text stringlengths 54 548k | label stringclasses 4
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where {{formula:bdfb2e79-09c3-411d-a820-0d2980c19784}} is the difference in black hole entropies before and after emission {{cite:fb6d509e2e15a1b4438ef0ed398362e17d5de2a4}}, {{cite:bf919cdd2a2667069d5f7ee1d724299f4e1143f8}}, {{cite:fd44e31c5e82102154594088c18dcfbf2606c0d3}}. It is shown that Parikh-Wilczek's procedure is also valid for the Rutz-Schwarzschild metric. When {{formula:7918af7b-52ae-4cf7-be6a-1b41f45f6c63}} and {{formula:56cbb1b6-2aa5-4d29-8b78-03509a6d1cb0}} , the result reduces to the result of Schwarzschild black hole, which is the same with that derived by Parikh and Wilczek {{cite:fd44e31c5e82102154594088c18dcfbf2606c0d3}}. Note that, for a Schwarzschild black hole, with Parikh-Wilczek tunneling mechanism, the quantum tunneling of massless particles from black hole horizon has been studied based on GUP {{cite:fb6d509e2e15a1b4438ef0ed398362e17d5de2a4}}, {{cite:bf919cdd2a2667069d5f7ee1d724299f4e1143f8}}. It is obvious that our result coincides with the one in Ref. [12] when {{formula:bc17480d-05c9-4c7c-a174-f9e532bc553d}} . We find that the above equation (36) gives tunneling rate's correction which caused by the varied background spacetime and GUP. When {{formula:fc52e7f7-8044-4615-9070-1c1fa782ab5c}} , the tunneling temperature
{{formula:bd40876d-1b1e-46a3-a431-177728ab3a07}}
| d | 2a9fd475d06097c7a1e7603007c77459 |
Structural optimization for the doped cases was carried out with the VASP code {{cite:7b0703bf29d1d78de66095c0c58aee198f92161b}},
using an energy cutoff of 600 eV. This code is efficient for the supercells, which
contain up to 50 atoms. The lattice parameters were optimized, while the
internal structural parameters were relaxed until all forces were
less than 0.01 eV/Å.
| m | 242136c5bf76c37202ad8070d83629ca |
It is also of interest to estimate the range of interaction in this material. In renormalization group theory analysis the interaction decays with distance {{formula:6fb970e8-dfb4-47fc-b6d5-3982cadfd0cd}} as {{formula:d4eb8199-9f1e-4656-b46e-93d9f0b9b0e0}} for long-range exchange, where {{formula:a103d50a-0554-40cb-a323-6ea1e88f6b57}} is the range of exchange interaction {{cite:7f16f2876005c076372792ade43a52af45317e4f}}. The susceptibility exponent {{formula:ed75465b-bc29-4a50-a8a5-b45782acca35}} is:
{{formula:7e771b6e-554c-42d4-bac4-3e5caf25e007}}
| r | b9c4cd10866b992efade8431eb14f862 |
Although such techniques are able to reveal useful numerical properties, they have been often categorised as too simplistic. In fact, a direct connection between the numerical discretisation of the linear advection equation and more complex three-dimensional nonlinear simulations can be everything but trivial.
The high-order schemes' research community has also produced substantial works on generalised forms of spectral analyses.
This includes analyses of linear advection on multiple dimensions {{cite:b2a2b83dd1c3919aee7faea957909f3803de2914}}, {{cite:59f600ff5bad385951a63949581143235f368144}}, {{cite:c142c446c7941d82e7fdef67bfc941c6f1059c75}}, of linear advection problems with non-constant velocity {{cite:b71b1d886f59caea1d4d6f7ec794204b6bafea7f}}, {{cite:fcb7c99d2a49dc6078c9b82a94947036214afedb}}, {{cite:b904a21489d3f21cf21419bc7cf4bd3e82bf6ba9}} and even of alternative eigenanalysis techniques, such as non-modal analysis {{cite:3ddc29aa018169b49d901f9c14bfb7e528858a1f}} and combined-mode analysis {{cite:0fc2275c84ccdb96f8429537fd594169e169e2fb}}.
Nonetheless, all of these approaches commonly involve a semi-discrete form of the linear advection equation, where only spatial numerical errors are considered. The main goal of the present work is focused on a fully-discrete formulation of spatial eigenanalysis where also temporal errors are taken into account.
Despite the fact that some recent work has been presented regarding fully-discrete temporal eigenanalysis {{cite:f836c69518895b392d93c88999383a1c28c10acd}}, {{cite:cf0bfb9f20653b41ceae73b7187d98854cbd5805}}, {{cite:b390037cb830b7831a03a1a37b2e070ad3e14dfa}}, the full generalisation of spatial eigenanalysis including a temporal discretisation remains, as of yet, unexplored.
Even if spatial errors play a critical role in the simulation of turbulent flows, the interaction with the temporal counterparts is everything but obvious. The temporal discretisation can significantly affect the spatial errors, leading to much different results in terms of accuracy and stability of the numerical simulation.
| i | 6887c0c72488ed822c2d16cbc9fb4c0e |
Autonomous driving {{cite:6085aab6915ca208467ccebc9d329693036849a6}}, {{cite:c19940073a02ab85a01ddf03f99f539746218b10}}, {{cite:71090118318ff29afe1e7427bfadead7690526ba}} has received considerable attention in recent years because of its potential to ease congestion, reduce emissions, and even save lives.
However, the timeline for the real-world application of autonomous driving is still uncertain due to the unsatisfactory model performance.
One main reason for the limited model performance is the limited size of labeled data, as collecting a large amount of annotated data is usually expensive, especially tasks such as object detection and segmentation.
Semi-supervised learning (SSL) {{cite:318aff4e6d6cb1f9da501c2d854dfef7e220064d}}, {{cite:45915455ff7cdba62219a1ffe6dd1ac8914811d1}}, {{cite:1fbac5cc51fd4eb90caa4a2beb86ffc4c403a269}}, {{cite:5099536cc07ee9f7e6775bbaf322627e2d374f97}}, {{cite:87c06188d05ee8497427d8038d9ea4d358b25ed3}}, {{cite:9e996c645731e3a824930bc5c979be1459d045bc}}, a paradigm to use abundant unlabeled data to improve the model performance with limited annotated data, is a promising technology for autonomous driving.
| i | 89ffb5a0577bee09748b617851d293d6 |
Egocentric view and generalisation
The use of an allocentric (rather than egocentric) view did not improve generalisation or demo variant performance for most tasks, and sometimes decreased it.
tab:short-results shows the greatest performance drop on variants that change object position, such as Layout and Jitter.
For example, in MTR we found that egocentric policies tended to rotate in one direction until the goal region was in the centre of the agent's field of view, then moved forward to reach the region, which generalises well to different goal region positions.
In contrast, the allocentric policy would often spin in place or get stuck in a corner when confronted with a goal region in a different position.
This supports the hypothesis of {{cite:69482eb8094cd5311d51a21139129c1a575c23f0}} that the egocentric view improves generalisation by creating positional invariances, and reinforces the value of being able to independently measure generalisation across distinct axes of variation (position, shape, colour, etc.).
| d | c939930576fec29a7dfff502fa5882fe |
We considered three ML algorithms proposed in the learning from imprecise data literature, namely: k-Nearest Distributions (KND, also called Generalized kNN) {{cite:603987806ca8a40359a3880825f7f811834f77bd}}, Support Measure Machine (SMM) {{cite:babef24f29f67364248007631aa942f79600178f}}, Weighted re-Sampling Forest (WSF) {{cite:30a3efd100057ac9738cb68cf2d51df1af6943d6}}. See also Appendix C for hyper-parameter settings for the considered models.
KND denotes the generalization of kNN to distribution-valued instances, namely we used the {{formula:9a4d724a-1808-404b-9531-d26a37168dc8}} schemeSince Mahalanobis' distance takes into account only the mean and scale, using {{formula:ad44e45c-9a59-4e08-9467-4a9102cf8385}} scheme would result in the same algorithm. and Mahalanobis distance:
{{formula:eae6967b-4fd4-47b9-b9e1-0683367180bf}}
| m | 79332d4117ff6966e4bbfd9c200ca2d3 |
Since the flows considered are turbulent, the numerical solution was found as a large eddy simulation using the explicit filtering method. Detailed information of the numerical procedure are provided in R. Varadharajan{{cite:38884fd406e7a74755e189347f4433fe38719f2c}} and S. Ganesh{{cite:4f330f403f0014da5bc1006e5e68901ab90a4ccf}}. Essential requirements for this method are that a high resolution numerical method be used along with a high resolution low pass spatial filter applied to transported variables after every time step. This approach to LES has been used successfully, for several types of flows, by at least two other groups {{cite:24ce5c19179679e96484328cb927632bc13e03e8}} {{cite:5864379acdb0a9c549a4a409dc3a970f38a822ea}}. Here, a Cartesian grid was used with a 8th-order compact difference formula for spatial derivatives, split into a forward and a backward step extending the method of Hixon and Turkel{{cite:8a14a1ef1df0ae1443ebc83c444b321bccb26991}} {{cite:ec6788c3ac4ef330c2f2b75c860eece501565c1a}}. Time-stepping was by a 2nd-order Runge-Kutta(RK2) scheme. A one-parameter fourth-order compact filter {{cite:489f32817b3b4d719c09c0eed5630abf1095bac6}} was applied with filter paramter {{formula:adab2223-3e58-4cec-ae59-15657bbbb0ed}} in the stream-wise direction and 0.498 in the cross-stream directions.
| m | 871f2d6aa4d2d1fdc9579b2dfc0fc9ed |
Results on CelebA-5. We further verify the effectiveness of our method on real-world class-imbalanced datasets. The CelebA dataset has a long-tailed label distribution and the test set has a balanced label distribution. We use 300K Random Images {{cite:1cda6fa1d109e11eac9ce4fba673aca9525c941f}} as the open-set auxiliary dataset. Table REF summarizes test accuracy on the CelebA-5 dataset. In particular, the proposed method outperforms existing data-rebalancing methods and is able to consistently improve the existing state-of-the-art methods in test accuracy.
| r | a055a76d75a1a09a1c61cbc0a608ef73 |
For the evaluation of the quality of our synthesis procedure, we
must measure the Hurst index for each direction in the generated field
and to compare with the {{formula:6f0bba3d-7684-4000-adbc-00a72228c213}} value used in the construction. For
this, we apply a modified version of the Directional Average Method
(DAM) proposed in {{cite:cc64f4373fc72e733507a269a8a6282ec202f251}}. As said before, this method
was developed to estimate the orientation-dependent index {{formula:b743ef47-13b4-4dc9-88ea-dd8fe7771667}} in
anisotropic Gaussian fields. It consists in obtaining a 1-D signal
that is the average over all the lines orthogonal to a given direction
{{formula:0e2c08eb-3e18-43ac-a55a-353b35db5e32}} . The estimated Hurst index of this signal must be about
{{formula:e5ae864f-c6ca-4632-8c9e-80a3f4cd3017}} , where {{formula:4a6cc171-59b4-42b2-868f-6f831c559ae9}} is the desired parameter to
characterize the field. In order to get the 1-D signal we proceed
as follows. The matrix representing the field is treated as a monochrome
image. We rotate this image by {{formula:f5d307d2-b297-4e8b-a4dd-e15e13982fee}} in a clockwise direction,
by using an image processing operator that includes a bicubic interpolation
{{cite:6a9ed774a5f9e41673dcf57c2e7406f72d41bfaa}}, but others methods can also be applied.
The output, expressed as a matrix, is large enough to contain the
information of the entire rotated image, from which we extract an
inscribed submatrix whose columns represent an approximation to the
lines orthogonal to {{formula:0b285785-51d2-486e-a5c4-5ade934d813a}} in the original data. This procedure
is ilustrated in figure REF . So we can directly
get the output 1-D signal by taking the average of each column of
this submatrix. Finally, we estimate the Hurst index of the signal
by using a method of choice. This process is performed, in our case,
for each one of the {{formula:6d67b788-ee91-4bbc-81f0-987af9e97b3a}} angles used in the synthesis by curvelets.
| r | 75e2ac05ebed07209741563aa16c35a7 |
We use the Dirac cone model to describe the dynamics of the TI multilayer structures. In the model, the linear Dirac cones are assumed to be present on both the top and bottom surfaces of the magnetic-doped TI layer as well as the undoped TI layer. The Hamiltonian is written as {{formula:99d2af27-29a3-4f55-a452-63a81898a42e}} {{cite:1c2a1f962336c7994413f5322f3098b42b6ddbfa}}, {{cite:89036e703272cfb20e41d56a644f858c1fd0e976}}, {{cite:beab3fd60ff5bd303c02feee719d6ea2b9eb5c0c}}
{{formula:cde42617-589e-4b17-ab2c-b383b96868e5}}
| m | 49c88b30f9225089e9191d5a25ec99ed |
To address the above issues, we propose the first self-supervised DNN-based BP for solving COPs by seamlessly integrating BP, Gated Recurrent Units (GRUs) {{cite:232deb9ac41bf7bbfe3c05b8ad7fc64da1358b39}}, and Graph Attention Networks (GATs) {{cite:7f04ced388346db693274729a8fcba525bc715dc}} within the massage-passing framework to reason about dynamic weights and damping factors for composing new BP messages. Specifically, we make the following key contributions:
| i | 8af7077a53dfc4455efaa5622d5dfb4e |
For simplicity, we chose networks of similar size in our simulations.
However, the presented results are not contingent on network sizes in the ensemble and largely independent of the particular functionality (underlying distribution) of each SSN.
Their applicability to scenarios where different SSNs learn to represent different data is particularly relevant for cortical computation, where weakly interconnected areas or modules are responsible for distinct functions {{cite:a22c56b7b8a457f6c874bcae3c1b9e3a6504fda4}}, {{cite:421e9f2a5ebc7bdd06fcb62aeb13ddd7281c88a7}}, {{cite:97e5d4295f1b83a179a8809dc1f1c392e0efadb8}}, {{cite:f8940f32460e28f8ddc118b12afeddaf251b03df}}, {{cite:4b431bb6077a00ef609a2ff599e8db20edfecfb3}}.
Importantly, these ideas scale naturally to larger ensembles and larger SSNs.
Since each neuron only needs a small number of presynaptic partners from the ensemble, larger networks lead to a sparser interconnectivity between SSNs in the ensemble and hence soften structural constraints.
Preliminary simulations show that the principle of using functional output as noise can even be applied to connections within a single SSN, eliminating the artificial separation between network and ensemble connections (see fig:figS7 and Video S3 in the Supporting information).
| d | b0502ea5d9c8a9dcd8ac760cbb8e87a4 |
Stanza is a state-of-the-art and efficient framework for many NLP tasks {{cite:8530e9eccc2d77ac482a4d81eb9f3c14a3afd978}}, {{cite:7a6d79d4b50f061510a2d2b439db17a996748574}} and it supports both NER and syntactic tasks. We use Stanza to train NER models as well as syntactic models (tokenization, lemmatization, POS tagging, dependency parsing) on TB2. For more detailed information on Stanza, we refer the readers to the Stanza paper {{cite:8530e9eccc2d77ac482a4d81eb9f3c14a3afd978}} and its current websitehttps:// stanfordnlp.github.io/stanza/. We use Twitter GloVe embeddings {{cite:2de4ae55b50ba1759a6c4b7b10a14c95b664c3a9}} with 100 dimensions in our experiments and the default parameters in Stanza for training.
| m | 79e22cdae66598301a44254b83574c1a |
Arguably, a crucial factor for the limitations of existing methods is the fact that most methods use weak 2D supervision from landmarks predicted by face alignment methods as a form of guidance,
e.g. {{cite:3fd51c5245020c09d9ec748b4fef5023d1e26a2f}}, {{cite:d54e33ad55f2ac4949913861257c607cf05b8606}}, {{cite:a89a31c5b0c79eb622f19758cd30963b78f0ddac}}, {{cite:fbb7efab98aab1bd94f3c0350cb52521449ba233}}, {{cite:e567fe7502f01fac7b700c9006a8aa394ecd3e48}}, {{cite:f74cbcf0e9dd2312dbda98d6538e0d82e194a95d}}, {{cite:d2f2b8aede75b04f7068ed509d663558c8580f98}}, {{cite:dac5e663d97b4ad5a9e193a68a289c470ea5827c}}. While these landmarks can yield a coarse estimation of the facial shape, they fail to provide an accurate representation of the expressive details of a highly-deformable mouth region.
