text stringlengths 54 548k | label stringclasses 4 values | id_ stringlengths 32 32 |
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We also re-analysed available radial velocity curve. Our solution seems to be a little bit different according to the results found by {{cite:7016114b5c20db8b03532f7cb01dfb675232eee8}}. The differences should be caused due to the orbital period used in this study. Here, the adjusted period is a bit different from the one used by {{cite:7016114b5c20db8b03532f7cb01dfb675232eee8}}.
| d | 38df20f3da5c165b8f3f53bfca650380 |
We have also checked that our calculation for topology {{formula:a03f0592-661d-464c-93e1-29b675431ddf}} agrees with the results in ref. {{cite:b29cb8c4387f23427aa30de004018298b23cd7cb}} by comparing all integrals with numerator powers of -4 (which is the highest numerator power computed in that paper). Ref. {{cite:ea565e39f773084ee32d8ec6a6e3d11704802d07}} has claimed to compute the planar integrals with numerator power -5 with the help of the program FIRE {{cite:a91b3b4254bbfae873bd234bbeb0afde55e6de02}}, {{cite:1a95342dec63dd8b7067c15f992ffa152fbd78de}}. However, since that reference does not provide explicit results or details about their calculation, we are unable to compare.
| r | fad8e3174c5662fb165d8a8539b166fa |
Let {{formula:ce2fffcd-50f1-4ef1-8962-2ba0ea7f6bbe}} be a prime number and {{formula:62082584-0dfd-4d2f-b954-7f174a35ceb0}} be a power of {{formula:e1adf8e2-989a-483a-b935-97a886dd51ef}} . Denote by {{formula:2bec24bc-8f68-4709-8fea-90458bfebf7b}} the field of rational functions over {{formula:bedf03ed-5cf9-4892-b8bd-ed839482975c}} . An imaginary quadratic field extension of {{formula:abb4c53a-6c06-47ed-8cd0-4045c7590c37}} is a degree 2 extension of {{formula:8a5c7a51-43b3-4859-967a-0a86ddfa79b3}} in which the prime {{formula:33d6a9b8-c1de-4f2c-b1fa-66e617089301}} is ramified. The question studied in this note is motivated by recent results of Ellenberg, Venkatesh and Westerland {{cite:4c6f8f72106bef9ad78aaff7ff8fc73f8f52eb7e}} on the distribution of class groups of imaginary quadratic field extensions of {{formula:6dc4b4ef-a01b-4546-9395-23217da73c7d}} . The story begins with predictions made for the distribution of class groups for imaginary quadratic number fields made by Cohen and Lenstra {{cite:affa28ba99d9f46aef9b465812a0a70b45ccb100}}, based in random matrix theory. The work of Cohen-Lenstra led to significant developments in the field of arithmetic statistics. In the number field context, the predictions are far from proven unconditionally. We consider function field analogues of such heuristics in positive characteristic. The aforementioned results of Ellenberg-Venkatesh-Westerland show that the Cohen-Lenstra heuristics in the function field context are true in the large {{formula:99de8b36-32e6-48e7-a206-805bb6c003b3}} -limit. We refer the reader to loc. cit. or Theorem REF for a precise statement of the result.
| i | 2c153e77dc70a8a5b7438b7b159409e3 |
Our GPDs are based on the PTE effect where an electromotive force directly provides a voltage, rather than a current {{cite:60c49c49b5558bf88ed8ba0f5bbc267e21b54072}}, {{cite:b40a56f3b5baa4cf09c1e0d19fb5af3ec8105da9}}. In case of Ge, an additional TIA is needed to convert the photocurrent into a voltage for further signal processing {{cite:3bd06a453a23cb0ebea8d4159cdce89c038ca7f3}}. In the TIA we consider a feedback resistor {{formula:c5e1fc6e-19fa-46ae-a41c-762b7e65a72f}} = (90V/W)/(0.5 A/W) = 180 {{formula:930150f0-98ae-4fc9-916e-5efde755db4e}} , which assures the same {{formula:bb73b78e-b21e-474b-bda8-59d469b08bd9}} for same optical input power in both cases. Neglecting any noise other than thermal noise produced by {{formula:6b10202b-a396-4ff6-bda2-c5a1c6431ea3}} , we estimate for the conventional receiver a lower limit for the sensitivity {{formula:725d7f59-9d74-446d-97d0-2458aada1831}} {{formula:de5dfe45-9e30-4908-918b-0bf795062f39}} W {{formula:48a42821-311b-4f23-92a1-42fa69e25d41}} -19 dBm at a bit-error-rate (i.e. probabilty of false identification of a bit by the receiver decision circuit {{cite:22f052bebeab443d05dd68f52094202969b02606}}) BER = {{formula:2ce4f41c-8bce-498f-9610-7e17a3149b48}} . Here we calculated the thermal noise current as {{formula:042cba59-0f1c-49d3-ad16-8ef403fdcdbb}} ={{formula:b08e6312-566e-4b5d-95a4-b437a4eb44bf}} with BW = 12 GHz, as in our GPDs, and a {{formula:66dec0de-1faa-4584-9f3c-edf88360e47a}} factor (i.e. required signal-to-noise ratio to get a specific BER {{cite:7e6d4a180a848ec4bdff09c84509b226ceb6d69d}}) {{formula:7182cd20-2bc1-4b31-badb-74c83233b706}} 6 from {{cite:22f052bebeab443d05dd68f52094202969b02606}} BER = {{formula:07836f17-7e3c-4756-8c61-fece452eb6c8}}. For our GPDs, we estimate {{formula:15ae4e18-9dc6-4a74-a89b-0818ade721d7}} = {{formula:07b6942c-9b51-4969-8a45-a118159d83db}} -16 dBm for same BER and {{formula:45888208-e67b-4829-b2da-81b0dafdd2fe}} , where {{formula:6e440230-928e-4911-9076-ede23272e138}} = {{formula:efd3437d-3644-4041-b770-5911c2d5406b}} and {{formula:14d2fb49-3235-4032-930b-4307db8d44bf}} {{formula:5311833f-99f4-4c04-a719-075e051d18d3}} is the total device resistance. Thus, the {{formula:d8ff1161-f2fd-4d5f-9135-e99653eccc12}} of our GPD-based receiver is on par with mature semiconductor technology and could be further improved by reducing {{formula:8230e23a-18c7-4ff7-afe3-c241309811c9}} , which dominates the total device resistance, thus being the primary source of thermal noise. The natural generation of a voltage makes the need for a TIA obsolete, with a reduction of the energy-per-bit cost and system foot-print.
| r | 83b02d945bd0c171a9edc643c76a4ef8 |
where {{formula:df8dd0d2-8bf5-4707-930b-6788eeafab0c}} is a given function and {{formula:beeb82ed-8b83-491b-803d-03898014c8a7}} .
The purpose of this paper is to show the local existence and the uniqueness under new conditions.
The existence of solutions to the more general quasi-linear wave equations has been widely known since the 1970s.
Kato {{cite:f149629e540de42185772c0019068522d03094f4}} and Hughes, Kato and Marsden {{cite:007da8d4f57c19d8808c9eed5174847d31364b75}} have shown an abstract theorem about the well-posedness
of the system of general quasi-linear wave equations in {{formula:6344e0df-bd0f-48c0-a0d2-fdeec1ca6827}} Sobolev space.
In 1 dimensional case, the well-posedness in {{formula:54cb69b5-9b7c-4e8c-8f0b-114f1ba5d7b4}} class for first order hyperbolic equations has been studied by Douglis {{cite:a6b081f158bca2fbf6c1b67778191005929e9895}} and Hartman and Winter {{cite:1752d26b0bc99accc9807b64756e475207233ded}} (see also Majda {{cite:a8aee63809563e23f1eed7904f12536da8bfcace}} and Courant and Lax {{cite:3b617123e17c3503de11cce30a1ac66dc7b21915}}),
where {{formula:6b824125-1d5f-4902-a5e3-2ea2f4269f6a}} is a set of continuous and bounded functions whose derivatives are also bounded.
In order to apply these results to the existence problem of (REF ), the following assumption is required:
{{formula:9d1cbdfb-1293-484d-84a3-dd83d7bc9aa4}}
| i | 7555a95d0e41d500701972238ddd8be5 |
A schematic of the setup is shown on fig. REF .
It enables standard single-tone microwave optomechanical measurements {{cite:fed00a2feccdbcfbcab223e4d5e38424d0b60914}}, with the additional ability to artificially tune the microwave cavity effective temperature (or population in the quantum language) thanks to a Noise Generator (NG).
This NG is made of two High Electron Mobility Transistor amplifiers (HEMTs) in series (total gain {{formula:cb601d38-679c-4d36-acb5-9848b5774805}} ) connected on one side to a 50{{formula:b58870f9-0234-40ca-af68-df5ea7a0be29}} Ohm load, and on the other to a {{formula:16d514a5-0e5b-4b6f-a8ae-850cd459a1d0}} filter {{cite:026596860113ef93e2d92b1079fa5ff3059dcbf4}}.
At the frequency of the cavity {{formula:bfebef64-8477-4e8c-89f3-a5b7fd97d282}} , the applied microwave noise spectrum is essentially flat, with an amplitude {{formula:605f7b62-9bfa-4e6b-9e21-3dfb3f077afb}} that can be quantitatively expressed in terms of photon number {{formula:6646c381-85e3-430a-b268-739005a76319}} .
The noise level is tuned by inserting fixed attenuators, which lead to an uncertainty (from screwing/unscrewing) of about {{formula:59ab6cac-15a1-48f7-b121-6c2a5d7c2543}} in noise level.
| m | af506c99a663e51b47d0d5677362f144 |
When all the {{formula:d07004ba-c0a3-4fca-9759-623ebd0a36ba}} th order partial derivatives of {{formula:3c7394ec-29d3-41f1-afd0-bb799a4c950d}} exist,
let {{formula:7c1d04b4-9fb6-4d11-b1eb-31a52cbf3f8e}} denote the {{formula:47f8b8a1-4502-4cb6-a937-96219d9c2532}} -way tensor of {{formula:dc8627da-8eda-4a0d-9c84-dbf2d8bfba7b}} th derivatives;
in particular, {{formula:792d8b50-6412-4fed-b397-f6cf2a2e90f0}} , {{formula:6a346586-464f-4642-9f45-63534c4e6561}} , and so on.
When these derivatives are continuous, the order of differentiation does not matter
{{cite:b645ecac2ed25c4884f1bde40da78a63de0d73d2}}.
| r | 3eef5eca9853c8383699ce4f6de5092d |
The existing hadronic interaction models give different predictions for the shape variables. CORSIKA {{cite:8509f580a8af51283fa16b054c4e9408bd39009a}} was used to simulate proton, helium, nitrogen and iron showers with the EPOS-LHC {{cite:e0e2d16879602aca90d7455681c8b7c9532ebe7b}}, QGSJetII-04 {{cite:5d9c1e419ef103fb4a0909aaab00653263c84acf}} and Sibyll2.3c {{cite:d90197a65f89352d646074e84c5118ee480a960a}} models. The evolution of {{formula:a97e7da3-460b-44d6-91e7-4cbae0fa5437}} and {{formula:be66c7ed-cd20-4bce-8fb1-e2c8749b08f3}} with energy, along with their respective systematic and statistical uncertainties, is shown in figure REF . Both the asymmetry, {{formula:d278b186-cfe0-4954-8f11-ab6cd9c4d816}} , and the width, {{formula:c06379f8-57a8-4340-ba14-0cfd5927106b}} , in data agree well with the predicted values for all models. For the asymmetry, all models give similar predictions, and the results seem to point to the composition becoming heavier with energy, although current systematic uncertainties still hinder any composition claim. For {{formula:60761402-dbee-4cc6-b0fc-ff6d427344f3}} , data is consistent with a linear increase with {{formula:9d265fc8-5e1c-4d1e-bd7d-eaaf69e610e7}} . {{formula:f59f6066-45aa-425c-a853-ff8580eb8e0c}} is compatible with the predictions of Sibyll2.3c for all compositions, but points to a lighter composition if compared with the other two models, that predict smaller values of {{formula:bd2171bb-d1ca-46e6-8922-1c36096de9b0}} .
| r | 7cc28e6c630f37a31de27998a8ffc4cd |
The proof of Lemma REF is an application of Hölder's inequality for the trace ideals (cf., e.g., {{cite:d3d18f4081d866f5d6af78a61c2d5853388f384a}}). Lemma REF then combines with Lemma REF to yield the following analogue of (REF ) for {{formula:59624dea-d44e-44a9-98da-a4b87ec11f31}} .
| r | d1e4d9df917b437b7bcf69cc9e6bddea |
For year-long QPOs, their indication for the existence of a binary SMBH system
at the center of AGN has been intriguingly discussed
(e.g., {{cite:d4ed653c40d5e87ca374ec53389b1949e320b8b0}}, {{cite:7ca0fcc45e68966ad484ad991db2b000728e9a53}}). The secondary SMBH may induce
an observable periodic signal, which reflects the orbital periodicity of
the binary. However the period of 176 day is rather too short. The intrinsic
period at the local galaxy would be {{formula:7b35be30-21c2-42e3-8839-6f57f0a41daf}} days.
