text stringlengths 54 548k | label stringclasses 4
values | id_ stringlengths 32 32 |
|---|---|---|
Efficient spectrum utilization is another key issue for JCAS systems that needs to be addressed. Spectrum efficiency in wireless communication systems can be significantly improved by operating in a full-duplex (FD) mode, which is being considered for the next-generation wireless systems. Specifically, the FD technology could potentially double the spectral efficiency with respect to the half-duplex counterpart, as it employs simultaneous transmission and reception using non-orthogonal channels {{cite:dd95db9f82a38f2cc58a2c2fd1a04198bdef69ca}}. However, the non-orthogonal operation creates a self-interference (SI) link between the input and the output antennas. Owing to the overwhelming negative effect of the SI at a transceiver, the FD technology has been previously regarded as an unrealistic approach in wireless communications. Fortunately, with the recent advancements in transceiver design and signal processing techniques, the SI signal can be successfully suppressed below the noise floor, and therefore the FD technology becomes feasible {{cite:6cb64969b24c37710159b540a63179de46f9c26e}}, {{cite:5d9cf14fa1ea6977f6e9587d7289582a8fc33529}}. However, the performance of the FD radio in large-scale multi-cell networks is additionally compromised by the increase of the intra- and out-of-cell co-channel interference. Several research efforts have been carried out to study the effect of multi-user interference on the FD performance for large-scale wireless networks, and several techniques have been proposed to mitigate the additional interference caused by the FD operation {{cite:6cb64969b24c37710159b540a63179de46f9c26e}}, {{cite:6171a9e32a47567e9d6409b1324befd6f84fc8c9}}, {{cite:03a1360975817aa99a28e5061f9531961fedf254}}.
| i | 2ab1457d9d72b0d056e7b55a67e99bcc |
The finite volume method (FVM) {{cite:db01aa5489c4f10becbd6e38cca16a66280f18a8}}, {{cite:50e86fe91b1744e0e68b5f462a14e5762431502a}}, {{cite:138e157a793a2b35d015d782fa91209840095a88}}, {{cite:4c71efb30a752db75f81a6ac91a0451437009c46}}, {{cite:7c06837c3aa1a3ceeb5c0855c694ed311b5c98d0}}, {{cite:3d021c3acb8fb4539dda051646b23e26a3e7dbb2}}, {{cite:f84358c300a643e8942fd10298ab4647afb9056e}}, {{cite:5e3d12a237eae5c2c44727e638cdd59fed357122}}, {{cite:1bbdd9bbae15fca01c9e82b609649d000abe056e}}, {{cite:27652c451fbe3b14f9f584d8e46e32adfdf0bd80}}, {{cite:b3e51dd16bf00e684c5453b637d702a5efe6a753}} is one of the main numerical methods for solving partial differential equations, which is known for preserving the local conservation property. Till now, many progresses have been made on the stability, error estimate and superconvergence of the FVMs. The linear FVM schemes have been well studied on any spatial dimension {{cite:ffdf43310413a6caa920b7c2b49eaa73ffd51d0a}}, {{cite:ce800ca38b4933b25cd28471e8a1f9ee4bfb9d17}}, {{cite:614dfae06191647a426100c42c7bf2136570e390}}, {{cite:a8b58835e3cfbdaef9c995c0c2e01154c5d8d9ba}}, {{cite:87c5cec1715c027d92d500f29c87296fc2eb1ef4}}, {{cite:428905c0de0236ef0498b43e5e68e1d4170dd5ad}}, {{cite:7b1fdcd9e04e05427dbda9c9cc37436db2af9fc1}}, and complete results of arbitrary {{formula:b7d52006-c77b-4cad-925e-39a839f836c5}} -order FVM schemes on one dimension (1D) are given by {{cite:5b0ee286c232596a7df7bfcc8cffa07b2b738260}}, {{cite:344e061e1713565942d9693f3e910989c87e301d}}. For high order FVMs on triangular meshes, {{cite:f1f3c20538d4d1edab9ccd000264f47d2053d1f6}}, {{cite:13686a9913d4e6c3680370a1136d62a16c9586cf}} present a unified analysis of the stability under the assumption of the minimum angle condition, which restricts the minimum interior angle of the triangular elements. While, for some quadratic FVM schemes, the angle value of this condition is improved by {{cite:7b1fdcd9e04e05427dbda9c9cc37436db2af9fc1}}, {{cite:48c1faf56ae63badcebc734a399dd879699762e9}}, {{cite:1931b7e0e47b47cd9bfc77ed9262cdacf5f3b074}}, {{cite:1ff57a0193dffcd0f15c65dcf9b345cacef650ca}}, where {{cite:48c1faf56ae63badcebc734a399dd879699762e9}}, {{cite:1931b7e0e47b47cd9bfc77ed9262cdacf5f3b074}}, {{cite:1ff57a0193dffcd0f15c65dcf9b345cacef650ca}} are based on a new trial-to-test mapping. And, through proposing the orthogonal conditions, {{cite:cd59bb527ed39c9f4193c4bf0b72fba1da893b27}} carries out optimal {{formula:c3381671-5ab8-45ce-ad99-b4592db07fbc}} error estimates for arbitrary {{formula:8ed14cab-b00f-492f-bbdd-07619df8f229}} -order FVM schemes on triangular meshes. For the FVMs on quadrilateral meshes, {{cite:4dbfb1dc253ef14b83b5051c08cbb12848d27e08}} proves the stability and optimal {{formula:f6d4226d-5a6f-4a5b-89f5-a65ef65cb5e7}} error estimate of the biquadratic FVM schemes, and {{cite:e83255a29cecfcd760cf126e463666d3f14005a5}}, {{cite:3802e30dfa2bd4e6e27f59113790d1a6a0c97564}}, {{cite:1eb5a672a5b0fb63d5ebcf1c67bbea6c14d21654}}, {{cite:863072b34b1099f921475c5b26651e8acf06dd54}} present the stability and optimal {{formula:d5c4a336-c8f2-4fb4-b9da-0999622d5cec}} estimates of arbitrary high order FVM schemes by considering the bilinear form of the FVMs as the Gaussian quadrature of the bilinear form of the finite element methods (FEMs). The dual meshes of the schemes in {{cite:e83255a29cecfcd760cf126e463666d3f14005a5}}, {{cite:4dbfb1dc253ef14b83b5051c08cbb12848d27e08}}, {{cite:3802e30dfa2bd4e6e27f59113790d1a6a0c97564}}, {{cite:863072b34b1099f921475c5b26651e8acf06dd54}} are based on the Gauss points. Compared with the big progresses in 1D and two dimension (2D), the FVMs on three dimension (3D), which has more applications in practice, are mainly concentrated on the linear schemes {{cite:ffdf43310413a6caa920b7c2b49eaa73ffd51d0a}}, {{cite:b44b9cb802740cb451d04d299187190f7db2887a}}, {{cite:6c8b46595b4082449812262a0cfcc48787073eb1}}, {{cite:bb9ab8da0c040fed9bf7b0b9fd9473ba546878e7}}, and there are few results of high order FVMs on 3D (see, e.g., {{cite:d15872da8cbbc5eaee66242c3be4bae1ab3ee8fd}}). Specially for the quadratic FVMs on tetrahedral meshes, no result has been published yet.
| i | bab4af7f912033ed8aa4996fd2238c72 |
In both cases, {{formula:4ddcc9b9-8b4e-4c22-9280-5d6652194de9}} is the number of independent fitting parameters and {{formula:9bb8575a-e1d8-4ebd-9fe6-9ab83db6696f}} the number of data points used in the analysis.
To test the effectiveness of a dynamical DE model (versus the {{formula:3837cc16-49e7-484b-a0e6-aca6d84e6e49}} CDM) for describing the overall data, we evaluate the pairwise differences {{formula:ab1f147b-1452-4c3f-ab31-05378f6b971d}} AIC ({{formula:8fd3aa93-2b81-4a4d-94fd-98ae02e293db}} BIC) with respect to the model that carries smaller value of AIC (BIC) – in this case, the RVM's or the XCDM. The larger these differences the higher is the evidence against the
model with larger value of AIC (BIC) – the {{formula:57ec4132-82f2-46ae-afdf-0d620b77bb87}} CDM, in this case.
For {{formula:23db9756-a5c4-4272-8f8c-3a68bb56e1d8}} AIC and/or {{formula:2ddc3081-b2f9-4060-9105-58f939ae7e21}} BIC in the range {{formula:8fc61d93-2252-4aa5-bf40-4c6e993e2acb}} one may claim “strong evidence” against such model; and, above 10, one speaks of “very strong evidence” {{cite:9eaed187bd3f6383bc50c64822df9de90b2a2edf}}, {{cite:8c52ed716f4f667255494001d50c7599ed753635}}. The evidence ratio associated to rejection of the unfavored model is given by the ratio of Akaike weights, {{formula:f469966b-fb2a-4b35-aeb8-8246ed79d663}} . Similarly, {{formula:e45a9a6a-2786-4b1f-bd22-41db599bac8d}} estimates the so-called Bayes factor, which gives the ratio of marginal likelihoods between the two models {{cite:8117bf895f6fc4b2e6a879b6033ec667ef84dce9}}.
Table 1 reveals conspicuously that the {{formula:b9adb801-167d-4f2f-a829-3a59010f3358}} CDM appears very strongly disfavored (according to the above statistical standards) as compared to the running vacuum models. Specifically, {{formula:9f330f70-46c3-400d-a8ec-54db6fca7fb0}} AIC is in the range {{formula:03484448-11ea-4667-a7b9-6236ddac4ec6}} and {{formula:6cdf4edc-5018-46f7-b46b-8da18cda19a7}} BIC around 15 for all the RVM's. These results are fully consistent and since both {{formula:2327cbe5-7775-49d9-b573-6e98b0cce17b}} AIC and {{formula:52649592-ce21-4362-b292-c897d0882859}} BIC are well above 10 the verdict of the information criteria is conclusive. But there is another remarkable feature to single out at this point, namely the fact that the simple XCDM parametrization is now left behind as compared to the RVM's. While the corresponding XCDM values of {{formula:b0288c95-994f-4f99-b118-fc2054c3e5b2}} AIC and {{formula:90ec97db-1216-4617-adb8-a6d87428a434}} BIC are also above 10 (reconfirming the ability of the XCDM to improve the {{formula:f07cf5ff-a678-4244-9231-ff2baa0aa8bb}} CDM fit) they stay roughly 4 points below the corresponding values for the RVM's. This is considered a significant difference from the point of view of the information criteria. Therefore, we conclude that the RVM's are significantly better than the XCDM in their ability to fit the data. In other words, the vacuum dynamics inherent to the RVM's seems to describe better the overall cosmological data than the effective quintessence behaviour suggested by the XCDM parametrization.
Being the ratio of Akaike weights and Bayes factor much bigger for the RVM's than for the {{formula:3da85bca-a9c4-4062-a210-22b8fbee3411}} CDM, the former appear definitely much more successful than the latter. The current analysis undoubtedly reinforces the conclusions of our previous study {{cite:a4b237e0f2612dceb2968bc44a1eeff1fc334c3c}}, with the advantage that the determination of the vacuum parameters is here much more precise and therefore at a higher significance level. Let us stand out some of the most important differences with respect to that work: 1) To start with, we have used now a larger and fully updated set of cosmological data; 2) The selected data set is uncorrelated and has been obtained from independent analysis in the literature, see points S1-S7) above and references therein; 3) We have taken into account all the known covariance matrices among the data; 4) In this work, {{formula:17150aa1-f9e1-4ce4-a507-241eeef4b22a}} , {{formula:a26f3924-6e35-482f-ba55-13c905a70e30}} and {{formula:7afe8a14-4fb8-43b2-b697-3c6cfc166b67}} are not fixed a priori (as we did in the previous one), we have now allowed them to vary in the fitting process. This is, of course, not only a more standard procedure, but also a most advisable one in order to obtain unbiased results. The lack of consensus on the experimental value of {{formula:e6025225-5495-4f64-949d-dee1a3c1f691}} is the main reason why we have preferred to use an uninformative flat prior – in the technical sense – for this parameter. This should be more objective in these circumstances, rather than being subjectively elicited – once more in the technical sense – by any of these more or less fashionable camps for {{formula:9368395c-1426-4ac3-8246-4a9af5b5f0c3}} that one finds in the literature, {{cite:215404f4b9ecefd1b99db02c56804efc87bb8fca}}, {{cite:ad970b84d6435a14aaf1f30a03ef68d861da1458}}, {{cite:0e72c41f18be063a8c89ce2bd8946506a17bbe79}}, {{cite:f878f99abc1c49db4a514f9be0e1c8c5bc9c794b}}, {{cite:b0843e65b68bd43bf22f41fb26d2b23f1c8e7466}}, {{cite:1af10036d3cd3969dc0097c409eabe1cdcb38a8c}}, {{cite:1e0a05971d4affd43d8a0aa8511855833d334be1}}, {{cite:6b2bab36d28e38592260bef4c457e6301ebdab7f}}, whose ultimate fate is unknown at present (compare, e.g. the value from {{cite:1e0a05971d4affd43d8a0aa8511855833d334be1}} with the one from {{cite:6b2bab36d28e38592260bef4c457e6301ebdab7f}}, which is {{formula:87f1efca-9fba-4f28-9f23-06165798938e}} larger than the former); 5) But the most salient feature perhaps, as compared to our previous study, is that we have introduced here a much more precise treatment of the CMB, in which we used not only the shift parameter, {{formula:887f7653-8147-4ec9-abe6-6b4bf92ab8d8}} , (which was the only CMB ingredient in our previous study) but the full data set indicated in S7) above, namely {{formula:f7f6fb5c-7d5c-4568-a24b-273d370f0044}} together with {{formula:bc816569-fc48-449d-9dbd-7e90759e64d3}} (acoustic length) and their correlations with {{formula:37ff8ba1-98a8-42dd-9d2c-6d9adc4e5b0d}} .
{{figure:2c6f0e1b-7011-4940-8c16-dd803b9b1503}} | d | bb615805f8331adf56f44946a9992658 |
In the end, we draw attention to the progress on black hole stability problem in recent years. Linear stability of a Schwarzschild or a subextremal Reissner–Nordström spacetime has been shown by {{cite:69145a063b10eba4415d79338a6a60609eaa314b}}, {{cite:b45c55025f6e42fc3fab5f438ac2f4583d2cc958}}, {{cite:4e6197bec3f11123810675df026a341615f061ca}}, {{cite:19d940af9e8ddde5ba9653ab614b3eff927463f1}}, {{cite:104937601eb892c02b89676f7b70f16dcacee609}}, {{cite:54a0f01a68adf7a164b8d703d12d086b4ca81acd}}, {{cite:6060b3788496046dffd6b2dd272b3a7485326dbf}}, and linear stability of a slowly rotating Kerr spacetime is proven in {{cite:e4e13ee92fd404514cd4acbbb8873a57107c8808}}, {{cite:54ed96c2d021704f9665b813d1c7c9d5fb6a38fd}}, {{cite:5ad1b850bc31d37c13059f0774801be84d94913b}}.
For nonlinear stability results, we refer to {{cite:7a3ec0cf4e2c99e47ad910bc07b8ab634feaef41}}, {{cite:b8850a3b391bc91d8b22f88deeadeed4b03236e6}} for Schwarzschild, {{cite:a0bf9d0815f08d470dd625ff4e1117ab5b051435}} for slowly rotating Kerr-de Sitter, and {{cite:cd7cd3677875425f9bce56afbc063a9053b3788d}}, {{cite:09f072e53f8d17abc6ec42df1d6d43bfa171e8f7}}, {{cite:891c52f80553151bcc9ef722cfcbd761676a8580}} for slowly rotating Kerr.
| r | 6a49f6be8b80ab9847248eb78010a5a0 |
Controlling the charge state of an individual quantum dot can be very important for quantum technologies, where the undesired switching to a different charge state precludes interfacing the electronic spin to photons {{cite:2d42bb9014c323ea9e038cd44b24a9ba8cb2405f}}.
Boosting the decay rate now brings the colloidal nanocrystals on par with the fluorescence lifetime of NV-centers in diamond {{cite:dedd0e0b08b01b172dd5d85a17c30a0705ad2882}}, and epitaxial quantum dots {{cite:638316091debe5e5770a31ca094fabae1f77f741}}, and could open a path towards coherent emission at room temperature once the decay rate becomes faster than the decoherence rate {{cite:bb7f29564c7edb8fe9f4d308f5a1f2fb48c08317}}.