It is also important to note that the shapes of the human mouth are perceptually correlated with speech and the realism of a 3D talking head is tightly coupled with the uttered sentence. As a result, a 3D model that talks without the lips closing when uttering the bi-labial consonants (i.e., /m/, /p/, and /b/), or with no lip-roundness when speaking a rounded-vowel (such as /o/ /u/) has a poor perceived naturalness. In EMOCA {{cite:5007acb0efc7034afff590da22770d659f47b0fa}}, some significant steps were done in improving the expressivity of the 3D reconstructed head, however the perceptual emotional consistency loss only affected those movements that correspond to emotions. Furthermore, this method did not predict the jaw parameters as well, resulting in poor articulation.
| i | d4ccf867f23eca00cab2ef172d2965cc |
All these arguments must be evaluated in the context of accretion-decretion disks expected in some DPVs. Since the tangential impact should accelerate the star until critical rotation, we might have a disk with an inner boundary transporting angular momentum and matter outside and the outer boundary transporting mass inside. This kind of relatively massive, self-gravitating accretion-decretion disks are starting to be studied by {{cite:499cb25fdc8a30d8827a390dd3a6e868ae40dd79}}, {{cite:4b63fea7dfbff089d899e7c9b2be85d9602a4755}} and its importance in the field of algols,
double periodic variables and other close binaries remains to be established by future investigations.
{{table:de624450-a255-4d9e-9f6a-8dea51116975}}{{table:445bff62-d132-42d2-9ebc-767b820ae1d5}}{{figure:cffa986b-6bad-4021-9d4c-2b205bcaaacd}} | d | 5a34c7e0959882b1a5a903c54291e0eb |
It is also possible to use our operations in conjunction with other strategies, including dimension reduction, quantization and tree search {{cite:c3759c5156d71d85f5a2c8adc89af1539565ac44}}, {{cite:560d5c6c2d0281d4410434aef3efa3385b2131e3}}, {{cite:e6508811c1bc4833886907a304675c95a64d56d2}},
because many compressed domain search methods use brute-force distance computation on its auxiliary data structures before performing the fractional search.
We note that heterogeneous architectures with off-HBM storage such as host-RAM or even SSD {{cite:bff82244843655804b86ff639098ee7c48bb4460}}, {{cite:6e4cd8fae7b739ae0580119e1f9eae784cf59ade}}, {{cite:0fb73da8bcc61a34d0d16f7b334c7566ce1fbf3b}} are great starting points for future research.
| d | 71a303a456103d6b50ca60f5540c0978 |
The estimation quality of {{formula:d34e96f9-ed52-435d-b6ee-71231551cdc6}}
determines how well the relation between {{formula:6cd088a2-e7e8-48d3-a832-24f3aff54e0c}} and {{formula:80f19dc3-ecb3-4a9d-9206-9088acaa559a}} is captured.
Besides the regression method,
the starting epoch {{formula:1f5257b9-6384-42b4-907d-15b564685877}} of the observations also plays a role in the estimation.
As shown in Fig.REF (b),
we evaluate the impact of {{formula:7db47390-e569-4039-b4cb-54bd9b7df494}} on {{formula:ef769226-c99c-4563-9c2b-a2d0ebc29c63}} of our approach.
It goes as expected, when the length of learning curves is fixed,
a higher {{formula:a3c2aa1f-9c29-4d21-8eaf-734931579328}} usually produces a better {{formula:86245120-6141-4d32-9c03-c8b1ead2717e}} .
Since our ultimate goal is to predict with the early observations,
{{formula:70f791f6-5203-4ae9-a7a2-db12f27cd238}} should also be constrained to a small value.
To make the comparisons fair,
we view {{formula:8648979b-5055-4a92-955d-852404aff669}} as a hyper-parameter,
and select it according to the Bayesian information criterion (BIC) {{cite:f9441d875599569645a362a9235bd6246ac6cc96}},
as shown in row 3 of Fig.REF .
{{figure:4dca4be8-3b72-43bd-8ef3-c6368570876b}}{{figure:f612ebdd-d70d-499e-8cf0-8327e8559ee8}} | r | 58516117e1a7a22a68df14718a99eca8 |
In our work the idea of how performing the qubit state reconstruction is similar to that in Ref. ficheuxtomo, that is to read the resonator dynamics. In fact, the functional relationships linking the qubit dynamics to the resonator evolution, that we have derived from HEM, bear some resemblance to those used in Ref. ficheuxtomo to interpret measurements. The main difference is that in Ref. ficheuxtomo the bath has not been explicitly considered, while, in this paper, we have exploited its effects on the qubit state reconstruction. Moreover, the LME used in this work takes qubit and resonator on the same footing. Finally, we have introduced dissipation and decoherence through the presence of an Ohmic bath, without describing a measurement apparatus. A generalization of our study to a more realistic model, including the measurement process description, deserves future investigations {{cite:452e349079059700fa085d24a27a987c894aea92}}, {{cite:893778f7e9def76a1ddbfc9c249e3fe6c79a4e97}}.
| d | 36abfa51a97ea51e2729976d09ab7e5f |
{{cite:70bb27b254e9af55c02134e95f787e2b022824ac}} in the 1920s found that hanging heavier weights from a muscle led to faster firing rates from neurons inside the muscles. This is where rate coding originated from, the idea that information in nervous systems are communicated in the form of average firing rates. This is surely one form of communication, and usually assumed to be what the ReLU activation function is modeling, yet several other temporal codes are known to be used in BNNs {{cite:d2953a5a58507bce96b9e95798f03b2bec39c470}}. As evidence that DNNs use rate coding are the numerous successful ANN-to-SNN Spiking Neural Networks, often thought to model more tricks from the brain conversions methods rely on replacing activation values in DNNs (e.g. ReLU, sigmoid, and tanh) with rate-based coding {{cite:10baf251bdc1aa9c2eb2d889d4c45921c2a872ad}}, {{cite:7358af9890843fafa3bb7402dea1b1f7dac2def9}}, {{cite:d7d9b829edde6b7ecf0a4adfc8daf2fd2a1d6ab5}}, {{cite:2dd0665ad56263474ceb6c6aa18dc2a031eab525}}, {{cite:1241cdc2be8615580ca825500a0de65e4b190f21}}, {{cite:d81751a8938901d030be60c4b2fb3ec704864f21}}. Many of these approaches suffer little accuracy loss from the conversion process, and can be implemented much more efficiently on neuromorphic hardware {{cite:2dd0665ad56263474ceb6c6aa18dc2a031eab525}}, {{cite:1241cdc2be8615580ca825500a0de65e4b190f21}}, {{cite:d81751a8938901d030be60c4b2fb3ec704864f21}}, {{cite:c1db99dec6397f7b9eb0cd1b6bf299cf94d8e61d}}.
| d | 5a23040b9d757c730c1924180b5082d8 |
The Multiconfigurational Time-Dependent Hartree Method for Indistinguishable Particles {{cite:f0478760c8f721f3dd67cf6bdf8ab14ec93ff969}}, {{cite:4f12a45cd7f7967b307d11f142c7055680691d2a}}, {{cite:7b55c5efd4b184da4203e409880ab5d01652b4ed}}, {{cite:cd7d4f3d8bf54ca459d2a3ad3dd9dc18b3f8ae91}}, {{cite:5c11a4295e7494aaa7f6f91b65853e67947d3898}} is implemented in the MCTDH-X software {{cite:6bbeb47b9146ba825f30d5d2ead65429c8f82892}}, and can accurately simulate cavity-BEC systems. We consider a general Hamiltonian containing a one-body potential {{formula:7a4e9f31-6915-4532-a158-8f75a77c8662}} and a two-body interaction {{formula:6a5f3929-d99c-47ba-86ba-98da6fd11fd1}} :
{{formula:69c10fd3-f7b6-4a2e-9815-a3e7354bba79}}
| m | 18c082bc8c0a92d5f87b8f3ab92cb952 |
Affordance Characteristics. As part of the niche environment that humans occupy, object properties seem to be understood by humans in terms of their affordance characteristics, or in other words the opportunities and limitations that they offer to humans {{cite:bd9e1d916b14d2285391829df1ac01a4e16866d6}}, {{cite:cf85d0bfdae6ee8d0c7f375dd7a14b93c7d63ade}}. ART has shown up weaknesses in GPT-3 to understand object affordance characteristics through Necessary quality, Order of size and Order of intensity. Severe performance limitations on Order of size appear consistent with evidence for GPT-3 and other NNLMs using CSQA2 {{cite:c591cb9884b55e873ab709e19654284dc33d0cc0}} as well as earlier work on BERT for the task of scalar probing {{cite:647e2dfdece37235248c3d8b5830891cb65a1d86}}, and supports the view that there is an algorithmic weakness in the ability of language-only distributed semantic representations to capture affordance characteristics {{cite:f50bca93a98796391de7e97a40ceadb1f594a733}}, {{cite:7b6af9e0e7e25892953351bf105c83d5ca5ede6c}}. Our finding is particularly salient in the light of strong human performance and low human variance for Order of size and Order of intensity. Davinci's apparent progress in Associated quality hints at a situation whereby the largest GPT-3 model can generate potential affordance characteristics for objects, e.g. can a person walk down a bus? but without being able to engage either the inference processes or underlying conceptual representation that underlies human physical common sense. For example, understanding the physical qualities of a bus that enables walking down its central aisle possible such as the frame's hollow structure, overall size relative to a human body, density, motion and so on.
| d | a920916baf9498efba58cfc12fcfef84 |
Lemma 2.1 {{cite:99573a9f490c09d40d194658fa60fa516598ac5d}}
Let {{formula:00cb4773-dea6-405b-9ecf-51eee90a4ece}} be a cyclic proper subgroup of a finite group {{formula:357666f7-f03b-4915-8f0b-d9499c698216}} , and let {{formula:98f80525-8a3b-4ce7-95c3-36b201561e96}} . Then {{formula:a45dc43e-db9f-4e34-94ed-6af8004312ae}} .
| r | f9b0e59c900f9348e456594d95ecd6bb |
Despite their usefulness in many applications, LASSO and SCAD also have certain
shortcomings with respect to VAR model estimation. LASSO is likely to give
inaccurate estimates of the model structure when the sample size is small
{{cite:ff194ff0073a3976c7a7abd9c4937c6fd4e1d638}}, {{cite:0b59c3757dd64264ec0386fb2803a408f0355f0f}}. In particular, the structure estimates obtained
by LASSO tend to be too dense {{cite:4c10601f203e6c675b93b44952769732a49ddeb9}}. While SCAD has been reported
to perform better {{cite:127fbc0c61ac34e08a4fba8dbf600ca0d39bc5ad}}, it still leaves room for improvement in
many cases. In addition, both LASSO and SCAD involve one or more
hyperparameters whose value may have a significant effect on the results.
Suitable hyperparameter values may be found through cross-validation but this
is typically a very time-consuming task.
| i | 4129d87591a8f38d29598081af37e160 |
Finally we envision that the present findings can be applied to other two-dimensional semiconducting or insulating layered materials that form tubes, as it is the case for transition metal dichalcogenides.{{cite:916ea737b9641e3398a191cb987527a3cb0875f2}}
| d | 952373a8703fb04198285f8d3aba6a0f |
We compute our timing results using a Intel i5-7600 CPU @ 3.50GHz CPU,
and a NVIDIA GTX 1080-TI GPU. We use square style and content images
scaled to have the edge length indicated in the top row of Table
REF . For inputs of size 1024x1024 the methods from
{{cite:2c611dde9f9f781475bdac9ff37f6107e5dd5050}} and {{cite:787c27b5934c91d51e8883dbc4d5b64f2b8c2083}} ran out of
memory ('X' in the table). Because the code provided by the authors {{cite:861f988922914a19ea93efc83b3e7ace989c51f1}} only runs on Windows, we had to run it on a different computer. To approximate the speed of their method on our hardware we project the timing result for 512x512 images reported in their paper based on the relative speedup for {{cite:2c611dde9f9f781475bdac9ff37f6107e5dd5050}} between their hardware and ours. For low resolution outputs our method is relatively slow, however it scales better for outputs with resolution 512 and above relative to {{cite:2c611dde9f9f781475bdac9ff37f6107e5dd5050}} and {{cite:787c27b5934c91d51e8883dbc4d5b64f2b8c2083}}, but remains slower than {{cite:ad5495370b670fc47eb985122f7dbb09930e530e}} and our projected results for {{cite:861f988922914a19ea93efc83b3e7ace989c51f1}}.
{{table:40d2ef6b-1a3e-40c0-9259-e3e139f9102c}} | r | 4f51179ab821de7347d0d29f1f4af0b0 |
The overall segmentation results are presented in Table REF . Results show that our method achieves the best performance in terms of both OA and mIoU metrics. In particular, when compared with the competing method in this specific task, MeshSegNet {{cite:5dd6e72009f8ebe81ed27e3aeb2d5430d764640a}}, which directly consumes the combination of coordinates and normal vectors, the proposed TSGCNet still increases the segmentation accuracy by {{formula:17e42df5-7d66-4ef3-97f7-fa6dcad40855}} and {{formula:a660d0ed-95b3-484b-92e7-6e9daa844e7e}} on the OA and mIoU, respectively. Additionally, our method also significantly outperforms the graph based network DGCNN {{cite:62cd0b1b964ddf246f5470f8185520d0c2782f02}}, demonstrating the effectiveness of the proposed two-stream mechanism that can learn more discriminative geometric feature representations for accurate tooth segmentation.
Furthermore, despite the varying shape appearances of different types of teeth, our method is able to present consistent superior segmentation performance over other approaches by a large margin.
| m | 8d3db2e4053553ebb628a430af259096 |
A major challenge in EnKF is generating and evolving a large number of ensemble members of the dynamical model in time. The accuracy of the background error covariance matrix in EnKF (which affects the performance of EnKF) black depends on the ensemble size {{cite:fd17a34471e6e49fb6c528bb07dbf86ec8464134}}. For an accurate estimation of the background error covariance matrix, the number of ensemble members should be of the order of the number of states, black {{formula:31158c3a-4658-489e-af13-08dbecb44670}} , in the system, black which can be large (e.g., black in the weather system, {{formula:26039861-9386-4ed8-8140-55f24791e9ea}} {{formula:89f42b9f-e2e7-4165-b9f1-5725ee2c02ff}} ). However, evolving such large ensembles over multiple time steps becomes computationally intractable. Thus, fewer ensembles are typically used in practice ({{formula:553f94bb-6b1e-4c0b-bd27-7bb002938e11}} in operational weather models {{cite:6629bb91debe36adb6f0c5753110fb0c4f2b126e}}). These covariance matrices, generated from a smaller number of ensemble members, are rank-deficient and suffer from sampling error that degrades the quality of the estimated initial condition (often referred to as the “analysis state"). For this reason, various ad-hoc localization strategies black have been proposed to remove spurious long-range spatial correlations in the covariance matrix {{cite:c99a51c743fc95b3437b2093dfb5678334fd0fb1}}. However, in this process, one may also remove physically-consistent long-range spatial correlations and this can adversely affect the performance of EnKF black and thus, the quality of forecasts {{cite:ea8866abcda3e5c633eb0843eebe0e91cc007b97}}. There are other methods to estimate the background error covariance matrix without evolving a large ensemble, e.g., the stochastic Galerkin method {{cite:3fb0b3c079f1d5356444e4dd0fa457dbaf1815a6}}.
| i | 477140173d010e646e1e63490b590fcf |
We use additive attention {{cite:ad002ad7788024f69244291139fd1af3658dce81}} to obtain the gating coefficient. Although this is computationally more expensive, it has experimentally shown to achieve higher accuracy than multiplicative attention {{cite:47e19072f32e90ae36c142e27d37630c7ef7ed0d}}. Additive attention is formulated as follows:
{{formula:0add2e7d-f707-4e44-bf59-338cabee52ce}}
| m | b109dde1878c7c25176e6bdaf26f4c90 |
Given a planar phylogenetic network on {{formula:e88ec940-8d80-45cd-9ebd-49e049dee589}} ,
let {{formula:2bb27a23-5441-49c3-84e6-065aa0c6da73}} be the digraph obtained from {{formula:f55f5989-fc4a-4945-b1b8-3e88e14264f1}} by adding
an additional arc {{formula:46d0bbbe-3086-48dc-9ba7-91663d4c12f6}} for each element {{formula:7a984ccb-0f3d-46bb-a9e9-d63cf04e6859}} in {{formula:b6909f0e-9329-43c4-b5ae-d265c9ba4297}} if {{formula:c02d05b8-fea1-446b-a0cf-4f0d0e6ef035}} is not already an arc in {{formula:85e4526c-dcb0-44fe-a5c1-b18a6f3e18e2}} .
