cite:3f26c4fa32ab41656e8b56129cf51fffafc229a9}} and nCETQ15 {{cite:60d78f5939ab4005fcfb40a6193dde2d4f0fffc3}} nPDFs (the latter tends to underpredict the data below 5 GeV/{{formula:6552603f-3f67-4d02-82a3-c0f69664d213}} ), as well as by models using gluon recombination as the CGC-based calculations {{cite:a4972d8afc4ca002971664274e5e2a64d4cada32}} or parton energy loss in cold nuclear matter in the framework of fully coherent energy loss (FCEL) {{cite:542224dbed2096364c87f326690da8d04e6a0add}}.
| r | 2e3a4445718ea8a30d0b7fb9dc9c65ee |
Frequency conversion and comb generation in optical resonators and microresonators are transforming research and applications of nonlinear and quantum optics. They impact precision frequency metrology, modelocking, soliton photonics, quantum and classical processing of information {{cite:3249bd8eead9743f2e62ff16562777d241e7a663}}, {{cite:15b76121464830a83bf2c1194d6f1303dfd5df35}}, {{cite:e00c09ebccbd6ba964ddca0454f21fb96e869cdf}}. Microresonators made with the materials possessing the second-order, i.e., {{formula:dcb24f29-844b-4eb5-ae4d-c45e906aec1f}} , nonlinearity allow generating frequency combs at twice or half of the pump frequency at the comparatively low input powers, see, e.g., {{cite:c0dc7d3675b057709beda4c90306a33cef037286}}, {{cite:79677cd65363e2e68b70cceb5b5fc84c1b2be490}}, {{cite:c30d979b7983c4825e9883ae01e5599dc58484a5}}, {{cite:49ec7cf3ec1a38635fb6108ece10604eeb47317f}}, {{cite:de133fdf71060f51ed2aed31addffc8dcedc4afc}}, {{cite:ab3c219919314424dcaaaf84391ded633a066cfa}}. Another advantage of {{formula:78aee660-64e4-488a-8096-33218524e89b}} resonators is that the side-band generation relying on the {{formula:ff50bfcb-3b65-4661-9b4b-d5ec99743560}} effects does not critically depend
on the dispersion sign, which facilitates working with visible and near-infrared sources.
Though the generation of {{formula:2077184c-71d1-40f9-873b-06eb66df56ab}} solitons in micro- and bow-tie resonators has been demonstrated {{cite:49ec7cf3ec1a38635fb6108ece10604eeb47317f}}, {{cite:b4d1029a25c94148d8f6dae0c8669cf3c12eb6f0}}, it remains far from being as developed as the soliton techniques in Kerr resonators {{cite:e3fda411f42a6a343293056dd5515b9bac6ebf8b}}. This, in its turn, hinders the development of applications of the {{formula:8c947fea-641a-460c-8a03-20b70c29ccbe}} based soliton modelocking in microresonators.
| i | 38e6f402a1c51fb2ed27b636caa3456a |
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