The period suggests
a very tight orbit (a binary separation of {{formula:2b6a67bb-e919-4024-a61c-a85639aed165}} 0.001 pc) and a quick merging
time scale ({{formula:62fe909f-4a48-4637-9d9f-d07ea41b6c02}} years) due to gravitational radiation, where
the mass ratio between the two SMBHs is assumed to be 1 (see details
in {{cite:edf0298dde9aa06d1f9718ad5e3ab7d12d635aca}}).
| d | b06c1a0d95a3df4a360871ccd75e5548 |
To extract the mass {{formula:b0309538-70e1-4bf2-a53d-adcf36c94a85}} ,
one can carry out the numerical analysis of sum rule (REF ),
with the aid of input parameters
{{formula:3ddad8db-879d-4465-adeb-d0a68e6a683e}} ,
{{formula:6fe8bafc-a2c8-4272-9459-c17dfaefd738}} ,
{{formula:b8b8f1c8-20b8-42b9-b02e-9c9a1b5cf9f5}} ,
{{formula:32079666-a3c8-4e2d-a582-f255c8f4aa05}} ,
{{formula:8b31d143-79ba-453f-b741-7c28b431d007}} , {{formula:150147a7-2f01-4fb9-b70e-834c553fc72d}} , and {{formula:8fd02601-af26-4c5f-aca2-cf69dc97fc70}} {{cite:40613e4da7dce7e8b1a25493face8b7c34166d38}}, {{cite:398376f7d5a72c6c1f1a771d4d7b855938238707}}.
Besides, quark masses are taken as {{formula:4e843e09-7139-4720-a79b-34b5d5386ae0}}
and {{formula:d4661d61-b6dd-4937-ae16-47552e9e3aac}} {{cite:19f9455240f383680f1860561b3ebb33a2298269}}, respectively.
Keeping to the procedure of sum rule analysis,
both the OPE convergence and pole dominance should be inspected
to find suitable work windows for the threshold {{formula:c5506806-0e00-4561-9714-047ad061b881}} and the Borel
parameter {{formula:9b207b0c-c071-4851-92e4-7049b8299432}} .
| d | cdbb3e3a9f3af889bb14a97790867994 |
The implementation {{formula:a627d265-afb8-4d75-823b-dafa95f6f565}} can also be improved by improving the algorithm for Riemannian-distance estimation in {{formula:236b2269-d751-4353-b56c-e08934f6e945}} . The construction of the {{formula:6e04901a-c848-4e2a-8ef9-bcdb0ded3a07}} -nearest neighbor graph {{formula:c02e0995-ad9c-499e-ab23-c3ff0d9ef091}} is stable (assuming {{formula:5a1a2e5b-2183-44b6-8e40-5c4b9a1b2719}} is in “general position”, as in Definition REF ), but it is much more sensitive to perturbations than one would like. Additionally, we note that sometimes all {{formula:e0eabea1-7004-454f-9d97-a7d279a95b60}} -nearest neighbors of a point {{formula:c4574589-1ce5-426c-9a26-6eefcd75a4a4}} are in the same directionBy “the same direction” we mean the following. Within the injectivity radius of {{formula:873e0dd9-fe34-486f-a168-f84cc07c1ba6}} , the exponential map {{formula:c55a0c28-1288-4f16-a66c-837024b61926}} is a diffeomorphism {{cite:607cae922649c5787674e3534fff5dc6683a441a}}. Two neighbors {{formula:66382a94-cdd4-40b5-a2cd-fff1f110d5b2}} , {{formula:aac96410-3d8f-49a3-adb3-018365e66bb2}} are “in the same direction” if there is a {{formula:26eedbe7-a238-44ea-a507-64f90250d944}} within the injectivity radius such that {{formula:5ccbd071-2fdf-4e06-87b9-f407a2bcdc42}} and {{formula:10c21e2d-59cd-4027-a50b-c892a2e8d994}} for some {{formula:ea8b1374-8bc9-4a0b-90c1-6d80e3f9a150}} . More generally, if {{formula:7d313a84-3087-415e-aa41-222a2e4d0e42}} and {{formula:4d0c91d4-25ef-4792-a4e5-c045946af21a}} , then the angle between {{formula:d9f60846-7577-41d1-a86c-f18af71dfb8e}} and {{formula:3bdb1aba-2e05-4287-a0f6-2b9e7c8ca162}} is a way of quantifying how close in direction they are. relative to {{formula:bf75275f-e6fd-4300-bc8c-04df31dc9460}} . This leads to problems such as the following: if {{formula:99b2bd11-ab55-4b4c-ac74-f90ab4854b5b}} is a curve, then even two adjacent points {{formula:d7d46a51-4ef5-4d06-a3b5-8b965aedd84c}} , {{formula:c0cbf206-103d-417d-8101-36ffbafee85f}} on the curve may not be connected by an edge in {{formula:198ad545-bcbb-497f-b4df-af498c93fc13}} if the parameter {{formula:3d2d0ff2-5a19-4c39-933d-45c3d7bbba6c}} is too small. (We observed this in Section REF when we tried setting {{formula:8e434fa7-5d49-4341-ac6b-4af2bf843bf4}} .) A solution would be to estimate the tangent space at each point and to connect {{formula:90758aed-0c6b-4018-8d1f-c29a68d7093b}} only to nearest neighbors that lie in different directions. Such a modification could also improve Riemannian-distance estimation in widely-used algorithms such as Isomap {{cite:69929f56fb7ac7190a251c0501bb4c1f0560658a}}.
| d | d395b90a2d47c5e91f6ac3fd76d5510e |
Seminal studies by Kroner {{cite:670e81fe6d1c937b2735464787952dd96881cb47}}, Edelen et al. {{cite:06e3ccd430ae6daa84290ec4c93e7d002f55f9c7}}, and Eringen et al. {{cite:78912a70be8d1e10092f309dbde79d26c4d4a04f}}, {{cite:1731fe6366943ee0cf0e5d299c0c2411f8cddefb}} laid the theoretical foundation of nonlocal elasticity, and explored its role in the modeling of nonlocal size-dependent structures. The mathematical description of the nonlocal continuum theory proposed in these seminal studies relied on the introduction of additional contributions, resulting from long-range nonlocal interactions, in terms of a convolution integral of the strain field in the constitutive equations. Over the years, several researchers {{cite:31f2bcf5db14a82895137292814405581140a666}}, {{cite:b3c8f3dd21bc74cbafceca59506f48af76493825}}, {{cite:bab78d83a6fe6a8f6b8e2e11cf2ebcfb1d548455}}, {{cite:bd0bb6fbea818fc096e376ec25a84e48bd7e5f9e}}, {{cite:34e39597a242b546a4d42cdd6644b6a8cd6e1aaf}}, {{cite:dbdd5e2e791dd7ee1d157dd586b0482203163bf2}}, {{cite:2db97550d8f5b911b4856dbeca74d3e86624cb76}}, {{cite:cf20bf8658d7e78151dcacac5b1529a08e1c9590}}, {{cite:a4b89800bf0972aace64c0a6a2d983172d7b68ff}}, {{cite:aa38bd444ce2fa73e214ecbdbc5bb2082f759187}} have proposed different modifications to the formulation presented in the seminal studies {{cite:670e81fe6d1c937b2735464787952dd96881cb47}}, {{cite:06e3ccd430ae6daa84290ec4c93e7d002f55f9c7}}, {{cite:78912a70be8d1e10092f309dbde79d26c4d4a04f}}. From a mathematical standpoint, these approaches belong to a class of the so-called strong integral methods that capture nonlocal effects by re-defining the stress-strain constitutive law in the form of a convolution integral of either the strain or the stress field over a certain spatial domain (the so-called horizon of nonlocality). Depending on whether the nonlocal contributions are modeled using the strain or the stress fields, the integral methods can be classified as strain-driven {{cite:78912a70be8d1e10092f309dbde79d26c4d4a04f}}, {{cite:b3c8f3dd21bc74cbafceca59506f48af76493825}}, {{cite:bab78d83a6fe6a8f6b8e2e11cf2ebcfb1d548455}}, {{cite:bd0bb6fbea818fc096e376ec25a84e48bd7e5f9e}} or stress-driven approaches {{cite:aa38bd444ce2fa73e214ecbdbc5bb2082f759187}}. Further discussions addressing the origin of nonlocal effects, existing theories of nonlocal elasticity, and their applications can be found in this recent review study {{cite:50ac0ec576015b9d9de9dd24a57188ad410adbb0}}.
| i | dd2669f67264c0ebd2e118685e57dd06 |
A well-known neural waveform model called WaveNet-vocoder {{cite:845d16c60657a7f12afae3637191a79877d624bd}} uses a dilated convolution (CONV) network {{cite:c504c065340893ce70a0c6296985bf14383ea053}} to produce the waveform samples in an autoregressive (AR) manner, i.e., generating the current waveform sample with the previously generated samples as condition.
Although WaveNet outperformed traditional vocoders {{cite:657d95d43a4c82bb137eb37df267d3717fd42185}}, its sequential generation process is prohibitively slow.
Flow-based models {{cite:de327219f52a057a16662b584d9f692b0cfee04b}}, {{cite:b4ce308ad2fea387574ea8b5ffb75e60fc72cb96}}, {{cite:f3ecda23150b91eb345c4f2e7e5374815090dec6}} convert a noise sequence into a waveform in one shot.
However, some of them require sequential processing during training {{cite:de327219f52a057a16662b584d9f692b0cfee04b}}, which dramatically increases the training time {{cite:cc438592dc6a9570e8358e1362031d70ca2742f4}}. Others use knowledge distilling to transfer the knowledge from an AR WaveNet to a flow-based student model, which is complicated in implementation.
| i | 0b69f00941d00b1b15b47d3467e0ee30 |
Furthermore, RGQD also has a strong anisotropic nonlinear response, depending on the orientation of
the EM wavefield relative to the elonged side {{cite:21a4aa32bbb3b5df2722c2ffa94a69732fc1b92c}}, {{cite:6396052cb118da86c79d31b61fa390f1772ad4d7}}. For RGQD at {{formula:82bca3e3-c6bb-4beb-834a-a1fec548db59}} and {{formula:c93692d9-1879-4c20-93f6-956e751bd7e6}} , the harmonic polarization
direction coincides with the incident wave polarization direction. At other angles {{formula:f7581f81-6d98-4035-a738-f92236f460bf}} ,
harmonics appear with polarization vectors perpendicular to the pump wavefield. To reveal the dependence of the HHG spectra on the orientation of the EM wavefield in Figs. 5 and 6
show the HHG spectra for different {{formula:f06bccf0-1ab6-416d-aa94-c43d8329fd45}} of the pump wavefield relative to
the {{formula:49937aa7-5828-4b14-a213-01c89c2a3f2e}} axis in the RGQD of zigzag edge for {{formula:11cf31fb-4bdf-493d-90cb-cd2ac2c6d17e}} , for {{formula:0ad3ec0c-b039-46c8-aa65-63a4023328a7}} and {{formula:5e9cc4dc-f147-4f63-addb-c9f22aa2aa9f}} components, respectively.
In contradistinction to the isotropic HHG spectrum for unbounded in space graphene at the low-frequency pump wave, the spectrum
is anisotropic at a high-frequency wave, when, due to the symmetry of the carbon hexagonal cell,
the optical response with respect to the driven field polarization is periodic with a period of {{formula:d078e548-05ad-4723-a498-5b9164c80663}} {{cite:b41a41af4732e4c30be830331cf72b8a1758c6e7}}.
For the RGQD we have strong anisotropy. In particular, for HHG process in the case of more than the
first eight harmonics for the {{formula:face5506-63e0-4a36-9c68-a8bd8a27804a}} component the angles {{formula:29dbb966-1432-436a-8e1c-64b3485b477c}} are preferable, while for
the {{formula:f6a30be1-e0ca-4af6-bbfa-f996aafa50a9}} -component we have a maximum for the angle {{formula:96cee18c-2375-440f-ba44-092b6d0e0c29}} . Moreover, different polarization angles lead to different maxima in the harmonic spectra
and cutoff energies. In Figs. 7, 8 the same is shown for RGQD of armchair edge.
For this case we see a completely different picture. In
particular, for the x-component the angles {{formula:da0c4d5d-de9d-41bf-a253-9071de2e89ab}} are preferable, meanwhile for the {{formula:c218074b-79ac-4c29-ac89-3d9421ebf13e}} -component we have a maximum near
the angle {{formula:804b1e15-9233-4dcd-bc3a-dd99650b2121}} . The latter is also a
consequent of the rich spectra of eigenstates in Fig. 2 with different symmetry. Note that during
the generation process, only odd harmonics appear in the RGQD, regardless of its orientation.