If {{formula:dce12951-7d81-4d31-861d-a7b67ec5ef9d}} is tip planar, then it is straight-forward to see that
{{formula:d4643ae7-841a-4e0b-9065-63031adedd3e}} is planar, but does the converse hold?
Given a normal network {{formula:e5a350af-cbf9-4306-9956-5a034d19c4a9}} , we define {{formula:f989b2fc-f1f9-4083-9a62-0a806d6afbea}}
to be the network which is obtained from {{formula:8d44b1e5-ed2a-44dc-9b4f-fb936a67563e}} by collapsing
any arc {{formula:3731e437-c64f-458c-b39a-b4411c19cc45}} in {{formula:72e20ae9-02c9-4cb0-bf79-dc6e1ecdf0e8}} , where {{formula:13eb15f0-55fd-465b-82d4-cd394dc8d3d3}} has outdegree 1 and {{formula:b5c05778-cc2a-4bcf-b08f-f36e7a9c9550}} has indegree 1.
Note that that {{formula:11b09980-c53c-4456-99c2-3c90e322474f}} must be regular (see e.g. {{cite:62613848eb39938118ff60031a76bec6bce633e5}}).
Is {{formula:be32adc8-3d9a-470e-9f5c-15eb047eda48}} is tip planar if and only {{formula:947c8112-0259-41c3-90ba-d516f0ca7c4e}} is tip planar?
Is there a prepyramid cluster system {{formula:f509bfb3-963c-4f1e-8796-773aa4834fe9}} such
that {{formula:60ff857f-b991-4d12-9f63-b2a3c93eaee0}} is not upward planar?
Although there are some general algorithms for drawing
planar, upper planar, tip planar and outer planar networks (Theorem REF ), are there more
specific algorithms for drawing special types of planar phylogenetic networks
such as tree-child networks?
| d | 94d3ee23686c8c4f6c71e922b36776a4 |
Some other methods such as BYOL {{cite:4eae6e4b0b07396d2d588e443a61e3c94b64d1e3}}, SwAV {{cite:274fc66fed8e3224523b26e8c521b9ac0a5b08eb}}, and SimSiam {{cite:c46464f9c1fc40d9f82b1f0284d6af7814de14c0}} are recently developed to learn self-supervised representation using only positive examples. For example, BYOL (as shown in Fig REF ) used a momentum encoder that prevents collapse, and a predictor that induces asymmetry to cluster positive examples.
| m | e0e61ffdc69b1ade7a6e0db2da397e1c |
The next generation of CMB surveys such as the ongoing Simons Observatory {{cite:c04fabc2bde8aac322b20ae730777df29e845799}}, {{cite:8077bcc171e85a7940ba3b7f80e34cf8ce388b37}}, the upcoming CMB-S4 {{cite:6156ba402f15c65d6a74f430914f70077453f54e}}, {{cite:ee74948a5cf5d6e310381a7bfb72e5aaab530d5d}}, and the futuristic CMB-HD {{cite:a5d600abf301923b442194cd76920ab88d332066}}, {{cite:06c3a8e99d54b91e64f668be942dfcb19aa3901e}}, and galaxy surveys such as DESI {{cite:7bc55efb964a677cb58c2bf0f1bc25644ac2bebf}}, the Vera Rubin Observatory (VRO) {{cite:ce396d07a4837f55fd0d0b525428b60adf348f80}}, and perhaps then MegaMapper {{cite:1a0ed3651b2ae2da0327f9861f21414bcbcc995a}} promise to greatly expand our ability to infer the fundamental characteristics of the Universe. One exciting new opportunity is to use the CMB as a back-light, observing the effects on the CMB of scattering and lensing by the intervening large-scale structure. These interactions include the thermal, kinetic and polarized Sunyaev Zel’dovich effects {{cite:20c5f4f4371003851e9b2b0c8fefc1a541ed566a}}, {{cite:b719548d9b822d5104b8e427a6b54e285c66f7a4}}, {{cite:88ad6e92536a11f4e2b4c1978a369786fff4f2bf}}, {{cite:e996cc3e9a4dab9be8d074ed6b7ef7f3d51c6b0d}}, {{cite:b3da185584d81351d8dc0d9b78e967f5561e75b7}}, {{cite:95a992ad791f02393f7b343cd73f497976885bce}}, {{cite:5c01c028aad77c0adaf47eb48ad0be11eb626fbf}}, {{cite:0e3f1087d04fef90f3fc68890c47bc7b78258af1}}, {{cite:ebe4c395500eb42e91171484ccf9bde7478fdcc8}}, and the
integrated Sachs-Wolfe effects {{cite:377a73d36e00a172a5721ffd5da4b0d399458115}}, which includes the
moving-lens effect {{cite:fb8810d392388e14c253d87432c9e48ad3da98f2}}, {{cite:5907869b2274c6415840ed625cf42751c67982cd}}, {{cite:440c1c39ce63c215f23b8d742f89dc072306b4b8}}, {{cite:934dffb0868ff17006909426cbfb849e6f4fa915}}, and weak-gravitational lensing (for a review see e.g. {{cite:a32a932809e23181b4b987c82f39010787dc5603}}). Each of these effects can provide new insights and constraints on cosmological models.
| i | a4e3ddfa50eb1a7fcbd472b845b7e48b |
Limitations and future work Blurriness of the NeRF results is a big limitation of this work, despite using cone-casting from Mip-NeRF. We believe further improvements such as {{cite:ab1fe14daba8e09d2636bf940d61775f05224274}} can help in reconstructing sharper estimates.
Another limitation is that the photographer capturing the scene ends up modifying the light field ever so slightly by casting shadows, creating reflections off of shiny surfaces, etc. Unfortunately, the intensity changes this creates are too soft for existing shadow detectors {{cite:788cc53f57dd663f056020984582dab3979f4a4f}}. Methods modeling transient changes {{cite:3673c5bac0b79bd633f667d77b3b34eb59a9643e}} could potentially be of help. The finetuning for each camera introduces additional effort though only once per camera. Future research can improve generalization across cameras, perhaps using multiple cameras for training, or through other data augmentation techniques.
Our approach learns radiance and view synthesis in two independent steps by specialized networks. Exploring how both can be done simultaneously, potentially in conjunction with geometry and material estimation {{cite:130a534e43aa389807c4fb8694e5cd1f7eb042bf}}, {{cite:a84ae064c4ac2a2c92630903c6c1532978be9b8e}}, is an exciting direction for future work. Finally, recent efforts have demonstrated how to significantly shorten training {{cite:c8a740a3c61e32481eeed2995c37996b37aa5166}}, {{cite:e4a8fb262453b4d1d7d1846d94cebba022a5dd62}} and inference {{cite:8a49c37a0600bb4027a465739cae8d4f29e34a37}}, {{cite:c87f89308af41a04b78b3d2325a8ad937c9dc43d}} times of NeRF-based approaches, which can be incorporated into PanoHDR-NeRF. By reducing the time between capture and visualization, PanoHDR-NeRF can be used for AR/VR applications such as virtual tours and VFX generation.
| d | 9c32b207fce538d62863a3f762eb11d4 |
In this section we will discuss the limitations and potential societal impact of our contribution. To start with, our theoretical analysis relies on being able to compute a Kantorovich potential {{formula:45168f4e-5523-48ea-87df-5657b0519444}} for the pair {{formula:237c3041-771a-4c10-89ed-34e5c5cdcb79}} . Given recent results in {{cite:77e7ac1f807053cc78400d4d075634a235242f5f}} showing that the optimization problem for learning critics from {{cite:d52509f7efea4044838fc0dd7af0427040079a8c}} actually returns a function that solves a congested transport problem, which is distinct from a Kantorovich potential, one may ask to what extent our theoretical analysis applies to the types of critics learned in practice. The distinction between these problems decreases as {{formula:9d5bc2a4-7d71-4728-ab21-6db466fcee98}} gets large, so we suspect that our assumption of being able to compute a Kantorovich potential is reasonable for the {{formula:b7e910bc-06ba-4a8e-88b0-b288d38af553}} value we used ({{formula:80035433-7a46-4955-b05f-d2b10a40a001}} ), but this is certainly something to consider, especially for the smaller values of {{formula:a6437b9b-ba0e-4b6a-81ff-3221a306392d}} typically used in the literature.
| d | 24b2106fbf658c1e9d869e3fad3f7f72 |
Advocating a particular version of this idea, Silverman & Mallett
{{cite:c3337cb07068dce404d55fadf26e84eb90bf0961}} suggested a symmetry breaking mechanism for
the production of such a particle, based upon a real-valued scalar
field. Although in this case the symmetry breaking mechanism
provides a nice example of particle production in a universe with a
cosmological constant, symmetry breaking with a real scalar field
generically produces a catastrophic domain wall problem
{{cite:aefcba97d900296cb99f4f474d4c8b66f74e1038}}, and this example would seem to be no
exception {{cite:eaef0b73880ea05619719ee6398cfeaeaaeb2035}} so this is probably not a viable
scenario. However, these papers consider the possibility that the
Dark Matter component resides in a Bose-Einstein Condensate (BEC).
The dynamics and possible observational consequences of a
Cosmological fluid with such properties has been investigated
{{cite:519fbd33dd2b851a8df6f888a1a72cfc17e2bc1e}}, using techniques developed in the field of
condensed matter physics. The equation describing a BEC is known to
condensed matter theorists as the Gross-Pitaevskii (GP) equation, but is probably
more familiar to cosmologists as the nonlinear Schrödinger
equation (NLSE).
| i | 062400f3c913996ca036718b04b0b516 |
For more information about hypercyclic and supercyclic operators and their proprieties, see the book {{cite:6fd2f612f2408bd8d6e05734606f18bf9df39d72}} by KG. Grosse-Erdmann and A. Peris , the book {{cite:cb86e829c7af6b40a36b7a0e65d84d5875536615}} by F. Bayart and E. Matheron, and the survy article {{cite:0d0e123ba70eb0e7fb29079e840ab3425f8f93d8}} by KG. Grosse-Erdmann.
| i | 09c508fdc5626e03b310debeb384b885 |
SAM Implementation:
Given a pixel query map {{formula:74c3c9d6-d1ba-4637-95bc-2220a8fab5a4}} and the corresponding encoder features {{formula:60cdf9fc-6c92-4095-be53-bebde9c1b55f}} for a particular scale {{formula:44c6aa9b-66ad-49e6-94f1-9f28cedd25dd}} , we first perform a {{formula:04f7a8dd-1cfe-486e-8b3f-45df4679887a}} convolution {{formula:94e30402-eabc-45ef-aa71-aab6d36cde2f}} with {{formula:cce656ed-166c-486c-ba75-cd1c2bb3697e}} channels on both {{formula:cd4b64ae-e232-4573-8747-eac433293aaf}} and {{formula:8182799b-e3a4-4019-889f-26faaaeaa13e}} so that the number of channels of the pixel queries generated from the decoder features is the same as the number of channels in the encoder feature maps. Post the convolutional operation, a query matrix {{formula:cc01a0f8-4027-4356-bf13-47a0dbb5d9e1}} is obtained from {{formula:d685d8ab-9411-4fa3-bb9b-a25b147404bf}} , and the key {{formula:90afd7e8-5be6-4670-af0b-9c276b87af37}} and value {{formula:86f34140-7625-4e91-aead-b7b677728ac5}} matrices are obtained from {{formula:7a75ab99-338a-4e92-a3d6-aa7abc96cf13}} using the weights {{formula:23d915ad-ab0c-4109-9ec4-2ccbd71d366a}} , {{formula:99b5e31f-0c3a-4a9c-8459-b961021c1003}} and {{formula:35e35208-be50-49a7-bb6c-145d504f8c21}} implemented using MLP layers.
Since it's not computationally feasible for a query {{formula:c85b690b-9f38-44fe-98fe-8d1855981f87}} corresponding to the pixel query at location {{formula:1ebf7c06-d4b2-48bf-a676-f146d5bf9bc4}} to attend to all the keys in the matrix {{formula:37978a39-2d98-4b89-9592-cb2f9a220509}} , we restrict the attention to a window as suggested for Swin Transformer {{cite:cf713d65c5df498b7d5bd0e1af558361ab15b6f3}}. {{formula:cdf24004-78d5-4616-a5de-7b164cbe6687}} , {{formula:928f8c4f-fabb-4c82-b11f-171e633acfb0}} , and {{formula:2dcd36a4-487c-4781-85f3-70e64d522c94}} matrices are first divided into windows of size {{formula:8ad03b1b-7ab1-4d0d-a4aa-21b922b4753b}} . Similar to {{cite:cf713d65c5df498b7d5bd0e1af558361ab15b6f3}}, we use {{formula:3b7c04eb-e884-4794-958f-6a275f312f4a}} . Let {{formula:42577ea1-27af-4a0d-9bc0-fe11e81158b3}} , {{formula:6539d3be-9ed0-4a60-9f4d-42adfb2e26b8}} , and {{formula:65c9a21b-fb4f-4eed-bb23-cc073a92edfe}} be the query, key, and the value corresponding to the pixels in window {{formula:6b214fe0-e218-4418-8d8b-8505a9e41b68}} . We compute the output as follows:
{{formula:9d2ec8b6-40eb-4e36-b1d3-b8890d7267c2}}
| m | 0205c229fe7edd9689c41257c2d72b06 |
If we would like to confirm that the event was in fact caused by a dark remnant, we would have to wait ten years and use the Extremely Large Telescope to take high angular-resolution follow-up observations of this field to try and identify the source and lens as separate objects.
If the lens is a neutron star, it may be emitting radio signals which are to weak to be detected by modern-day telescopes.
We could try observing this area with more sensitive radio telescopes in the future.
However, it it worth noting that only a small fraction of neutron stars can be observed as pulsars due to the fact that one of the magnetic poles has be aligned with our line of sight.
If the lens is consisting of two neutron stars, the system might emit gravitational waves that could be detectable for upcoming ESA mission Laser Interferometer Space Antenna {{cite:3713d31b3169dac144fb60aecd0f1880ea8b1abe}}.
Another option would be to wait for the final Gaia Data Release.
Based on {{cite:ec994a97179ef0727aafe02d84c6b3706287ab64}} we expect that accuracy in the along scan direction (AL) should be between 0.3 mas for the brightest points and 3 mas for baseline magnitude.
The largest astrometric displacement of the centroid of light due to microlensing occurs for {{formula:e276b774-c0e8-49db-a520-0bb1bead05fb}} and is equal to {{formula:c168ff72-019e-4e95-bccf-c486374bd95c}} .
This gives us maximal astrometric shift spanning between 0.45 mas and 2.82 mas for the GF+ and 0.26 mas and 2.34 mas for the GF-.
This means that astrometric microlensing might be marginally measurable by Gaia.
| d | 159950db29a4a5bfb402e004181f60b9 |
In this study, based on the formulation of ALBERT as a discrete-time dynamical system, we analyzed the trajectory properties using short-term and long-term analyses.
In the short-term analysis, we first demonstrated that token vectors began to synchronize after a certain period, and suggested that it was caused by the attention mechanism of the Transformer's encoder.
Recent studies have showed that graph neural networks {{cite:6fa34c5a360f81c6e61e26d66f8cda3161dc400a}}, including the ALBERT's attention mechanism, can cause over-smoothing and eliminate the difference among nodes with the deep architecture {{cite:1f35fce5979571ad594b0f9df7a3cf4d3738bcdb}}, {{cite:c597ea3a212f95a0bdf5b47bea81b6b453cbe1aa}}, which is consistent with our empirical results exhibiting token-vector synchronization.