An intensity-switchable nanoscale light source can find important applications for optical signal processing with very stable giant quantum dots, where the switching speed is usually limited by the decay rate of the quantum dot, which can here instead reach GHz speeds when the exciton is maximally charged.
| d | e8b29c593686fd0036e709744e42cb4b |
Table 2 shows the performance differences between different variations of the Wave-U-Net,
with different numbers of layers. No fine-tuning was performed to obtain the results shown here, which explains the difference between the 10-layer Wave-U-Net in Tables 1 and 2.
The results suggest that fine-tuning does not make a meaningful difference, except on the CSIG measurement, and that performance reaches a peak around the 10- and 9-layer models, smaller than the best performing equivalent model for music vocals source separation in {{cite:4a1547806b29a59fcec6b0f683065fc88e965c60}}.
This is likely due to the size of the receptive field, where for speech the optimal size is probably smaller than for music.
| r | a2a4be6a0ab4546c8d96d80382226dc6 |
Note that {{formula:3e3f402d-5bad-4687-870d-726fec04d5e8}} -isoshtukas for connected reductive groups {{formula:865069b1-f137-4546-9cbb-e7e1d22a806f}} were recently studied by Hamacher and Kim {{cite:32a0e0655b7904bef8b75563344674cfd992f0e1}} from a somewhat different perspective. Namely, they defined isoshtukas as {{formula:4da9c872-7a1c-4cec-a394-202085c20ebd}} -torsors {{formula:5244687a-be0f-4464-a958-7d4cb2ad0392}} over {{formula:fa5fb48f-5a99-4859-b8c1-8fd4e20de673}} together with an isomorphism {{formula:bc5146e5-3b69-402a-896a-9b43fdb4009b}} and classified them very explicitly {{cite:32a0e0655b7904bef8b75563344674cfd992f0e1}}. Since {{formula:0655f81c-d658-42d0-9a16-43eb2042256c}} is connected reductive, then {{formula:d996f258-f0fb-4509-b944-b379da7d2851}} by Steinberg theorem (see {{cite:ee3b7804e27ab377f96f4283c2919a260215fa95}}). Consequently, any two fiber functors on {{formula:48656763-9572-48db-97e4-65b34bd77391}} in {{formula:6f66d1a3-d67e-462b-a9dc-397f8794d56c}} are isomorphic and the set of isomorphism classes in {{formula:5c92afa3-1977-4c59-8ce9-ff4f6ec2db16}} can be computed after fixing fibre functors. A standard Tannakian argument (see {{cite:67fd3a379e55be4551475fcd6a322a32743f148c}}) shows that the set of isomorphism classes of {{formula:4539a22d-9228-4761-bc37-d0e2f8520a6d}} -isoshtukas of Hamacher and Kim is given by {{formula:41dcb49b-457c-4922-a821-de8f13f81763}} .
| r | c4e2fac39a37fbd8873f04c48d77ae24 |
Since no radiation was detected with the numerical code used here,
our numerical results suggest the mathematical existence
of true breather solutions.
The solutions constructed here are also different from the sine-Gordon breather
in the sense that they are propagating, and have a well defined phase and crest velocity,
similar to the two-parameter family of mKdV breathers. In contrast, the sine-Gordon breather
is a one-parameter family of stationary breathers.
Nevertheless, it is possible that the breathers found in the present work also feature
very small radiation which may be below machine precision,
and in this case the breathers found here would also be approximate in the mathematical
sense, i.e. decaying after a very long time.
On the other hand, the question whether the breather is an exact solution
or a slowly radiating meta-stable state may not be of much importance
in practice. Indeed while it has been shown for example that the Peregrine breather
is unstable to virtually all perturbations {{cite:8fd6c414962266bca9b21894613998e6f5369f22}}, {{cite:7e279fd10e0efd21a1777b0702c865a81b3286ab}},
breathers are nevertheless observable in the laboratory {{cite:53a2aff6572442b6f46aaf4d2f82bf212bb854ca}}.
Moreover asymptotic model equations such as the KdV and Whitham equations are generally valid
physical models only on a time scale inversely proportional to the amplitude
{{cite:8ebefc5d11999c03ed85561342e4396f34f340db}}, {{cite:a2546bc4639379560842e1c3e635b9b1633a2abf}}, {{cite:5bb801af3d8ef42235dcf581a4c05c0b67c79dfa}}, {{cite:96e095b90a228da701d5b67199097ae0586ae3e0}}.
| d | 81fc25b4a99d80069e59e2aa35a5cd50 |
We describe in this section the solutions of the shooting algorithm in the case of two controls. We first recall some results about the continuous limit {{cite:eb7b301a92966b671bd98a56ecb11c0ad2dcf921}}, {{cite:9c959f8a458ba51ae7dfaa8090653ddfd9e73ea4}}. In this limit, the optimal equations can be integrated exactly by introducing spherical coordinates {{formula:70329605-5e91-4072-80f3-08a2672a956c}} such that
{{formula:b03c02f7-e5f1-4661-8b24-bca50982f982}} , {{formula:ff9bf8fe-dcf2-4160-9554-13ffc0f5c070}} and {{formula:85453209-f5b4-444a-89ed-2b868262d37c}} , with by definition {{formula:f4bf57bc-c00f-4697-85b6-9e8d51c8bf50}} . Using the generating function {{cite:ba86134be9c274e06427f5fe940e3ca768f64b9e}} {{formula:37a3c577-f1df-4bf8-b208-990053cd87c9}} , we deduce that the conjugate momenta can be expressed as
{{formula:0d46e30e-2ef9-4a7d-bd60-6034de03d05f}}
| m | a182d7f1e54b910f4e0e178ca959c8a5 |
The proposed method in this paper is compared with the method proposed in {{cite:6876a15e8e68ed51bcbf72a80a96e1d4690d3fe0}} as well as {{cite:6649830107ddbdd5e66474af78e1d5dc8499dcea}} in finding a Safe Corridor (SC) between the same starting and goal points in 10 randomly generated environments. The comparison metrics are volume covered, number of constraints per polyhedron, number of polyhedra per SC (genericness), computation time and SC safety. The mean, max, and standard deviation of the relevant metrics are shown in Tab. REF . The difference in the metrics between the 2 safe methods i.e. {{cite:6649830107ddbdd5e66474af78e1d5dc8499dcea}} and our method, is also shown in Tab. REF .
| r | c50b9b2d087bd62afccb5a8a90fe2d6e |
As in {{cite:bae1320d6274d195e7ae68c24547673e68d735bf}}, the computational domain extends over {{formula:8f19cff5-37ce-4afb-a10b-12756ce92461}} and {{formula:09833ea8-f27b-4a5d-834a-21e2851c95fc}} , with the same Dirichlet boundary condition {{formula:2b68f9df-4b7c-42ea-bf63-466063e0dab3}} at the inflow {{formula:042c3f96-31db-42ec-9fd3-02700f55203c}} , `top' {{formula:85b7f5aa-7784-4f9e-a85a-3b5ead620e31}} and `bottom' {{formula:48237f23-c2e8-4815-8eb5-8c35e8d3bd09}} boundary conditions. A standard outflow boundary condition {{formula:899dd9b8-5d14-4101-9d21-7c8b013a2265}} is used at {{formula:e7b60ffa-5a45-4ba8-bdbc-9ee4735a920e}} , which is similar to the stress-free boundary condition of {{cite:bae1320d6274d195e7ae68c24547673e68d735bf}}. The boundary condition on the cylinders is obviously no-slip and impermeability, i.e. {{formula:d750c212-c01e-48c9-81f8-7fc0c44e177f}} . The freely available software FreeFem++ {{cite:6a9d2940ea481c69f6bb8f5fd6dc939e73238222}} is used to time-march the incompressible Navier–Stokes equations discretized on Taylor–Hood finite elements; {{formula:7b52fec6-71a4-4e5c-8316-190393b16432}} for velocity components and forcings, and {{formula:971d1e97-2282-4299-8f96-1a65a22131fc}} for pressure. The mesh comprises {{formula:2a522ee4-fbe4-4311-8f7d-9fbf0f429a4c}} triangles, {{formula:cbca08f4-8aa2-4d44-93bf-c8aabe079e62}} vertices and the total number of velocity degrees of freedom, including both components, is {{formula:d05aff63-01b4-4df7-afff-0d8f70a9321d}} .
| m | 8b521c314c89ac25ec5bd851d36f8654 |
Qualitatively, Theorem REF is identical to the original basic container lemmas {{cite:ead3c52abbc00749d6e5cc9c58edcf62ed26811b}} and {{cite:5e7528a191be4aa8607e81e5890f3bf900d71192}}. Quantitively, however, it is a significant improvement of these results. In order to demonstrate this, we shall present four applications of our new theorem to problems in extremal graph theory, discrete geometry, and Ramsey theory that had previously been attacked using the original container theorems, obtaining an essential improvement of the state-of-the-art result in each case. We discuss these applications and the relevant background in detail in the next three sections.
| i | 6cb8487aba2d51da1cd01c845f137465 |
In this section, we describe mMonoT5, a multilingual variant of monoT5 {{cite:c67fffc65a054d410fd7df5e8a0f300cfebf6b26}}, which is an adaptation of the T5 model {{cite:c957f94eebe3bcbad1d4622ebf9934283a74e3c8}} for the passage ranking task. We first finetune a multilingual T5 model {{cite:db1c0c693d3042e9190ba7f642e630e1f48a74ae}} on the mMARCO dataset {{cite:cc1acda0e1e33110133d519fe8151c385f4f96e6}}, which is the translated version of MS MARCO {{cite:a51ed50dc4ef3fdbc81737702e019acd3eaf63ea}} in 9 languages. The model is trained to generate a “yes” or “no” token depending on the relevance of a document to a query.
| m | 3382e9666cfbf784640d6c61e1ca742f |
See {{cite:80b3c1cbd6c9cacc0c9830f769969257199d4643}}, {{cite:e4e61c5566942a655f114ab13200856171bbb7dc}}, {{cite:8fdb0c5ab72c6f4ae752cbbedb2ea0e6a419a338}} for the proof.
| r | f8c33e574a3d0239ebae4d67183ba2ca |
Two released BERT {{cite:8dbd49a205c45322332a8b6f31932dfe9f288b7d}}, BERT Large Whole Word Masking and BERT Base, are first used as pre-trained encoder and baselines for Span Fine-tuning. Compared with BERT Large, BERT Large Whole Word Masking reach a better performance, since it uses whole-word masking in pre-training phase. Therefore, we select BERT Large Whole Word Masking as a stronger baseline. The results indicate that Span Fine-tuning can maximize the contribution of span-level information, even when compared to a stronger baseline.
| r | 0b7d8a7643f1ff4fc894cd9962352780 |
We prove that for super-resolution measurements it is possible to achieve a quantum advantage demonstration even when the measurement is approximate (with a system-size-independent sampling error), based on plausible complexity-theoretic assumptions similar to ones used in the "quantum computational supremacy"
literature {{cite:15162e48c4ce965fc1ae6c04a623cbceca6b139e}}, {{cite:eb21e632b0128064e0577e9ef4800bcc9a4f33c8}}, {{cite:21ee979efcb74c340ef896bd85fde07d19da9f80}}, {{cite:ad0411e5893f073d8eb339a629041bae0900adee}}, {{cite:3fba3db8ce32e535cb69edb5bcea869804cc1246}}, {{cite:8e887925b7b1d7ec8c8f59663a0f8b9d268e413f}}.
The quantum advantage originates in the super-resolution measurement of a simple 5-local cluster state Hamiltonian on the 2D square lattice on product state inputs. The protocol can be implemented using the quantum simulation scheme of Ref. {{cite:21ee979efcb74c340ef896bd85fde07d19da9f80}} and requires the short time-evolution of a nearest-neighbor on a 2D square lattice, suitable for implementations in, for example, optical lattices. Moreover, this scheme can be efficiently certified using reliable single-qubit measurements. These results open up the possibility of near-term experimental demonstrations of quantum advantage via energy sampling.
| d | 4e3c0584bbf30084d1f0e8143df7fd74 |
Table REF shows the quantitative comparisons on the Set5, Set14, B100, and Urban100 with factor {{formula:98616da7-6898-4e4c-b628-c77f9f1864e5}} 2, {{formula:970864ba-89be-4ec1-b519-7ab08dd4f12c}} 3 and {{formula:0c00922b-01f3-4612-bd9c-8576443f8f8f}} 4. As illustrated in Table REF , our approach surpasses IDN with a clear margin. Specifically, our approach outperforms IDN with 0.11 dB and 0.46 dB under factor {{formula:71f7953a-6ba0-48cf-9f9b-d8f6d69c30c6}} 2 on Set14 and Urban100, respectively. Moreover, our full model surpasses IDN with 0.22 dB and 0.08 dB on Set5 and Urban100 under factor {{formula:39b6ad80-8edf-48ac-938f-6fd8774d4a5e}} 3. As IDN is an efficient SR framework, our model still owns a superiority among state-of-the-art methods, which inherently verify the effectiveness of our model. When compared with the remaining models, our approach outperforms them by a large margin on Urban100 in term of the PSNR metric. A similar trend can also be observed for the SSIM score. Specifically, as illustrated in Table REF , our approach achieves 0.50 dB, 0.36 dB, and 0.30 dB improvement over MemNet {{cite:bbcdbe293d70f4e1a07b14e200ce300a00cb73ff}} on Urban100.
| m | e087b5f083f2f91e98c793b67fe0f01c |
Note: Instead of the covering number of {{formula:bfec0403-4c8b-46ed-99de-11a7a2089cd2}} , the above result needs the following metric entropy result of the interval {{formula:d64fc777-b163-4ce6-ba14-a0b58895c944}} (see Prop.4.2.12 in {{cite:c3ab3d6c0931fd076525b6b3a7abbeb78407c2c5}})
{{formula:a1fa43e1-bf4e-4dba-811c-819171701270}}
| d | 7d5a77cc33cf065c74062d44cd4a1b3c |
TER is not restricted to grid-like environments. For instance, consider a LunarLander task in OpenAI gym {{cite:8836b1c72ef73aa1ce8b108d54ef1e30e4f8aab9}}. The goal is to control the aircraft to land on the planet. Though it is not a grid-like environment, we still can build a graph to maintain predecessors of each state in LunarLander for TER.
| d | 6a78c679451537d51278fb1df3dbe626 |
On the other hand, the secrecy rate optimization problem has been intensively investigated in recent years. Because phase shifts of the IRS can configure the wireless channels, it can greatly improve the secrecy rate {{cite:9e10da8b36624517b166a175f212c3ad3f9d8019}}, {{cite:8e73fa5e37f19f216ad406d8e1860e37d586ad9e}}. Specifically, an IRS-aided mmWave secure single-user multiple-input single-output (MISO) system was investigated in {{cite:9e10da8b36624517b166a175f212c3ad3f9d8019}}. In {{cite:9e10da8b36624517b166a175f212c3ad3f9d8019}}, the IRS's phase shifts were adaptively adjusted to strengthen the received signal at the user but suppressed the eavesdropper. In {{cite:8e73fa5e37f19f216ad406d8e1860e37d586ad9e}}, a robust secure based on block coordinate descent (BCD) algorithm was proposed for maximizing the secrecy rate in an IRS-aided mmWave MISO communication systems.
| i | e40b3698648ec6b21111d5ffa5b24e27 |
Unsupervised Domain Adaptation (UDA) aims to reduce the domain shift between labeled and unlabeled target domains. Early works {{cite:ddb337a850e639c3b75ed871dfcf81bde0360571}}, {{cite:0bb51ad53d9759174f713eba8259f3560a432807}} learn domain-invariant features to link the target domain to the source domain. Along with the growing popularity of deep learning, many works benefit from its powerful representation learning ability for domain adaptation {{cite:acb2c0acafbbb6bfeca298b26c3877cae6d84882}}, {{cite:a1025565cb589e38d907bbfa3a56002a697a679e}}, {{cite:379cf47dbdcd62dfc38a0d3c9c73f022e6afe6c7}}, {{cite:2e0c1bb8572d0292402b79e62130c595f2477892}}, {{cite:b868bd52934de136d96c07da80b89d01baa9d7e3}}, {{cite:6c9ea05683ff377fd4d9111eee4ae58abacd3f58}}. Those methods typically minimize the distribution discrepancy between two domains {{cite:9cba924ecf5d364ce245f9873457f3c2661b0306}}, {{cite:a1025565cb589e38d907bbfa3a56002a697a679e}}, {{cite:379cf47dbdcd62dfc38a0d3c9c73f022e6afe6c7}}, or deploy adversarial training {{cite:2e0c1bb8572d0292402b79e62130c595f2477892}}, {{cite:acb2c0acafbbb6bfeca298b26c3877cae6d84882}}, {{cite:b868bd52934de136d96c07da80b89d01baa9d7e3}}, {{cite:6c9ea05683ff377fd4d9111eee4ae58abacd3f58}}.