This is due to the inversion symmetry of the sublattice of RGQD.
{{figure:e97c6de6-107e-41c0-9d9c-db922d5e4bfa}}{{figure:7132b30b-ce4b-4620-9b61-e733f48f9b0e}} | r | bacdfeae0561d4063df43536a728724d |
In this article, we propose a two-step procedure to find the balance between pooled and stratified analysis in basket trial design. In the first step, we treat it as a clustering problem by grouping cohorts into clusters that share the similar treatment effect. In the second step, we use shrinkage estimator proposed by {{cite:6ee2bf4c62dbcc6b29197de0465dbff9058d732f}} to estimate treatment effects for cohorts within each cluster under exchangeable assumption. For clustering, we adapt the mixture of finite mixtures (MFM) approach {{cite:834e716273b8ecb4b2b37166f1e3ae9a63ba3387}}, {{cite:377b21c784836b4ea909f9919cbcce867fce2ef4}}, {{cite:1400c4b13fafb92950914c89032aa5def2bee483}}, which admits a clustering scheme similar to the famous Chinese restaurant process (CRP) but alleviates the drawback of CRP by automatic model-based pruning of the tiny extraneous clusters leading to consistent estimate of the number of clusters. The contribution of this paper is three-fold. First, a full Bayesian framework is developed and the clustering results yield useful probabilistic interpretation. In addition, we establish consistency results for the estimation of clusters for the binary data. Thirdly, high probability of selecting the correct number of clusters and the better estimation performance than benchmark methods when heterogeneity exits between cohorts are empirically demonstrated.
| i | 69d92eed21366c6353fa39adfa70ce5b |
The observation of a significant dipole, together with the lack of significant anisotropies at small angular scales, implies that the Galactic and/or extragalactic magnetic fields have a non-negligible effect on ultrahigh-energy cosmic-ray (UHECR) trajectories. This is in fact expected in scenarios with mixed composition where the CRs are heavier for increasing energies, in agreement with the trends in the composition that have been inferred for energies above a few EeV {{cite:3492c1d76cc7615e82f8f84d09687ce35e23cac0}}, {{cite:7769d21236fd5ce1f2ca5c4c1c7062208abfc68f}}, {{cite:3de49bc0c6fe85cd36c2b058282b62b744cb4804}}, {{cite:70e3044e477dcdd11518b96849f721c89072ec27}}. Extragalactic magnetic fields can significantly spread the arrival directions of heavy CR nuclei up to the highest energies observed, even for nearby extragalactic sources, washing out small-scale anisotropies while still leading to anisotropies at large (and eventually intermediate) angular scales.The root-mean square deflection of a particle of charge {{formula:7bfaead9-a7e7-4d10-8fb9-e3dacb99d58e}} and energy {{formula:d1e9810e-c0ff-4769-81db-10d43da087e4}} in a homogeneous turbulent magnetic field with root mean square amplitude {{formula:d6b94a93-ccf7-44a1-8914-bd4d314fc008}} and coherence length {{formula:cf003b3f-f44f-4b18-bd1e-51f2dd3f35f5}} is {{formula:9c0b23fe-7012-4425-9c64-7793349ce74a}} . For instance, oxygen nuclei with 30 EeV coming from a distance {{formula:26838214-939c-4fe0-99c8-8162f7a0a440}} Mpc are deflected by about {{formula:908cf874-330c-4e33-b956-78c472a35c57}} for an extragalactic field of 1 nG, which is consistent with the bounds from cosmic background radiation and Faraday rotation measures {{cite:5995f8301da3144744fc330108d6c95e8c9e7f69}}. The Galactic magnetic field is also expected to further modify the arrival directions of extragalactic CRs, affecting both the amplitude and the direction of the dipolar contribution to their flux and also inducing some higher multipolar components when the deflections become sizable. It is not yet clear whether the dipolar anisotropy observed arises from the diffusive propagation from powerful sources in a few nearby galaxies or is instead reflecting the known anisotropy in the distribution of galaxies within few hundred Mpc {{cite:8089345f0cc1799261214e2d142c46daceb185e9}}, {{cite:0ea3e7e4d9e087023d9bba4e6272c5a214b21a5d}}, {{cite:2c609dea99c343c3aab35c32d650e34baf103761}}, {{cite:a64d43d9b126c358efaa3f210bd8b4dbe5ae7df9}}. A detailed study of the amplitude and phase of the dipole as a function of energy, as well as the possible emergence of structures at smaller angular scales, should shed light on the distribution of the sources and on the strength and structure of the magnetic fields responsible for the deflections.
| i | 1f73ee87611b15aa6d3a672c801136f1 |
We follow the scheme depicted in Figure REF , as follows.
From the simulations we obtained RSDs as functions of time for samples
with different parameters (inclination degree and rotation speed). We
first fit these data using hyperbolic functions. Then we select four
characteristic times and use the LASSO method {{cite:783fe02c0d071ddee30b49825d150e238cc1e5bc}} to fit
those characteristic times from the parameters. In the end, we make
predictions with fitted functions and new parameters to get new
characteristic times, thus RSD vs. time curves of new parameters can
be determined.
| m | 3410e1e077a917ae4dbd15d2092c8532 |
In this section, we introduce our deep geometric model for motion forecasting. The model is based on Graph-WaveNet {{cite:b2ba3d0209e8125990e91fbbdfa5dd5def80c003}}, a spatio-temporal extension to the original WaveNet {{cite:46f726f98fd07f6c203153e2439118ffd4b08745}}.
{{figure:5baa7ba0-b22a-4128-ba7d-cb87141cacbe}} | m | bae80ace250d15ea8d5f0a46deb24bee |
Our template-based method leverages a deep neural architecture, which takes a single background-segmented person image as input and regresses posed and deformed surface meshes for body and clothing which match the performance in the input image (see Fig. REF ).
Before training, a 3D template of the person with separate cloth and body geometry as well as a multi-view recording of the subject performing various motions has to be acquired (Sec. REF ).
The technical core of our architecture is formed by two prediction networks, PoseNet and SimNet, that are trained to regress body pose and cloth deformation, respectively (Sec. REF ).
PoseNet, introduced by Habermann et al. {{cite:4209880bfe41170786e0a40b70f4c1c084956042}}, regresses skeleton joint angles and the root rotation from the input image using multi-view 2D joint detections as weak supervision.
The proposed SimNet predicts the surface deformation of the cloth template by regressing embedded graph parameters from the same input image.
In addition to multi-view image data, SimNet leverages our cloth simulation layer as supervision, which encourages physically plausible deformations (Sec. REF ).
{{figure:98a8618c-bf41-41e1-a1a0-e0bd1aba69d8}} | m | 4a61b09ba894f468a43d4a0c679f8d91 |
Datasets: We use the full Librispeech dataset {{cite:a804e41e216e0ac59a694bcf49717a29e0a74249}} for pretraining a character based SA2SR. The dataset contains audios and transcripts for around 960 hours of audio, and we generate the proxy sentiment labels using text-to-sentiment RoBerta model trained on Twitter sentiment data {{cite:f9a56183658828d0d1f9494d23639bae6ff978f4}}. We extract LFBE features with 40 frequencies using {{formula:6a027893-f6a9-4bff-bf01-07aa8d47bd07}} window and {{formula:02ae1087-efd7-4c4d-ad55-a7d80fad4c0a}} steps. Hence, for SA2SR pre-training, an input tuple consists of (LFBE Features, transcript, proxy label).
| r | 37dc8ac185057bad877296a625bccdb3 |
Being social animals, human users are inevitably vulnerable to the efforts of the social bots.
Studies have shown ubiquitous social bots {{cite:7da0f27b3b121a8df49262d4f6dcbd7e87f36a56}} distort online discussions, and particularly those about politics.
During the 2010 US midterm election, primitive social bots were used to attack some candidates {{cite:c5191d7d53831556cb237a7ca35d20f5fec964a6}} and spread tweets with links to fake news websites {{cite:535307c6a8a054dd0d24627788566367f360390c}}.
A similar pattern emerged in the 2016 US presidential election, only with more sophisticated bots that aimed to effectively push their messages to the target audience {{cite:f4948ca6b840c325a11d39366fe6c3496b4392f8}}. In particular, bots were most active in the core of the misinformation-sharing network {{cite:c1b7d63c72079dc995ccb763005bf55959f2d399}} and effectively amplified the spread of low-credibility content by posting it within seconds and by targeting influential accounts {{cite:6b75a3bd0cbd29817a5b9088214a917015be53f1}}.
Analogous automated campaigns were reported in countries around the globe {{cite:8e66ace5c9e459fd8d6f4155f1a8b795e66c5f45}}, {{cite:410ebd3ef24564f9a0ee552dde73ad7e080e5ad7}}.
{{figure:50a2b658-3248-4723-b8a1-5d39b2646798}} | i | c11206f252ba0e2df17178cf7216b8f0 |
Probabilistic questions.
Weighted automata and its extension as nested weighted automata, or automata
with monitor counters are all measurable functions from infinite words to
real numbers.
We consider probability distribution over infinite words, and as a finite
representation for probability spaces we consider the classical model of
finite-state Markov chains.
Moreover, Markov chains are a canonical model for probabilistic systems {{cite:a4d64ebceecc035320f57348dc747ae19778195a}}, {{cite:b2795ecf1730f95f492f9ccb9aa9f52d882997bc}}.
Given a measurable function (or equivalently a random variable), the classical
quantities w.r.t. a probability distribution are: (a) the expected value; and
(b) the cumulative distribution below a threshold.
We consider the computation of the above quantities when the function is given
by a nested weighted automata or automata with monitor counters, and the
probability distribution is given by a finite-state Markov chain.
We also consider the approximate variants that ask to approximate the above quantities
within a tolerance term {{formula:3c11e170-2356-4612-8286-ce1b6ca98479}} .
Moreover, for the cumulative distribution we consider the special case of
almost-sure acceptance, which asks whether the probability is 1.
| i | 6501d36912410cb46b81c70e5dc0b48b |
It is worth considering whether our results are affected by numerical resolution. There is a fair amount of evidence to suggest that simulations such as ours do not accurately track halo survival after they have lost a significant ({{formula:6ce24f97-c3a6-47f8-b00d-dd31349bb445}} ) amount of mass, with {{formula:c6b30643-3ba8-41ce-860b-864caaced2f0}} particles appearing to be a critical limit below which halos disrupt unphysically {{cite:114cfb12a0c149854208b3f80cad7e2ea2fc29c2}}, {{cite:4b07777d869ec46819fba4362c6bd08ca543b8b5}}. In terms of halo counts alone, this effect should not affect current cosmological zoom simulations significantly, since accreted halo mass functions rise steeply with increasing mass, {{formula:f9da3d3c-1beb-400d-a4c1-747097c258de}} {{cite:7c3f8d1eddf8f39464c9ef4abee35000b0e4869e}}. This means that for every halo of mass {{formula:ab217a71-1795-4f9b-ad98-f3efd8580686}} that was accreted long ago and has lost 99% of its original mass (100 {{formula:e64d7f9b-2dce-4ca2-99a1-9f9fb18b979d}} ), there are as many as {{formula:18192651-baa6-4af0-bc9e-06fd8bd47b9a}} halos of mass {{formula:5d2f1d8b-8e4b-4be0-aec3-e584896a9cea}} that were accreted more recently and that can be accurately counted. As discussed in {{cite:4c6b02f1ec125320f9395d6600deb2c4f7157b7e}}, convergence tests suggest that our halo counts are mostly complete down to {{formula:511fed15-5f92-4558-8828-6dacf1139288}} km s{{formula:cbc276ad-4eca-44c3-853f-58ea9397942b}} , or only {{formula:ad7c247d-e858-4390-a494-f5597a1ce0f1}} particles. Of particular relevance to this work is whether or not internal halo structures, e.g., {{formula:1983a883-e041-4908-978f-21020abbbeb4}} distributions at fixed {{formula:197ca471-333d-4cef-958b-36c9471ca81d}} , are tracked appropriately. We have limited our analysis to halos with {{formula:c2f28059-c337-4b5b-b934-40ded7a02b37}} km s{{formula:f4c24072-e38b-46e5-9613-0bc5ed5100ed}} , or {{formula:d13930a6-1073-4406-917d-474521e0fbe8}} particles. According to the results of {{cite:4b07777d869ec46819fba4362c6bd08ca543b8b5}}, these should be fairly well resolved. For Draco and Ursa Minor, we are looking at halos with {{formula:0636f217-7405-489e-b254-3630ce15c4e0}} km s{{formula:c8c453b6-80db-447e-a0da-034e8a791082}} , which have {{formula:e6cca6ae-661d-406a-b835-a3f374701e2a}} particles, so quoted results for these interesting systems are likely robust. If anything, we will be biased towards missing halos with lower {{formula:e17dddc2-31b7-47c5-a13f-ea65e764b80b}} values at small pericenter. For example, {{formula:64a1347c-edef-4ec8-b731-3fa49017567d}} would imply {{formula:d78d2fb2-27c7-498d-aba2-a2ae44ae235d}} mass loss. In the unlikely event that this this bias is significant, it would mean that the measured trend would become even stronger at higher resolution. This will be a topic to explore in future simulations.
| d | cf629eb27820fe551148bdf804afd775 |
Among a wide range of algorithms, YOLO is a one-stage object detector that utilizes a real-time end-to-end approach to predict bounding boxes and class labels at once {{cite:31ce7f51995fc7ee78f4a3dfeec3c06110697259}}.