We also measured three indices to quantify the transient properties and found that:
| d | 693bd98a891d2f54a85529b406a91508 |
In this section, we evaluate our proposed SpFDE framework on benchmark datasets, including CIFAR-100 {{cite:7176c497304b646b12294fb1afce452dcfdcf31e}} and ImageNet {{cite:010bd509add75a992b2caf3ae0f28e90b6de8395}}, for the image classification task with ResNet-32 and ResNet-50.
Note that we follow the previous work {{cite:f174daf53bde4c5e5705cbf2b560cbe7425dbb0a}}, {{cite:728c971e12cd9e232a1b99e34571d7e600d7454d}}, {{cite:4b34162f79383940910552fd100ea9460e32bf4f}} using the 2{{formula:96ed49e7-c650-4787-acfd-3dbbbe339c48}} widen version of ResNet-32.
We compare the accuracy, training FLOPs, and memory costs of our framework with the most representative sparse training works {{cite:4b34162f79383940910552fd100ea9460e32bf4f}}, {{cite:728c971e12cd9e232a1b99e34571d7e600d7454d}}, {{cite:fba8730b4c3a33f83ff8448062dfbff5003a7ac0}}, {{cite:d084ca8196eade3880c56397e1e70b5424f4ad9d}}, {{cite:bedbb2316457c419669c3d221c5039c49069b813}}, {{cite:486a0c9c7b96708111d3caa0f4f81f443f25c677}}, {{cite:9bc96b8f46ffaf4315d729a8fc068981288ca69a}}, {{cite:f174daf53bde4c5e5705cbf2b560cbe7425dbb0a}} at different sparsity ratios.
Models are trained by using PyTorch {{cite:8dc92611173c72134a8435f8c1d2444a185af5fd}} on an 8{{formula:017d923a-6ff8-4bda-9281-f74b5f8dd7d4}} A100 GPU server.
We adopt the standard data augmentation and the momentum SGD optimizer.
Layer-wise cosine annealing learning rate schedule is used according to the frozen epochs.
To make a fair comparison with the reference works, we also use 160 training epochs on the CIFAR-100 dataset and 150 training epochs on the ImageNet dataset.
We choose MEST+EM&S {{cite:f174daf53bde4c5e5705cbf2b560cbe7425dbb0a}} as our training algorithm for weight sparsity since it does not involve any dense computations, making it desirable for edge device scenarios.
We apply uniform unstructured sparsity across all the convolutional layers while only keeping the first layer dense.
More experiments on other datasets and the detailed hyper-parameter setting are provided in the
Appendix .
| r | 61160a00c0bb9a45fc07950aa52fa876 |
In the first task of legal text classification, the best option in this task is determined based on experimental results, for example, in this way we found that multiple strategies can be used to get around BERT’s limit to sequence length of 512 tokens, but the ‘head & tails’ strategy where only the first 128 and the last 382 tokens are kept performs the best such as the work in {{cite:848113443d8a7759d454681f7f650af443b66083}}. Tables REF and REF summarize the over all results of our model compared to three BERT variations for Arabic language on the classification task with two datasets namely, SJP and BoG. On the dataset of BoG, AraLegal-BERT, outperformed the all models by 0.7% in F1-Macro average higher than the highest model of the three, which is ARABERT-v2large. Similarly, our model also outperformed the rest of the models in the SJP dataset, with a good difference between it and ArabBERTv2-large, which is approximately 0.4% in F1-Macro average.
| r | 2f03caa0b19066e91a8b32161b131ee4 |
In this section, we evaluate the performance of mmWave VCs using NOMA at road intersections.
In order to verify the accuracy of the theoretical results, Monte-Carlo simulations are carried out by averaging over 10,000 realizations of the PPPs and fading parameters. Monte Carlo simulations are carried out, and they match perfectly the theoretical results, which validates the correctness of our analysis. We set, without loss of generality, {{formula:b151f80e-9f67-438b-9e9e-7290b59ad148}} . {{formula:06e69e84-dc8e-470b-8bd8-3ddbeebbec96}} , {{formula:0a924152-ecde-4027-84bd-009d10fdc885}} , and {{formula:84c36fd0-cf5a-4fd8-a967-755dac29c896}} , {{formula:a7fc56e2-2326-4fad-b44a-ed03c19f1e91}} {{cite:c218c6953871f1aa93a4007c1a666846235f01d2}}, {{formula:55d0dd63-d87c-4939-b9ba-8952fd21d1ba}} . We set {{formula:81c634c5-1481-4ac0-859f-a12b3c4d136c}} , {{formula:baf91e29-cac8-4b9e-ba91-56b0e927fb44}} , {{formula:d3ccb3e3-482e-4e02-af73-7103c8cb10b1}} , and {{formula:1150a1aa-e358-4ce7-a09b-4c6c8db95e15}} . Finally, we set {{formula:473f7af8-cc0b-4cdf-8a34-d936a7b4453b}} dBi, {{formula:79be57d3-68f0-4ee4-b991-24c3f2746de9}} GHz. Unless stated otherwise, we consider mmWave VCs using NOMA in all the results.
| d | 3db6a5dad61ffd272fbc1a7b971a7b24 |
The recent detection of gravitational wave signal GW170817 originating from binary neutron star (BNS) merger by the LIGO and Virgo detectors have opened up a new era in multi-messenger astronomy {{cite:19100ca6262b7265d238166f8f1e96f104f3a568}}, {{cite:a8fded46b65eb3546931499d5b4ac7acbb586182}}, {{cite:76e2e14d82eebad4b5eeb547ea48f2e195745c8e}}. Additionally, short gamma-ray bursts (SGRBs) were also detected by the Fermi satellite GRB170817A indicating the presence of huge magnetic field in the merging event {{cite:b2cb4c3598f08cf6bf8fc95db68edf99c9daf529}}, {{cite:021d0d99912a45f0b9732d06bdec89d4ac860dc0}}, {{cite:aff0bd6dcf888ffc84a27e2a0d9db0b86e473c9c}}. These mergers are unique astrophysical objects of significant sources of gravitational radiation, electromagnetic as well as neutrino emission {{cite:a6a19a2b8148b483ef59acea934cfdda1bff2bf7}}. They offer a novel avenue to study highly non- linear gravitational effects blended with complex micro-physical processes; serving as Einstein's richest natural laboratory {{cite:c2eee9a1d84134abad93b5bd26fe194d68e05019}}.
| i | d74d1af574b1d6332c358824736145c6 |
Towards this aim, the initial work {{cite:afd7083224867e79ff06a1dbfc54c8dc5689d2f2}} proposes a framework that explicitly incorporates the noise into a numerical time-stepping method, namely a Runge-Kutta method. Though the approach has shown promising directions, its scalability remains ambiguous as the approach explicitly needs noise estimates and aims to decompose the signal explicitly into noise and ground truth. Moreover, it requires that the Runge-Kutta method can give a reasonable estimate at the next step. Additionally, irregular sampling (e.g., when dependent variables are not even collected at the same time-grid) cannot be applied, which can be highly relevant when information is gathered from various sources, e.g., medical applications. This work discusses a deep learning-based approach to learning a dynamic model by attenuating neural networks with adaptive numerical integrations. It allows learning models to represent the vector field accurately without estimating noise explicitly and when dependent variables are arbitrarily irregularly sampled.
| i | 59e6c50733e69f03d446232f393d2510 |
Here we provide more visual examples of the sequences generated with RIVER. See Figures REF and REF for results on the BAIR {{cite:3d1c38fb87b18ca574d29bf095efacf2501af97b}} dataset, Figures REF and REF for results on the KTH {{cite:cb06277c1c98053b9fe31a928cf804a6feed6fcf}} dataset and Figures REF and REF for video prediction and planning on the CLEVRER {{cite:5dfa1bdad8378691dbd1c4c028b735d677f98e0a}} dataset respectively. Additionally, we highlight the stochastic nature of the generation process with RIVER in Figure REF .
{{figure:f796e570-ba1b-42b5-983b-71f48e07a76f}}{{figure:c79c720b-eafb-4850-b843-99671091cd2f}}{{figure:89c2ee38-abe3-4b3f-80da-86d89f3d60f1}}{{figure:b1ec14e5-f301-4de0-821c-4fa59e352fe6}}{{figure:83ea5359-6ed7-45db-b66c-2fad99f6c8e5}}{{figure:a253d055-efc3-42a0-944c-5801dc5e8720}}{{figure:90e7479d-4662-4f9d-9e37-cd0002f89001}} | r | 6afc0c3091ebc5568aa8670bbf836d8a |
We designed a CNN that could accomplish the dual tasks of ECG beat regression and ECG
segment arrhythmia classification. First, the network architectural requirements were posed as
an optimization problem, which we solved by using Ray Tune library {{cite:4997c2f7e5256880e6a818d3a5d6fc6b82853db1}} to
choose the best performing configurations. Neural networks with different permutations of
user-defined hyperparameters were trained on the regression followed by classification
tasks. The value of validation loss of individual architectures with specific combinations of hyperparameter settings was expressed as scores. The aim of the optimization process
was to find models with the lowest score for the classification task. For optimization training, the
following options for hyperparameter settings were considered: batch size, 50 and 100;
the number of convolutional layers, 3, 5 and 7 (these were common to both regression and
classification tasks); the number of channels in the first layer, 8 and 16 (this number was
doubled in every successive layer until the maximum, 128); kernel size of the first layer, 64
and 128 (this number was halved in every successive layer until the minimum, 2); kernel
size of max-pooling layers, 3 and 4; inclusion of batch normalization layer, yes and no;
number of classification layers, 1 and 3 (which were added in the classification task);
the number of neurons in the classification layer(s) or the last layer in the case of regression,
1000 and 3000; inclusion of residual connections from all convolutional layers to the first
classification layer, yes and no. Async successive halving algorithm scheduler {{cite:c311dbc6bfca489af0e796781893e2edf34146c3}} was used for hyperparameter optimization, which works by evaluating multiple model configurations and dropping not promising ones based on initial training performance. This allows for time and resource effective search given large hyperparameter space. The hyperparameter search was carried out for approximately
12 days. Upon completion of the optimization, the best architectures and training processes
from those evaluated were chosen.
| m | 467710b6360f41309c6dfb98f03cc8da |
Metrics.
We use the matching precision (%) metric here to evaluate the dense correspondence estimation performance. Theoretically, it presents the correct correspondence percentage by {{formula:d10dab6d-ecc8-480b-8524-4e325624a6d4}} ,
where {{formula:ffdec588-0cdf-4092-96b3-2d594a8c88c3}} is the Hadamard product, {{formula:6aed2cd6-a48d-4be0-ad6f-ba07e311d3c9}} , {{formula:ddbb0ae4-093a-4165-bac8-ff76f8f1e966}} represent the predicted and ground truth matching matrices, respectively. In actual application, this metric is often relaxed by confirming the correspondence as a correct result when the distance between the predicted corresponding point and the real corresponding point is less than a threshold. Here, we propose a self-adaptive threshold as
{{formula:8eca3097-b9f4-49d0-8b98-d84d19b375cf}} , {{formula:4bd14630-efd3-4470-a605-8f2a8466c059}} ,
where {{formula:982ac581-480d-44f9-b175-d62e28d6ca48}} is the Euclidean distance between the points {{formula:f373f394-1bcc-4434-a53e-4a9c6a0df7d0}} and {{formula:fe427d0f-f913-4da4-bc24-7868c5bbffc2}} , {{formula:0968940f-7c16-4acd-a48b-642ddbb44d72}} represents the K-nearest neighbor. In other words, for {{formula:b4c1cee0-304f-43d3-8a01-9b66f71db05e}} -th point {{formula:39345661-694c-40df-8ac0-6032b38e180d}} , {{formula:6a17ad98-2448-44dc-9b0a-7f07cd0f0ae8}} is computed as the mean distance of {{formula:46895af5-da7d-485e-911d-b9e0f3c2c0dc}} nearest neighbor points.
Meanwhile, for a fair comparison, the metric of per-point-average geodesic distance {{cite:10b78edcb24333ab27c849af9664232b64c3d3f6}} is also used for the methods with 3D mesh input.
| r | 7f6c9be070eafba4300c3ef55983c7f9 |
Until recently, SNNs have been restricted to simple tasks and small datasets due to instability in learning regimes {{cite:f83ee568f4ee5ec27f6efa65a02428e19ef1e1f6}}.
Recent development in new spike learning mechanisms {{cite:b1b74d48e87de2c90c15ff24c333fcdebfda582f}}, {{cite:f8e65a45c6c5dcbea16175b72e372e544486d634}}
has made it possible to design SNNs for real-world robotics applications. This coupled with neuromorphic processors such as Intel's {{formula:8e2af1b8-41db-44a4-bd83-c2cbffc791b4}} Loihi {{cite:25b7a853af2d5e01b31339c5654414fb8d1012e3}} and IBM's TrueNorth{{cite:a188471c52a5f55c6113672fa3d0c132e66bd081}}) along with neuromorphic sensors such as DVS {{cite:0995a546fd33db030e7f414d2d0b23ebfdb98b18}} and ATIS{{cite:5ff241bf6c43edee5fe089e306456f9e9007803d}}) have made it possible for producing real-world prototypes, drastically enhancing the appeal of such technologies.
| i | 5183f0aefe09fc7a2600b383046475fd |
Features-only: The simplest way of incorporating pre-trained features is to directly use these pre-trained features as the input for the decoder. The decoder of the original model is adjusted to fit the dimensionality of the features.
Concat: Concat simply concatenates embeddings {{formula:1b17643a-a425-4568-b06e-e3f2c6d2d2a2}} and pre-trained features {{formula:8130900a-da89-4392-969b-73cdaa822df4}} along the {{formula:2fa1f7f5-c1a9-49f3-ad2a-1fe7a820c732}} dimension. The pre-trained features, therefore, act as a supplementary of the embeddings and the embedding space is transformed into a joint feature space. The decoder then has the flexibility to decide how to leverage the information from the joint feature space. Since the concatenated embeddings have a larger dimension along {{formula:d2756929-cce4-4dad-8b4d-e4b7a7db285c}} than the original embeddings, the first layer of the decoder will be adjusted to fit the dimensionality of the new intermediate representation.