{{figure:ad0695ca-fd95-4658-a87d-2a9b81ce52e6}} | i | 3e54bb54d60b54955f87200c62f4f050 |
where {{formula:959c6ee6-a34c-4317-bf9f-b8f3e316c8dc}} and {{formula:09e3041e-493c-4875-a8ea-a2cdd1261f20}} for {{formula:54866432-2cc0-4114-a1e3-b3c0812c39b5}}
is the wave vector of perturbations with the wave number {{formula:ff1d84aa-8b4e-4f50-b20f-c3674b039567}} , and the number of Galerkin terms {{formula:875c203f-4a7f-454f-9bdc-38609ee669fe}} in the above expansions is chosen large enough to meet numerical convergence. For each {{formula:6fd3dbe0-a5af-48e4-83dc-246359877865}} , the functions {{formula:447b08de-c11d-4106-82f4-73b866ddfccd}} , {{formula:1dda1c0f-1f0b-451a-908b-adf7b62e014d}} , {{formula:b0ca4bd2-cc57-45d1-b7bf-afe8cd61c7aa}} , and {{formula:bb9ffe9e-637c-4f43-9a11-7dce4ac80049}} are known as Chandrasekhar functions {{cite:dc6505600418e3a32b95e4885d161e9b98fa0f4d}} and are defined as
{{formula:4055cb45-dbb4-4490-8057-a917eb2ed54e}}
{{formula:0101f441-17da-421d-8f92-084ac1494c10}}
| m | 94e5c6ce5203868298ae27c26a5c2f09 |
Carbon-footprint aware NAS. The EC-NAS-Bench dataset reports several metrics per architecture, as shown in Table REF . Combinations of these metrics and the use of MOO could allow for the exploration of architecture spaces that have interesting properties. For instance, NAS can be performed to directly optimise the carbon footprint of deep learning models. Although instantaneous energy consumption and carbon footprint are linearly correlated, when measured over a longer duration ({{formula:e5239d56-dccc-49e7-a81e-01fbfe3aa35f}} 5m) these quantities differ due to the fluctuations of the instantaneous carbon intensity {{cite:af99619212f6cc2c1f519401536754ae2c691a19}}. These carbon intensity fluctuations are caused by the variations of the power sources to the grid {{cite:2a83d33f79b035b06256913a0573c9cf25b4aefb}}. This can have implications when training models for a longer duration or on cloud instances that can be distributed over data centres in different countries {{cite:9c3388e930e0b9e4e382e798a7ed7433651340cf}}. By reporting instantaneous and aggregate carbon footprint of model training in EC-NAS-Bench we facilitate the possibility of carbon footprint aware NAS {{cite:3f82046d85b7ac2ab802cd96e9b53f95633901d2}}. In this work, we focused only on energy consumption awareness to work around the temporal- and spatial variations of the carbon intensity.
| d | f6c4ed3ddfd473e82057728b77411d0c |
In this learning paradigm, we do not need a large amount of images labeled by attribute labels. Instead we pre-train our CNN model using a self-supervised learning paradigm. Here, we use the MoCo v2 self-supervised learning {{cite:4111a9ef2659c3c4973149f1e9cb00b0da354fac}}, as it is a strong and efficient self-supervised learning method. Specifically, we use SimCLR {{cite:721a3cc3512b9b481b5a7e4037038d75ccd58a3e}} style data augmentation for the unlabeled images in the contrastive loss, and follow the implementation details in MoCo v2 where we use a two-layer MLP on the top of the last feature layer to map image features to 128 dimensions, and then use a momentum updated model to calculate the key features in the memory bank. Here, we stored 128 mini-batches in the memory and each mini-batch contains 128 samples then the size of our memory bank is {{formula:c52a9ce8-922b-4ef9-9475-eecda40c81d7}} . After pre-training the attribute network, we select only a small number of images and then label the selected images with attributes to fine-tune the attribute network. For this study, we conducted experiments on two publicly well-known person ReID benchmarks namely MSMT17, and CUHK03.
| d | 369c8daf7be2c787b92ec81fa82a0346 |
On this note, let us once more consider the quantity which
Eq. REF measures, namely the distance of {{formula:cc8334a0-f7ec-40c4-ba25-bfe0bf789ad3}} from
{{formula:4f535c11-517b-4b9d-8e0f-4bc45dd6b085}} relative to the distance of {{formula:8bd49482-133e-4788-9267-2f42d7b86497}} from {{formula:d3c1a97f-e433-433f-9ed7-063fab0da102}} . Referring to
Fig. REF (right column) and Fig. REF (A,C),
we can see that samples {{formula:db819add-3392-4f05-a835-1c2d6f544c4e}} which are more like those in sample {{formula:b67c4786-82dd-4119-aec8-1c78cffd523c}} have
a distribution that lies to the right of samples which are more similar
to {{formula:f8e5dd29-a08a-48a2-9829-e1c4440a7d32}} , as expected; for example, in Fig. REF (A,C),
the distribution of null (not in {{formula:aaf2198d-2330-432c-b66c-4a4609a1b3d3}} ) CGEMS cases (dashed red line)
is shifted to the right with respect to the distribution of null CGEMS
controls, as might be expected from Eq. REF , i.e., the CGEMS
case {{formula:c4275499-5d34-4a2e-a082-f55d3140b223}} s are closer to CGEMS case {{formula:ad2379d7-ced9-4358-88db-dc15cd36948a}} s than are the CGEMS control {{formula:c875b2ee-faa1-4a52-a9f6-40587bdbb8a4}} s.
Although this difference is not statistically significant, one could
imagine that it may be possible to select SNPs for which the shift
is significant, i.e., a selection of SNPs for which unknown cases
are statistically more likely to be closer (via Eq. REF ) to
the cases in {{formula:205902d1-a6ea-4f5f-b8d3-3030d58adef0}} and unknown controls are statistically more likely
to be closer to the controls in {{formula:b586169d-812c-428a-b9a8-662c8635e210}} . In this case, a subset of
SNPs known to be associated with disease may potentially be used
with Eqs. REF , REF to predict the case status of
new individuals; conversely, finding a subset of SNPs which produce
significant separations of the test samples may be indicative of a group
of SNPs which play a role in disease. Because this type of application
would use fewer SNPs and would involve the comparison of two distributions
of {{formula:d4b66bf3-1a6d-406a-af34-3ba947afc50d}} (cases {{formula:3fe4497b-f448-44e2-9701-d98af8b19371}} vs. controls {{formula:15327399-fd77-4e25-8aea-42ad18b0f9ef}} ), it may
be possible to circumvent some of the problems stemming from the unknown
width and location of the null distribution described above; still, much
work is needed to investigate this possible application. If successful,
the metric proposed in {{cite:8de113cbfe90c70ab6c89f6c60db11e93aa3d85c}}, while failing to function as a
tool to positively identify the presence of a specific individual's DNA
in a finite genetic sample, may if refined be a useful tool in the
analysis of GWAS data.
| d | aebaef1c93f792786a8c162b843b6e39 |
Table REF presents results on SDD in the short term setting {{formula:65e0d4c5-199d-47ca-9257-f3a8c5c5a3f1}} seconds, {{formula:b0885aeb-d43a-46b0-b379-712e9ca8b4e8}} seconds. We follow the standard split from {{cite:37ed19bd4c097cd0383bd3db949269fc63f7f338}} and report results with {{formula:585e7ed0-55d9-4b8d-919b-8c1fa79e9064}} . Since there's limited aleatoric multimodality in short term settings, we use {{formula:c626b54b-0266-4167-9af7-bf412d0f800a}} thus being comparable to prior works using {{formula:b91ee02c-a324-4c5e-a364-3491b3566fef}} trajectory samples for final evaluation. Table REF shows our proposed model achieving an ADE of {{formula:9be34931-b08e-4b85-ae02-aad213c04412}} and FDE of {{formula:fd4f27a0-803f-4403-90e0-5f8b19daf037}} at {{formula:bfe8913b-9940-4bee-a00f-fdf65fe361e7}} which outperforms the previous state-of-the-art performance of PECNet {{cite:23c8e85a2c68c7e11b51830d133f24321a5cfd33}} by {{formula:37b8a3b2-ad59-425b-9a84-a9fdaf669067}} on ADE and {{formula:9f321792-1807-4679-94ec-67f194b6fe0a}} on FDE. Further, at {{formula:2efb6a2c-9e91-4db2-9dda-00678b49b45f}} it achieves an ADE of {{formula:e1d2c15c-9082-4940-a968-ef350219038e}} & FDE of {{formula:dad864ae-7309-46f0-be89-8898155a437d}} outperforming previous state-of-the-art performance of TNT.
| r | dd0f685d7c8df8b5f46e91841e082311 |
The general framework and results obtained in this paper
motivate applications to a variety of exciting problems in different areas of interest.
In mathematical GR, potential applications include
the analysis of waves on black hole spacetimes,
analytic compactifications,
and possible generalizations of the Chen-Teo instanton.
In gravitational wave science, it would be interesting to make
explicit connections to modern techniques
used in scattering amplitudes and quantum field
theory {{cite:09d3d1d81424e136f7ca81cf216a39274e412eeb}}, {{cite:4943620cebb1f86abed5bca6cc7e6b25a131183a}}.
The relation between Kähler potentials and
the Newman-Janis shift motivates further investigation
into the geometric origin of this trick,
together with connections with its interpretation
as a generation of intrinsic spin {{cite:1650eb7e2b0a7de437541825ee42e8218c84d89e}}, see also
{{cite:ae4dc6360bba08834ed89403fa57296f4fea04af}}, {{cite:74e951a26403763cee8f4273135c6e06a374335e}}.
A detailed description of dualities in the Plebánski-Demiański family
will appear elsewhere {{cite:73bcc312544945b62fc8eb43dc2c0fc4832f3d68}}.
| d | d5cf45b7927959a0617d65b0552dddd5 |
To understand the real nature of the BLCCs, {{cite:dc28d589d0f8578f9698472fda92cbbb27f8d65c}}, {{cite:870be4579c83bc57731d8b6d543c8502ba0c85b5}}
performed an HST imaging survey of 20 BLCCs in M31's disk. As a
test case, {{cite:dc28d589d0f8578f9698472fda92cbbb27f8d65c}} presented details of the data-reduction
pipeline that will be applied to all survey data and describe its
application to VDB0-B195D. They estimated the object's age, by
comparison of the observed CMD with theoretical isochrones from
{{cite:d9819aefcb9676b58a242e8b223f014d6dcea538}}, at {{formula:39be3dca-830a-43d4-9152-810b51ec7c9a}} Myr. In addition, they constrained
realistic upper and lower limits to the cluster's age, independent of
the adopted metallicity, within the relatively narrow range from 12 to
63 Myr. Using Maraston's SSP models of solar metallicity
{{cite:285fa27045a2b83bf218294aea8c66761b428a77}}, {{cite:5261a07a68db7bb9f7b9b5da94e82be267da110e}}, {{cite:41571e32aaddbf65c531aca2ca35b578efe95a22}} and {{cite:ed39c6d73778d03b60628cacb551caae80e55f45}}
IMFs, and photometric values in the {{formula:673e9fbf-ee19-4c65-9070-e0a782b63209}} and 2MASS {{formula:43d7238d-6ba3-4ad8-86da-e80e8aa5a4eb}} , {{formula:a4ec3dd2-e264-404c-8a9c-7ae5bb55ea90}} , and
{{formula:4b9f579e-f134-4a39-91dd-c505c276401d}} bands, {{cite:dc28d589d0f8578f9698472fda92cbbb27f8d65c}} concluded that the mass of
VDB0-B195D is {{formula:6c21fc19-51bc-45fe-9cc6-8a6715aff91b}} , with their best estimates in
the range {{formula:e4fd0dd6-154d-4dda-8b56-2c54140af4c1}} .
| d | 6fee06a2db5d3945f2ac5e5f61b2898f |
We give results of regular (natural) decision trees, TREANT {{cite:9d6d5130a75cdf6686a94915070b557d3b91dad1}}, Chen et al. {{cite:d461dc462a21b32909f0c8e2caf39f8f31d81fbd}} and groot on fourteen datasets in which we compare predictive performance and run time.
For natural decision trees we use scikit-learn's {{cite:18a5406652cd9dfeb42d91f67ed67e0192d3da40}} implementation as it is widely used for research in the field.
To compare against robust decision tree algorithms we run TREANT and the heuristic from Chen et al. that computes the adversarial Gini impurity using four representative cases. All datasets can be retrieved from openML except breast-cancer, their specific versions are listed in the tables. Breast-cancer was imported from Scikit-learn.
{{table:da66c427-9378-4787-bb89-30dc97561862}} | r | 47cefb5593312a5c97c982a1d7782101 |
Shor's quantum algorithm for order finding in modulo {{formula:3b91d4ac-fda7-4138-b2e6-e08a1928a832}} requires {{formula:c0abbdc2-10bc-464c-9b68-37a43b3be853}} quantum operations with {{formula:f2964b7e-9ee5-41f8-aa8e-bf5f37f23735}} uses of modular exponentiations. The main subroutines of Shor's order finding algorithm are modular exponentiation and quantum Fourier transform. Modular exponentiation needs {{formula:e7113654-01a5-4dc0-b1b6-a8bfb6a49b4c}} multiplications, hence {{formula:450a5be9-be8e-4ee2-9b06-8d4558abc1bf}} is the total complexity for a modular exponentiation while quantum Fourier transform is quadratic in {{formula:69ff7547-22ef-410b-be01-46d951abbde2}} , see {{cite:f0722be107b83d5b13c51682f99a1188de14029e}}.
| d | 50d1d8a52bef1572b6299dbc42d28415 |
Later on, similar methods were introduced to reduce the bias of IG towards features with large number
of values. The extreme case is using an feature with an ID code. It is clear to see that knowing the
ID code we can precisely know the class of any instance in our training set. The problem is that we can
say nothing about a new instance which will have another unknown ID code. One of these methods is gain
ratio (GR) in Eq. REF used by C4.5 decision tree induction algorithm {{cite:dcdafcf9c28ffecfc024948a174f7c7c892b2eea}}
which normalizes IG by the amount of information needed to predict an features value (the entropy of
the feature). But there are also various other proposals, among them there are entropy distance
{{cite:bb548083da6c0389949c7b5ae95ef6124967082c}} in Eq. and the Mántaras distance between the class and the
feature in Eq. which was proved to be unbiased towards multiple-valued features.
{{formula:43fa7e37-d7f3-4cd0-8381-60c4a803a947}}
| m | 18f409e11f0751fba5818e79c7e8611c |
Pose Encoding on a 2D Manifold. The first challenge lies in encoding the input pose information so that it can be leveraged effectively by the image synthesis pipeline. Prior methods employ global pose parameter conditioning {{cite:1c813a225f17c9f99888da084cbb9db80782350b}}, {{cite:db21e607f2c30398f79866e73316544223961051}}, {{cite:a216b9440b7b9ba6a11e610b47720add844c425a}}, {{cite:fdb62117efbe0e9cc0ccec61b8e05e663730aef4}}, or Peng et al. {{cite:041ea489e0dfb3fa628f155a5dc47f343ae591bd}} learn poses in a 3D sparse voxelized space by SparseConvNet {{cite:04c65b952d23a845a74348f30ef2be09068b88f3}}. For better pose generalization, {{cite:b537be96a081c86ce3405d65ff63318ae5c078d6}}, {{cite:d722168c4d61f32aa734b27534691b07050ad391}}, {{cite:8cc72b3af72ff040cc2b29bded9a0be5d6b4dad7}} learn motions using skinning weights via a backward (or inverse) skinning step.