At the time of writing this paper, many different versions and variations have been introduced.
YOLOv2 has improved the performance of the first version, including low recall and small object detection, by using batch normalization on convolutional layers, improved classifier, and anchor boxes {{cite:90eff1bef31f00e161e34659b11230b4d6fe3783}}.
As the fast approach introduced in YOLOv2 decreased the accuracy, YOLOv3 appeared with a robust backbone, allowing it to detect features at three scales {{cite:89a90eb95fe17fbe20094c2cf87df79050f8224f}}.
Although later versions of YOLO are not considered official, their developers have changed the architecture of YOLOv3 to improve performance and accuracy.
In YOLOv4 {{cite:80ab871566de7100c610f38188bb5a7efc4be7a2}}, the primary focus is on enhancing the object detection stage, resulting in ten and twelve percent gains in accuracy and performance, respectively.
In 2021, the fifth version was introduced as compound-scaled object detection models trained on the COCO dataset {{cite:a53541b83cf39e08f1a16c408087f72decd3e89b}}.
YOLOv5{{cite:337d6a7059506ef86191de8dd18b32f1bf51f9e3}} is implemented with the aid of the Ultralytics PyTorch framework and Python programming language, making it a super fast methodology to train.
| i | b7857a387d4fd7af397815d379fa596c |
We trained networks of spiking lif neurons using a supervised
learning approach which we call “SuperSpike”. This approach generalizes
the back propagation of error algorithm {{cite:7b285d21d99f43faf9fbf200163a285fbecb1f8f}}
as known from the multi-layer perceptron to deterministic spiking neurons.
Because the partial derivative and thus the gradient of deterministic spiking
neurons is zero almost everywhere, to make this optimization problem solvable,
we introduce a non-vanishing surrogate gradient {{cite:ba5bcad1f77e9e463fb0cac1c04cc9f001a22e46}}, {{cite:ded47457d240b04fd85e9a1fda506e20a40c59ee}} (cf. Eq. REF ).
All simulations were run with a temporal resolution of 0.1ms using the Auryn
simulation library which is publicly available {{cite:5e1846ecc32cd495239d01a7aace909022dc59b7}}.
| m | 30b59e1a2e1c2e46fa2ab061025fff8f |
First, let us deal with the definition of the overlap (REF ) (referred to as symmetric overlap). In Fig. REF a, this local measure is shown in the case of a link connecting nodes with significantly different degrees. In such cases, for {{formula:7a03f385-12e6-465d-ba1b-f6ddcd6f8177}} , Eq. (REF ) can be simplified to {{formula:fd4ee2fe-eca8-48df-a621-47506da5602e}} , which shows that it is strongly biased towards nodes with high degrees, distorting the image of the common neighbourhood as seen from the perspective of nodes with small degrees. This drawback of symmetric overlap gains importance in networks with highly skewed, fat-tailed node degree distributions {{formula:36185d35-2a1b-49a5-9dd4-10b2008c7b34}} . In such networks, as brilliantly exploited by the degree-based mean-field theory of complex networks {{cite:26d63ad125d6b4cebfc68ad3457ffdb3dfd5f66c}}, {{cite:7b4800d3a712e5d82a31ae473620ec79a8132b70}}, {{cite:36c38c5cd1d6a93e3641850aa4ccf2f07a197283}}, node degree distributions for nearest neighbours are even more fat-tailed than the original distributions {{formula:27caba02-8fc4-43b1-ae51-e118e8a252e5}} . As a result, the number of edges in such networks connecting nodes with high and low degrees can be very high, leading to an unintended overrepresentation of strongly connected nodes by Eq. (REF ).
{{figure:fefcd95e-22c8-4a2e-ac29-91fdbefa40e8}} | r | c5f4cbb719eadb43b9ea72d55106811d |
If we allow for violation of faithfulness, then {{formula:7b8e0164-d2b1-4e60-b73c-1af81cc653fc}} and {{formula:3c49f8e5-44f4-4b28-81b4-4cc814f7387b}} can still have a latent confounder. An example of this case is given in {{cite:f170a23d11a8f9ed489ad3a7f67c8bc844729e2d}}, which we discuss below.
| d | 007393b64a8fe6dfb452c6c3d3f0b1af |
We implement a fully connected neural network with the machine learning library KERAS {{cite:8115d1eb437ffaec684026047c316846ab3baf7b}} using TENSORFLOW {{cite:36a6aec40a0a5ea6d47a0cc20fb03f08240ce2db}}, {{cite:dfbb4b371c19206eb7fd18806bf56595cbd874bd}} as the computational backend. Our neural network comprises one input layer, three hidden layers, and one output layer of neurons [see Fig. REF ]. The two adjacent layers are fully connected, where each neuron in one layer is connected to every neuron in the previous and next layers. The interlayer connections are represented by sets of correlation weights called weight matrices. The inputs to the neural network are the snapshot spin configurations obtained through the Monte-Carlo thermalization; that is, the {{formula:46e9ed57-cb64-4ca8-93a3-68b57bd0256b}} and {{formula:ff2e2a05-3c57-4535-af46-0953ac1827c4}} components of the planar discretized spin vectors {{formula:8dfdf5a9-4a07-41b2-ab9e-ee8655fef6b3}} at all sites ({{formula:2a496ede-3ad3-4490-8790-969fab429ad3}} ) on the square lattice. Therefore, the required number of nodes in the input layer is {{formula:1040ebc5-0498-43ed-909f-a9b8f933c857}} . Meanwhile, the answer labels are given by the so-called one-hot representation of temperatures. The temperature {{formula:7d4f4d22-e8d4-46ff-b570-897c23ddbdae}} ({{formula:459fe8da-7080-417c-a2e4-d6fa2d7da63a}} ) is represented by a vector {{formula:82c73434-10be-4c62-b449-d326a1f45a06}} with 300 components in which only the {{formula:ec748dab-2501-4f68-bc0e-dc8f2f1ba90a}} th component is set to unity while all other components are set to zero. In other words, when the temperature is {{formula:62212059-b529-404c-8bdb-0b8c6960e6d8}} , the {{formula:8728cd48-2706-494c-a4e5-0daefd60218b}} th component {{formula:feff74b0-c503-447c-8981-32897d74b205}} ({{formula:2be9106c-b0b2-483d-8cf2-24e1add28e23}} ) of the vector {{formula:3c78eaef-8dcd-47cd-ab2b-e07408774b1a}} is given by {{formula:920135a7-a20b-4f40-801a-fd3cfac4deb4}} , where {{formula:64e435ba-dee5-48ae-9ce1-e61b0bb47f1c}} is Kronecker's delta. Each node in the output layer is assigned to one of the components of the vector {{formula:39700a0c-e371-43f3-8ac9-10449d0c0ce3}} , and the number of nodes in the output layer is thus 300. Typical numbers of nodes of the three hidden layers are 2000, 1000, and 300. As the activation function, the rectified linear unit (ReLU) is used for the first and third hidden layers whereas the softmax function is used for the second hidden layer and the output layer.
| m | edd47ab185383ece2c62addb207220dc |
Mahalanobis distance: the Mahalanobis distance (in logit / feature space) measures the distance
between a sample and class-conditional Gaussian distributions estimated from in-distribution data.
It has been used to detect OOD samples in classification task {{cite:d17a372d028329259a9f9cc749d639433f26a335}}.
In this work, we adopt this method to 3D object detection and experiment with logit layer and multiple feature layers.
| m | 004dfcd3222029322c78b4bfcab3dddb |
Loop quantum gravity {{cite:5e1a6c549fa5413478680ffd741cffb987b214e8}} suggests that, for quantum gravity in four spacetime dimensions, areas, instead of lengths, are the fundamental variables. In this approach the areas have a discrete, asymptotically equidistant, spectrum. This leads to interesting proposals for the origin of black hole entropy {{cite:64e29987523c218f105de682171f0d1671acf274}} and resonates with more recent developments on deriving geometry from entanglement {{cite:bead8e55b52da21dae4d0bf5bf06b8ae3409ccfc}}, e.g. via holographic tensor network states {{cite:e5927cffdc150e442f09d30c6113521f067cb20a}}.
| d | 45bfa33eb35b827ed448160ac5e2a0b4 |
In this paper we develop a novel efficient attention mechanism using input dependent sparsity structure in attention computation, motivated by the analysis showing the sparse nature of attention {{cite:f703d561d9854eccef2c2ee315ce9e0dcfac5614}}, {{cite:f2910bc4421edbccab47945d77e5ab0417f2e13e}}. We propose to use decision trees to efficiently compute attention by only retrieving the top nearest neighboring keys for a given query. Decision trees are low cost, hierarchical non-linear models that have been popular in both supervised {{cite:be69057f89fc778eb35be3578fc620e67a90473d}}, {{cite:f05c173e09335721a6af6148d107d05e83e568ac}} and unsupervised {{cite:82781288bdfbfaaa90f979804a49f963e669ec88}} learning. Given a vector, each node of the decision tree decides whether to navigate to the left or the right child depending on the sign of a simple linear projection. We learn decision trees in each attention layer of a Transformer model so that a query pays attention only to keys that map to the same leaf nodesLeaf nodes are the bottom nodes of a decision tree with 0 children. of the decision trees. We refer to this as TF-Attention. Such sparse decision trees that retrieve only a single leaf node are typically hard to train due to their discrete nature. Further queries that pay strong attention to multiple keys result in bunching many keys together in a single leaf node creating imbalance. The key computational advantage of decision trees is realized only when they are balanced.
| i | 0d1a817ce6b447bb9b8a1eaad0e6cd3d |
For approximately fifty years particle physics has dealt with a conundrum:
The electroweak hierarchy problem, the apparent unnaturaness
of low mass scalar particles, or,
why is the Brout-Englert-Higgs (BEH-boson) mass, or weak scale, small compared to e.g., the Planck scale?
This has driven much of the thematic research for half a century,
from supersymmetry {{cite:645e6dc16c0f7d1731462e4d5ebf8b0368022b70}}, technicolor {{cite:4381a9bc10af44b5f559cc4f746d7749bdf647c9}} and extended technicolor {{cite:d17a71429f180615e228e00a935552c50c40d0fe}},
top condensation {{cite:65e904ab8b8a2b926a28ce7cf8e14a5fb442f96f}}, {{cite:ad4e3b33e7d04b397cabecb4a87de58f959aebd7}}, {{cite:86a610610409e09b12f274bc1f2ec9fa73dc4d48}}, {{cite:e0284a693d81ab29002ad7165df3a969cb857a3f}}, “composite models”
(where the BEH-boson is a pseudo–Nambu-Goldstone
mode {{cite:c621ce2920e1695b8e2e7da06b5482a206f20d2b}}), etc.