FiLM: A Feature-wise Linear Modulation (FiLM) layer is originally proposed as a general-purpose conditioning method to assist visual reasoning, which is difficult for standard deep-learning methods {{cite:7a114b42e347d61063888955c6bd320a2ce959f1}}. The success of FiLM leads to its successful usage in several audio-related tasks {{cite:b0822f489f7ef7c282f7103916807744e6003586}}, {{cite:b60b41c4ac39d5ef9fd2654a0c9d59b37ee1681e}}. The FiLM layer influences neural network computation via a simple, feature-wise affine transformation based on conditioning information:
{{formula:80e9df7f-4f22-44a6-86b3-1e8f24ff08bc}}
where {{formula:0ad2e7d6-5892-4df3-902d-7c721cafe3e2}} and {{formula:efae0967-fa8f-4ae8-93f8-b85dd4a1a6fa}} are calculated based on pre-trained features {{formula:7f297483-381a-44ec-887c-ecc3cf738f61}} . We use a simple linear layer for the functions {{formula:5d9f2d0a-3cb2-4321-817c-4a801c046dcd}} and {{formula:759f7c02-4ae3-47e5-aa72-4cd46cd646f8}} to compute the transformation parameters {{formula:615f89d9-03e3-4de9-947b-2a06dcb1c002}} and {{formula:ebcd8ae8-2742-4970-882c-87afea9d05ee}} . The resulting embeddings after the transformation are {{formula:959f3235-f850-479c-97fc-8a2b9bdd1b2e}} .
| m | 44ed2c2432bd669f4816344d104e2fcf |
According to the latest experimental data of 2020PDG {{cite:da744c063b364054b5e5704156f0d652eee87a3c}}, the {{formula:a3cb1a92-e86a-48fe-b705-365a52389785}} decay branching ratio is {{formula:a41dbad1-dc17-48eb-9a29-72d4a025a601}} , which coincides with the calculation result in this paper, {{formula:4c43a8d1-a222-41ce-ae21-d4b824d90bbe}} . As can be observed from the numerical results, the resonance {{formula:e4c42d96-e0ba-469d-9031-fa789694c9b5}} is the main contributor to the decay {{formula:e11984db-4e41-48b8-bb5e-3c79e04f2fcb}} , accounting for approximately {{formula:8d2345a5-8108-4d27-b5f0-592f05753bcf}} ; while the contributions of the {{formula:dfb2f9b1-c90e-47c7-9b51-25b3871c453c}} and {{formula:481c9a34-855c-4429-82b9-7ac7c760e639}} resonances account for {{formula:9995b4a6-87b9-411a-afba-01f54eee62b4}} and {{formula:207a2920-fd9d-4d1a-8ca9-7b09ceb114d9}} , respectively. Moreover, the interference contribution items of the three resonances amount to roughly {{formula:a96d67cf-51bf-4811-81fe-4720dfd76fe6}} . The {{formula:86c92bdc-c092-4ecc-af56-c09adad9b540}} resonance is also the main contribution source for the {{formula:92227e31-1c34-499c-a550-cc1dc6c616d9}} decay, accounting for approximately {{formula:ba5228c0-015e-4b07-98b7-fb04c3fc43d5}} of the total decay branching ratio, while {{formula:96efdf48-b5e1-4d97-a654-16f247cfa152}} and {{formula:5ec09b97-d51f-4e4c-95a7-3fb217aee76d}} resonances account for {{formula:fb2065d9-afad-4425-95ee-a27933149d6a}} and {{formula:1a479712-4596-4f47-a44c-e831bb76dc0f}} , respectively. Furthermore, the interference contribution items of the three resonances amount to roughly {{formula:0011d8ac-b856-4127-af05-6700bd090c94}} . According to Table REF , there is a small gap between the decay branching ratios of {{formula:eff3c689-e31e-4463-ac1f-6581de2cc740}} and {{formula:6852857f-5665-4355-94de-547009a55168}} . This can be attributed to the fact that the resonance {{formula:109702e0-defd-4d9f-8915-e09128f18bc2}} has a large width.
| r | a5028ec3c25af8b37299fa53e66927a0 |
Limitations.
One limitation is that LiVT can not be deployed in an end-to-end manner. An intuitive idea is two branches learning to optimize the decoder and classifier simultaneously, like BBN {{cite:d0d6f6209261ec5856f96b632daa184ed8bbd333}} or PaCo {{cite:9bd61a1bbc950e791e44c3b79a479be6f4bf5617}}. However, the heavily masked image prevents effective classification, while dynamic mask ratios exacerbate memory limitations.
| d | 00f7588a3a0d44f65ad2befd344077cb |
Random forests can be understood as local adaptive likelihood estimators for
the conditional parameter function {{formula:bf8d6d3e-6a93-4eea-a3d1-4cf4f2dd6d66}} for a patient with
prognostic or predictive variables {{formula:795842ed-4303-4c99-8625-72aa16e7ac0b}}
{{cite:9260c1083dd19818cacf6d9c852c83861bde1fba}}, {{cite:0744f0fc907ab8f97e2d3831592fdb660fe699a3}}, {{cite:785a1d3e68b65ef8f3bc1238b571132b28ce812d}}:
{{formula:f04cd590-4132-4ca7-9e2c-19932efa4bf0}}
| m | 468e4a520852bc588ec39368a07edd83 |
In this work we concentrate our efforts to explore three quantum properties: i) entanglement, ii) EPR-steering, as an entanglement-based correlation, and iii) quantum discord, as an above-entanglement correlation, in bipartite two-qubit states affected by various quantum processes. Specifically, we report on the dynamics of EPR-steering by means of the Costa-Angelo criterion {{cite:e2ec51d54c66d0d57ca90855c6353be32cc2e376}}, quantum discord quantified by means of the interferometric power of quantum states {{cite:9b0fae8744a2a82655f3a821ebf0821b059d9ed7}}, and entanglement quantified by the concurrence {{cite:1736d2e99f6a895abd1a9b7759cb358e17490e6d}}. We present a systematic analysis of these quantum features under different noisy channel scenarios, as well as under entanglement swapping protocols. First, we show that relatively straightforward noisy channels can still induce nontrivial dynamics in the form of sudden death as well as a death and revival of EPR-steering and entanglement. Second, we show that whilst noisy channels generally reduce the amount of quantum properties present in the system, swapping protocols on the other hand can increase the amount of such properties, even to the maximal amount allowed by quantum theory. These results therefore illustrate how quantum processes can affect the quantum properties of physical systems in both negative and positive manners.
| i | 9882e06a642287da73288dc0876d59d1 |
With EnCluDL, the statistical inference step is performed by
the desparsified Lasso.
In {{cite:910e92dfbb529ed18cf13d54dfd771e55afae06f}}, another ensembled clustered inference
method that leverages the knockoff technique
{{cite:02012c5a01098f59058247963c4e4c8cada40ed2}} leading to a procedure called ECKO
has been tested.
However, formal {{formula:5b2353ab-4c4e-4cf3-a493-70df7b3b823d}} -FDR control guarantees have not been
established yet for this model.
It would be also quite natural to try other inference techniques such as
the (distilled) conditional randomization test {{cite:2606983faff6b8fb7ad5f0c09ac4f3356f14d9d7}}, {{cite:5d9ae986db67280a08601a0916d557f13bc8126d}}.
| d | f57ce8647bbe1684eb3bf0150e0f5d5d |
A common method for constraining EBL absorption is to take the observed spectrum in a region where the EBL is unabsorbed, extrapolate that to a region where it is absorbed, and take that as the highest possible intrinsic flux {{formula:a87d9d68-7e3b-4651-9a1d-23c63f23eaa5}} {{cite:e01f5703e239526e7f73de32ca5ca09ca70b5a82}}, {{cite:0987b69dc6933e07e40a9d1841c29b6fae18ecce}}, {{cite:841cce9c7a67da03444ac4e6f8f1dbbc9b2d6316}}, {{cite:489cbb6770e1e1ac68ec0dc285a181f4f027293a}}, {{cite:7510d544014e5e2c19ff479a3b474d46088b672d}}, {{cite:974979364224d448a2a6f5b12bf22238d5fee053}}, {{cite:dc2badf7ae7f2ae7bd56f102454b24acb77a9518}}, {{cite:56bd15904957919bb313cf02c6f64275e58496f5}}, {{cite:7212de4728348c00a868ff62638ad2a3f99c5c50}}. We note that in the 0.1 – 1.0 GeV energy range, the EBL should be completely transparent to {{formula:01505277-e28a-4b56-981c-b8830a07f70d}} rays in all EBL models. At higher energies, the intrinsic flux is attenuated as
{{formula:a32531ef-d4fc-4376-8a17-ea61ce2072a6}}
| r | a34c0ea892f3ef3fcde7e29dd4afdf41 |
Recent years have seen increased interest in hatespeech detection to combat the proliferation of toxic language spreading on social media platforms such as Twitter and Reddit. Many datasets have been annotated based on human-written social media posts {{cite:5960e92c4b167c6da46ccca165fd8ae4f3bfb116}}, {{cite:5921ed033bb0963b759fce36f2ba271e16258397}}. Individual work might focus on one or several specific aspect(s) of toxicity. For instance, {{cite:fc6db9413a3266c2a7f452a8d35dbf568f9a9665}} annotated Facebook posts on covert aggression, {{cite:27c7f9f4ee1f2ac7aa981156c7a64b76e7f0a03d}} studies cyber bullying. {{cite:80cabf64b73e08604f8d1c0f0346e23992f6d53c}} and {{cite:0d94025a1075e3ca8c6c9583f91f02e2c56bf751}} provide multi-faceted labels regarding the targeted-nontargeted and individual-group distinctions. {{cite:885c870ebc3cde57b9d2ce01bc3e624161843fbb}} explores a dataset where toxic comments are organized in six classes: toxic, severe toxic, obscene, threat, insult and identity attack. Various bias detection methods have been investigated in the literature, including keyword-matching {{cite:0e9587bef39f6eae979849bd186bd15dc8227c70}}, traditional machine learning classifiers (such as SVM {{cite:4df557b2cbc8efb9c7f8032fe462e6a2217ecf37}}, {{cite:8d76f22793d6ff77e4b8a6106f4edc238ad7df63}}, logistic regression {{cite:59468358c2604fb9466563c6a749a4fdf3025903}} and multi-layer perceptron {{cite:59468358c2604fb9466563c6a749a4fdf3025903}}), as well as Convolutional Neural Networks {{cite:885c870ebc3cde57b9d2ce01bc3e624161843fbb}} and the most recent transformer-based approaches {{cite:b3b3564bf16a2f7485a400e45fdaa82a68f58b3f}}, {{cite:26218844361f21803a417ffa1e98e36b79bd6e5f}}, {{cite:3fd1fc3cd540a8fb0bceda93bfc9f547cbe07ae9}}.
| m | 31401cea42893610eaeee8646f2f1e1e |
NGC 3393: The starting spectral model for this source is provided by the work of {{cite:e1cbd74f2578e128cfe7b7a4d82b20cb869055e6}} and {{cite:fc8affad75f4471458a5e842e1cb7ee1cb34e5e3}}, who fitted the NuSTAR spectrum with both MYTorus and Torus models. The results obtained with our baseline model are broadly consistent with the results presented by these authors with a slightly larger value of {{formula:5858d784-27c8-404b-8cc1-b0bd4d6804df}} ({{formula:f57308bd-0e33-497e-bfc8-b15261da1d92}} vs. {{formula:7b0e09e5-d609-440b-9f8a-ac452aae0b7f}} ). The 2–10 keV observed flux is {{formula:fc3f0db5-b757-48d7-86c6-7ab6920024b8}} , and the intrinsic one {{formula:79c099ff-a7c1-463b-a78b-cdbd94c841e2}} .
| r | b532afaa5f65f933e63636da696aefb3 |
Similar to the offline method, the end-to-end method is designed based on SQLova as well. For the condition value subtask, the start and end position of condition value are predicted through a pointer network. The difference is, the representation of each cell is the output of an bi-LSTM encoder with BERT{{cite:615242871d255980d4274e961947f40cdba1dcb9}} lexicon embeddings as inputs, and the bi-LSTM is shared for all cells and trained respected to the loss of model.
| m | ee5e3e2777a0950dc9e91fcc07ccad00 |
The Markov decision process (MDP) is a fundamental mathematical
model used to handle stochastic dynamic optimization problems
{{cite:71de1858bcb3305cdfc8044322bc96579c680466}}, {{cite:c279eb9d843ec8cb8b73f1872c88e0f75bdf27a5}}. The study of MDPs in operations
research is multidisciplinary. It is deeply connected with
reinforcement learning in computer science
{{cite:70156de8ccc7f84b5cd9a144eea75442ccbb38bb}}, {{cite:8f2da121cdca2bfe1608a3c12b822c40915a412a}}, optimal control in control science
{{cite:a73351b6a1ffe4b1d48ecfb230e80666b7ce757b}}, {{cite:7732d044c295b2c7edfec2771cb7aa2cc3912ff4}}, and dynamic discrete choice modeling in
econometrics {{cite:4a5985df088b36eefecab13589a72864ff9f6692}}, {{cite:fbd14ec90797dfd7202c09d208672a55e3e2ceee}}, etc. Traditional MDP
theory focuses on the criteria of discounted or long-run average
cost, where the principle of dynamic programming plays a key role.
However, for other optimization criteria, such as risk metrics in
finance, the corresponding optimization problems usually do not fit
the standard MDP model and specific investigations are needed case
by case.
| i | f9b3ca05d085a56e382718f578a3eb00 |
Deep neural networks can be used to approximate hyperbolic partial differential equations.
The construction of heavily over-parametrized functions by deep neural networks rely on the foundations of the Kolmogorov–Arnold representation theorem {{cite:1e66b99538edf4716a8edfe39003c73bcb9ad4cf}} and the universal approximation of functions via neural networks {{cite:33fb9b43934a58349204d1ec4dc9c421a726095f}}, {{cite:149f082711989dc928bc1441722f1e20856cc3e7}}.
For the data-driven modeling of nonlinear PDEs, deep neural network architectures such as convolutional recurrent autoencoder (CRAN) can be efficient and useful for constructing low-dimensional learning models {{cite:aa3229ee014985a745eb85ef5a9db52b0ca215d4}}, {{cite:2326965dbcdba28ec3a908d4edb872c3dcd4e11f}}, {{cite:c23250254e08002f02b1fa9f02bc9b8ed7ecfc30}}.
CRAN is a fully data-driven approach in which both the low-dimensional representation of the state and its time evolution are learned using deep learning algorithms.
Convolutional recurrent autoencoders have been shown to perform well for unsteady flow and fluid-structure phenomenon {{cite:165e93e2aa0a5c05136f8057d1321d50b067599c}}, {{cite:2326965dbcdba28ec3a908d4edb872c3dcd4e11f}}, {{cite:c23250254e08002f02b1fa9f02bc9b8ed7ecfc30}}.
On the other hand, the ability of current CRAN architecture to learn PDEs with a dominant hyperbolic character relies on learning low-dimensional manifold with convolutional autoencoder and evolving these low-dimensional latent representations in time via RNN-LSTM, which can pose difficulties to generalize for the various physical phenomenon characterized by hyperbolic PDEs.
The current work build upon on our previous work on the convolutional recurrent autoencoder net for the unsteady flow dynamics and fluid-structure interaction {{cite:2326965dbcdba28ec3a908d4edb872c3dcd4e11f}}, {{cite:c23250254e08002f02b1fa9f02bc9b8ed7ecfc30}}.
| i | 21a4c788bc2e5901d05c5e86a3af6651 |
where the values {{formula:6602cfb0-6f7f-4d6f-b166-4415c90659b1}} mb at 2.76 TeV and {{formula:eff42263-7ee3-48ea-bad3-0aa7aae3dd19}} mb at 5.02 TeV have been considered {{cite:b889c7f62ddc646836539139afebf13965ec286b}}.
| r | 8e4baa2f4b119e8c9f74fdf43604c560 |
In a bipartite quantum system with density operators {{formula:e3fdf651-ae3f-46a6-83ce-94b8d952e31a}} in a Hilbert space {{formula:0f098100-217f-43e0-a51f-641c8bfdc0a6}} where {{formula:47b29a93-1b4e-4343-b9dc-e78c6ec787fe}} so {{formula:af7f8884-adb1-4b5f-bb26-5e1a1f344273}} , a {{formula:99bfb2ea-0c2b-4736-8036-980da5582dcd}} system has {{formula:1d30f4ad-ca48-483a-b6e1-3a2f2193cece}} , and the entanglement of any {{formula:9b5683ce-bd8c-4156-a342-f900a76a0555}} in {{formula:0ea397bf-396b-4dfd-88b8-3a5085cc480d}} is given by the I-concurrence {{cite:cc89bf94f348d16001ffa733990696ce866fd8ae}}, {{cite:4ed130f2f4997794111b676ad005192283ae901a}}, {{cite:c73952b0ba807d703e75d72d6ae1a1464ff1f469}}, {{cite:c5a53d772c39226ef9077ec34f7c6cb9029c3b1f}}, {{cite:7552bf7e52ed8295b75f50766942ce1841774602}}, as (from [sec:App.A]App.sec:App.A)
| r | 206870a8e99cba4de53ef482aa577151 |
The vision system is hybrid in nature with two different methods, a machine learning object detection and a classical computer vision method, each of which is designed to operate depending on the relative distance to the landing pad. In the long-distance, the machine learning object detection method is applied to identify the landing platform (the ship), and an image-based control is utilized in the autonomous flight control system. In recent years, there have been many studies to develop algorithms that guarantee fast detection as well as higher accuracy, which are essential to reliable UAV operations. Various algorithms and architectures of Convolutional Neural Network (CNN), a class of deep neural networks, have been proposed such as Region-based CNN (R-CNN) {{cite:b367c69007fba458e2329494b40b13297df1b260}}, {{cite:116f37c4ede3827d11c6779e1ab87d2e731e9ac7}}, {{cite:b89cff32605ddaba36d9a5dbfda02865b8472ddc}}, Single Shot Detector (SSD) {{cite:62a0856e725127427bfefea78ed1170437b15097}}, and You Look Only Once (YOLO) {{cite:ab28502c5b9ed76264db23fddf445aa0d02d1d5c}}, {{cite:d52b8f130c1304d9021c2dc6b513389914307319}}, {{cite:4b3b3517e63368b344d1a2b6c690ceb90a572f1d}}. R-CNN is classified as a two-stage detector that combines region-proposal algorithms with CNN to extract 2,000 regions via a selective search, then classifies the selected regions on the image. Later, its variant Faster R-CNN is introduced to improve the detection speed by replacing the slow selective region search process. Meanwhile, SSD and YOLO are classified as a one-stage detector that regards object detection as a regression problem by taking an input image and simultaneously learning the probability of an object class and bounding box coordinates. According to the studies that compared the state-of-the-art algorithms, YOLOv3 demonstrated faster detection performance than Faster R-CNN and SSD {{cite:4b3b3517e63368b344d1a2b6c690ceb90a572f1d}}, {{cite:6b4ba95541581e4e917592efbf9ead0a3236fbd1}}. Hence, the YOLOv3 algorithm is selected to train an object detector that is able to detect a ship and a horizon bar in real-time. It is not only visually tracking the object but that information is relayed in real-time to the autonomous flight control system. Once the object is detected, it provides the object position and its bounding box in the image to the autonomous flight control system. Even though the actual relative distances are not estimated, the size of the object and its position in the image are sufficient information to control a UAV to approach the ship from a long distance. The verified maximum range is approximately 250 meters (820 feet) when the object occupies an area of 1.8 x 1.8 meters (6 x 6 feet). Considering the range is proportional to the object's occupying area in the image, a typical small ship where the rear-side occupies 15 x 15 meters (50 x 50 feet) area can be detected from 17.3 kilometers (9.3 nautical miles) away.
| i | 0ae448dc1731f0026e77da96e14c3982 |
Improved GANs.