Skinning weights are not powerful enough to represent complicated deformations due to arbitrary motions and various clothing styles, however, which may cause averaged and blurry results. In addition, changing topology is challenging for backward skinning used in {{cite:d722168c4d61f32aa734b27534691b07050ad391}}, as it is not able to model one-to-many backward correspondences {{cite:82ec79d40b86ecdb1a78b63a9863b9ff77d8ec9f}}. In contrast, we encode motions on a 2D UV manifold of the body mesh surface, and the dense representation enables us to utilize 2D convolutional networks to effectively encode pose-dependent features. We define a set of geometry and texture latents on the 2D manifold, which have higher resolution than the compressed latent vectors used in {{cite:cd56f708fd446e48ad650bd50c4317df339abbf0}} to enable capturing local motion/appearance details for rendering. Since our method does not employ backward skinning, we also avoid the multi-correspondence problem.
| i | 56d18cf228e7fd66db9ed2c99db19fd6 |
The solution of the {{formula:673a784d-b5fe-4d72-871c-46bc18cf11d0}} -subproblem involves keeping the {{formula:1edd3975-1c02-48c8-bbf6-31260d06f241}} largest magnitude elements and zeros out the rest. Inspired by {{cite:806b8eb1856227bc0578a4877a9330ef57ee70e4}}, we can obtain
{{formula:ad1acd5c-be63-4c67-be1c-a1994a326a64}}
| m | 7cf07cd6b83a3d271df2d69994faa74e |
Following {{cite:7d16163749bbb8c6b8303df3813185b21e915b03}} we use positional encoding {{formula:38d96116-96a5-4da7-979f-4cd9ac066178}} for both scene coordinates {{formula:c5685fac-1411-418d-86fc-f0176fc11085}} and viewing directions {{formula:8e62c281-bb64-4faf-b35f-f7d5b0a3904b}} to capture high frequency details. We employ 10 frequencies for {{formula:8c6e4756-fe74-42d3-8f2d-312e275ac3d2}} and 4 for {{formula:3520671c-926e-4103-9570-e15af53db5a4}} .
We design the architecture of the decoder to take advantage of the fact that the volume density {{formula:73ba3734-b34a-47a5-a078-1c04c22789da}} depends only on the 3D point {{formula:0a671f8c-a106-41e5-88dc-487f091cecff}} and shape code {{formula:b416b32a-8476-4aa9-9b0a-405e80d58845}} , while the RGB color depends in addition on the viewing direction {{formula:9834a659-72ff-459f-a040-34d9f8f3f368}} and texture code {{formula:dcf9ab84-e54e-4605-9dc7-cca6024e7805}} . The first layers of the MLP {{formula:b7720f0a-6f54-4b7d-a627-6275f06c38b8}} map the input 3D coordinate {{formula:fcef6330-8f44-4000-ad1f-217e14604dde}} and shape code {{formula:f2a0610d-eb64-411a-85f8-c3be00399266}} to the volume density {{formula:3c3942e9-2302-4b5b-9ffd-684e0e6298d0}} and an intermediate feature vector {{formula:df73c86e-12cb-4748-8690-faa5b8cc9e84}} . The second part of the network {{formula:28b1fb74-433b-4441-8152-2232f6de7d5e}} takes {{formula:0bb0705c-5afc-4037-ab45-93a7dc3dc513}} and {{formula:aef524d1-c130-4aaf-8032-e82bc8be327b}} as input and outputs the {{formula:7748f51c-c7a7-4ea6-8743-16726c95f666}} colour as shown in Fig. REF .
{{formula:b2c0b166-f70a-4b66-827d-92a25130b197}}
| m | 1b76caaab540a2ded3dda14eddb8b1b8 |
There are many techniques that can be utilized to solve the system of linear equations produced by each iteration of Newton's or Broyden's method for finding roots. Two widely used methods for solving a system of linear equations are described in the following sections, and we refer the interested reader to {{cite:cc83803044bb6a8f0f29683e53799d0e8655802a}} for more methods and details regarding these methods. For a visualization of the basins of convergence for Newton's and Broyden's methods, we refer the interested reader to article {{cite:6360779a816b2ee561b559df670361d67faeafd4}}.
| m | 39d63be94a18dd71f75b07eabd652ef4 |
Then, we let {{formula:932a5d08-e29f-4e4a-b3d5-d6840980d0ea}} denote the number of residual errors that fall into the {{formula:78458d00-6250-4650-9a44-431a631a01b6}} interval, so that obviously {{formula:8ad5f6fd-82cf-4a25-b5a4-fe735d9813c4}} . Following the routine of Otsu's method {{cite:b2a9093e9ed4963f0e56b4327b510a8754794704}}, we normalize {{formula:e49300eb-9ebb-4f57-b431-5f79b4545069}} as {{formula:0a0101de-6274-4af0-ac90-0f32ce02730d}} , so the probability for a random residual error to be lower than {{formula:917a9b9d-9d15-4204-9353-ee69c6aae331}} can be given by:
{{formula:758b2d5e-ca7f-4c75-9ac5-9aacc32d043e}}
| m | c4a5e0e7282dd18afc870efa71453cfb |
Many modern RL methods use deep neural networks to parameterize the policy; this is referred to as Deep Reinforcement Learning. Typically, deep RL methods cannot be used to train policies using real robots because they require huge amounts of training samples to learn useful policies, and collecting this data on a real robot would take a prohibitively long time. Furthermore, during the training phase, RL policies employ exploration, where they select random actions to find potentially more optimal policies. This exploration usually results in collisions with the environment, falling over, and pushing joints past their limits. As a result, training an RL policy on a real robot is generally avoided. As an alternative, fast and accurate physics simulators are employed to train policies fully in simulation. However, RL methods trained in simulation generally suffer from the reality gap (also called the sim2real problem). When the policy (trained in simulation) is deployed on a real robot it fails to produce optimal, or even stable, behaviors due to mismatches between the simulation dynamics and real robot dynamics. We will examine some common solutions {{cite:a8955e7673286fd40385bcad223e23a658f40e8b}} in more detail in the summaries of the papers.
| m | 12efee04f77e62e4a4d7dc23b09fbfc1 |
In this section, four datasets are adopted in our experiments, including ShanghaiTech A, ShanghaiTech B{{cite:e6c47bb63138cfb1dc5cf8f713cb8e5aaf31dd6d}}, UCF-QRNF{{cite:0dde039fb318b3d2217f5a3eef5604b5564cd218}}, and UCF_CC_50{{cite:df325d2faef36dfc395ad9bdd173158c7f3f1ba7}}. Firstly, the evaluation metric and datasets are introduced, and then the implementation details are described. Subsequently, the proposed NDconv is compared with state-of-the-art methods on the four above-mentioned datasets. Finally, the ablation study is conducted to explain the meaning of parameters in experiments.
| r | 9171b178bc6e06e8fa12d17dafa09126 |
In the smart grids context, usually there are reasonable forecasts of the statistics of the uncertainties and a knowledge of the systems dynamics. Therefore, using a structured function approximation such as Model Predictive Control (MPC) scheme can be beneficial. Indeed, MPC uses the predicted information and model to provide a reasonable but usually suboptimal policy {{cite:4a775d620cb92402052c6a05f2faeac03f27f32f}}. Moreover, MPC is able to handle the high-dimensionality of the forecasts. In {{cite:7112460d63c848955ae66072c7c2cff218aeaf8f}}, it is shown that adjusting the model, cost, and constraints of the MPC could achieve the best closed-loop performance, and RL is proposed as a possible approach to perform that adjustment in practice. Recent researches have developed further the combination of RL and MPC (see e.g. {{cite:dbe5d6b8baa47c4ae56ba6cd2ff85e8d54b17548}}, {{cite:b7ad6eced28cb79bb94570cc370ce619ce9a6ba9}}, {{cite:47c2b91171b4d717131deff5a0f2bb2f097a1f2a}}, {{cite:cd71d4dd79989e1349a4d3dabb097064258bd85b}}, {{cite:d60090803b761de21ae6d73454daa497070f5997}}).
| i | 9626d431e98da30e278ad248bb07b375 |
TGIF-FrameQA is an open-ended QA tasks based on
TGIF {{cite:93802204f7cf4f71d95a94f1ff736116d7d9f361}} dataset.
TGIF {{cite:93802204f7cf4f71d95a94f1ff736116d7d9f361}} contains 165K QA pairs on 72K animated GIFs.
FrameQA requires a model to highlight the fact that questions in this task can be answered according to a video.
The answer comes from a dictionary of words of type object, number, color and location.
| r | 89431b84483f2955b5f629d6f48c6995 |
The mean field limit, roughly speaking, is an infinite-{{formula:80f4f379-88d0-4300-82c7-1e741507e876}} approximation
of the model. An important question is: how large should the number
of neurons {{formula:0d6e7e18-699e-4eb9-9727-f743503b22be}} be? It is known that under certain assumptions, one
only requires {{formula:3e25af9c-7c1f-4de0-8b10-4f104d7ab290}} independent of the data dimension
{{formula:31c205c3-ac44-4f16-af69-711660388b32}} {{cite:d256fdbeb3855f95fc1ae4c16b3ec8f7c09c0f47}}. Unfortunately those assumptions fail to
hold in the present setting. A key fact is, unlike previous works,
here the “Lipschitz” constant of the modelStrictly speaking, our autoencoder model is non-Lipschitz in the parameter,
and neither is its initialization chosen to make the model effectively
Lipschitz over any finite training period as done in {{cite:d256fdbeb3855f95fc1ae4c16b3ec8f7c09c0f47}}.
This adds more complications to the analysis. The statement may be
interpreted as that the model is locally Lipschitz with a constant
that grows with {{formula:c9ad234f-0312-4989-bb21-80ca530d7761}} . Without taking the statement in the strict sense,
we stress on the underlying difficulty dealing with the dependency
on {{formula:254db399-6f8c-4d24-ba59-32e11b49d79d}} . grows with {{formula:61765c06-8da4-40da-be1b-c13df4f213b3}} . This not only poses a major mathematical challenge
but also leads to a fundamentally different result. A naive adaption
of previous analyses would lead to {{formula:ed67ffaf-8c38-4746-95da-1fe9c15aed42}} undesirably.
A major technical feat of the paper is to show that one only requires
{{formula:225c6edf-3b46-4b6e-a3b0-74c948860ca9}} . Proving this result necessitates
a new argument which, unlike previous analyses, crucially exploits
the structure of the gradient flow learning dynamics. In fact, we
prove so in a more general framework of a broader class of two-layer
neural networks. Furthermore we believe that on one hand, {{formula:4854917d-5bf3-44a8-aef6-27e1f4a89ea1}}
is generally sufficient, and under special circumstances, so is {{formula:5bb0110a-4d18-44f4-abd5-1e5aaf910ba5}} ,
where the quantity {{formula:eb138dce-12c0-4702-b0cc-0117f78c7f8d}} is characteristic of the data
distribution. In general, {{formula:97394b03-d956-425c-96a4-bf3f4bd415c7}} can be on the same order
of or much smaller than {{formula:f168a1d9-4d50-4474-a933-5b93e09576ad}} . On the other hand, we also conjecture
that {{formula:bf10bfe2-751d-4200-928e-76784bbf05ab}} is necessary, and hence unlike previous
settings {{cite:3a0269b0a5a57db317ebeb616e3f42204994795b}}, {{cite:d256fdbeb3855f95fc1ae4c16b3ec8f7c09c0f47}}, here it is generally insufficient
to have {{formula:1826d82d-2bb4-4a59-9eb5-d7d89e5aa162}} .
| i | 4913a7bb438b72ec08f754eea0ff35cc |
Hyperspectral image (HSI), a three-dimensional (3D) spatial-spectral cube, which is rich in spectral information, has been widely used in applications such as face recognition {{cite:c37462689e404228a76a9605ed971520066d5ccd}}, remote sensing {{cite:2095d166542792ade76bb3b3033bcb2ba28d02d1}}, food surveillance {{cite:3bd1c09b720dfec6f2c2212d8a0d2cfd1c9e0bb3}} and so on. Typically, a spectrometer is used, which scans a 1D-line or 2D plane to capture a full 3D image {{cite:ae0eabc64f523f9df026a3b0f5d7dd4c7d1ce91a}}. Though it can achieve a high spectral resolution such as 10 nm or less {{cite:e417d981146459996d9f8c86b72c61afd6ddc23e}}, it is time-consuming and unsuitable for dynamic scenes {{cite:6398b71ebf469bce2fc29d34dad2e6584b10b5bb}}. Therefore, it is necessary to improve the efficiency of hyperspectral imaging for the dynamic applications.
| i | 2d32973aab814a89b4d5e0b3231753dd |
To assess the performance of PG methods applied to variational compilation, we have run three different numerical experiments. We generated several random shallow quantum circuits with depth logarithmic in the number of qubits and known connectivity graph, which acted as the target unitary {{formula:dabdc35a-5d77-48f1-a08d-9554d1fc9c33}} , followed by a circuit with the same connectivity graph and depth, and randomized parameters implementing another unitary {{formula:d088e773-d86f-42dc-be2d-553ab8af8dd8}} . This setup is physically motivated because in the absence of error correction, circuit depth of NISQ algorithms is bounded by the inverse effective noise rate, which means that only shallow circuits, i.e. of constant depth, can be realistically considered {{cite:77c6ee2cd446025d28d82e91f85dda2509efce5a}}, {{cite:f7a2381ae9d81b75c03ec915b67ab049f2e55543}}. Practically, our choice for this setup stems from the need to evaluate how close the performance gets to its theoretical maximum. Given that most unitaries have exponentially long circuits {{cite:f494da1bb819355aa739606cf8710af5fa767dbe}}, sampling operators in {{formula:fb4dac89-b7e7-4fde-a3b1-256b9b9048a7}} , instead of explicitely defining a quantum circuit, would almost surely result in the optimization getting stuck at indeterminate values of the cost function, which would in turn lead to a poor characterization of the performance. Finally, since barren plateaus will arise frequently in logarithmic and linear depth quantum circuits {{cite:ded500c99e265f23aa884158daacd5e0c841b458}}, we expect this choice of circuit depths to still constitute a good testbed for our method.
| r | d63ba0264f52a0db8526b63cff63b92d |
Our model combines the advantages of both the seq2seq and the sequence tagging models, while alleviating their problems.
On the one hand, while seq2seq models usually suffer from over-correction or omission of correct tokens in the source sentence {{cite:bda20799c9a375d05f6af658410623095d109248}}, the proposed sequence-to-action module guarantees that the model will directly visit and consider the source tokens in {{formula:1a11bdeb-9dfd-48c6-81eb-e90eda04e32f}} as the next predictions' candidates
before making the final predictions.
On the other hand, comparing with sequence tagging models which depend on human-designed labels, lexical rules and vocabularies for generating new tokens, we only introduce three atomic actions in the model without other constraints, which enhances the generality and diversity of the generated targets.
As shown in
the case studies, sequence tagging models usually fail when dealing with hard editions, e.g., reordering or generating a long range of tokens, and our model performs well on these cases by generating the target sentence from scratch auto-regressively.