The discovery
of the BEH-boson in 2012 at the LHC, and the apparent lack of
any nearby new physics to act as a custodian, has exacerbated the conundrum. The BEH-boson
appears to be, for all practical purposes, an approximately massless (e.g., on the Planck scale)
scalar field. This is seemingly anathema to fifty years of post-modern theoretical physics.
| i | e5a0e88cf7465cf25984c45cae314a05 |
High-quality whispering gallery mode (WGM) microcavities {{cite:b2db271b44738c0b9c517a093d12808eca2705f1}} have potential value in investigating fundamental physics and practical technologies such as cavity optomechanics {{cite:6a1497f0d74470735eb7eaf3967714c76b5985df}}, {{cite:40da899077a1aa490d91379cf2eb617bc96216aa}}, {{cite:f96c4d097f9371a24d1a1a6920bcd56411b8a2a1}}, {{cite:1349cc158b72c714d3c7ee4d6d9b02e4405b7ae6}}, {{cite:a1268bba8d7f678646718cc578f721f560f4d13c}}, {{cite:cfcd7ed886bac8733121e24a288c91526c4c6861}}, {{cite:20eff4136f4d7adbe5466763acd3baef1c761b5a}}, {{cite:ad91fe36b280814a8304b2cde9e4c5a9401a517d}}, {{cite:e1d76a602efa2ac85c5701265672b5770672dae1}}, {{cite:a6f9b302ffacc36f9e3e3601586453be72b037dd}}, {{cite:a0120837eb8d07c52050220c67c925cd745b847a}}, {{cite:e8980102b11365786e2de4038e3f679ea9e5b8c0}}, low-threshold lasing {{cite:bdee45fee0406fcfb3ec4c3f95d3bf39820ef637}}, {{cite:bd59801e7ca6ecbc351a21ca2259b7c005c481f7}}, {{cite:c10adc64503c7ad340049d26c883ac44b733ea80}}, {{cite:9dcc3aeab47d961a3f3c9d10ee3a68a27a9281a4}}, {{cite:0bc6078a0b17667f23fd1b45ae0a2264c9ea9947}}, {{cite:e1142736526110532504ac19f6313019a63c6bff}}, quantum sensing {{cite:46d4b0c830b651dcf83cbd49dc3955fcdb37d1f7}}, {{cite:8f4b0c5512a2e5b8959526088bfc74d1c4596692}}, {{cite:af119bea59b2f3d0163cd5fe34639d4a0cab4cea}}, {{cite:33118fd2795ad46cb684a5aace2206ef65d4d725}}, {{cite:6fe045550d64a132c93dd3dc5bb60eff920d3e8a}}, {{cite:55fdf4485cb3bb00837d93e624defc608a14c84b}}, {{cite:11369c8cef7fe1f01d7d23d2da034e9fb75a7918}}, {{cite:941ef0fa1a108c2ae980c0b8fe1692a919dee162}}, {{cite:d891e25458e0f7bc259e19a8cd7f443810b3ab0d}}, and nonlinear optics {{cite:472fc9f588c8a73c43aabf7c5fe263d90b772f2c}}, {{cite:f96c4d097f9371a24d1a1a6920bcd56411b8a2a1}}, {{cite:93f4b37e8b4a734111923400fedce4872f27a039}}, {{cite:62b0a750ea4e33c939d017f5d5fd1d34179da3de}}, {{cite:6d31a04b52d6d7f29695f69731b1749cfb9e3f33}} due to their ability to enhance light-matter interactions. Characterized by exploring the radiation pressure interaction between optical modes and mechanical modes, optomechanics exhibits rich physical phenomena such as optomechanically induced transparency (OMIT) {{cite:40da899077a1aa490d91379cf2eb617bc96216aa}}, {{cite:e1d76a602efa2ac85c5701265672b5770672dae1}}, {{cite:f96c4d097f9371a24d1a1a6920bcd56411b8a2a1}}, {{cite:df71111413f72eed50d1742f1de895979e347b17}}, absorption (OMIA) {{cite:e1d76a602efa2ac85c5701265672b5770672dae1}}, {{cite:f91d6d486aea871464b978badf3af1a8650db51e}}, {{cite:dd3b9e4d61c3a5c760fc397287bfdc3eba8af624}}, and optomechanically induced Faraday effect (OMIFE) {{cite:88297fe15b3f2566f57f2fbf5ae305d654496569}}. These effects enable a new degree of light control and achieve arbitrary tailoring of the input lights in optomechanical systems. Further, the additional degree of light control allows varies of applications including state transfer {{cite:5770d67db5a8970b305a3fe1706e02a9161689ab}}, {{cite:99f0d286c9fbd025e320bdd990ba8e3fd1f43cd0}}, {{cite:4555d295b5bf3e4740aa04b024a1dcb70b3e5206}}, {{cite:d4b418e9b1bcffee3f9c46aff4cc788eb90b6f51}}, {{cite:0cf4a85f39e89a018e3cf6681ade19448c032ebf}}, optical routing {{cite:f0fec0f6c92884de264851edbe3acdba7de55d88}}, {{cite:1c919a0cf7bf6391a3dd0dc3374aa38548ffb9fb}}, {{cite:a25d7b6e56f3169c1073851bd9db09728d2f61ed}}, and entanglement generation {{cite:cb2a7c4bff211dd9678ee02cd8bc8103602c763e}}, {{cite:a242d4ae831858444d2c5fec04bfd0949e7ef2af}}, {{cite:7e2aaae39bd14ef9c1b7d0fd07fb79941b28310c}}. Besides progressing in many applications such as frequency comb generation {{cite:314c46c94a9ec144195bb09967ffcf64d1ac76f9}}, {{cite:dd06da405b6bfc1a3e78e8e54d5bc58d05ecec10}} and light storage {{cite:ad91fe36b280814a8304b2cde9e4c5a9401a517d}}, {{cite:dce4a5e4469859529561833138c924015401c6bc}}, optoemchanical systems provides a promising platform to study polarization behaviors.
| i | 3f06b98c0cf3a0f9fb8bfce99da55663 |
Cross-modal Fusion:
The encoded unimodal representations are fed into a cross-modal fusion network, that uses a set of attention mechanisms to capture cross-modal interactions.
The core component of this subsystem is the symmetric attention mechanism, inspired by Lu et al. {{cite:5fcf4f8166255d2406b212bf38c08e224980da1b}}.
If we consider modality indicators {{formula:4ac52e21-498e-42d8-905f-3977603123a4}} , {{formula:feb105d6-ba24-4fdc-af95-8b258f0011b1}} the input modality representations, we can construct keys {{formula:d7065341-7fa5-45ea-b8fb-d9fcfbb79fa0}} , queries {{formula:a14e6969-cedd-437f-8cb3-28aeb1bbab43}} and values {{formula:c38873c0-bee0-4c52-a60a-68c706769be5}} using learnable projection matrices {{formula:1c3ccf65-ddf4-4cc8-a57a-51adf788ea3e}} , and we can define a cross-modal attention layer as:
{{formula:ef318b11-9d19-492b-bd64-61be3ef4d2f6}}
| m | 81d22ec38b97074ac5128b58c89ded29 |
where {{formula:8a29c8f9-fb62-4dc6-9f49-11e6d335be98}} acts as a regularization strength balancing between the two objectives in Eq. (REF ) – the regularization is necessary because it is numerically difficult (or even impossible) to find a counterfactual {{formula:2899945a-8065-4b8b-a553-4bb01645b3ed}} that yields the exact mapping {{formula:01531733-4ee0-4d1a-ae38-393f1b992563}} , we therefore have to specify how much difference we are willing to tolerate.
Note that convex quadratic programs can be solved efficiently {{cite:d1d73160024c46a223c47d48729138052dd9e9da}}.
| m | 46160dedab7ac917dfd1e9ba24ff1a90 |
For sake of completeness, we also compared our method
with an anomaly-based detector that performs forgery localization by looking for general traces of manipulation, hence not focusing on DJPEG compression artifacts. In particular, we considered a recently proposed deep learning method, named MantraNet {{cite:4b6c8466ba9ecf9e327890793f31377894559c97}}, based on anomaly detection, that performs joint image-level detection and pixel-level localization of forgeries, regarded as local image anomalies.
{{figure:6bcaffdf-06f2-4b06-9ddb-f968632428f1}}{{table:e7f9ce73-3ec3-4e19-9b92-484fb90dc25d}} | m | dd9fed940377575213bf3d30796d03e7 |
Finally, we note that the discussion of holographic entanglement entropy can be framed in terms of `bit threads'
{{cite:432c7e1fda23cc3fc162d1436627312b341515c0}}. In the de Sitter setting, this leads to two distinct proposals: the monolayer {{cite:848d4930994854116d45fbdd4e344df4f8697416}}, and bilayer {{cite:61296367bea676cad97f4f8537cf33ee0deac3de}} approaches for entanglement entropy – see {{cite:8ebbd5afb0d1be911b8ff6fc6fad9693b3ca77b2}} for a discussion of the differences between the two approaches. However, we note that there is an analogous `gate line' description of complexity=volume {{cite:85f87f8f3f545257c0498949dcc03f227f23156c}}, {{cite:9478f8401805836dc7f29d9bd186b89c9a069559}}, {{cite:800e4acda2b0d5442fdee5d054b81dd5c77dc588}}. Hence it would be helpful to examine this description of holographic complexity in the context of de Sitter space and explore if analogous subtleties arise as were found for the holographic entanglement entropy.
| d | 9d1cbfa7f9540e662c422445829ede10 |
Energy-based Score Function To mitigate the issue of overconfident softmax probability in MSP, we propose an energy-based score function to push apart score distributions of OOD and IND samples. We first briefly review the energy theory {{cite:5e0a5ca48fcea4bd9e741f36f060ed87cb64560b}} then explain our proposed energy-based score function for OOD detection. The previous energy work {{cite:5e0a5ca48fcea4bd9e741f36f060ed87cb64560b}}, {{cite:338c74029a07ea32bc8e9d390c66c5cc16fc3b93}}, {{cite:0526767e38be587d2e2be20d9cc267b5fde15dc0}}, {{cite:eeb72743c173f2284c365d56ece712db0210f3d8}}, {{cite:9158cdf0b5687f7304674030dca27dc410862a40}} aims to build a function {{formula:abbfacfe-30a9-4cb8-9f30-140ccdb15cd9}} which maps a sample {{formula:cc84da62-d604-4618-9983-d85f449a631e}} to a single scalar called the energy. Given a data point {{formula:8cae26ca-2ee3-4a5f-98c5-e16aabd1692c}} , the energy function can be defined as follows:
{{formula:83ba2f7e-913c-4453-a5b1-4c14834fe31d}}
| m | d97ac741005a33eeae7aa1eadd62e447 |
In Fig. REF , we compute {{formula:ef9fc084-1ca0-4ae2-b9fb-16b9ea8c75fc}} after each iteration, where {{formula:7f57f3e6-4679-4386-a6f8-382c277da107}} is the dominant eigenvector obtained from eigendecomposition as in {{cite:49d48f6cb105f1582ac9d121da33c45a5e8fba19}}.
The MAPI iteration converges to a vector very close to the actual eigenvector because
{{formula:a3e3be13-a045-41c3-b950-0d821e128e96}} is very close to zero as shown in Fig. REF for {{formula:bb29646a-2511-426e-978e-cc3847d682ba}} greater than 20.
However, {{formula:41475d11-ac98-4dbe-aa99-2930a039f5bc}} obtained using the MAPI method is not exactly the same as the eigenvector {{formula:55cfb3a2-597f-49a7-86d0-9ab6ecc55bff}} as we see from Fig. REF whose vertical axis has a different range from Fig. REF . This is expected because we perform the iterations in the Reproducing Kernel Hilbert Space (RKHS) domain. Nevertheless, based on our observation, ranks of the entries of {{formula:5162d888-479b-4f27-a1f8-7e5996c50bf0}} obtained from the min1-PI
are the same as the ranks obtained from {{formula:8cfed243-58b9-4792-8c98-daecb937160c}} of the RPI. After 100 iterations, {{formula:1eda5d87-21a9-4f82-8df6-4b3abae84d52}} =[-0.1433, 0.4171, -0.1166, 0.3863, 0.1285, -0.1315, -0.4330, -0.2097, -0.5770, -0.2106] from the RPI and {{formula:2c8717c6-c258-4dcd-ba8e-1c3a50f9c401}} =[-0.1649, 0.4166, -0.1371, 0.3887, 0.1480, -0.1508, -0.4306, -0.2359, -0.5362, -0.2370] from the min1-PI. When we order from the largest to the smallest, both vectors produce the same ranks {2, 4, 5, 3, 6, 1, 8, 10, 7, 9}.