Despite the high-quality generation, GANs suffer from the “mode-collapse" problem, wherein they fail to capture entire modes in the real data distribution.
For instance, a GAN trained on the MNIST dataset – a collection of handwritten digits from one to ten – might neglect a subset of digits from its output.
Furthermore, training GANs can be tricky sometimes {{cite:7f1a777c846c5032418a60360050d868c5cb100f}}, {{cite:087f06ec7fa4dd940b479791b66a531522039f23}}.
An interesting line of solutions includes an implicit maximum likelihood estimation training objective {{cite:ddf3c4e0dd581bd0ce52738560a6a146f2e71c30}}, {{cite:40ff7ba8e347f591a53ba86da602a39225578775}}, {{cite:ac878a522fc0e4f20d01e72090325eda06add7b1}}, which insists on the use of full-recall GANs.
| d | 492409368f7634af80aae2faf8e4ae20 |
+ C9(s PR b)( )
+ C10 (s PR b)
( 5 ) ] .
Here {{formula:4d6e96a3-49fa-4db9-bf01-5eff9e588415}} and {{formula:6ff8e781-40f0-4865-b7d0-3d2a7865da9c}} are the new physics WCs which are assumed to be complex in the current analysis. Following a penurious approach, we ruminate only those scenarios where either only one new physics operator or two operators whose WCs are linearly related, contributes. We call them as “1D" scenarios. Under this assumption, we perform a {{formula:8870a0bf-99d4-441f-a898-6846860414d5}} fit to identify solutions which can accommodate the current {{formula:10b3d0f5-5b74-4284-b944-036a22b822f3}} measurements. The fit is performed using the CERN minimization code MINUIT {{cite:b9fc24f52ffa56d655f8f817b49e6410ff7e332e}}. The {{formula:28fd232e-037f-452f-86db-aa02544e1090}} which is a function of new physics WCs is defined as
{{formula:1cd949ec-36ea-4b10-9e4c-3fc5c85c7f1d}}
| m | f62a2b4275fbf17b3e7d6b4702b6b663 |
Making sense of the fundamental quantum nature of matter withing the context of General Relativity (GR) {{cite:2e9face8779c189eed9b86e970739a7934d91eff}} is the holy grail of modern theoretical physics. Intriguingly, discrepancies do not restrict to the UV where ignorance is easily acknowledged, but are already strikingly present in the IR picture of gravity, where according to a Wilsonian effective field theory (EFT) point of view everything should be well understood. The most prominent example is the cosmological constant problem {{cite:3e388ae418b99f28944e927c2e3fcb120a377ff9}} which has gained a new twist with the evidence for an accelerating expansion of the universe {{cite:79f5eed1042d0dd64ad2f326475423654d230030}}, {{cite:9093e9ce835cad877bff8d4a109abcaa5f9eb79e}}, providing the main motivation for a multitude of proposals of low energy modifications of Einstein gravity {{cite:075653d79c23441ef1268e27b803a3eb64b7c498}}.
| i | 99aeae75bdf5cd10517c1af638929b2c |
In survey data, informative sampling designs are accounted for in unit-level modeling and inference through the use of sampling weights, as done in the Horvitz-Thompson estimator for population inference {{cite:bdc1b9d04be8b1c18e049213c16a2026ef785808}}.
A general approach for likelihood-based inference with survey data and informative sampling designs is the use of pseudo-likelihoods, where each unit's contribution to the likelihood is weighted by its survey weight {{cite:8d1d08c78b4f2a165d95b4a5e949363e85a9b556}}.
We note that the term “pseudo-likelihood" was first introduced by {{cite:f94516c215b648e08ce51aee0c053a4ff2558ee8}} in the context of analyzing data having spatial dependence.
His approach leveraged Markovian properties of auto-normal models and approximated the likelihood as the product of marginal densities.
While the pseudo-likelihood is not the true likelihood function except in the case of independence, it is a computationally simpler method for parameter estimation than traditional likelihood estimation.
See {{cite:edf73a78aa56fb2b406d7f8825509991a33ace17}} for a more detailed review of modern methods for unit-level modeling under informative sampling.
| i | fe4f50f93727b38b1856cd4083fcdf53 |
Table and Fig. REF present the quantitative and qualitative results of state-of-art methods on the NOCS dataset respectively. The comparison points include learning-based methods relying on a category-level prior, such as NOCS {{cite:c92cdf03f7753fb9547107fe3f89217138520137}}, KeypointNet {{cite:1725d013314f1ee9f749f24c0e606ec79f415f33}}, and 6-PACK with or without temporal prediction {{cite:8befb2228b7cc623d66bbef18828e679d65ff6ea}}. These methods are offline trained on both real and synthetic training sets, which are rendered with 3D object models extracted from the same categories of ShapeNetCore {{cite:12e6853001849f18cfecf58ab4d14c043ac72d1b}}.
In contrast, ICP {{cite:19d532ffc643afd2f1d5714bfa5e884f915404a3}}, MaskFusion {{cite:10e8424da98c2b4874a5342f7a6cda1da66748bf}}, TEASER++* {{cite:42ab29f4c23c1697a11849af5d11b75552f70d69}} and the proposed BundleTrack have no access to any training data based on 3D models.
| r | 1a4404d57d947de74848abde7ad9e5db |
Finally, it would be interesting to extend the approach developed here to more realistic models of active particles. This includes studying other models of active particles such as active Brownian particles, which typically model many types of self-propelled colloids {{cite:dd2b594b00cf6986ed15f19418452faf438789c4}}, {{cite:078043abb37f2c9742b8dd990d9212ac3aa70e6a}}, and run-and-tumble particles, which typically model bacteria {{cite:5acd7f9efbdc18df4cb13932b69dbcc641b0e58d}}. More generally, it may be interesting to study models where the correlations are not exponential or the persistence times have a broad distribution, as has been seen in some bacterial systems {{cite:e7af7092e5a35db58d576973791905a6a33d353a}}. An important question is whether there are critical differences between the many models of active particles, for example, when interacting with boundaries. In addition to studying different models of active particles, it would also be interesting to include interactions between particles in our approach. It has been seen that a simple repulsive interaction can have significant effects on the density and pressure of active particles {{cite:d5fc8e2f55f98884b8093ee45cd184c770229e41}}, {{cite:77414e2c044712b1b9437a5e24bcd562c06779d1}}. Similarly, as was discussed, interactions may affect the transport of active particles in corrugated channels {{cite:7cda6a32a47978cdab0d1b061c4263667e5e975d}}, {{cite:d9479e44587a038f2977e06be27f601d14ed033a}}.
| d | a04f24ab98c543dae246a5a96df2a12a |
In this study, we introduce the term Face Area Lightness Measures (FALMs) to be any technique for characterizing the intensity of light reflected by human skin in the facial region, as measured by a sensor (this has been called many things in previous studies: lighter/darker-skin {{cite:7df3012e5a33cddc24fca0513d79df81b76170be}}, tone {{cite:f0c7a38a0cae4229501dd4afefb5137a75bc12db}}, {{cite:f8c445d5c4ed0442eedc7e9d3b1c72c43ff1d88d}}, {{cite:f817a51f66cfd1afccf01cd87888f515a08af058}}, reflectance {{cite:bc5f4d4fb15ed183a9c46e6b2a15e3874235bbe1}}, etc.). We assess variation in FALMs estimated from images taken in various environments, at various times, and on various devices and compare these measures to ground-truth measurements from a calibrated dermological device, designed specifically to measure skin lightness. We then explore the suitability of FST as a proxy to FALMs by comparing ground-truth FALM readings with subjects' self-reported FST. Finally, we perform data simulation and modelling to show that poor FALM estimations can result in the erroneous selection of categorical demographic race as the significant explanatory cause of performance variation, even when this variation is primarily driven by FALMs.
| i | 0743a39a410910c2c0ca02f9b10a8d4d |
A future challenge is to apply this approach to more complicated and more realistic implementations of the Faraday effect, paramagnetic materials in particular, with
typical spins of order {{formula:d3cce30c-f362-44dd-aa0c-596e32da69a9}} and significant dependence on temperature {{cite:a9c03256083e393b42b8cca5c08e7c1cc96c5ad3}}.
| d | 8c716eaf5ca510b05e4b90835b2a1809 |
Production of the structures {{formula:ebaf7acf-da68-4c48-8289-f03ca0a7d335}} and {{formula:d7143972-9ce4-4d32-8e04-27daf38ab6e0}} in {{formula:75332d6a-91b5-4801-8318-0406705c594e}} meson's weak decays
were analyzed in Ref. {{cite:d1ff739ca822e89400c304f8b8a6dd8611eb6a50}}. The central idea and main
conclusion of this work is that production of {{formula:95fcd059-9cbd-4f28-ae77-7fa6c3d2469f}} is dominated by
color-favored processes. It was also argued that competing models for {{formula:6ec1658d-f817-4846-85b0-fd26a29bbb7f}} can be unambiguously discriminated due to differences in features
of their production and decay mechanisms. Similar problems were addressed in
articles {{cite:26e76587ea14e299c273af63b414de759db71e89}}, {{cite:2d5a0df6072d61d5132af5e610eca30074c90161}} as well.
| d | e4526c8deff87ece43bc3b297dce0d16 |
We use approximation estimates for the projection {{formula:61327341-10f0-49da-b4b6-03bc347bc883}} , and an inverse estimate (cf. {{cite:7ec16fa2d3c775359e2a8352228f618f7282c701}}) to conclude that
{{formula:eb00c542-2655-4091-a3e8-cdb91fb4c47c}}
| m | ca8f7a82517c623a2cbb00db39a88011 |
Optical-atomic clocks, which are among the most precise metrological instruments currently available, provide continuous-wave (CW) laser radiation that is stabilized to a narrow-linewidth atomic transition {{cite:9ec273eede622eefcc0c674e02291a137af2534c}}, {{cite:b227ffbfa9e0fc34e4c52b972fac2c77ffdcd643}}, {{cite:d9bf0bd837d8594b6ab5f66ec1f737d834320baa}}, {{cite:7207f5f8b14543b830af7bc53f64390f0e728a43}}, {{cite:385c19bd0958abb61b83a423f7dfc1659d5815c8}}. Optical frequency transfer over optical fibers provides an ideal solution to coherently transfer the stability of an optical clock to remote sites {{cite:be3a287dd93aa9e912bd7fa7b23f7619b8023af6}}, {{cite:ccdba291aead03e59d3cc61293f88b43c23b11cb}}, {{cite:4bf2e4a11f1f3f3cbe03450c976d1d50f56ac639}}. This optical-frequency transfer capability was developed for optical clock comparison and timekeeping {{cite:464ffca1e0c3805665491dae10331512bb5692cf}}, {{cite:26f40f12a208fae040d03e646342a2622b1697e3}}, {{cite:3c2e3821b9e9e915ee8cc7d03b0084ec6d111710}}, {{cite:10b082537bc3f105ec663133e27bd27b9bf79b08}}, {{cite:afa2be2c0cf16371fd76d19e567f89317deea52d}}. One of the most common ways to implement optical frequency transfer is the active phase noise cancellation method, in which the fiber phase noise is detected by comparing the local optical signal with the round-trip signal and the compensator is implemented by actuating the frequency of the transferring optical signal {{cite:be3a287dd93aa9e912bd7fa7b23f7619b8023af6}}. In many applications, multiple-node optical frequency transfer is usually required {{cite:6ff4b0de7f89d6742ec298084062d8f56afdebc8}}, {{cite:81e56737dc59b337b82f2fc1702756f9d66f52e4}}, {{cite:700f2896c1f1e231c75e933738c37efcdb30fd5c}}, {{cite:cbd0b05b5357839db3c33123fed733482791dc77}}. To address this dilemma, a pionnering work was demonstrated that can provide coherent optical-frequency signals at intermediate sites along a bus topology optical fiber link {{cite:220576ac5a0eb9b6343d7bccaf75ee17bc0731e4}}, {{cite:dba5e5e779d0a2fb9ae7e9e284ee8dbdb0930748}}, {{cite:35d93e00e80be8fb67c2c0dcfc8dd70fae944f6b}}. However, this approach is limited to the fiber link with a bus topology. By contrast, many applications require the transfer of signals from a single master site to multiple remote sites over a fiber network with a branching topology such as the planned Square Kilometer Array {{cite:6ff4b0de7f89d6742ec298084062d8f56afdebc8}}, {{cite:81e56737dc59b337b82f2fc1702756f9d66f52e4}}, {{cite:700f2896c1f1e231c75e933738c37efcdb30fd5c}}, {{cite:cbd0b05b5357839db3c33123fed733482791dc77}}. An excellent scheme and its extensions {{cite:b7d9cd3d6485ca152fe627065a5434ea337135f0}}, {{cite:ba3f89070bea96365e71562a15e83a86d42db673}}, {{cite:aa66c510d9972b979d52b3155e085b476657e01f}} for fiber phase noise cancellation at the remote sites have been proposed and experimentally demonstrated. In these schemes, the phase noise for each branching fiber link is obtained at the remote site by heterodyne beating the first-pass fiber output light against the light that transfers through the fiber for three times. The phase noise of the single-pass fiber output light can be compensated by using the detected phase noise with the active and passive phase noise cancellation techniques {{cite:b7d9cd3d6485ca152fe627065a5434ea337135f0}}, {{cite:ba3f89070bea96365e71562a15e83a86d42db673}}, {{cite:c83ada265d738bfa1a17b5603820aa0611f9141b}}, {{cite:35d93e00e80be8fb67c2c0dcfc8dd70fae944f6b}}. In these schemes, transfer to each remote site is simultaneous and independent, addressing the performance entanglement of all the remote sites of the after-mentioned multiple-access optical frequency transfer techniques {{cite:220576ac5a0eb9b6343d7bccaf75ee17bc0731e4}}, {{cite:dba5e5e779d0a2fb9ae7e9e284ee8dbdb0930748}}. This has the advantage that if a single stabilization servo fails then only a single remote site will lose its stable signal. In our previous work, we have demonstrated optical frequency transfer with passive phase stabilization over a branching fiber network {{cite:9fa8be31fb90e19ddef71910df0f908f609b87be}}. The technique possesses the advantages of an unlimited compensation precision and a fast compensation speed and free from the effect of servo bumps on the spectral purity {{cite:c83ada265d738bfa1a17b5603820aa0611f9141b}}, {{cite:9fa8be31fb90e19ddef71910df0f908f609b87be}}, {{cite:35d93e00e80be8fb67c2c0dcfc8dd70fae944f6b}} as opposed to the active phase noise compensation based optical frequency transfer technique {{cite:b7d9cd3d6485ca152fe627065a5434ea337135f0}}, {{cite:ba3f89070bea96365e71562a15e83a86d42db673}}.
| i | 43c939576fe027ceab5a5eec256c1fcd |
In the rest of this section we will present some of the final SEDs
resulting from our simulations. A larger collection is shown in
{{cite:35d7f66d65384b9b01f8fd90c2023abd40f9adf8}}. The SEDs of each model has been averaged over
the time interval {{formula:cd64e15c-ff7f-4286-864c-5f0a6d3adc85}} s.
| r | 2b127abed0c3734d8361e5f67ab1db15 |
Deep learning methods are also exploited for the task. Specifically, the detection of visual relationships using a Deep Relational Network {{cite:f852bce60ad5cf452c0f4e0a17edd366a3022166}}, a deep reinforcement learning model for detecting relationships and attributes {{cite:096ff2b3c36987d513385bb15b16b162cc9a7ca8}}, a message passing algorithm for sharing subject–object–predicate information among neural networks {{cite:6e08a394405440f73f0d85e7b929c988ee03a8d3}}, and an end-to-end system that can exploit the interaction of visual and geometric features of the subject, object and predicate {{cite:7b9a976c1147444daa549792385f4fb86234a95f}}. However, the above systems cannot utilize the visual/geometric features of the subject/object and additional background knowledge together.
| m | f524824aacfca2754bfc52055b39c57e |
In this section, we compare our proposed method with other five state-of-the-art crowd locators in two congested datasets (QNRF and SHHA). The compared locators are TinyFaces, RAZ Loc, LSC-CNN, IIM and DCST. Specifically, TinyFaces is trained via official project with default parameters. RAZ Loc is adopted from {{cite:14d118ebd3552609b5a33261690350777a703f63}}. LSC-CNN and IIM also come from official implementation. The performance of DCST is from arxiv preprinted paper. The performance (Localization: F1-m, Precision, Recall; Counting: MAE and MSE) are arrayed in Tab. REF .