In addition, we choose the term “action” instead of “label” because the proposed sequence-to-action module does not need any actual labels to be trained, instead it is trained end-to-end by fusing the probability with the seq2seq model.
| d | 9f3151553a5850efdd67094454a56a2b |
Despite the complexity and difficulty of amplitude computations, which grow exponentially as the scattering particles and/or precision (loop order) increase, incredible progress has been achieved in recent decades, especially in planar {{formula:8ade2d63-e132-4f56-a3c5-732972feb880}} supersymmetric Yang-Mills theory (sYM) due to its considerable symmetries (c.f. {{cite:29de7a7c43ca7697a051b53dfd6eac2aa92ce562}}, {{cite:50cdcb17b1238bfca8149c0fc31458462975664a}}, {{cite:85553f9544ef6a6be82bee1491e71c827a2b7485}}, {{cite:00af05cc2f568b7c6b8b69da1aed665822329838}}). The four- and five-point amplitudes in planar {{formula:1b73b584-cc26-4bbc-a254-0ab3b5521dd8}} sYM are captured by the well-known Bern-Dixon-Smirnov (BDS) ansatz {{cite:65ce62327bb130ba63a26fb7841038d8da8e1881}}, as well as the infrared divergences of scattering amplitudes {{cite:56ce75c976849cff6b1d5e300fd485293e3e2340}} for all multiplicities. After subtracting the BDS ansatz, scattering amplitudes with more than 5 particles of the theory are finite functions of cross-ratios, and in particular are expected to be multiple polylogarithms (MPLs) {{cite:cd02985c8c120b89920c210218bbe2a07092b124}} of weight {{formula:ec5cd34f-1f70-4ba2-af91-b7476c101917}} at {{formula:8d3aa547-f2e0-46d1-9599-df7ddc34efad}} loops for MHV and NMHV cases {{cite:bc15eb85033203f543ff87e40bdbb682723503cd}}. Remarkably, the first “non-trivial” amplitude – the 6-point amplitude (or hexagon) – has been fixed up to seven and six loops for MHV and NMHV cases through a bootstrap program, respectively {{cite:b1baf973402412a8ff2d8b904f31632eb78d7a8e}}, and the 7-point amplitude (or heptagon) has been fixed similarly up to four loops for both cases too {{cite:4d6bb3e4df92a0675e1ac9303af8928412e74d54}}, {{cite:7d6047302ccc18a6a6937a5ace4050ab962bf908}}.
| i | 4e950ba06b5dd2027d16d641d658c2b8 |
Despite showing video as the main application in most of our experiments, our method is invariant to the order of frames in the sequences. This is a result of using a zero-shot strategy, in which the underlying models are trained per frame. Examining the results, the generated captions display a logical order. This is not surprising, since ordering frames is typically not an extremely challenging visual understanding task, and is also used as a self-supervised task {{cite:fd3dd4a0e9aab11fcf994d7e338aecbec0125d46}}. Evidently, the information that exists in both the Language Model and the CLIP network is sufficient for generating sentences that adhere to the natural order of events.
| d | dcfea902873d0eba485374ef045c830d |
Unsupervised learning of an acoustic model (AM) has a long history from the Bayesian model to the deep neural network (DNN) system in the field of automatic speech recognition (ASR) {{cite:50e8eb150a88b12b52c4694288e7b3c6b1ea49e0}}, {{cite:3cf79b5568bea1cd9e0ae5ead65c28471d28c28c}}, {{cite:244ce733fe299fb1f21fe2bb889602a91318db95}}, {{cite:1abb5920aefeb7f26fce12199780e17d6a6464d2}}, {{cite:6a1a19df311c515f50e6e213863ed3a878e71ac0}}. It is typically done by transferring knowledge from stronger teacher model(s) to the student model {{cite:60a9fe244e2508e8de3743543fcd677423ad7f10}}, {{cite:812579a36803974859080b19699105a6c4ee6378}}, {{cite:4dd8ed5cbad56a72a8f73c712c699897c5b69dfb}}, {{cite:fc4a838c15ee2d82fe354b185c013a270f91372b}}, {{cite:15018fc9c5491fede0ff04c1a47f49b382ac2e00}}, {{cite:781710a131d9cecb12cb8172d1ea4addedffce65}}, {{cite:dbf052810d6cc52a0ae6fa0b7647109a07cc1a18}} or adapting the seed model pre-trained with a sufficient amount of labeled data {{cite:50e8eb150a88b12b52c4694288e7b3c6b1ea49e0}}, {{cite:3cf79b5568bea1cd9e0ae5ead65c28471d28c28c}}, {{cite:244ce733fe299fb1f21fe2bb889602a91318db95}}, {{cite:18dabf70f9341c5423118dc7079d8f9001c31c38}}, {{cite:4c849a374811afd32424131205e3f72d9d1d0c82}}, {{cite:4748cc29ec1293418c95aaafb8d9a9f108b58661}}. Because of no need of heavy decoding processes with teacher models, the latter self-training approach is perhaps preferable in many situations such as on-device personalization and federated learning scenarios {{cite:379e445e4cebda8600f327c4775de31e0b51370f}}, {{cite:945eb66caa715db34a3c89285fa58c059f321d57}}, {{cite:4276654f334df3a955c98fbf64bc2aa3228f8c5d}}, {{cite:d2a9cdd34d444fa943b7bff8bfb0ccf168afaaee}}. In this work, we thus address the self-training task for AM without an additional bigger teacher model and parallel adaptation dataThe definitions of unsupervised learning and self-learning vary in different applications and fields. For presentation purposes, we will refer any model optimization methods without manual transcripts as unsupervised learning even if the initial seed model is pre-trained with labeled data. We will say self-learning is a special class of unsupervised learning techniques which optimizes the seed model without another teacher model..
| i | 5ab3d6fe8326e88c4cc142d45f1990c8 |
Several methods can be utilised to measure different {{formula:18f5e2f6-0edf-443e-b717-804267fc83c0}} violation observables in these decays {{cite:0e71cc0af749e195c75c1fa35cd5491b89f0bf8d}}, {{cite:5c438ccb34c14a68f9bc311c81a80230bfe38821}}, {{cite:d66f28eeffb17af220de53bd53c77b29f3f47590}}, {{cite:1869b620f81209d55c5dcb1b0be54f71ba33a709}}, {{cite:387d710e8c984d95377b8d6d3935d53d2223c33b}}, {{cite:15ee84f2058862e941bd201eed7735d4ef201ddf}}, {{cite:e9dc9e13ea82da71b9c6879ee30c4179cca7d348}}. The measurements are then typically used to place tree-level constraints on {{formula:57bd782e-5d4b-41fc-8e5f-e11d48ed220e}} without the need for any theoretical input.
The current world average value of {{formula:e1926c21-f887-4ae2-a22c-d73fc06d0b55}} {{cite:71b0b9333855efe529dcd32c1a4faf684123b2ca}}, {{cite:9052c8021251ef90d1068fd483a17f3cc989e42b}}
is dominated by measurements from the LHCb experiment {{cite:da233f2f9c398ed8319e38477bfe88b57371879d}}, {{cite:3ecdbee66571f7f62aa2d06a2fcc1f9722f24c6e}}.
| i | 1323e8de02dbbd076c98078b54819f8d |
In centralized asynchronous communication methods, the network overhead is concentrated in a few parameter servers. Therefore, decentralized gossip-based methods have been developed to spread the concentrated network overhead to every worker node. DP-SGD {{cite:59adad2e0b7b9cbcf4a4f5305d78a1f894ba6b55}} is a significant research on gossip-based distributed deep learning. This method shows that gossip-based communication methods can achieve similar accuracy as AllReduce-SGD when the number of worker nodes is limited to a small number. ADP-SGD {{cite:8ba1ffc47f726751137ebb00f5632519f23edadf}} is an asynchronous version of DP-SGD. It shows that asynchronous and decentralized distributed deep learning can achieve convergence accuracy similar to that of AllReduce-SGD.
| m | f82f21bb6614dca3217cd6bc03cb1455 |
Step 5 - Distilling knowledge from the original model: Once the compact model is obtained after resource allocation, we follow the common practice in network pruning {{cite:77ff43683cf52f280bbaf9567a5b14f97c7bd52f}}, {{cite:6e71af80bed2ac9a533925d9518abe477e077236}} and start to train this model from scratch with both hard label and soft label supervision signals. The hard label denotes the ground-truth one-hot vector and the soft label represents the softened probability distribution from the original cumbersome model {{cite:9a892583d407c4fa0cf8ba13a715e636ff4fca9e}}. By distilling the probabilistic knowledge from the trained unpruned network, the small compact model can learn better representations and exhibit better generalization capability after the training phase. The final loss function is written as below, which is comprised of the hard label loss and the distillation loss:
{{formula:c8029837-9f84-4a0e-97a1-99575e9487f8}}
| m | e1b639d570599a050dcad8bfcf33e8ed |
Recent papers have proposed fusing E2E models with LMs trained with text data (usually referred
to this as fusion), including shallow fusion {{cite:fce7b25abbb5ba0ccba6f11cd77070dd6e7785e5}}, {{cite:9b6732c69e368025df35df5adf98b58f2233a70e}},
deep fusion {{cite:fce7b25abbb5ba0ccba6f11cd77070dd6e7785e5}}, cold fusion {{cite:1b160ad789dcad33aa5a369c3f9197046825bbf5}}, component
fusion {{cite:33c2716666c9bf76164037e0fd8c822cb00a4cba}}, etc. Most experiments used neural LMs, and some used
n-gram fst LMs {{cite:9ee4324e6cc71fe58e3cf87706ef76efe2ed25fa}}, {{cite:fd0cfb88068696aac1babb81fc47347d75e8a4b3}}, {{cite:fce7b25abbb5ba0ccba6f11cd77070dd6e7785e5}}, {{cite:6454bdd16acdbbc5a23f37c59ff1f489a409f9db}}.
See {{cite:1701d50a373327aa6b608a874407cc0d13cacef1}} for comparison of some of these approaches.
However, these experiments were performed with standard non-streaming
attention models. Fusion approaches with streaming E2E models have been
unexplored, and it is unknown whether the observe gains on attention-based models
could be translated to streaming models.
| i | e5ba9245b0b7d769d1a20aedc180f7da |
The good performance of the algorithm is the result of several choices. First, the use of voxel-sets as input for our experiments instead of other shape representations such as meshes; indeed, due to the statistical properties of our large datasets, the voxel representations leads to highly stable embeddings, they are easier to generate and to maintain than surfaces, and allow to exploit the full volumetric information of the shape. Furthermore, the fact that they are regularly sampled contributes to the convergence of the Laplacian embedding towards a “geometric-aware” eigenbasis {{cite:233dd5ba3c68e5c1cdb2acfbe5665fde71df1725}}. Second, the definition of a local graph-connectivity allows the treatment of the otherwise difficult cases related to self-contacts and topology changes. These cannot be handled when completely connected graphs are defined since a self-contact would imply changes in all the pairwise distances. Furthermore, locality gives rise to very sparse Laplacian matrices and thus to an efficient calculation of the eigendecomposition (we use ARPACK). Additionally, the initialization is usually good for EM to converge in a few iterations. As a consequence, the procedure is time-efficient, and that whole matching procedure of large voxel-sets takes only a few seconds.
Finally, it is important to mention that our method can be applied to other type of data since it relies only on geometric cues and does not use the photometric information as suggested in {{cite:6914ac8bc0e5fb8b0f77da4062e2d0bafae159f0}}.
| d | be488662bbf777da2cb80aac50c882d8 |
To our knowledge, only a few of the previous studies considered the effect of the AGN contribution on the morphological classification of their host galaxies. {{cite:582ce4299793ef7cb37a575a81b95672fd24204c}} studied the effect of AGN on the rest-frame colours using a sample of X-ray detected obscured and unobscured AGN in the Extended Chandra Deep Field-South (ECDF-S) at 0.8 {{formula:666def83-37d1-4e52-b81f-7226ee3e85e4}} z {{formula:2fc48086-471b-4c8b-abcc-f7e91b21d944}} 1.2. They found an insignificant effect of the AGN on the galaxy colour in the case of moderate luminosity, obscured AGN, with a more significant effect for very blue, very luminous AGN (sources out of the blue cloud being classified as quasars, see their Fig. 1). A similar study considering the effect of AGN on the host colours has been carried out by {{cite:17dc84e91b1bba5be02c3cbb971a39b8caf2cf17}} for AGN of moderate X-ray luminosity up to the redshift of z {{formula:5cb6b95e-8f43-4e66-8d20-c8aff145f965}} 2.5; again significant difference is found in the distribution of U - V rest-frame colour between active and non-active galaxies. These results go in line with several others showing that in moderate luminosity AGN, the AGN contribution to the total optical light is not significant {{cite:80e3fb39a8d9d4b5974f5715e01221ea955f5378}}, {{cite:6335949bc30fa44466a3cf047ec2e71a378b3c3c}}, {{cite:c5832de25ca06463fcec1a0baf170ba6b70a714b}}.
| r | 1d10a88df30a09bfa2606fa3fd599d5c |
Comparisons with the state-of-the-art.
To verify the effectiveness of the proposed ReconFormer,
we compare the proposed method with 7 representative methods, including conventional compressed sensing (CS) based method {{cite:a8fb10b53e3363f8b1ca54d6441f54132bd8cc05}}, popular CNN-based methods – UNet {{cite:5c1bf049eaafbfc0cf8e9cc853a9b65fbf107bcf}}, KIKI-Net {{cite:c1cd172444673c822c55fa78e3bcb4910318a4db}}, Kiu-net {{cite:fd788d9483c45ef452bc9be85c5312db548af237}}, and D5C5 {{cite:028487d79084dad94d3faa2d2e16a72a22d396f7}}, state-of-the-art iterative reconstruction approaches – OUCR {{cite:c1222d65ddf78d9d92563be3640934c191231eed}}, and vision transformer model – SwinIR {{cite:b10b7376e7751845b7ff36d62eb432f517789f1e}}. For a fair comparison, methods (UNet {{cite:5c1bf049eaafbfc0cf8e9cc853a9b65fbf107bcf}}, Kiu-net {{cite:fd788d9483c45ef452bc9be85c5312db548af237}}, and SwinIR {{cite:b10b7376e7751845b7ff36d62eb432f517789f1e}}) that are not originally proposed for MRI reconstruction are modified for data with real
and imaginary channels and a DC layer is added at the end of the networks. The unrolling length of all iterative approaches is set to 5.
| r | dda7cbc62ce06e7565a141b68599b926 |
In this paper, we incorporate these changes in the adult speech spectrum through LPC Segmental Warping Perturbation (LPC-SWP) and Formant's Energy Perturbation (FEP). We use this modified LPC spectrum to obtain the augmented children like filter-bank features for model training. Steps involved in the proposed method are shown through a schematic block diagram in Fig. REF . The range of warping factors and formant's energy scaling factors are presented in Table REF . Warping factors for vocal tract length perturbation (VTLP) and uniform LPC Wapring Perturbation (LPC-WP) based baseline systems are selected based on studies in {{cite:55b4b65da744ef1a405c096806b507b35f930694}}.
{{table:428781d3-6a66-424e-84fb-d1477d37429d}} | m | 011a0bfd800756d893fd2c858328a066 |
We compared the performance of P-TD {{formula:2093e75a-a60b-4484-b23d-588af6a5660a}} using 8 different voting rules: Borda, Copeland, Kemeny-Young (with weighted and unweighted majority graph), Plurality, Veto, Random dictator, and Best dictator.For formal definition of the voting rules, see {{cite:7467d397b1d96227421c4e5d4e7529cefea4862d}}, or Appendix REF .
| r | 0b7b94c20a36b24be9e75aac9fd4b498 |
Pretraining ever larger language models is a research direction that is currently receiving a lot of attention and resources from the NLP research community {{cite:8dd6a95589d65c8b859fd8ffa785087a4f91bca5}}, {{cite:02471ae66eae5ee9fe5e5b07e7fb6b94a886d249}}.Be careful, everyone is on small, specialized models these days -ds Still, a large majority of human languages are under-resourced making the development of monolingual language models very challenging in those settings. Another path is to build large scale multilingual language models.Even though we explore a different research direction, we do acknowledge recent advances in small scale and domain specific language models {{cite:d7c5521246d755a53d30fcc01e66fac585a724a8}} which suggest such models could also have an important impact for those languages.I feel this contradicts our point here: I've already mention similar approaches in the related work - However, such an approach faces the inherent zipfian structure of human languages, making the training of a single model to cover all languages an unfeasible solution {{cite:6aa091a0c18c47e7203d3530330aca48e86842fe}}. Reusing large scale pretrained language models for new unseen languages seems to be a more promising and reasonable solution from a cost-efficiency and environmental perspective {{cite:678f73cb00fb1fba653420c5fcdc2524791674a6}}.
| d | 5a7443b1f771932baae60eac404becde |
Soft thresholding has been widely used as an efficient denoising approach in signal processing {{cite:6afdb8ecad7714ad517275fdc9e21fff19b7bb36}}, {{cite:2f06f3e22a80edc1bcd4fc076356bd301da54b38}} and recently has drawn attention from deep learning communities {{cite:a40bc35fad6026d5bed4aebbd6cd84ec83da4fe5}}, {{cite:d326a033b8bde23a4354e35f3397e2cf03f9a6af}}. The core idea behind soft thresholding is to use thresholds to distinguish real signals from noises, while the input signals below the thresholds are zeroed and the others are shrinked. Since determining the task-specific thresholds requires significant expertise, Isogawa et al. {{cite:a40bc35fad6026d5bed4aebbd6cd84ec83da4fe5}} proposed a neural network to learn the global thresholds for all inputs, and the learned values are fixed after training. Zhao et al. {{cite:d326a033b8bde23a4354e35f3397e2cf03f9a6af}} designed a residual shrinkage network to produce dynamic thresholds for different inputs. In particular, the thresholds are designed channel-wise and shared among all pixels, and then soft thresholding shrinkage is leveraged to denoise the data channel by channel. However, since the data collection with respect to each pixel can be treated as an independent process, the optimal thresholds for each pixel must be different from each other. Therefore, the global or channel-wise threshold may not be the best solution for denoising the photon counting data.
| i | 93cc72c7c24cd58b13fc3618c5653c9e |
The discussion between the width and depth of deep neural networks is an essential topic of research. Researchers have focused on the correct approaches to increase the depth of DNN, which in turn increases the accuracy.