Therefore, considering that our min1-PI converges significantly faster than the conventional power iteration and the min2-PI is identical to the min1-PI if all values are non-negative, our MAPI can be employed in the Google PageRank algorithm {{cite:17042d4ba274a33f6981a2417e25270887cd27dd}}. We will discuss it in Section REF . Moreover, if we want {{formula:d53803bf-a90d-4f46-bbee-55ef2eaebcd3}} to reach 0, we can optimize the vector via the MAPI first and then switch to the RPI for further converging.
| m | 20ba9b396870e776ac87deac0a407ce8 |
For completeness, we recall the notion of relatively prime self-adjoint extensions (see {{cite:8887be605d5b4d1ec066fc4c1645994c224d67f6}}).
| r | 264449609395ea6b269f76f1b87ccf94 |
In preliminary experiments, we searched for an encoding to describe action sequences for a walking robot. The results show that using MAP-Elites to generate a diversity of sequences, then using a VAE to learn a representation leads to an encoding that can accelerate future optimizations by several orders of magnitude. Nevertheless, using the representation during optimization, as described in this paper, did not accelerate the quality diversity optimization as much as in the high-dimensional arm used here. One hypothesis is that the regularities in action sequences are harder to recognize than in the arm experiments, especially at the beginning of the process. For instance, it might help to use an auto-encoder that is especially designed for sequences {{cite:716accb4bed0180df5460b8d922e0c96fa3c22d0}}, {{cite:69980d16da54b88015a5ac5f7bb3cf4956e70110}}.
| d | cdff6f798598d1aac8d60faf4ea5669b |
To address the choice of model dimension, we developed, building on {{cite:4428ca3d4299554fe19f6c384ddd82ba9bc8da8f}}, a practical procedure based on separate SVD of the shared covariance part and the study-specific covariance parts. The choice of the number of factors remains an important open problem. The most common method for choosing latent dimension fits the factor model for different choices of {{formula:ca0f3bf5-31bb-4243-8db4-63d67f60b030}} and compares them using selection criteria such as BIC. This approach presents many problems especially in a {{formula:4e0b4815-ad8c-4a7c-bafd-3990c8782c0b}} setting where MLE is not duable. {{cite:abc65500b1feb85f38d6d8e8228bbb7f49e5a618}} proposed a reversible jump MCMC to estimate the number of factors in standard FA, but this method is also often computationally intensive. {{cite:4428ca3d4299554fe19f6c384ddd82ba9bc8da8f}} developed an interesting adaptive scheme that dynamically changes the dimension of the latent factors as the Gibbs sampling progresses. In our approach, we develop a practical approach where we have a balance between retaining important factors and removing the redundant ones.
| d | 354ec424fd2e7e102320a2c39dce68e3 |
At {{formula:1b5b2798-6cd9-435c-8a71-6dc16f0dddef}} , as showed in figure REF , strips and perforated lamellae emerge as stable phases near order/disorder transition. When {{formula:8964b18f-beaf-4455-8bdd-fda120015b21}} , NCSLM is observed. NCSLM is an ABCBA lamellar structure, though the width of the two B layers is different. NCSLM was observed in flexible ABCA and ABCD tetrablock copolymers{{cite:4a2e9610bec6b2c688317e279f547d8043a8382a}}, {{cite:6206f7c2b4c9defbfc29b8d4c8b31cf3c1f607ca}}, {{cite:765278fcfeaf982e7cf854700dfb1dc24d031edd}} and in the blend of AC diblock and ABC triblock copolymers {{cite:7bb75ab5d23460e4c9838f20bf28520c8504b724}}, {{cite:1740f893d62a91ebb8d03d584a40f10cdaa96a3a}}, {{cite:4417e1ba2690f33dd2ab737c91ff759ca0a89d3f}}, {{cite:a8a9b9f349ad00a5a37da896193b987f306bc1cd}}, {{cite:6cb2aa5de0fb2bb183d7b460a20a3ca28f79d0cb}}. However, it is found for the first time in coil/rod block copolymers. It is noted that the difference between the free energies of NCSLM and CSLM is very small (no more than the order of magnitude of {{formula:600ac5ec-2383-4f3f-9b14-ea26cf0a3eec}} ) when {{formula:e2d9d6ed-3046-49f8-9174-6da0d6ee59a0}} [seen figure REF (E)], i.e., CSLM and NCSLM are degenerate structures. Above the region of degenerate behavior in the phase diagram, the relative stability between NCSLM and CSLM changes with an increase in {{formula:8efa15f0-1a3b-40f5-b476-ceff6d9cdab1}} . When {{formula:1adbc85d-a4d0-454f-b721-f1b21c64e784}} is increased, firstly CSLM has a lower free energy than NCSLM, and then NCSLM is more stable than CSLM. This is similar to the emergence of the stable micelle C at {{formula:cf0f9517-ecf4-4bdc-8ef6-4fd6cf228eaf}} . These behaviors are in reasonable agreement with the cylindral/ spherical structure transition in coil/rod/coil ABA triblock with increasing the interaction between rod and coil blocks {{cite:7c97d7a9fb59fc46117a8464d7408dc38aab5405}}. The mechanism for the emergence of NCSLM will be discussed in detail below.
{{figure:4384923d-c544-4b25-ab19-2b9cf3246521}} | d | bfd1593e7881d576aacbbff1a582fbc3 |
Predicted segmentation masks were post-processed by applying 3D morphological closing and extraction of the three largest connected components. To demonstrate the utility of our loss penalty term, we compare it to other successful methods in Figure and Figure , using error maps and the following metrics: global Dice score (G-DSC), boundary Dice score (B-DSC), and its relaxed version which expands boundaries by a certain tolerance. Our method produces high-quality segmentations, with accurate results even in regions with significant partial voluming (intercondyle notch, tibial condyles). B-DSC of our proposed loss shows a significant improvement in edge detection ({{formula:7c48879a-0298-4897-8926-4789800bcccf}} vs Dice loss {{formula:717d7fee-3f4d-44a1-9d6c-53b21473ac30}} vs {{cite:6fa04552b83e5935c57cdc929557089337641d64}} {{formula:01a5b38d-8923-43d0-b27c-e6bcb6f4c8c6}} vs focal loss {{formula:26d3ad73-9088-4f41-9063-26d4052dba2e}} ). This superior performance is maintained globally (G-DSC) ({{formula:a8b98a3b-589a-47d5-be15-6a0ea63a3802}} vs Dice loss {{formula:30f8529b-46ff-4cd7-a0ef-1be78cdff050}} vs {{cite:6fa04552b83e5935c57cdc929557089337641d64}} {{formula:d061353e-3ba7-41b8-86f3-3144e360983b}} vs focal loss {{formula:c63fe87c-ee58-4915-8752-f3ec4782ae9a}} ). We observed that guiding the network with a shape-aware loss function is a promising method to improve segmentation performance.
| r | 21b3b7d1ea85332aad45b59964eeabc1 |
Human feedback for judging simplification quality is more consistent for sentences, compared to longer samples, such as entire documents.
Metrics such as BLEU {{cite:4fa073d52819bf852a72c216517cc902ffab4d21}} or SARI {{cite:56814097c4ba36b8de107e82f74209f8ba39a10a}} rely on (aligned) reference texts for automated evaluation.
Prior alignment of sentences limits the length of input samples, which is essential for algorithms with non-linear runtime, or length constraints.
{{table:6ab62bc9-09da-453a-a278-eaf9134fa8d1}} | i | d0f33ee3606734813ecda52b96cc5de7 |
In this paper, we explore the mechanism to enhance the anomalous current caused by a background magnetic field in the spacetime with a boundary. Usually, the anomalous current is suppressed by the mass and the distance to the boundary, which are the main experimental obstructions. Remarkably, we find that the high temperature can greatly enhance the anomalous current and make easier the experimental measurement. For free complex scalars, it is found that the anomalous current is proportional to the temperature in the high temperature limit. Interestingly, the coefficient is just the current in lower dimensions at zero temperature. Thus, for any given charge carrier with a fixed mass {{formula:ba4f4891-36d2-4db2-96e3-a1a67d710018}} , one can always produce a detectable anomalous current by increasing the temperature. We look forward to the experimental detection of this novel anomalous current. For simplicity, we focus on free complex scalars in this paper. It is interesting to generalize the results of this paper to Dirac fields. It is also interesting to study the holographic anomalous current at finite temperature following the approach of {{cite:ff4f5df36d5cf3a1f87f4727c9561ae13a3d624d}}, {{cite:d38d4765e9d65f6363a57f5ea031769d03fd9fd4}}, {{cite:ec876a9e68476cabb5bac904af3e590d2de48e45}}. Note that (REF ) shows that the anomalous current at zero temperature in four dimensions is related to the renormalized current at high temperature in five dimension. This implies that there is an “effective Weyl anomaly" in the high temperature limit in five dimensions, which is consistent with the Kaluza-Klein mechanism. According to the Kaluza-Klein theory, a 5-dimensional Euclidean QFT with a small period of Euclidean time {{formula:a6168877-8d2e-496e-a7e7-fa237e00097d}} behaves effectively as a 4-dimensional Euclidean QFT, which is expected to has a Weyl anomaly. We hope these problems could be addressed in future.
| d | 9a25549d8dabab265f8b307948c63367 |
We first describe the scan method in section . The results for the global fits
are presented in section . We begin with a comparison with CKMfitter and UT{{formula:1cab52d7-dfac-40f2-9764-e77146602604}} ,
employing the scan method to extract CKM parameters using inputs standardized for the book Physics of the {{formula:55b1a916-feb6-488b-83ba-027165c61085}} Factories {{cite:800357c9bf2febfadfb4d272b211c0b9089b84a2}}.
Then we look at the current situation using inputs from PDG12 {{cite:97131d2eb8bb18f954ec48db431ff391a958c4cc}} and HFAG {{cite:89690e7ea8cf7ca61750fb3392d89f2eebfc3a87}}, investigating the question of consistency of the results with SM expectations. We call such fits “baseline" fits. Their characteristic is that the {{formula:6efd9454-bc28-457b-b500-495e354e1d11}} function has of the order of {{formula:2f47354c-e773-475a-abd3-0645a451f06b}} terms and {{formula:0eae8215-1dbb-4cd1-a75d-30edbbf55d81}} fit parameters including explicit inputs for {{formula:ea361567-77d2-4afb-9099-1a6167789140}} and {{formula:133a81bf-6859-4064-85a7-c735162de3e8}} . To take into account the correlations between {{formula:ab58c9cb-6c3f-4606-9390-56495b14e4f1}} and {{formula:34ea9200-eb4d-4d79-81a3-93dd6e114cec}} or {{formula:f9df7f71-2f05-4387-a652-985edd16f208}} and {{formula:83e08bbf-7e6d-4e16-9ba6-6af86878d34d}} in the extraction of the parameters of the unitarity triangle, we perform a fit in which we replace the inputs for {{formula:7628e328-a18a-44ea-9b0c-3b0fed4290aa}} and {{formula:39a3a4c0-53d0-4cf5-9fd1-bb5e606e21c5}} by branching fractions and {{formula:9428455b-d049-49d0-a926-e5866f634d8e}} asymmetries of {{formula:38d5c44b-bd15-4159-b532-1f98afb8ac7c}} decays to pseudoscalar pseudoscalar ({{formula:7fd8c155-1962-41e3-9842-ce9b26b3d144}} ), pseudoscalar vector ({{formula:3a6acb6b-9fb9-4720-ab52-495110491471}} ), vector vector ({{formula:0201e926-2b71-4bfe-b298-d176c8594660}} ) and {{formula:b5001cf9-4e96-46b5-82e3-7864c6c3821f}} pseudoscalar ({{formula:16702c0c-83c6-4b82-9344-b5045fa71596}} ) final states and {{formula:782635a3-3281-43dd-b318-d0c324603dab}} decays to {{formula:defe57f5-e625-49ef-82ab-11c95c9cdf15}} , {{formula:f63d9dd8-de31-4281-bff4-05e00408b312}} , and {{formula:5e855262-5096-44b8-b03a-93b841e13ba4}} final states. We refer to the latter as “full" fits. Thus, we are able for the first time to include the correlations between {{formula:56fb4a2c-6542-4846-8371-86a0c5ea3787}} and {{formula:096d49e6-1632-471c-b5e5-8ec02e2e3d83}} and {{formula:c255d949-95fd-4a23-9c2c-869d99c20150}} and {{formula:7a82d197-eae9-44cb-8087-7593c7ce1c45}} in the extraction of the parameters of the unitarity triangle.
| i | bb61020a1a93bf4bf0890d00966a08c0 |
In {{cite:5202d57aeff390599b8980b5f8cde871cf5f5a5c}}, it was shown that a stacked self-attention mechanism could achieve state-of-the-art results in natural language processing tasks {{cite:323f6f57a6db82b8d33ab3a5d364c153c3119757}}, {{cite:bd66ec3be43cd6ded8daea9d8c841489ff054f2e}}, {{cite:d3568b93e8087142ae32662f687a5ebf330a0c2a}}. In addition to the stacked self-attention at the encoder, the Transformer network {{cite:5202d57aeff390599b8980b5f8cde871cf5f5a5c}} uses a multi-head topology, where attention functions are performed in parallel at each attention layer. However, the stacked self-attention modules compose a serialized architecture of the Transformer network, where it can learn from previous layers with attentive information. With a deeper utterance-level aggregation network, the speaker embeddings will have greater capacity and become more discriminative. We conjecture that, if multi-head topology is applied in a serialized manner, more layers can be stacked and capture more robust speaker characteristics.
| i | 998eab98eabfbac9ccb67c55586b1930 |
The Alfvén waves lead to non-linear interactions which are crucial for the dynamical evolution of a Kolmogorov-like MHD spectrum {{cite:cd4efa0a858fb8eaedfc8372fd42800fb89e5002}}. We have also performed a power spectral density (PSD) analysis for all IMF vector components. It depicts Kolmogorov-like turbulent nature (The PSD analysis follows {{formula:c1239630-1da0-47de-be31-494dcaf143de}} spectrum) for
the frequency range between {{formula:d512da8c-aa1a-4ea7-9bba-606a971c7f37}} Hz to 0.5 Hz in the
studied the shock-sheath region. Thus the existence of Alfvén waves with the Kolmogorov-like turbulence depicts Alfvénic turbulent nature of the shock-sheath. Thus, we observed the continued cascade of energy from large scales to smaller scales of wavelengths and eventually to such small scales that the plasma no longer behaves like a fluid due to a change in velocity and magnetic field fluctuations. At this scale, the particle distribution is affected by the magnetic field which may lead to plasma heating through resonant interactions . We opine that the plasma heating in shock-sheath could be associated with an above-discussed process.