In SHHA, our proposed method achieves first place on F1-m and second place on MAE. Comparing with instance segmentation crowd locators IIM and DCST, we outperform them (76.0{{formula:d0f206ad-8a57-4940-b612-8d9232ef9d32}} vs. 73.9{{formula:4890b74c-7702-4a89-b8d3-310b558d6f02}} and 74.5{{formula:c2116dde-ed83-443e-b22f-d6169d6b72c2}} ) only with VGG-16 being backbone network. In QNRF, our work achieves first place on localization and counting. Significantly, the VGG-16 version of our work surpasses Swin-Transformer {{cite:bea1ff29a28977a45091805c2a0c1a4a9f539cd1}} based DCST (72.6{{formula:0bcfc0ca-1da4-46f9-9503-ec71d4285703}} vs. 72.4{{formula:e92f8da9-aa18-4539-9d78-97301e09e0e6}} ).
{{table:2cbc180e-1230-421e-b403-0ecc0c4d3ccf}} | m | 52d77a565a6de8003771d808d69b96ee |
where {{formula:c82bd220-dea3-44fd-a4fc-f544382b8ac0}} , {{formula:651712e2-709f-4f8b-9381-bf7f373e4c19}} is any reasonable input function or random process, {{formula:86af5886-4ef3-4cc8-adc0-bab78be5a096}} is the scale parameter of the continuous wavelet transform (CWT) in the {{formula:41811659-c942-4920-b60c-01f01e611d23}} -th layers, and {{formula:4cb36346-1c40-4207-a6ce-fd4c000ce31f}} is a nonlinear function modeling various neural activations; for example, Rectifier Linear Unit (ReLU), arctangent, and several others {{cite:70a488d54bd4ff1f5f05587f10a1afe5bdcfd46c}}. We may apply a suitable low pass filter to the {{formula:b6ad7e88-2bc3-4c9d-aea0-8ab1c0e3f720}} -th order NAST and obtain the {{formula:169a1fb7-46f7-46dc-b2ac-1f2c95738604}} -th order NAST coefficients.
Here, when {{formula:72ebc535-6127-4b08-b1e3-a98d09c08fbc}} , we recover the traditional ST.
In {{cite:63de7e0f38c4476c9af19c784f8b4c0851d75275}}, such idea has been implemented with several theoretical properties explored.
Note that in {{cite:63de7e0f38c4476c9af19c784f8b4c0851d75275}}, the activation function is followed by an extra pooling layer, which we call the pooling NAST and it is not considered in this paper.
The authors in {{cite:63de7e0f38c4476c9af19c784f8b4c0851d75275}} showed that the pooling NAST exhibits vertical translation invariance in the sense that the features becoming more translation-invariant with the increasing network depth. Note that the translation invariance of ST shown in {{cite:d5abdc9ca0b50fe573a2cc348c6d5d7ebdac2f98}}, {{cite:f483d108d5c2d4c65166181876b1f54e065001a7}} is the horizontal one, in the sense of the features becoming more translation invariant if the wavelet scale parameter {{formula:ed01657e-34ac-4e04-b67d-e7520c70b100}} increases. For input functions satisfying the deformation-insensitive property {{cite:63de7e0f38c4476c9af19c784f8b4c0851d75275}},
a deformation sensitivity bound is also derived for the pooling NAST. However, the authors of {{cite:63de7e0f38c4476c9af19c784f8b4c0851d75275}} only focused on deterministic functions.
| i | 3aa2f307865c3ca4cebc76a8f29b9f70 |
For text pre-processing, we used a hybrid phrase detection algorithm based employing a dictionary as described in Lui et al {{cite:ee53b73a5853f47b3a8d811c4e390eb05ac14997}} and based on an approach described in {{cite:bdae901ace7b1086c0f7f170d5c841191d1b22d0}}. First, we seeded the co-occurrence detection algorithm with entries from the candidate therapeutics list such as“folic acid” and “fluticasone propionate”, since these precise strings are already known. Then it applied a count-based equation to identify additional phrases. We normalized each phrase to a form where spaces were replaced with an underscore. This approach increased the likelihood that concept phrases such as “monoclonal antibody” and “recommended dosage” would be found.
| m | d1e1dcbee7693b80596449f25c5b043b |
The Bellman completeness assumption is about the closure of a function class under the Bellman operator. It has been widely adopted in RL literature, be it online RL {{cite:381a13ee7f9dee8f00fd06121931bc5121d2aae3}}, {{cite:29b97db45d4f9c0d08532474360362f93e026c16}} or offline RL {{cite:ad45ff090100c3a5372bcf73ed6ea18df5971d28}}, {{cite:2b1a780893bba765ff3e6ec4b0754d3a8452b491}}. Some classic MDP settings implicitly possess this property, e.g. linear MDP {{cite:42a96fd43ec046c72d0d00a27ff8f69f3d53615f}}. Note that {{cite:25df0b531908b8c661dc9c945688cc23798f8ded}} show the necessity of such an assumption on the Bellman operator to regulate the Bellman residual: Without such assumption, even in the simple setting of linear function approximation with realizability, to solve OPE up to constant error, the lower bound on sample complexity is exponential in horizon.
| r | 124df99a9b0b10eaaa5c3c61f8d40dd4 |
where {{formula:30c4b369-82ed-4f7a-9a99-dec15e046fbd}} r
depends implicitly on {{formula:8b8568a8-1790-4a43-8958-2e9f5e47a0d2}} , {{formula:cd28413b-9774-4722-a0e6-22ebce5fb9c0}} .
We may view the vector {{formula:d0c83a94-65e5-4f52-ba9f-a6ac87f7ecee}} of the space {{formula:685844e3-3432-4f99-a02b-62835b24088d}} as a
section of a fiber bundle over a collection of non-intersecting punctured discs
{{formula:5abb3b02-e74b-451d-b436-baab94fe66bd}} , {{formula:3b176bb9-6602-469e-86b3-f64ab10916e0}} ,
with an {{formula:81550f45-9ddd-4480-822e-72fd404acfd4}} -valued fiber
{{formula:ad95b5e7-7e81-4a8d-9127-0f7a988e909e}} .
In this paper we explain how to construct the vertex operator algebra {{formula:8f2f7c7e-172a-4546-a4ec-b766fc9f9983}} -bundle mentioned above
in the case when it
carries an action of the group {{formula:55fac392-96f9-4d85-a182-0d95f500964e}} of local
coordinates changes in vicinities of {{formula:2a596652-3c59-49f8-af65-e5e7b12d2551}} points on {{formula:d965f705-50b3-4f45-9b55-245ae9be9f64}} .
This means that the action of the group
{{formula:552db4f2-dbad-440d-aee8-2dd0a850fd1c}}
comes about by exponentiation
of the action of vertex operator algebra {{formula:dad9f5b1-f43d-4430-8d56-b21d3d5902e6}} ,
{{formula:bebab94e-c0d1-4aa7-9764-e34a69906a61}} ,
via the action on {{formula:f127a954-ac31-489b-85f3-1dd45108e27a}} .
The representation in term of formal series in {{formula:8912fb87-de0c-4ce4-ae63-d65b1fd32eb6}}
allows us to find the precise transformation formula
for all elements of {{formula:8a1cc98c-85a1-49a6-a941-741af51b3474}}
under the action of {{formula:041159f9-8383-4d83-b4b7-be613d268d04}} .
We then use this formula to give an intrinsic geometric meaning to sections
{{formula:ce6f0f26-aa07-42a1-8651-9f0df46bca5e}} of the fiber bundle in coordinate-free formulation.
Namely, we
attach to each admissible vertex operator algebra module {{formula:4e3b3fd7-a242-4267-b226-6aedf9e4bc85}} -module {{formula:b80f86d1-3b5d-41b0-8335-3f0d50df9fdd}} (i.e.,
satisfying certain properties)
a fiber bundle {{formula:9098c503-e411-4add-97e5-e64d21c2d72e}} on an arbitrary smooth manifold {{formula:48410f81-b4ab-4273-93d3-df5296d8886e}} .
In Section we show that the bundle {{formula:e1c86b52-eba2-40fc-8609-62fdabcb62aa}} constructed is canonical, i.e., its
sections do not depend on changes
{{formula:a6932ee2-1ddf-45a4-a783-e1432c8512ba}} of coordinates
around points {{formula:cc265a97-7f6b-4b94-8c1a-f08cacef172c}} on {{formula:e5a414d5-a539-4ed4-bbe2-a7b5b6bc0c1c}} .
To keep elements of {{formula:90dfca2f-e789-469e-9d9f-528faf9663c9}} coherent with respect to actions of the coboundary operators {{formula:eb63e4bf-1c25-4bdf-a917-bfe0b7e3b672}}
shifting indexes {{formula:7ce672fd-5836-4c46-ba70-5d02dc3621a7}} and {{formula:4f653a00-e376-4ad8-8555-f1ef4654378b}} ,
we apply certain analytic restriction on their characteristics provided by values of non-degenerate bilinear forms
of entries in {{formula:349595ee-31cb-4680-b6cb-4eae0d4bbdd8}} -vectors.
The spaces {{formula:c9f6e4c7-a5a7-4163-994c-f5868f795c6a}} are defined on cosimplicial domains chosen on transversal sections of {{formula:3f041fe7-07d4-4770-9750-1415783e8d5c}} .
Then we formulate definition of
the category of vertex operator algebra bundles defined on {{formula:1150f728-031b-4f1c-8adc-a52b0e7e89c9}} .
The spaces {{formula:82f4ad55-b851-48b7-87a4-eba181c9449f}} associated to the category {{formula:9496b519-82ad-4e18-b9a3-4966174e7595}} of admissible {{formula:b5462237-642f-4e0b-96f6-6f73690b746f}} -modules
defined in Section .
The spaces {{formula:a713d1a0-9d64-4e00-86c9-c5b2d0ad7fbf}} of vectors of characteristics {{formula:5f0399e5-9d55-4383-8541-98eb7eb0c718}} of entries of vectors {{formula:1d688f02-fc2c-41de-b9d2-dabddecada7f}}
form {{cite:62299fde5ca2c9c8d1347ac7df9b130901ae06d4}} a double chain-cochain complex {{formula:929c8289-0416-4361-9315-3afd2e9c6d4e}}
where {{formula:d9d2cf54-ec1e-4496-9853-fc6ab25bb423}} .
The standard definition of cohomology of this complex is taken as cohomology of {{formula:5e4a31d3-bb98-4d1b-9fc3-7252def5db2d}} .
We show that elements of the spaces {{formula:25a9c7cf-f504-4af7-b4e4-5723e9074894}} are invariant torsors with
respect to the group of foliation preserving changes of transversal basis and local coordinates.
Though the construction of {{formula:15385aca-d39a-48ae-abdc-716c86b206e5}} -bundle does not depend neither on the choice of transversal basis
nor on the choice of coordinates on {{formula:72c33675-2219-4541-854b-5b69c3baa97b}} ,
it does depend on the choice of vertex operator algebra elements
as well as on a particular element of the category
{{formula:e2f7c06f-a63c-415c-8a75-3b12bf533e9b}} of admissible {{formula:1c36e9ff-829f-44f1-a53f-765dad44a82c}} -modules.
The construction involves
torsors and twists of a vertex operator algebra modules by the group of
automorphisms of local coordinates transformations (independent for each chosen point
on leaves of a foliation {{formula:c23f77e8-479f-46d2-b87c-b050c9a980cc}} ) of non-intersecting
domains
of a number of points on {{formula:a3666996-f070-4088-a58f-3f346b7dc3d0}} .
| i | 3c7f2db04c5e6889ec8e9d3304de4743 |
The vision transformers consider an image as a sentence. It splits each 2D image into the 1D tokens and models the long-range dependency between tokens with the multi-head self-attention mechanism. The self-attention has been recognized as the computation bottleneck in the transformer model. Its computational cost increases quadratically to the number of incoming tokens. As aforementioned, our approach is motivated by the fact that many "easy-to-recognize" images do not require {{formula:87eb90f9-ab1b-4ccf-aeba-c2bd47f74b2c}} tokens {{cite:5c8771e6aa18d95132538122896a51210cd238a7}} to correctly predication their category. Thus, the computational cost can be saved by processing fewer tokens on "easy" images while using more tokens on "hard" images. It is worth noting that the key to a successful input-dependent token-adaptive ViT model is to know precisely the minimum number of tokens that are sufficient to correctly classify the image.
| m | 0738b349bb09709cde53098f47523484 |
We now examine if the large amount of shape information contained in ImageNet pretrained models is equally distributed across different stages of the CNN.
In this experiment, we train one layer read-out modules on features from different stages, ({{formula:0aaf932e-87b7-4f38-8b5f-167b6ec0c7de}} ), of the SEN to examine which stage of a CNN encodes shape information. As shown in Table REF , the read-out module trained on the last stage features, ({{formula:de83e8c5-7c8c-4fdd-a8b8-64cb998a6f32}} ), achieves higher performance compared to the earlier stage features, ({{formula:5499c236-878b-4813-a3b5-336450627625}} ), for both Bin and Sem. This is to be expected, as feature maps from later stages have higher channel dimensions and larger effective receptive fields compared to the feature maps extracted from earlier layers. A surprising amount of shape information (i.e., Bin) can be extracted from stages {{formula:9dbd2ada-03d9-4b2b-91f8-77c1da9c995d}} and {{formula:6d33083b-d331-40ee-acfa-4dc2663767cd}} ; however, these features lack high-level semantics to correlate with this shape information,
which can be observed as the corresponding Sem performance is much lower. Figure REF reveals this phenomenon; the horse and person are outlined even for the early stage binary masks, but are only labelled with correct per-pixel categorical assignments in the later stages. Considering the non-trivial amount of shape information contained in the early stages, we investigate if aggregating multi-stage features encodes more shape compared to the last stage feature, {{formula:269e0ba2-e622-4b2d-a8a5-5904261317b7}} . Table REF (bottom) shows that training a readout module on multi-stage features significantly improves the Bin and Sem performance, suggesting that tasks requiring shape information may benefit from hypercolumn style architectures {{cite:804fe196053b421a0c3bd851dd4da59e553c0060}}. This indicates that some shape information is encoded in earlier layers but not captured in the late stages, which agrees with the dimensionality estimation results in Table REF , as around 12.5% and 14% of neurons encode shape in the first stage and second stage, respectively.