{{cite:48cfa138439987bf003ca72b2423286d1abac53d}} demonstrate that the width and depth are connected to the model capacity and enable the DNN to learn block structures which lead to good accuracy. Hence, by splitting the width, chances are that we could decrease the model capacity.
| d | 8393dd61ad9deb3de502cb6431f937a3 |
Policy gradient methods {{cite:dd6c7d72394d13603a6075c0351cfb0dd3e69654}} are a popular choice for a variety of reinforcement learning tasks. Suppose the policy {{formula:def1eeee-fa50-412d-9b2a-f46ab311198e}} of an agent is parametrized by {{formula:7f30d30d-0242-4d09-9195-788946d8c0fa}} . Policy gradient methods aim to maximize the objective {{formula:8e254e3a-bb85-4d67-916f-c68907e0131c}} by updating the agent's policy steps in the direction of {{formula:83f1f3d3-c2d6-45fb-b550-4890cadb910d}} .
| m | de7edb702de0696c7c0c29a37afa3f96 |
Lemma REF gives that the adjacency tensor (and signless Laplacian tensor) of a connected hypergraph {{formula:dfd0bc04-0d0f-4043-96b3-251633160b68}} (and {{formula:36e76006-6f12-4709-9f0d-f57fd4a7d2e7}} ) is nonnegative weakly irreducible, so {{formula:164f48ae-35ce-4129-a3cf-51e230396c30}} (and {{formula:24a57936-28fd-4f93-8e39-ce12466ae391}} ) is an eigenvalue of {{formula:87fa8136-ece8-41d0-a5d5-8d73d9de49c5}} (and {{formula:bce2faf6-b5e6-437c-80d5-a4563f560320}} ).
In {{cite:271b8fbb5b3f6e5292cf7aa89c04aee746768e62}}, it is shown that the largest eigenvalue {{formula:0979e256-406e-4441-8e85-83300fc2e777}} of {{formula:57ad3570-82b0-4dac-a506-a3bf6fda7458}} is between the maximum degree {{formula:ad63f96c-33fe-40be-8d04-7abb2ba4ca86}} and the average degree {{formula:a322c75d-9232-4a4c-ae61-d2f7ad2062a0}} of {{formula:d194d005-35ae-4ac7-afb4-af171db7f152}} , {{formula:a0c45e9a-d566-4a91-9e73-63a142f31b8d}} . By using Theorem REF , we also show the bounds on the largest eigenvalue of adjacency tensor and signless Laplacian tensor in terms of the degrees.
| r | 511f8943caf3e869d3f28c251f8e8fed |
A line of research in image-based robot manipulation learning relevant to our work involves the use of fully convolutional networks (FCNs). These works take advantage of dense, per-pixel calculations of convolutions and their robustness toward translation shifts of the input. Given an image of the workspace (often in top down view), the FCN outputs a dense, pixelwise action-value map, in which each output pixel corresponds to an input pixel in the same location, which in turn corresponds to a specific location in the workspace. Action-values typically represent the probability of task success in supervised learning or Q-values in reinforcement learning, and usually the action with the highest value is selected in evaluation. This approach has been used in works involving picking {{cite:b444dddf543c259a24fd80d02ecec8a9fd5575e1}}, {{cite:b2285c618c34fe01d363d8dddbd4aa7582ca3266}}, pushing {{cite:6a4ff2cba2e9ee9e01844ac5526cede9a5aef70c}}, throwing {{cite:6f247928fdff936e28d25e9ef2e5365971b21214}}, placing {{cite:3d0da2ebd1a6c67e4f10646d60c30f238901926b}}, various other manipulation actions {{cite:9633f9e64fb37293ad1f4fc1b7d5b3ff4478ead9}}, {{cite:3be8cc462857eccb779889eef7f8ab03a1056324}}, navigation {{cite:b67d5c34c54482774de1440fc0260df517a84457}}, {{cite:cf54edab357246fe6d46b77e4e4866aa94ea6e66}}, and language instruction {{cite:28dfe0ef324d698aecc751382adfe2d2223295b1}}. Our work follows this line with a focus on tool use.
| m | 0b34ef86466846ae36fedf5ca4a22fd6 |
We investigate the test performances
on various problems, comparing different choice of {{formula:0c2ae7a7-edd8-4034-aff3-478afad465d6}} . In the following problems, we apply the Gaussian kernel with median distance as bandwidth {{cite:e8a7de01dad7ab01074de9fcb30003b5679bb747}}.
| r | cc2ad8bf40a6cde038a61027cf20c277 |
Published by A. Einstein in 1915, the general theory of relativity (GR) {{cite:9ef1cf836065823cd7658a27de468db142f02977}}, {{cite:51178a78bbf5e50ab7d97214ae85d107bc09ae99}} has become one of the pillars of the modern physics and is very well tested both theoretically and experimentally. It can explain or predict different astrophysical and cosmological phenomena, such as those in the radiation-dominated and matter-dominated eras of the Universe (see, for example, {{cite:962bafc2ad6057e81b3c080d92dd47c6ffaf06fd}}, {{cite:8a50b5abea0063c92e995db0b567104e153704e7}}, {{cite:6794da22eff4a35c1fc9bc1133bfa041627ed0e2}}, {{cite:72159fa47b11f0d0c003788f6b3e6e93a7f984fa}}, {{cite:cea7b5e55e5bec1c93aea44f79918027fe21bda0}}, for some recent or new results supporting the GR)
but it fails to explain other phenomena, mainly in the acceleration periods of the Universe. The GR is still facing difficulties in describing the issues such as quantum gravity {{cite:6bcc2a257ecc7ef2640cc84db34447a6e9217006}}, {{cite:92cc8461a5e94443603768312aa35d73ea6a837d}}, the cosmic inflation {{cite:d9418b6c0202e05fb0262d058dccc53b48a2aff6}}, {{cite:92cc8461a5e94443603768312aa35d73ea6a837d}}, {{cite:3cbbcdc99d01d23922a59938e1c9869313a16e9a}}, {{cite:1fa371ec5706453b096f4f21636723199d39371c}}, {{cite:175757f8037654267b401bf4821ed5d1191effbf}}, {{cite:7dc91e72b3c698f1a58bc4cee5e5e1529c4a68e9}}, the origin of dark matter {{cite:4418ab1889fa181c084c43d7913fe2790c2f93e7}} (see also, for example, {{cite:399b65193b126e4f0d14f3e5d319c0faba4f9ae7}} in a particle physics aspect), the accelerated expansion of the Universe (called otherwise the dark energy problem) {{cite:1da1399461ebfcda397041277bc02dec3d3bf8e2}}, {{cite:bbea4116428b0b67c8bb6c966c75a501bd62d4d8}}, {{cite:3a95098373fc23bdbad43028cea56752091ce9d6}}, etc. These problems call for an extension or modification of the GR but so far there has been no satisfactory theory suggested.
To name a few famous theories extending the GR. The string theory (for a review, see, for instance, {{cite:4d5cbe47d8291189ac8e906ff63a527ae704e316}}) expected as a "theory of everything" is a very complicated ultra-high energy theory and weakly developed in the phenomenological aspect, therefore, it is very difficult for an experimental test. The similar situation is with a more special theory - supergravity {{cite:659976413bdc1c595334c9a28015e8ab4667c8e9}}, {{cite:a38e1abc3f93deca12f2012cf74f3457aa9300fd}}. However, these theories are based on the concept of supersymmetry {{cite:bbf8a823514eb0ec809a9191610a0727e406f270}} of which the LHC has not found any sign.
In general, to explain the formation and the evolution of the Universe is always a challenge in physics. One of the first attempts was made by A. Einstein not long after the birth of the GR.
| i | bf38c389d688bbfecb9e3cef9cc2faff |
User Study. Following the previous works {{cite:ac81bda89c3b1bd6b3b3f63fb598753ec6964a3d}}, {{cite:704a1375fe6335cc67ed3bed381fc359d2596316}}, {{cite:14c104630655011773d25f6bad9a20348f48d9f9}}, we conduct user study on Cityscapes dataset.
Participants have been informed their identities will not be recorded.
Each volunteer is given a semantic map and two corresponding images containing one by our method and another one by a randomly selected competing method (, SPADE {{cite:ac81bda89c3b1bd6b3b3f63fb598753ec6964a3d}}, CC-FPSE {{cite:f9011a649fd5f44c354e1bb99c0eb0b1ce1c25a7}}, OASIS {{cite:04c047fff4a0f674ac9096990c530c260fa1eeba}} or even the ground-truth image), and is asked to vote for the image with better visual quality.
The orders of the two images are random to avoid the effect caused by potential bias.
There are totally 2,000 questions for 200 volunteers, and Table REF lists the results.
Volunteers strongly favor (more than 80%) our results in contrast to the competing methods.
In comparison with the ground-truth images, our results still have a chance of about 17% to be recognized as the better one, further indicating our method is able to generate photo-realistic images.
{{table:33f39598-b42b-485c-935f-3f52f5f9cfb9}}{{table:e13065de-2180-4de7-953c-4c9dfa506b1d}} | r | 23aa82b30d9a74f1c7d766c1b94d06d0 |
Since an epipolar plane image (EPI) contains patterns of oriented lines and the slope of these lines is related to the depth values, many methods achieve depth estimation by analyzing the slope of each line on EPIs. Wanner et al. {{cite:1b18b0912705a9539cb8ddb255b4048d3737188e}} proposed a structure tensor to estimate the slope of lines in horizontal and vertical EPIs, and refined the initial results by global optimization. Zhang et al. {{cite:662e451febab6117dc0e14193d23f35f36fe698c}} proposed a spinning parallelogram operator (SPO) to estimate the slopes for depth estimation. Sheng et al. {{cite:c96fbe093e56ab6dfad599a66f0aff839d035d22}} proposed to estimate slopes using multi-orientation EPIs and achieved improved results over SPO. Schilling et al. {{cite:b61c6c5c32ffe36ede7db9b8335eefd810b7a5dd}} proposed an inline occlusion handling scheme operated on EPIs to achieve state-of-the-art depth estimation performance among traditional methods.
| m | 1db11ef087e6d53afd69aecec60e8244 |
The generalized Lie symmetry {{cite:d1046b3da70be959bc7c2f1b75802f00f8f129bc}} of the Euler-Lagrange
equations of motion is generated by second-order prolongation
vectors in the tangent space {{formula:4b451507-43a5-4f6b-a655-b7b5d553420b}} of the
second-order jet space {{formula:a8d8c079-4bd1-4f03-a8b0-2cf6d2305eb4}} . This symmetry is reflected
in the Lagrangian phase space description of motion, and the projection of
{{formula:8f8a1fe5-7e53-4e98-bec5-ea6fbedafcc8}} to {{formula:832e4fcb-c90e-49f6-8f8a-9a5efece341b}} maps these
prolongation vectors into the kernel of
{{formula:3c4c4983-9062-4da3-95a3-669e1900fb29}} . Surprisingly, it is not the vertical vector
fields of the kernel that generates this symmetry, as
may have been expected. Also surprisingly, the corresponding symmetry
group {{formula:d3bcd400-403b-492c-b7ff-fbf18ca5914e}} is not a symmetry
group for SOLVFs; action on a SOLVF by
{{formula:90bf2f98-657a-4c9e-a2e0-833c0b99eec4}} results in a vector field
that is no longer a SOLVF, nor need it even be a solution of
Eq. {{formula:38fbb676-61c1-4f12-94bf-0521865c4daa}} . It is, however, always possible to construct
from a SOLVF vector fields that do have
{{formula:8181444d-f4b7-443e-b069-83f93aaa852b}} as a symmetry group, and are
solutions to Eq. (REF ). These vector fields are the SOELVFs,
and they resolve the issues listed above for the SOLVF.
| i | 2e443385585c949f01384e703dc44b01 |
In this section, we use the Phragmén–Lindelöf theorem to prove a theorem on a class of meromorphic functions appearing in complex dynamics, namely class {{formula:c7654b64-adcf-4774-9dee-4910bd8d40ff}}; see {{cite:27d89c910fe7c9e9a54dca58e5f50bfa32c8a909}}, {{cite:38e097edca94c8f8b296bc3187bc57f1f4984866}}, {{cite:659bb5ee4cb5f29289cfcbc84e0fa27f0d86e2b0}}. For a meromorphic function {{formula:a37a9490-a38a-4c0a-bd90-4a96c4f52c9d}} , we say that a point {{formula:d926026e-0ab8-4d05-87d2-0d89c0209de4}} is a superattracting fixed point of {{formula:c7d6e940-0af0-49af-b351-9ae92181bd02}} if {{formula:ef7f2420-a1ff-4d6f-bbbd-774c2549bbf0}} and {{formula:a7a86a93-8ed7-469e-a84a-9433c60c1226}} . A meromorphic function {{formula:72a8a95c-c1fa-4d6d-be5f-12c692bd011b}} in {{formula:70523df2-e863-4a7b-be4c-60ee763e60e5}} has the following properties: {{formula:a73df9ae-9440-4d71-8655-b4de41f59676}} has finitely many poles; {{formula:9bc9a7ec-7dfc-4a60-b478-4d2ca4b89160}} has finitely many multiple zeros; the superattracting fixed points of {{formula:3dc9ca99-da99-4b20-93a8-c2ca2441baf5}} are zeros of {{formula:4bb87505-4293-450b-b719-f934b92309de}} and vice versa, with finitely many exceptions; {{formula:5f7487ea-0737-48ad-910a-2a35d10613d6}} has finite order. Then a meromorphic function is in {{formula:abc5a18c-4ddd-40e8-adb8-8a150f6e1efe}} if and only if {{formula:ba0e3d8a-5f59-40a3-8148-3f0a75c84bfe}} satisfies the first-order differential equation:
{{formula:b3c12870-0123-430f-a6a7-84bd3ce8370c}}
| r | 3108e4a25a66986f796cb303cdc97c5d |
As for multi-cellular organisms, the brain presumably fine tunes the synaptic strengths of billions of neurons to generate an optimal behavior. For this to happen, feedback signals should not only carry precise credit information to individual neurons but while doing so, they must not interfere with the activation/feedforward signals {{cite:8ef8402729555617d1f64ab9a3ab9205a6a327cc}}. How the brain does this is still unknown and many models have been developed to explain this phenomenon. For instance, some models invoke the use of error neurons{{cite:8d14612d50b44ba88f411e0a4536d675d5193734}}, while others assume a temporal segregation of activation and feedback phases{{cite:ec865bf6867f9b6d7d377bd8745728524b008290}}. Others propose a compartmentalization of individual neurons to spatially separate information as opposed to temporal segregation {{cite:f16ed0f410385d33d4533a3a36fd313861b58f7e}}. Our learning mechanism is similar to this last one. It avoids multiple phases by modifying a node to store two kinds of information - an activation signal and a feedback signal. The reason they do not interfere is because the system components can identify them by their chemical signatures - a universally observed phenomenon in nature. We have shown how the same network structure used to send an activation signal, can be used to send precise gradient information to individual weights. Therefore, our model optimises a cost function via gradient descent, something that deep neural networks already do to achieve human like functionality {{cite:07d15e5f2929e200bc93f464c2a9b6af465aa353}}, {{cite:b247254e21bbc54fcb46dd247a37cc0a61094e86}}, {{cite:1fdac84f61ebee226ee33b6e73419314a3cf1de8}}, {{cite:06e80858f593ed1dade306ac7962e1d6d1e477ae}}. In light of the reasons stated above, we think our model may ultimately help neuroscientists understand credit assignment mechanisms in the brain.
| d | 184f4cb8b3d6ec7c0569925042cfb659 |
Problem Formulation:
The input is a continuous recording of an EEG signal from a subject and is segmented into non-overlapping 30 seconds EEG signal called an epoch. Each epoch is categorized into five sleep stages: Wake, REM, N1, N2, N3 according to American Academy of Sleep Medicine {{cite:80461988b3906837f99022896a6644b85415a304}} guidelines. And
each subject’s EEG recording epochs belongs to one of the pretext/train/test
groups where the pretext group contains a relatively large number of unlabeled subjects compared to the less number of labeled subjects in train and test groups. Throughout our study, time-series and spectrogram are used as multiple views of the same EEG signal. For each EEG epoch, we obtain two time-series augmentations denoted as {{formula:9615db1c-f995-4a70-9fc5-583c67f4717b}} and {{formula:6b183ce1-4394-4b00-8df3-e47e5cd966ac}} . The time-series augmentations are converted into their respective spectrograms {{formula:974b5987-4554-4c47-9ec2-5b091da07756}} , {{formula:1e2314d4-67b5-4f16-b1c1-0ab51f54d634}} . The augmentations are passed into their respective encoders, which are time-series encoder, {{formula:b2c88b71-239b-4278-90aa-5f8077eaec3c}} , and spectrogram encoder, {{formula:45ad8d24-1cdd-4b3b-84a1-e763d9948da0}} , to extract their high dimensional latent representations. A separate projection head is used for the time-series and spectrogram encoder, which takes input as these high dimensional latent representations and maps them to the space where contrastive loss is applied on {{formula:61e75e22-b4c5-4d78-87bc-bad5d4d26b92}} , {{formula:097c96c0-51d9-4990-a4a4-b56ba43a287c}} . Applying the contrastive loss directly on the projection head outputs gives better results {{cite:2145ac787bf1e2a2105b1156e0aa8495e7c99c74}}. We use a variant of contrastive loss called NT-Xent {{cite:2145ac787bf1e2a2105b1156e0aa8495e7c99c74}}, {{cite:2003004871f0b66804213656c47163cf6ef8cf9f}} which maximizes the similarity between two augmented views while minimizing its similarity with other samples. Here, {{formula:d7530692-158a-48ff-94bf-fac2ef58404a}} is the batch size, {{formula:f43e5bb6-eace-4172-a031-717d25f8ca20}} is the temperature parameter, and a cosine similarity is used in the contrastive loss function given in (REF ). The function {{formula:016696b3-d174-47a1-853b-9eecbd36f056}} evaluates to 1 if {{formula:15bf42a0-6d48-43d2-b6ba-b6d8049577a9}} , otherwise gives 0.