| d | 9e2c92853914c22426b1058e77b8b1fa |
Our method uses weight sharing, that is, all fake-quantized weights and activations are obtained from a single float tensor, and are generated just once per-layer on the fly, i.e., we have {{formula:ea338162-2e2a-4b86-ab38-409b42c24317}} and {{formula:2aac75d0-5667-47cd-bbff-1b243389cba5}} temporary copies of {{formula:29d23a83-f6dc-42aa-8743-4411ad53f8ef}} and {{formula:87fc1fa3-1942-4f6a-9d20-018ca5191348}} during forward DNN passes. Thus, the memory overhead of our method
during training
is almost identical to {{cite:1943943b57869bea002590c51853d1cb686a15f6}}, except for the new {{formula:1395f3ef-5dda-4cb0-a22a-67f0ec13a5a1}} matrix, whose impact is negligible. A key difference between our method and {{cite:1943943b57869bea002590c51853d1cb686a15f6}} is instead in the quantization scheme, i.e., the function mapping {{formula:67686745-67fa-4f35-a639-30f7587f093f}} and {{formula:00d76b72-e987-40bf-b195-69886a60e4d2}} . Namely, we replace the original Gaussian quantizer used in {{cite:1943943b57869bea002590c51853d1cb686a15f6}} with the PaCT method described in {{cite:3bcb20c052f45b6ea4f35b21caff7cd3376dee31}}. The main reason is that PaCT layers are fully compatible with our deployment target {{cite:d362a469eb00e390c4fe6f0cf6735c7316a43c24}}. Further, we found that it also yields superior results.
| m | 7c350330863ef93f265481bdceb9e1e0 |
Distinguishing between the near-field and far-field is becoming increasingly relevant as modern wireless devices begin to operate in both propagation regions.
The most common near-field distance, known as the Fraunhofer distance, is
proportional to the square of the aperture and inversely proportional to the wavelength {{cite:28cffab10823527177d66819d8966c607a35f367}}.
To satisfy the data rate requirements of 5G and beyond, wireless systems have shifted to higher carrier frequencies and larger antenna arrays{{cite:bfb48c6f05c341004d482e6e1ae4a85332fceae9}}{{cite:2fafd775dd034eaa0e5928992f35010309d64d28}}.
For these modern arrays, the Fraunhofer distance becomes comparable to the typical cell radius. For example, the Fraunhofer array distance for a uniform linear array (ULA) with 128 antennas and half-wavelength inter-antenna spacing operating at 28 GHz is around 88 m. This is a good fraction of the cell radius of an urban microcellular and picocellular deployment {{cite:e0be48efa95301f07eec5cdba12c74b5d389690b}}.
In the near-field, the phase variation over the array aperture is non-linear in antenna index, which causes a phase mismatch when assuming far-field propagation with planar wavefronts {{cite:28cffab10823527177d66819d8966c607a35f367}}{{cite:1fadc5865e4a3267b004527f6494961b37cf2761}}. Inaccurate use of the far-field assumption can lead to beamforming gain losses that worsen as the array aperture increases{{cite:1fadc5865e4a3267b004527f6494961b37cf2761}}.
| i | bd27ee43daa8b0e3b79fe3e9ca26efa4 |
To summarize: given this state of the art from prior work, it is clear that alignment-based approaches can outperform mean-based algorithms at low deletion rates, but it is not clear whether, or how far, alignment-based approaches can be extended beyond the {{cite:c99680edd22ce74c2621e38c30a271937d6bf430}} results. Further incentive for studying the low deletion rate regime comes from potential applications in areas such as computer networks, where it may be natural to model deletions as occurring at relatively low rates. These considerations motivate the results of the present paper, which we now describe.
| i | 240a9adba592013a4606b1edefb17832 |
We present two models for the multiwavelength emission of Tycho, which both adequately fit the SED.
Model I allows for the weakest magnetic field in the immediate downstream region of the shock, {{formula:0774de40-4fce-448f-9c83-839cc26075e3}} , that is compatible with the entire {{formula:d238b5cf-fbb9-4612-ad46-9119a0542d6f}} -ray flux observed with Fermi-LAT in GeV-range and VERITAS in TeV-band {{cite:5cf997c292807604ff4b0c7f04a9ff39806f385a}}. In Model I, the resulting {{formula:42db6a3b-ac5c-4403-a54e-ef7dbce28a5a}} -ray flux consists of both leptonic and hadronic components. The magnetic
profile deeper inside the remnant is determined by advection of frozen-in magnetic field and corresponds to the MHD solution for
negligible magnetic pressure and energy density. As we shall demonstrate, this model fails to explain radio and X-ray intensity profiles.
| r | 1a717d94ecf034be795601f213538ac0 |
In our experiments, we use a different iteration formula based on {{formula:d05b07ff-231d-40cc-96e6-cb1f40652e1a}} -normalized gradients {{cite:f0d7640bf6d7c92dc0d99beeb9cf794f840e743d}},
{{formula:2fbb985a-cd40-40eb-a282-1d1310a6f33f}}
| m | 4b2d93756dbab6998a2af6499aead55e |
In this section, we present simulation results to verify the performance of our proposed distributed EM algorithm. In our simulations, we use the pairwise gossip scheme {{cite:16895ab7da7ce07579eb3ec6c538207df0b06e86}} in the Gossip Step of the distributed EM algorithm. Specifically, at each iteration, two neighboring nodes {{formula:95dac5b7-6f59-4045-811a-b185ff6dc482}} and {{formula:92bc0ae0-e508-4feb-85dd-777b69f8ba38}} are randomly chosen to compute the weighted averages {{formula:b3b57616-b00d-46c7-8690-1b4ea2be33f2}} and {{formula:093bfe11-b2cd-4b75-a382-17a622a7739f}} . For other nodes {{formula:6aa0d9be-d048-4c13-8e81-c0977a514e2a}} , {{formula:c445c9a1-0a3a-460a-98f5-958fef8b725d}} and {{formula:1a98c5bf-4f22-4699-a046-658c346c5324}} .
| r | 07f2ffd4da2ee30172b5e64783ce88c0 |
Thus, these findings provide the experimental realisation of fractional optical media. The results offer applications to engineering optical pulses and their use in data-transmission schemes. Further, implementing the FSE in the temporal domain makes it natural to include nonlinear materials, which is a promising direction too {{cite:d95d47adee7dc0d03faf56565043401387e23c92}}. Another relevant direction for the extension of the work is introducing an ingredient which may represent an effective potential function {{formula:cae06298-49cd-47fb-ae8b-43b40fab6d1f}} in the corresponding FSE. The potential, which may be complex in the general case, can be introduced using a temporal or frequency modulator {{cite:bc5fe19a55dbaca4494068ac359708b9ce0f672d}}, {{cite:171dd3d1bf3e12c9c4cac86bd29cd4e793d1bde8}}, or with the help of a nonlinear interaction {{cite:bb1516701c8ae1d4b5fe72b10f8841b99d53d7db}}.
| d | 2789ff373139ea0d9df0d1b38b09be8a |
[Ungapped hardness of Set-Cover from {{formula:bd500b83-e293-474c-9e3c-3ed525d8192f}} {{cite:048c2b2461faa935e94517e19adc6e987df696c4}}]
Assuming {{formula:8bef45c8-9699-41bc-91b8-6882d975df7d}} , for all constants {{formula:699a9d3b-a60f-4882-8f8d-2039dbff15d8}} and for all {{formula:1a12cf2a-5ac4-4200-841b-b0a3f6a73daf}} , any {{formula:bd541b79-1b46-4908-a931-da0866fb5a0c}} -Set-Cover instance {{formula:aee7dddb-d5c0-46e7-abb9-20b860f5a7b0}} cannot be solved in time {{formula:51a9bf37-f838-4c28-85ed-d17e75f0f7c0}} .
| r | b914fe98f2b75f4ca542fde90153ef04 |
It is believed that the ringdown waveform is dominated by the QNMs
of the compact object remnant. Thus, the detection of overtones from the ringdown signal allows for precision measurements of the characteristic parameters of compact objects like the mass, charge and angular momentum. Various studies suggest that the ringdown signal is dominated by the mode excitations of photons trapped in unstable circular orbits at the photon sphere, namely the photon sphere (PS) modes {{cite:d814b2065cf5351adbd8a9625bb068a9004a2822}}-{{cite:b03357adea94904e0892826c907422fabfb82134}}. These QNMs are directly related to the existence of the PS, and if the compact object is an asymptotically flat BH no other oscillatory mode is excited. For ECOs, on the other hand, although the PS excitations still exist at the early stage of the ringdown signal, as in the case of BHs, they do not belong to the QNM spectrum {{cite:42b498a269075467400d8bab2fd085909e492d86}}, {{cite:6bde821d0f878eb44298728e7ff1825be6e4d9ed}}.
| i | 73890ed30b2b1449922db56e6135e174 |
Recently, a new graph-based classifier proposed by Papa et al. {{cite:f7469139d78a0d6094a6d92a5f4eec4d20f94980}}, known as Optimum-Path Forest (OPF), attempts to fulfill the literature with a parameterless classifier, which is effective during the learning step and efficiently when performing new predictions. Several works introduced the capacity of OPF and its state-of-the-art performance, being comparable to the well-known Support Vector Machines (SVM) {{cite:6ac09859f42cca68df0c82ba4d76982d3a43eb9e}} in supervised {{cite:a80f0b9519fee58d0cb3bd98ebb6bcdd96297ad6}} and unsupervised learning {{cite:930592d99f92d7d2ef1af77187917a1a1860a581}} tasks. Additionally, it provides tools, such as graph-cutting and K-Nearest Neighbors (KNN) graphs {{cite:68aef9a359bd63080530e728a4b5b41a57de8cc5}}, to reduce the training set size with negligible effects on the accuracy of the classification. Nevertheless, the problem arises because there is only one official implementation based on the C language, making it difficult to be integrated with other well-known machine learning frameworks. Furthermore, there is a Python-based trend in the machine learning community.
| i | 630b5e1dce03230f8327b66d464f5292 |
To deal with the absence of keypoints (joints) due to occlusion, truncation and low-resolution in real-world pose estimation (as shown in Fig. REF ), we construct a multi-expert pose estimation system to predict improved 2D poses. It is fine-tuned with the pseudo ground-truth 2D pose generated by a novel Selective Spatio-Temporal Aggregation (SST-A) which integrates the pose proposals computed from several existing expert pose estimators. In this work, we select LCRNet++ {{cite:3d2ee93ac18d3311aed10ac50467f87a02dbf837}}, OpenPose {{cite:ae0c72681704b821425668cc4527c98210d872c8}} and AlphaPose {{cite:8b91561cd1b758c567f6063be33b741b723488cd}} as the experts. Regarding on our downstream tasks, we leverage the AGCNs {{cite:0c11e2639c5b3d0a18b22fc8e0575d7e3fb1a8c7}} to extract features for an input pose sequence that are used directly for action classification (for trimmed videos) or fed into a temporal model like LSTM {{cite:05e7bcf064f4848d66853ef614b8528740141fc3}}, TCNs {{cite:3f4bba2e653beb16af0b7194296d2a8db491e264}} for temporal action detection (for untrimmed videos). The contributions related to this paper are summarized as follows:
| i | 4e3ae1ec3786aecbc783c84d5b1b3e50 |
Our formulation allows borrowing of information across {{formula:abcf781d-199a-48d8-9af6-45c2a5d308d2}} and {{formula:7aa72c0e-8240-409d-ad7b-e28cb3619af0}} only when the corresponding actions are same, through an indicator function. A traditional nonparametric estimator will borrow information even if the actions are different, leading to higher bias, especially when the actions are nominal. Traditional nonparametric methods also suffer because their non-asymptotic terms become very large, especially in higher dimensional problems, as pointed out in {{cite:65629ecb3772f715e0a87ed3ed87eb2e97d117d9}} and the references therein.