{{figure:c783f86f-8b65-4e8c-bfeb-126d26b73eab}} | r | f368d8a4c6bcd9b5d80972c7d5d0e7e9 |
Visualization of the selected LRs. As shown in Figure 5, for the LRs in red, yellow, green and orange boxes in the query image, we visualized the {{formula:4bb3b674-0f46-42a8-950a-abc56bdb011b}} (i.e., {{formula:66018692-3541-4fa9-99e5-539ed697c4dd}} =3) most discriminative LRs selected by MATANet. In {{cite:7f51b632d9fb862a87f7c72e26a1bdaa2c220f9f}}, they will equally use the selected LRs for the final classification.
However, in our method, the LRs corresponding to these boxes are treated differently. In task 1, the task attention score corresponding to the red box and yellow box is 0.069 and 0.041, respectively, so the LRs corresponding to the red box will play a more important role in the final classification. Similarly, in task 2, the LRs corresponding to the orange box will play a more important role in the final classification. This is because the beak is obviously more discriminative than the wing in task 1. While in Task 2 the wing is significantly more discriminative than the beak, which verifies that our method can automatically select the most discriminative LRs in the current task. Moreover, it can be seen from Figure 5 that the scales of the dominant objects in different images are different, which may affect the performance of the model. This once again verified the necessity of our multi-scale feature generator.
| d | f2e0be5676d55f98e4d693ab4385de8b |
In this paper, we computed Lanczos coefficients {{formula:2cc041c1-6bee-4f9b-a675-92f0b28aa7a2}} and K-complexity {{formula:5db5a805-0e6c-4422-bf93-d72002668864}} of an inverted harmonic oscillator system, which is non-chaotic but shows saddle-dominated scrambling. As a result, we found that {{formula:3d46c851-3203-40d9-92a3-430753ec0cc7}} shows linear growth for small {{formula:1f98b18a-ab54-40f4-8f2d-21a0a7601130}} , and {{formula:d9224086-b046-4a9a-bd63-63303981853a}} has an exponential growth period in early times. Since this behavior is supposed to appear in chaotic systems, we conclude that K-complexity cannot distinguish chaos and non-chaotic saddle-dominated scrambling. This is in agreement with {{cite:068fe7f65b1711d88a842264e8f37a4e407145b4}}. We also found that in our case, the right side of (REF ) is saturated, while in the chaotic system left side is saturated{{cite:b9f31416c19e304b7094056bcf23ecb7cb31ce13}}. Also, we investigated how the saturation value of Lanczos coefficients depends on system size and saddle energy. Saturation value increased as system size and saddle energy increased.
| d | 06bbf42a941f944a958aa902efcc25ff |
[leftmargin=*]
Closer Ties to Unsupervised Representation Learning. Our segmentation model directly learns the pixel embedding space with non-learnable prototypes. A critical success factor of recent unsupervised representation learning methods lies on the direct comparison of embeddings. By sharing such regime, our nonparametric model has good potential to make full use of unsupervised representations.
Further Enhancing Interpretability. Our model only uses the mean of several embedded `support' pixel samples as the prototype for each (sub-)class. To pursue better interpretability, one can optimize the prototypes to directly resemble actual pixels, or region-level observations {{cite:b6faa25e77f4451b91f52e32c780ff5edc299937}}, {{cite:f597d07fd2479d28692390cfd58a221aed723a06}}.
Unifying Image-Wise and Pixel-Wise Classification. A common practice of building segmentation models is to remove the classification head from a pretrained classifier and leave the encoder. This is not optimal as lots of `knowledge' are directly dropped. However, with prototype learning, one can transfer the `knowledge' of a nonparametric classier to a nonparametric segmenter intactly, and formulate image-wise and pixel-wise classification in a unified paradigm.
| d | 027cfaf0ed2afb7beed0abe726372e76 |
Furthermore, the CSC and SPC pre-training improve the test results only marginally. We conclude that CSC can only be applied to dense point clouds and is less pertinent in the case of sparse point clouds, which are typical of the autonomous driving use case. For SPC there are two options, either not enough data were used to perform the pre-training, which would confirm the observation by {{cite:598b23ac9adbd91ec229a461f6149c4c4f5728f3}}, or the contrastive learning is not adapted as a pre-training task for sparse semantic segmentation.
| r | dd48ae16174e1332425940fa130c5c78 |
as {{formula:7f47fb8d-2919-4d86-a186-521534ed08c7}} , by our limit assumptions. Thus, Theorem 5.11 of {{cite:a6e58cd1726641a71c4ef5cd14ac0c43b6bba093}} may be applied to give
{{formula:af972e66-a3ed-484d-8807-cccc5826e17d}}
| r | bc7717b01bb621dab74ba7a1bd9bd92b |
Many cluster validation indexes have been proposed in the literature, often in
order to pick an optimal clustering in a given situation, e.g., by comparing
different numbers of clusters, see {{cite:991c395e1fb82dd5c446cf119033429b9efe7f56}} for an overview. Most of
them (such as the Average Silhouette Width, {{cite:54ca025de7d892090564efa4d8be710196030baf}}) attempt to assess
the quality of a clustering overall by defining
a compromise of various aspects, particularly within-cluster homogeneity and
between-cluster separation.
Following {{cite:5c666a141b82eab1ae9bcd88bc9b82e554c285c5}} and {{cite:dd29bd9b33072dcdeeed5207d2dd1a23262fbc31}}, the present work deviates
from this approach by
keeping different aspects separate in order to inform the user in a more
detailed way what a given clustering achieves.
| i | 4a29bc89c5bc7408a5106c92e510fa08 |
As for outlier removal of point correspondences, we choose RANSAC and NG-RANSAC {{cite:469c998d5e0d80d64d9aeced36d687d47fda19f5}}. We use the OpenCV-3.4.2 implementation of RANSAC with {{formula:25b0a471-f83c-41cd-a056-1a6cb19f9bbc}} , {{formula:20a1154c-e6dc-4e53-abc2-2f59caff735f}} , and {{formula:205b8466-a574-40a6-9e89-c3d0f89b9961}} with the five point algorithm and use the authors' code for the latter. For obtaining initial point correspondences, we use the nearest neighbor search and also SuperGlue
{{cite:b8217af5be458e7747e7a06ce8fc810604ee5d62}}. We apply Lowe's ratio test {{cite:53fecc3f28e5b355ef1ee1e8433b102fa086c31c}} with a threshold of {{formula:a986c031-ac34-48f9-bcf9-25f0d783e45f}} to RootSIFT, L2-Net, SOSNet, and RF-Net.
| m | 2e8c6062132c358752ae5ef2f0eed5cf |
The numerical integration of Equation (REF ) is implemented
using the algorithm introduced by Gunsteren and
Berendsen {{cite:6b7bd9d6cb283a10e53d4dd583d5ca27ba22a615}}. Our previous experiences with BD
simulation suggests that for a time step {{formula:904432c1-60f6-4d35-94e3-36969ea77c59}} these
parameter values produce stable trajectories over a very long period
of time and do not lead to unphysical crossing of a bond by a
monomer {{cite:90a59c60c2292987ef52b84f13a4ae51b4085dfc}}, {{cite:ccf80a6f03b277115daf668761d232844bf3f829}}. The average bond length
stabilizes at {{formula:fb3a098a-149b-4a6d-9827-19c0252c9ffe}} with negligible fluctuation
regardless of the chain size and rigidity {{cite:90a59c60c2292987ef52b84f13a4ae51b4085dfc}}. We
have used a Verlet neighbor list {{cite:ea8a1747ddf9baccf17ff060298536ea0af72acf}} instead of a link-cell
list to expedite the computation. In addition, the simulation runs for
the EV particles were done using LAMMPS {{cite:32b7982a6425e207daf478e7a04bec4bcc0dd3e0}} with the same
potentials for numerical expediency. We have checked that these runs
yield the same results.
| m | a4ee69577325e1163472f28f3e8649ff |
We present our main results in Table REF . In this table, we see that our formulation systematically outperforms the proposed baselines, as well as the ones it generalizes. In most cases, the possibility to add a layer or to consider higher-order interactions improves the performance over the existing baselines (MMSBM, Bi-MMSBM, IMMSBM and T-MBM). About the Spotify dataset, as stated before, artists are often added to a playlist in a row, leading to the probability of the next artist being the same as the one immediately before her to be higher. In this context, adding interaction terms adds noise in the modeling. This explains why the triple interactions version of SIMSBM does not perform better than its pair-interactions {{cite:e631ca7c4eb2a63e7c7e1eede8e4142160d771f7}} or no-interaction {{cite:71ce11fa33941ec6033a3e86f9671b8b4041b200}} iterations.
| r | 38c09c8b41d90dab42958d2be61384b5 |
Our spOccupancy R package fits spatially-explicit single-species, multispecies, and integrated occupancy models for potentially massive data sets. The package includes functions for data simulation, model fitting, model validation, model comparison, and out-of-sample prediction. Additionally, spOccupancy contains methods for Pólya-Gamma data augmentation {{cite:5ba7aba7a9a467f8e227caaf15da8e59e9e0bd09}} and Nearest Neighbor Gaussian Processes (NNGPs; {{cite:13c6e158713e7226254247aed184951793ac5998}}, {{cite:d400ec17bc43447be003348818bc75c5db3e4c76}}), two approaches that have either rarely {{cite:990e4bbca2e26ffe25ed2a9ab58e8b55af99821e}}, or never, respectively, been used in the context of occupancy models. We demonstrated via two case studies on breeding birds and one simulation study how these approaches enable fitting spatially-explicit occupancy models in a computationally efficient manner. We expect spOccupancy will serve as a user-friendly tool for ecologists and conservation practitioners to account for detection biases and spatial autocorrelation in assessments of species distributions and community patterns across potentially large spatial regions, and for large (e.g., {{formula:6bf12fe3-8a67-4e9f-9b54-2bfdfbd00022}} locations) data sets, which are increasingly encountered in species distribution modeling applications.
| d | 6fc3666d89bd2f3d9eb79cacee542d14 |
We first perform ablation studies on the impact of the output ensemble scheme, the proposed attention distillation bound, and the modality of unlabeled public data. Here we use the T1-weighted images from BraTS (B), fastMRI (F), and IXI (I) as private datasets and unlabeled T1-weighted images from OASIS-3 as public data; and we report results on the aggregated T1-weighted test images from B, F, and I.
From Table REF we can see the superiority of the importance-weighted ensemble beyond the average ensemble typically used in previous FL works {{cite:828e20eb2923b1e41d07a0ba73a9ed37ee92f29c}}, {{cite:aa3009830aee4327d49151cb5032b0c195b7b05c}}. Our proposed attention to upper/lower bound constraint further improves the reconstruction performance with higher SSIM and PSNR. In addition, Table REF shows the comparison of using T1-weighted and T2-weighted images blackof OASIS-3 as public data. The results demonstrate the robustness of our method to public data from a different domain (locally held data and data used for distillation are all from other datasets) and even different modalities (all three local nodes have T1-weighted images for training while public data is T2-weighted).
| r | 070f2446cb9d8c5228e4b049555acd42 |
Explanations of how to solve a task often involve a summary of the key decisions required to complete it, an ability referred to as selectivity {{cite:37d824d21619bf6d465da08f13943d31f76ec7b1}}, {{cite:0d2bfdf5befdace35858e1d4398243ca72b18126}}. Classic Deep Reinforcement Learning (RL) approaches lack this ability because all actions are reported when executing a policy. Recently, Complementary Temporal Difference Learning (CTDL) has been proposed which uses a Deep Neural Network (DNN) and a Self-Organizing Map (SOM) to solve the RL problem. Importantly, CTDL uses the errors produced by the DNN to update the contents of the SOM. In effect this results in the SOM storing episodic memories of states and actions that led to the largest errors during learning. We therefore use the contents of the SOM to generate task-level explanations as they provide an intuitive summary of most the important state-action pairs for solving the task at hand.
| d | 4ab7dfc309cd1ccb9236acd67bca17f7 |
Traditional equivariant networks, such as GCNN {{cite:58a40dcaefdbab7e64a70ff04a0709901c10f2eb}}, SE(3)-transformers {{cite:f6f4b6f863a074658c51faaebe0b8c131d9a5fa2}}, and LieConv {{cite:b8a453a6aacfb79c8862d2c3f6940487ae7ae3bc}}, require the group equivariance constraint to hold for each layer of the network. In contrast, for equi-tuning, we only need to ensure that the group actions are defined on the input and output layers of the pretrained model, which is a key reason for the simplicity and generality of our algorithm.
| d | 4e2f2e4e9fae1df6c402b660d2755e09 |
The island rule was initially considered for the two-dimensional gravitational systems where the explicit computations for the entanglement entropy of the Hawking radiation and the Page curve can be easily performed by using the semi-classical method due to the presence of the high symmetries. For the two-dimensional black holes in the context of Jackiw-Teitelboim (JT) gravity, the islands are emerged at the later times of the black hole evaporation and hence their presence makes the entanglement entropy remaining finite at the late stage of the evaporation process {{cite:76bd0cfca819434b56ad1ed3bc76a946b42859ef}}, {{cite:8e8b130e26d051daf371f7439a4396baaf72e219}}. The island consideration in the two-dimensional models was extended to study the asymptotically flat 2d dilaton black holes {{cite:c2386401e5d147e6895b084b8ed77cc4405e8313}}, the two-sided Janus black holes {{cite:b0838674c5304d5aded4dcaaddf025571c57b931}}, and the evaporating black holes {{cite:cb0d4639def083330b4da6053b4105f72c9d517b}}, {{cite:b9ac312821b162a4f52d96afda9af5e979ec233e}}, {{cite:e2c82fb5a272e14fcbf5ae50156f583a425de5e3}}.
| i | 5e18c329a23eba56f066df4d388d2f87 |
In this paper, we propose a novel approach to address this problem. Our approach is based on the notion of instrumental variable regression, a well-established method of resolving endogeneity in the econometrics literature, including endogeneity deriving from measurement error {{cite:8b5a3a0c64df8d1892f0bf81755b822849503052}}. We make use of a notably unique feature of this problem setting of applying machine learning followed by regression. Specifically, we leverage the fact that predictive machine learning models are typically trained and evaluated using data for which true labels (assumed to be perfectly measured) are available and which are used to quantify prediction error and model performance. This perfectly measured set of data offers a unique opportunity to overcome difficulties commonly associated with evaluating the validity of instruments.
| i | 966a9e35f661b21bc0e6efa4d82ccfbb |
An additional challenge is presented by the fact that the broad absorption profile associated with Damped Ly{{formula:158dfdde-37d2-4dd8-8e76-cb80e30b47bf}} (DLA) absorption systems (along with sub-DLAs) in the Ly{{formula:f7bf45cc-e16f-48f8-92a8-00bf67a50484}} leaves a measurable imprint on the correlation function {{cite:f6b617ded05761dabead1cec0ee7ce251b79d738}}. This can be somewhat mitigated by the masking and/or correction of known DLAs in the data, but not all DLAs are identified and their contribution must be taken into account in model fits to correlation functions with respect to the Ly{{formula:8810f17e-64c8-416d-b4b5-68dbc6cf5f90}} forest.
| i | 33cb0cd79f7264b6611899090533beaf |
Group DRO (*GDRO) {{cite:8381242382b35298154e37971f0b4e82c9dbe869}} provides DRO with the necessary prior that it must generalize to all groups. Similar to Up Wt, GDRO also uses {{formula:3d680286-7420-41f2-81ca-eaeddec35930}} and {{formula:4eafd718-c74b-4871-95b2-1d22c59d1b86}} to create groups and has been shown to work well with sufficiently regularized models. However, unlike Up Wt, it performs weighted sampling from each group and has an optimization procedure to minimize the loss over the worst-case group.
| m | 0cd957d94c00feb9720cd4c9bcbdc8d1 |
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