{{formula:fdceeba1-82e8-4871-82d6-3e7c1e37f326}}
{{formula:eec2d9e3-c910-460e-9191-d0eefa2427e8}}
| m | 8bac4dc45398a374d773425f66237806 |
The classical result of Wold {{cite:530291bb5f7c749e258fdc2b8ed3bdf86d883802}} asserts that given isometry on a Hilbert space is either, a unitary, a shift, or uniquely decomposes as a direct summand of them. Beurling {{cite:3ef8a1143e270a4b00f8c67f767a5480e67c1f8e}} proved that every {{formula:8db83e2e-2500-42d1-baa4-ed8e97c93b3e}} -invariant closed subspace of the Hardy space {{formula:643ba7da-1ffe-4134-a8b1-cb7ad5e964df}} is a copy of an inner function. One of the well-known implications of the Wold decomposition is that when the unitary part is zero, the Wold-decomposition gives uniqueness of the wandering subspace of a shift. Halmos {{cite:8e3696d695492ae4171dcdf90189bb476ff48968}} proved wandering subspace theorem, which is an abstraction of Beurling's theorem, characterized all the invariant subspaces of a shift. Richter {{cite:c47229f386f78d4f3aee17257e2adad3704ad051}} proved a wandering subspace theorem for an analytic concave operator which satisfies the growth condition that was explicitly mentioned and generalized by Olofsson in {{cite:9227868af128265169f3cf2294d291c07545230d}}. After that, Shimorin {{cite:d0e0ec5bf44c247e0843e6f1253fccdbbfc0c489}} provided an elementary proof of Richter's theorem by giving a Wold-type decomposition for concave operators that can be considered close to an isometry. Olofsson {{cite:9227868af128265169f3cf2294d291c07545230d}} extended Richter's wandering subspace theorem as follows:
| i | 099936192fa1202742f36888674cb76a |
In our first ablation experiment, we have eliminated all the enhancements in order to show the performance level of a baseline CNN on the CH data set. Since there are several SISR works {{cite:9807d7907338e68953e1871b5512b2538975dfff}}, {{cite:0d597fe015c24c97ecd6223b92d1f1f757b0dce8}}, {{cite:ca0647993ede4133fae7c3800adf0ba74c91a7a2}}, {{cite:06044f17b9785c10a9fc46f35c0164d10a4242a6}} based on the standard ESPCN model {{cite:49e5760ffc17fb56ffba38875f27cf657f4dbc23}}, we have eliminated the second convolutional block in the second ablation experiment, transforming our architecture into a standard ESPCN architecture. The performance drops from {{formula:e1ade2cd-1d2c-4521-bdad-c984837f3e5a}} to {{formula:dd9a5537-f7ce-43bb-b1b1-2cf0d22b26ba}} in terms of SSIM and from {{formula:affd5ee3-9dfb-465e-aae0-6f05a85d6117}} to {{formula:f555f7b1-3093-48c3-9c9b-4e6305cc09c5}} in terms of PSNR. In the subsequent ablation experiments, we have removed, in turns, the intermediate loss, the short-skip connections and the long-skip connection. The results presented in Table REF indicate that all these components are relevant to our model, bringing significant performance benefits in terms of both SSIM and PSNR. In our last ablation experiment, we used a fixed standard deviation instead of a variable one for the Gaussian blur added on training patches. We notice that our data augmentation approach based on a variable standard deviation brings the highest gains in terms of SSIM (from {{formula:32dd33f8-1298-4578-9fd2-95a35ee48eb5}} to {{formula:13e79c83-5004-4301-a94b-101a7f3ae4a5}} ) and PSNR (from {{formula:30980e42-30d2-4cf5-8565-aa68ab86ea25}} to {{formula:e23681a9-b071-4915-886b-2a91848f09a6}} ), with respect to the other ablated components.
| r | 1a4f24e5a28ad8daa75d9b76d656c5b1 |
In terms of the mass and time of sinks that form, previous simulations find different results. {{cite:905835434c9314aea8504a193b48185cf1b217d9}} find that the additional magnetic pressure leads to massive stars forming, whereas {{cite:2061ff5dc55f38f00cc0407d6c182a481a7c47e9}} and {{cite:0b536179dbeedbf33852e4e9c98ca09bb319ed92}} find the opposite. {{cite:74964e6963e7016e38e51010f03744ef9dc6f294}} find stars form earlier but {{cite:0b536179dbeedbf33852e4e9c98ca09bb319ed92}} and {{cite:2061ff5dc55f38f00cc0407d6c182a481a7c47e9}} see a delay. We clearly see a delay in agreement with the latter works. Our sink particles represent clusters rather than individual stars. At equivalent times, we see lower mass clusters in the runs with a strong perpendicular field. However if we take the time since the first sinks formed, the situation is less clear, and there is some indication that in the perpendicular case, denser if not necessarily more massive clusters can form.
| d | 35e82efa1f41223d0f7157b367ad1d4b |
The statistical significance of the dark energy dipole is
about at the {{formula:d4cdc0ba-6104-4054-89e8-7c38d937bee8}} level. The direction of Union2 dipole is
({{formula:c5979e39-b388-4874-bc43-12d7af366232}} , {{formula:8e064d3e-0dcd-4ed6-98ff-e5d2f7451164}} ){{cite:258947f3468fc2d16f1e391dbc2bbdfb4d8695b9}}, and the dipole and monopole
magnitudes are
{{formula:19d609f6-c0f7-4f8b-b7e2-a1f2be45fdcb}}
| m | 9400ed5bf3dbb46e03b343b8e1cb58cf |
Competitors.
We compared the proposed STL method
with three different modelling strategies:
(a)
Hand-crafted feature based methods
(GRDL {{cite:b4ecbf61b8a3d8d73a234a4df5a47b1088ccc072}},
UnKISS {{cite:3e642e376f1c6fd808c0a2700bce7370d5c37567}}),
(b)
One-shot learning methods
(SMP {{cite:6b62d6288c6dbe22c0c1319ac16245eca3372603}},
DGM+IDE {{cite:6037cf758360a8c3ae4be00787858fb2fb790182}},
RACE {{cite:fe15b72027976d5881331d7cb2e600ba4531561e}}),
(c)
Unsupervised deep learning models
(TAUDL {{cite:0ca9b1efb241f410f698787dd5c435097aacb150}},
DAL {{cite:44b38b68b50871aac5e4650bf3999eb8de25b879}},
BUC {{cite:7b97fb4712c40a098428f2f35c6449024dec9a11}},
UTAL {{cite:a56d4d62dd4cf00337bafbd832bbb0bc943b0ce7}}).
| m | 492e6b5bd226ccfe6e605cac74bb374a |
Successful models which account for the observed radius excess in hot Jupiters by additional heating must be
capable of supplying {{formula:7b318628-0e28-4135-9e1c-4f5da56b4959}} to the convective portion of the planetary interior. The proposed GEC model is capable of such heating, and produces planetary radii broadly in accord with observations (Figure 2). Variations in planetary mass, planetary composition (leading to changes in conductivity), planetary magnetic field, and stellar magnetic field may account for the range of radii observed in the sample. In addition, we note that it is likely that multiple heating models coexist, including tidal heating (for noncircular orbits) and Ohmic heating ({{cite:52d3708d59dc4b382441be0fad87be7cbe0bc460}}, {{cite:7cc3d00c1c1eef370e428de30ac7e9111c1994e0}}).
| d | b70746e1f90e65cdf34f8e236266e3b3 |
In this section, we show that the assessed SAT and TSP neural solvers are not robust w.r.t. small perturbations of the input despite the sound perturbation models introduced in sec:sat and . We first discuss SAT in sec:empiricalresultssat and then TSP in sec:empiricalresultstsp. We use the published hyperparameters by the respective works for training the models. We run the experiments for at least five randomly selected seeds unless stated otherwise. Since no directly applicable prior work exists, we compare to the random baseline that randomly selects the perturbation s.t. the budget is exhausted. Moreover, for our attacks we use Adam {{cite:7cf3ac1589da16cf31b6a4d41cec1ea22fa9f2c9}} and early stopping. For further details we refer to sec:appendixsatdetails and sec:appendixtspdetails.
{{figure:8437f24f-142d-498a-a89f-a40b9a499d6f}} | r | d8eaefafdc2fef896f23bc9ea9e806bb |
The No Translation baselines are worse still. Label projection uses hard supervision that affects model performance dramatically. This is likely because the binary labels we use as weak supervision in parallel data do not necessarily mean anything, and therefore cause the model to learn parameters that cannot generalize to actually meaningful test reviews. Meanwhile, Bi-SG is little better than random. We hypothesize that cross-lingual embeddings – if trained in isolation – are not able to mesh with higher layers of neural networks, which are often fragilely co-ordinated with one another {{cite:43b9efada7a58bd17d18acbefd56b16d6a0b8aab}}.
| r | b403b6c370d6139bd689584d52eaa781 |
Local smoothing {{cite:8c00fa65bbaa5a582aa5d5b20c78fe768d9100fe}}. Is a method that uses a pixel neighborhood to smooth out each pixel. For a given {{formula:2b85775e-3e6d-4a96-9e41-1bb65502dc97}} sliding window, local smoothing changes each pixel, center of the sliding window, with the mean, the median, or Gaussian smooth of the window. In {{cite:8c00fa65bbaa5a582aa5d5b20c78fe768d9100fe}}, it was shown that median filter is more efficient in projecting the ae back to the data manifold especially for {{formula:ab8c93d8-e67f-466f-8ca2-8f076fe4c169}} based attacks, since it is capable to remove sparsely pixels in the input image, and at the same time it preserves edges. In our investigation we use the median filter with {{formula:e11c2e6c-8197-4631-b392-403e837c0ad2}} window size.
| m | 0727a14bbbbc2e1067d133e9e5798499 |
For this task, we compare SBM-Transformer with {{formula:0799edd2-9445-46a3-a5cc-30bd415acf2c}} clusters against various efficient Transformers: Linear Transformer {{cite:a793c034771da511c4ada05254fda164d2a6f1ed}}, Linformer {{cite:01e67c4450647b89816d1ccad0c01ab7d4ed146f}}, Reformer {{cite:57f384a86f3d723ba4b4f818e253d331fbaf5df4}}, Performer {{cite:84e82de627f545b33aaacb3daa295a7dadc27272}}, and Nyströmformer {{cite:5c53ff8098f1e58fc7dd4d404a7341d109b5a414}}. Across all methods, we use a single-layer and single-head architecture with 32 hidden dimensions. Note that due to this constrained setting, the sole head must perform full attention to compare each token to all the others in order to attain 100% accuracy. All models are trained for 2000 epochs where a new batch of sequences is sampled on-the-fly at each epoch. We use a batch size of 256 and learning rate of 1e-3.
| m | bf8e4c1376ca33e5afdff09106dc7c70 |
In Bayesian settings, we start by defining a prior probability distribution over the unknown parameters, i.e., weights and biases of a DNN. Bayes' theorem allows us to infer the posterior distribution of these parameters after observing the training data {{cite:9ab8dc70e506da6c7c3ae0a59e37dbb59d794665}}, {{cite:9da468afaa7d4406257ad7457ffcef83957bf8b9}}, {{cite:91811d37af0e1527880a9183e856b801241682ce}}. However, inferring the exact posterior distribution is mathematically intractable for most modern DNNs, as these models do not lend themselves to exact integration due to a large parameter space and multiple layers of nonlinearities {{cite:7f6cad3140ebbd8be512676f729f2a2f832bc78b}}. One of the most common scalable density approximation approaches is Variational Inference (VI). The VI approximation method converts the intractable density inference into an optimization problem that is solved using standard algorithms, e.g., gradient descent {{cite:7f6cad3140ebbd8be512676f729f2a2f832bc78b}}, {{cite:9da468afaa7d4406257ad7457ffcef83957bf8b9}}. VI methods pose a simple family of distributions over the unknown parameters and then find (through optimization) a member of this family that is closest, in terms of Kullback-Leibler (KL) divergence, to the desired posterior distribution {{cite:a4c63cf3f70b25f1a788e92a13d3aafc9776af73}}. Over the past few years, VI has been used to estimate the posterior distribution for fully-connected neural networks, convolutional neural networks (CNNs), and recurrent neural networks {{cite:42a1e1d8df710d1fae1aef363d6b4cdee9e16c04}}, {{cite:3c7b4df7caa05d22596255688af959ccb8306f3f}}, {{cite:9ab8dc70e506da6c7c3ae0a59e37dbb59d794665}}.
| i | 77a6a2f1d1f65c62866e4c6249b6e8d9 |
Our framework, Continuous-Time Continuous-Options (CTCO), comprises a policy {{formula:1dc81326-ea7a-4080-a58a-7b2aab113dba}} , and a set of options encoded as a parametric model {{formula:073628f2-632d-490c-82ae-2ee5faeeaee0}} . The policy {{formula:4be15470-c085-46eb-b652-f76076ec7fb0}} selects options with variable durations and decides which option to execute only after the termination of the current option, allowing in this way, the system to determine the decision frequency dynamically. However, different option durations can determine the same effect on the environment (e.g., an option that outputs action {{formula:45903083-6811-411c-a5b4-98a87320cfcc}} for 3 seconds is equivalent to three options that output action {{formula:e03446dc-3604-479c-83f7-f31ca4bfa52e}} for one second each). Since longer durations are preferable for the learner in case of ambiguity ( it requires less number of decisions), we introduced a regularization factor that favors longer durations. We implemented the update rule of our framework by taking inspiration from soft actor-critic (SAC) algorithm, a state-of-the-art policy gradient method that includes entropy regularization to achieve efficient exploration {{cite:b5d56985ad36788524339cc9f9d06cbc5e97df53}}.
| m | e8859b8a4c8b0daaf22186abe43dc540 |
where {{formula:56449c73-30cc-4f61-80cd-788a41533ecf}} and {{formula:637db4e9-0674-4321-9a6b-bc14842de943}} are the sample variance and the mean of log-transformed data, respectively.
Also {{formula:bd4c5596-d748-4d91-8459-5545e901e976}} .
It can be shown that (REF ) and (REF ) are both asymptotically
unbiased and consistent, see {{cite:9fbb6c79bdd519d142e5f27430ea5b09698e1cce}}.
| m | 468cc45b72d51ca7b4d0ac40f529336f |
To assess the performance of the four considered pre-trained CNN models, namely VGG16 {{cite:93ca6d19bd1d1407fc6d3ed18b9dd79845d49abb}}, InceptionV3 {{cite:db1c471fe6502aca6c6e3fd2756fb11ebab0567b}}, ResNet50 {{cite:5b8b017a078cd672fb29838065c8627bfa43f68c}} and Xception {{cite:a56d1104309838b0daebb04a9a1b20f887e30575}}, we experimented with the UW fake satellite image dataset {{cite:854e26906af6d4d11c306b5ee8f75de307d865b7}}. We compared the performance of these four models to seven methods combining spatial, histogram and frequency features, as proposed by Zhao et al. {{cite:854e26906af6d4d11c306b5ee8f75de307d865b7}}. In addition, in order to assess the robustness against various image distortions, we also considered the effects of JPEG compression and Gaussian noise on the performance of each model.
| r | 8325b8db65937a2e6c563ed94e6cd7a0 |
For sparse DAGs, {{formula:922ecfd3-99c6-4107-8a95-44b38b29c152}} is a sparse matrix, and for {{formula:af2275a7-60f6-49ce-98f8-bd3338b21734}} , {{formula:aaf6f139-293a-4c45-a1f2-0b019a4c333c}} is low-rank. Hence, when the confounders are pervasive, it is possible to estimate each component through a low-rank plus sparse matrix decomposition of {{formula:35e10013-4e29-49df-9bd3-a6cd57193194}} {{cite:853012c269425ee7563bef3706c1eacd8cb88a8e}}, {{cite:e31f93bfb7686b9aab5ef1c7ad980510d2042032}}.
| m | fbc978af05613448981afbde05c91a72 |
In Fig. REF , the system outage performance is illustrated for various target data rates, when the large-scale channel gain of the direct link, {{formula:5c7fd9c8-07f5-4967-8920-4eb530ffeb21}} , is equal or less to the individual RIS-enabled channel gains, correspondingly. This implies longer (at least equal) distances of the direct transceiver links in comparison to the individual RIS-enabled ones. As expected, the performance gets worse for an increased {{formula:00aae146-07b2-4be6-bd82-4e2e89f628d4}} and reduced {{formula:2cfd8172-e9e4-458b-95a4-ff89d24398c0}} . It is verified again that the coherent scheme slightly outperforms the corresponding joint approach at the expense of a considerably higher computational overhead. Furthermore, the suboptimal approach under perfect CSI in {{cite:510d2b1eb59995ec7614bd74a06adab6e3bc1cef}} is presented for performance comparison reasons. In fact, {{cite:510d2b1eb59995ec7614bd74a06adab6e3bc1cef}} introduces a joint optimization method of both power transmission and phase alignment at RIS. However, only the phase optimization is implemented in Fig. REF (for a fair comparison to the proposed approach), as per {{cite:510d2b1eb59995ec7614bd74a06adab6e3bc1cef}}. Notably, the suboptimal scheme in {{cite:510d2b1eb59995ec7614bd74a06adab6e3bc1cef}} outperforms the considered random-phase approach; yet, at the cost of an increased computational complexity and a considerably higher signaling overhead ({{formula:053279dc-4390-4da1-b4d5-c72fc021407e}} against only {{formula:ba921a4a-4fa7-4ae6-9fed-ba022f7a8b9c}} provided by the proposed random-phase approach).
{{figure:26746c68-4976-4c5f-88cf-9050eaf49902}} | r | ce1ec97a1b653734d3a348b77e9e70f8 |
In this paper we consider the totally asymmetric simple zero range process (TASZRP) {{cite:04144f5ffeb2501cb3a0bf869464b847101b1248}}, {{cite:124f55f9c7f228e963177764dced193bf8bc3d13}}, which describes a system of indistinguishable particles placed on a one-dimensional lattice, moving randomly in one direction from right to left with the equal hopping rate on a periodic ring. The dynamical variables of the model are the phase operators {{cite:638f8e85b71884f24f442f9d7bab2abdd7cb81a3}} which can be regarded as a special limit of {{formula:861667e1-4ba6-4548-a6cd-9b40167030f5}} -bosons {{cite:2a8481813ffa8f4f8c417d85e60bb7cdf750de18}}, {{cite:0ce23fd10ff3e2708a7a5a85222462882101cf2c}}. The application of the quantum inverse method (QIM) {{cite:04144f5ffeb2501cb3a0bf869464b847101b1248}}, {{cite:124f55f9c7f228e963177764dced193bf8bc3d13}}, {{cite:f1f0b670ca8d2a58d01bd7e4db4c6c5221b1da8e}} allows to calculate the scalar products and form-factors of the model and represent them in the determinantal form {{cite:2078b6999e8a530a0cc130f2abb67c8822f6e1cf}}, {{cite:da8635d05a1eb223dfc2250e993ab155ed1f79dc}}. The relation of the considered model and the totaly asymmetric simple exclusion process (TASEP) was discussed in {{cite:da8635d05a1eb223dfc2250e993ab155ed1f79dc}}, {{cite:21fc60e69d59b55440dbf452bc7818b310ca3ba3}}.
| i | 84ca2de35ece484110376a95af4f6953 |
To the best of our knowledge, we are the first to propose an explainable end-to-end deep learning model to predict BCR over time after prostatectomy from TMA spots. We introduce a novel network based on self-attention {{cite:16cedaea019469fbe6eac0e019af666f0c8dc343}}, attention-based multiple instance learning (MIL, {{cite:6ca739bf467b48d0fdfc1e817b212fb04d65930a}}) and recurrent neural networks (RNNs, {{cite:cba02730ac90140b3ff6f595c2d0b0cc61531bde}}) for survival prediction, called eCaReNet (explainable cancer relapse prediction network). With an AUC of 0.78 on the validation set (0.77 on the test set) we achieve state-of-the-art results, while assuring calibration. Through evaluation of attention weights of the MIL layer, we further show that our model weights malignant patches higher than benign patches. In general, our approach is applicable to various cancer and non-cancer histopathology survival prediction problems.
| i | b62399a5720e3d68091e4ecd46b44a50 |
We foresee these detection concepts to lead to widespread tools for quantum optics and quantum information protocols when moderate photon-number resolution is desirable. For instance, these could be employed for state engineering based on measurement post-selection {{cite:b10b13f61cc237c50146351bfce2ef7a7310ec9c}}, {{cite:a6fd1433caffc1674f0c04821e42d445a73a2d66}} or to increase the computational cost of simulating Gaussian Boson Sampling experiments such as {{cite:04df6f83c5f42934b06ab978e8df0e3e49b95540}} as shown in {{cite:86bee0ad8543b35817086cf08379f0fa7f1752f1}}. An important next step is the development of fast and affordable electronics that can analyze detection signals on the fly, perhaps using a high speed field-programmable gate array (FPGA). These techniques will benefit from further advances in SNSPDs, such as potential improvements to dynamic range that allow resolution of larger numbers of photons {{cite:23b12150d94898c5aa18508716a4a435ad378091}}.
| d | 5dbed5d76c81874a7f6aea41f83256a3 |
Alternately, algorithm-level methods {{cite:3f4c09f1d2c7d64ddae71d69f54f160942cdb4f2}}, {{cite:3d46fd6aa94226239297f728fca181352a7078cf}}, commonly implemented with a weight or cost schema, modify the underlying learner or its output to reduce bias towards the majority group. Algorithm-level methods modify the structure of the decision process of how much to focus on under-represented samples. This could be implemented by assigning the cost matrix as a penalty {{cite:be9008b50e24e88e1874adc29ece1c360d753fbf}}. Moreover, loss functions could be modified, such as in the case of focal loss {{cite:1843ea24181df78b4a66cf8d20e9d890d9b9b04c}}, which reshapes the standard cross-entropy loss such that it penalizes the loss assigned to well-classified instances.
| m | c4ec303e4e9be5cad1c7b393572f7156 |
Due to their empirical success, there has been a recent surge of interest in using recurrent neural networks
and their extensions for solving NLP tasks such as machine translation and question answering {{cite:2a4bfafce019f331d662433ceee66d39dae72a47}}, {{cite:7681e9e9ff4b54fcf8a90d0244b4e54da0791c56}}.
These methods share the same spirit of end-to-end utterance-to-behavior
learning as executable semantic parsing,
but they do not explicitly separate parsing from execution.
This makes them architecturally simpler than semantic parsers,
but they are more data hungry and it is unclear
whether they can learn to perform complex logical reasoning in a generalizable way.
Nonetheless, it is quite likely that these methods will play an important role
in the story of language understanding.
| d | 75a716ddfe19123a37d8be6458e4be2f |
It is well known that the curvature perturbation ({{formula:3b3b2961-9869-40d6-9079-840792e637cb}} ) is sourced by the first isocurvature perturbation ({{formula:24d65255-ef8f-4c79-aa3f-897339dd4d2e}} ) {{cite:0fe81f7887ecfb6946410ce05d373915fe663aa3}}, {{cite:d197f35c828e4df2b5c2bd99fc8efc75b3216e0b}}, while the rest orthogonal perturbations interact via a “mass matrix” as well as through the curvatures that appear in the Frenet-Serret equations (see e.g. Refs. {{cite:a309cc7f6e40d56da39ab14788bebb6d3f61c310}}, {{cite:dbaeda9097ca0b8dcdb6ce3367fd20d4c3f313a9}}, {{cite:04c5979e1d14314254d29ed80dbf2917402c0a30}} for examples including up to three fields and Refs. {{cite:2b3e820221ac654503fb7bb8f31e165317658dbd}}, {{cite:6bcb90e8a1f2101ff6ca5ab7c708eac838d681a9}} for a formal discussion including an arbitrary number of fields). More specifically, orthogonal fields are coupled through the following terms in the second order action
{{formula:99f87d4a-efbc-4864-b6e3-46cbbf9ce50b}}
| d | 1658da2f9522c2755f598782c176a503 |
(see {{cite:e7e6a36c0c3379542c698016a2fbeaa55031c3d7}}).
Thus {{formula:351862bd-75a8-4b54-8683-9a929097f094}} of Weierstrass equations are globally minimal.
| r | 4eaf48c850b7e6d6d7a92aaeb0112c03 |
The sentence similarity algorithm used for this methodology achieved good Pearson correlation coefficient of 0.8753 for word similarity concerning the bechmark standard{{cite:efdf3c1f7a694bef4b0ecf17773c4be1f61549f6}} and 0.8794 for sentence similarity with respect to mean human similarity {{cite:85428f41ded2617ea002ff13c9872dbef74b21e3}}. The proposed methodology aims to use this algorithm and make it specific to the Learning Objectives. We use Bloom's Taxonomy to determine the comprehensive similarity between the LOs. We achieve this by establishing relative similarity between verbs.
| d | 81ce0bfb5084827a6a6f95167ecc6a76 |
Let us briefly comment on some braneworld black hole solutions and their possible relation to the solution that we have found above.We would like to thank the referee for pointing out these interesting results and references. While the CHR solution {{cite:518951ec788beedd36fadbb5403b0ae32dfa2f3c}} describes a black string with an induced Schwarzschild metric on the bubble wall, it is known to suffer from horizon shredding due to the Gregory-Laflamme instability {{cite:f18b438bdb22586e840c375e3e2270ffd780c8ca}}. A very promising solution is that constructed by Plebanski-Demianski solution {{cite:919936987b5b093c92a019e232fa4ec601a6984f}}, which is the AdS extension of the C-metric {{cite:37c3e3acb797ac8ba7005f31bd91b40ed663e54e}} and is referred to as the AdS-C metric. This is a four dimensional metric that describes accelerated black holes with conical deficit at one or both poles. These are interpreted as cosmic strings pulling on the black holes and accelerating them. This metric has been studied extensively in the context of Randall-Sundrum braneworlds e.g., in {{cite:daf0c5cbea389d9d31333c3338984477a0490d5f}}, {{cite:f8e02eddedd0751c4818c9d6a38b21157bccab55}}. Although attempts have been made to construct analogous solutions in five dimensions, to the best of our knowledge, there are no known analytic five dimensional AdS-C metrics. Since the four dimensional AdS-C metric looks like an accelerating black hole being pulled by a radially stretched cosmic string, it is indeed a candidate for a black hole on the dark bubble. This is a very interesting and relevant solution and we would like to construct a four dimensional analog of our present solution to compare it with the results obtained from the AdS-C metric.
| d | 8ed2e9617e1794f18d494aeb3cbd58d0 |
Gender bias and its reduction has been observed on GloVe embeddings {{cite:695b0e6f9c54eab91473dcb6ffdff1c4f8d4e7f4}}, {{cite:dd678dd3eae43d71f8bc9f5c8884feaf3d2d5458}} using different metrics {{cite:2e5fce991bc53ac5999951bdf69796eb7ee2084d}}, {{cite:dd678dd3eae43d71f8bc9f5c8884feaf3d2d5458}}, {{cite:864617e74f9a36bf6aa70ad348f11d604682043d}}, {{cite:3379b3c009bc3e3791877e5dc1eaa0131f0d62d8}}.
Each of these is projection-based, and begins by identifying a subspace represented as a vector {{formula:06146e42-c83b-4528-bc81-50de5877e482}} : in all of our experiments we determine with using the vector between words `he' and `she.' Some methods use an auxiliary set of definitionally gendered words {{formula:7e334fde-6f34-4cbb-a7b7-797618388f83}} (see Appendix and ) which are treated separately.
| m | e4933d2ca36b1e5b53bb19481b69c043 |
In this study, we find that DMD is quite sensitive to non-normality (see figs. REF , REF , REF , REF , and supplemental figs. REF , REF ), and to the existence of higher order nonlinear terms (see figs. REF , REF and supplemental figs. REF , REF ).
As to the question of which data-set metrics govern this sensitivity, in some cases shorter data with more initial conditions performs better (as in figs. REF , REF , REF ), and in some data fewer, longer time series produce better results (see REF REF ).
The challenge of non-normality has implications for the identification of fluid systems, as highly sheared flows are generally characterized by non-normal linearized dynamics, which was an original motivation for DMD {{cite:7d6cf5ff030c3b2cf29ca8dd3e28c3603e732a0d}}.
| d | 8f09557e6bf08938be5333d1fa57520f |
The generalization of various mathematical notions such as functions or even operators has importance that goes beyond mathematical curiosity. The Gamma function is a generalization of factorial for a real argument that is unique under certain constraints {{cite:6cdc60f20c07ef23ee32145f9935056ff6fb346f}}. It can even be generalized to complex arguments {{cite:b2628422cd676c252c7bf6953fcf2e307817a87d}}. It has been used in complex analysis, statistics, number theory, and even string theory in physics. Similarly, the Riemann zeta function was introduced by Euler for real argument and was later extended to complex argument {{cite:eb1e63d6f5dd2f6ebf52f0bcc7214ed9cdc9c6c7}}. It has turned out to be an extremely important function in physics and mathematics {{cite:046cbe41ca7b53b1238d4628447eb494dd724129}}. The notion of derivatives has even been extended to functional derivatives {{cite:e76ef7eb08d9e2b9cb31038112ecdf655f17c62a}}.
Another example is the q-deformation of numbers and functions {{cite:edad4643f3e001070c7c0f14d7c7e123d0a31205}}.
It has found applications in quantum groups and statistical physics {{cite:d86247efe9e5afe613ef1c42ed09f07d76d79f85}}.
Even q-derivatives and q-integrals have been defined. Of course, these generalizations need not be unique and different generalizations can be used in a different contexts.
| i | fbf35972273072e8c16fba1e3d342dc2 |
A fine-tuning with quantization constraint method {{cite:61f01f595982f57bba9b576f324f916bf68747b6}} is employed in our design. It effectively diminishes the negative impact of brute-force quantization while introducing more non-linearity. Different from the ordinary quantization method {{cite:f7d991cf5a0504ea317f76114988997ea20f48d4}}, we quantize the weights and bias before storage. This quantization method does not require modification of the TensorFlow source code.
| m | ffb98c6ab7304b002511366803764ea3 |
Aside from providing fundamentally new probabilistic perspectives on
GGMs,
our work also bridges the gap between frequentist penalized likelihood based strategies
and Bayesian shrinkage prior based ideas for GGMs.
The simple and highly scalable computational algorithms resulting from our latent factor representation
should also free up Bayesians from having to put restrictive assumptions on the graph structures to achieve computational tractability,
opening up new opportunities to adapt the basic GGMs to more complex and more realistic data structures and study designs.
A few such methodological extensions we are pursuing as topics of separate ongoing research include
dynamic Gaussian graphical models {{cite:d3e9763131f88ff455a2788fa3956cee6a945385}},
covariate dependent Gaussian graphical models,
nonparanormal {{cite:882ac3ed49fde5c810b33e7654dccb0c979d0553}}
and Gaussian copula graphical models {{cite:dc72ad232808804c7b81627199caf84f332fbe0f}},
etc.
| d | 13771a149bb700b6ea29f35310b46e4e |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.