{{figure:87adc890-b345-49f3-a65a-8bec2d544d8e}}{{figure:d64535ba-883b-4cb8-a5bc-5ad2f6c8299a}}{{figure:c5456e2d-bd69-473d-97f7-b6da8ff8b9a2}} | m | 13b14c67884cffb596ecacd1c4b17ca6 |
Similarly, there are several variants of SG-MCMC methods that have not been benchmarked against DGPs. Havasi et al. {{cite:600e882b2b5fbcc5b6aba90b5faeb3486254d609}} only considered the original SGMCMC {{cite:5a61d336c47e9c672f04c6d2f3be9f001c3b5a45}} approach. However, numerous variants of the method have been introduced that improve upon SGMCMC, some of which might result in stable training dynamics.
| d | 08d372f52d87919053909c7ec6365e30 |
Crucially, in the context of random networks of large width, LN's operation at each layer {{formula:3038c464-7fd7-4da6-9a11-23371b24c5cf}} does not compensate this mean shift. This stems from the fact that LN's mean and variance statistics can be approximated by zero and a constant value independent of {{formula:78b1803c-10bc-4fbc-bf27-01c96895d6d0}} , respectively. This means that LN's operation can be approximated by a layer-wise constant scaling independent of {{formula:c041cd54-cdae-4aea-9bce-c8af72bcd6b2}} .In this view, we would expect layer-normalized networks to be equally subject to a phenomenon of increasingly imbalanced channels with depth. This phenomenon would be driven not only by the succession of affine transformations and activation functions, but also by the succession of convolutions {{cite:a773db77c2ef4692c795684015f54b2fd8c1ecd0}}, {{cite:c705de64eddec6a190f3cbd760438b535207dd53}}, {{cite:395955ce5aa6735088b49ec788bb24139a29cba5}}.
| d | 0477f47677c38fb1d9f4cab8dcbbff56 |
Fig. REF and REF show that our GVS fills pathological regions with diverse healthy-looking tissues, which implies the reduction of the mode collapse. The research {{cite:68013a347e11d56b90753a9f545530636fcb52ec}}, {{cite:e1490900d555759465f8a811b49d9e9f12b491ee}} demonstrated that the higher dimension will exacerbate the mode collapse and meanwhile need more training samples. In the GANs, one image is a sample, and its distribution is high-dimensional so that generating such distribution is easy to fall into collapse. Our GVS treats one pixel as a sample. The dimension of its distribution is significantly reduced. Thus, the mode collapse will be effectively alleviated.
| d | f9f00f2824ee5c2924a98d85a01e2ac2 |
For the MIMIC dataset, we can see the models' performances in terms of both AUROC and AUPRC in Table REF .
In addition to the models we previously described, we also compare against the interpretable medical baselines of SOFA and SAPS II which are simple logic-based scoring methods {{cite:af0e4387d6e416682f5ef8f0464aac12311d6c4e}}, {{cite:3c3fea7f33f524decfe2860f2aec651159c4d5c4}}.
We see that the machine learning methods improve over the baseline performance achieved by the SAPS and SOFA methods.
| r | 557955de096f66aa8624d5b209817877 |
The above assumption measures the population diversity (heterogeneity) between the gradients. In heterogeneous settings, this bound indicates the similarity between different distributions. {{cite:25ef518355e5f9a9c538d43132acdd5742a95743}} show connections between heterogeneity and the Wasserstein distance between the distributions under certain assumptions.
| r | 3bd2037a236b4e15991f11cce51d0dc6 |
The small effect of the training dataset sex composition observed in our study is in line with previous research showing sex-related differences in MRI recordings to be limited and gradual {{cite:23b16ddf268619a2f2890ed6e29435524a03eec7}}, as opposed to the apparent sex differences in chest x-ray recordings.
Nevertheless, it is an important result that – despite known sex differences in AD {{cite:377fcc5887de29472ca2b5ef5de035109e380dcf}} – the training dataset composition does not appear to have a strong effect on male and female test subject performance, indicating that the employed feature representations are – to some degree, at least – invariant to this dataset shift {{cite:8efe7acc3a163a94fb8cdffb2d51098423b915fb}}.
| d | 624b26d455e90c736263dd29ba0e0640 |
The combination of all three techniques is applied in our experiments with 27 languages involved with the Transformer based model {{cite:7602ebada3f061d0ef437fcddf71c5b980c1259c}}, {{cite:d8e70d1f61c6a0f11ce06c87371a055f1ab416aa}}. In the process of learning these languages in different iterations, we were able to minimize the effect of catastrophic forgetting for previously learned languages, while the performance of the new languages are still comparable or potentially competitive with training all languages from scratch. Our contribution in continual learning, to the best of our knowledge, the first application in learning to transcribe languages.
| i | 89960a4175488e1854125589b35a1a88 |
Despite the pixel-level bit implementation is obvious by looking at the bitrate distribution result, the reconstructed image is less obvious. It might have something to do with the autoregressive context of {{cite:23680a8499171bc652fdfc6b1a049637e52a6a39}}. The autoregressive context of {{cite:23680a8499171bc652fdfc6b1a049637e52a6a39}} is a mini-size bit allocation with-in I frame. And this internal bit allocation might intervene our bit implementation.
| d | 05fc58289de18ceee9582803711bd21b |
Despite the wide applications of DCNNs in modern learning tasks, theoretical understanding of their generalization ability has been challenging.
Promising progress has been made recently.
An estimate of approximation error of DCNNs is given in {{cite:65753742c6c07634d67f4b8c0ca2dc375ebac7d2}}.
It shows that the approximation error decreases as the network depth increases.
This result is an important tool we use to prove Theorem REF .
In {{cite:2fed1c867242e446e98fe41ac1505b01bb933584}}, it is shown that implementing ERM on DCNNs yields universally consistent estimators, without any restrictions on free parameters.
However, explicit rate of convergence is not provided there. More recently, for learning an additive ridge function by DCNNs followed by one fully connected layer, a rate of order {{formula:f101a6ed-b8c9-48f4-8d18-2bdf73205e0f}} is obtained in {{cite:9df09ecd3313984b962579384ed8c32952dedd31}}. This learning rate is considered to be minimax optimal up to a log factor.
It is derived using an covering number estimate, which requires the filters and biases to be bounded, with bounds depending on the target functions space, filter size and sample size.
Some neural networks with similar structures are studied, for example, periodized CNNs in {{cite:6aa4558ba1db97ef98850910908bac9fbf94c612}}, ResNet-type CNNs in {{cite:ea06219eb55d27349662473e01330642676d1f3c}}, and fully-connected networks inducing sparsity in {{cite:44a58cede10a2f917acf95d4fa12dcdd92b9a355}}.
| d | c6af83c47460085e1c9d8438519c81ed |
To prove Theorem REF , we note that any finite set of time-frequency operators parametrized by a collection of finite points on an integer lattice in {{formula:4e8749fa-81ad-481b-9d23-5dfbdc08ca3a}} , forms a collection of pairwise commuting operators. As such, the Spectral Theorem {{cite:438f78d1493a649180f42b38be8f28805d5be6db}} guarantees the existence of a unitary operator which diagonalizes the operator
{{formula:79b46c0c-afad-49cd-9071-8deac6ac0e11}}
| d | 9d8c582f4b0c3d34e7db175d8348636e |
In this section, we experimentally prove that ADC is more suitable to human pose estimation than deformable convolution (DC) {{cite:b196533919fdfcd73e764151974dd580debd9ca6}} and scale-adaptive convolution (SAC) {{cite:0d193dd138230a5df8cb17a139b50d19c5886865}}. Comparative experiments are performed on SimpleBaseline-Res50. As shown in Table REF , although DC can bring an improvement on the baseline, its performance is inferior to that of ADC. As we have discussed in Sec REF , the unconstrained and independent offsets of DC may cause the input and output feature maps to lose their spatial correspondence, which potentially hurt the accuracy of location. SAC can alleviate the size inconsistent along spatial dimensions, but involves little multi-scale fusion along the channel dimension, which is more important in HPE. Consequently, the improvement of SAC is lower than both DC and ADC.
{{table:7dd2fa1b-ef9c-4503-88cd-62bd6d55abdc}} | m | fdea12781231481e86cb0d6e17facd9f |
Open-domain dialogue response generation (RG) models aim to provide human-like natural language responses given dialogue histories {{cite:9d7f1dc5a258d40975b5003db0999b3ef1d4fddc}}.
To improve generated response quality, many studies have been conducted to develop knowledge-grounded RG {{cite:2edfaacebc964a47f6f68c69d044b61fe5dd918f}}, {{cite:37360a6849c4f13330c3af32621eb3b4e422bce8}}, personalized dialogue agents {{cite:ecd5f787aa04a6bfcb0f5f7c8cea7eb25085cc03}}, empathetic response {{cite:51a91717c31a513dd87ee622fe6b2cab25fba0f5}}, etc.
For all the above-mentioned directions for RG, large-scale dialogue data geared towards the specific goals is crucial, since most current state-of-the-art neural RG models require training on appropriate and large data.
Therefore several datasets have been collected to support such research efforts such as knowledge-grounded dialogues {{cite:2edfaacebc964a47f6f68c69d044b61fe5dd918f}}, {{cite:37360a6849c4f13330c3af32621eb3b4e422bce8}}, PersonaChat {{cite:ecd5f787aa04a6bfcb0f5f7c8cea7eb25085cc03}}, and EmpatheticDialogues {{cite:51a91717c31a513dd87ee622fe6b2cab25fba0f5}}.
Producing natural and logically-coherent responses given dialogue contexts involves making commonsense inferences during the communication. For example, if someone says “I'm going to perform in front of a thousand people tomorrow...” the listener is likely to conclude that the speaker is probably feeling nervous and respond by comforting them: “Relax, you'll do great!”
In contrast to other efforts to make RG models more empathetic or knowledgeable, there is a lack of commonsense focused dialogue data for both training neural models and evaluation. An ideal dataset for studying commonsense in RG needs to simulate how humans have multi-turn conversations as much as possible. Existing commonsense-focused work in RG uses extracted post-response pairs from Reddit {{cite:e2c6a5aa8c905f3240d4ec6f94548ff9ff575fcf}}, which are single-turn and rough approximations for real-life conversations.
| i | 90cf3c641708c65391f8170824fb468e |
Decision trees {{cite:b375f0a2c4ae02e94ef66140ba9e5e281ec36ae5}} (DTs) are generally considered to be an intrinsically interpretable model family {{cite:69d3d2f73b58c3cfe762113fbf5a429da0a83df0}}: sufficiently small trees can be contemplated by a person at once (simulatability), have subparts that can be intuitively explained (decomposability), and are verifiable (algorithmic transparency) {{cite:269f2f0ddee9876cb8284419e2423c30d39cafcf}}.
In the RL setting, DT-like models have been successfully used to represent transition models {{cite:e11c6649d34de9558e7f47364b675342c1edd121}}, reward functions {{cite:b12e83b279a2691d7fdfaced45b643508f92fb3d}}, value functions {{cite:3705abb916f7b0e6e8d2247d95942ed68e3d1ed7}}, {{cite:fb433941e97918d7f42340bc3f06f91233b25acf}}, and policies {{cite:374148a41e9c54ed7b93c80f231379cbae1d9dfe}}.
Although learning DT policies for interpretability has been investigated in the single-agent RL setting {{cite:374148a41e9c54ed7b93c80f231379cbae1d9dfe}}, {{cite:64868ef91d616f674639463ab618be2ea3eca9e5}}, {{cite:0f6db5e67629520211da0e8250c015b3f582a557}}, it has not been explored in the multi-agent setting.
| i | 20902d2f127ef211e589a059270a922a |
Scalar fields are ubiquitous in modern particle physics and gravity models, including inflation theories and dark energy scenarios {{cite:dd8199f453f3929991fcde774105c2c8b422a998}}, {{cite:4474c32bb16e5d3a79987d92643845d4428a5618}}, {{cite:ca8ab4cc94deff8a70ce3b8502c5b0510e269344}}, {{cite:6fc67eebb73c50963db33d8f8f519cf0a65f0e62}}, {{cite:eaca2bcc57c196f36dbbb9b116d8f3e1858c20a3}}, {{cite:d43224aa689ca9d0ca7ae2d0474a44194d2d61d4}}, {{cite:60ccf3145cab4209f32a2f15252dd110fde949b9}}, {{cite:f97817fd2d5d5db69bcfd9c1da64c80381721f3b}}. In many cases {{cite:6927bcadd883aba1d3b3e3529fb1fe76de1bf357}}, {{cite:17a48b9d69e64c6114246d4382163d2efcefc2aa}}, {{cite:e9b591ee4a1bf5698e7b34cf3ef756d39a026ed4}}, {{cite:02fb844bb0e1bed093e5c2e8c8255dc3e776c2ce}}, {{cite:088f81d0c7482abb93d9832573e81097e6021be6}}, {{cite:3453e77af81261ddea78492b0b0a963be7d4bd3b}}, {{cite:763d1fe15a01bb8196f2af0abeb1cc53c723e1bc}}, {{cite:cae2811ac3ed414f3c43c16bc6bb16ce58fedcf6}}, {{cite:26cfca656bf36bd91a4a2a2838a15f52319b51b0}}, {{cite:e9e620420a295cb2965aa2a5921dbd3e227a6961}}, {{cite:7f080ad643b4062ceace8b3b4e757ee78b8cdb56}}, {{cite:2adbcd3059719e7fc4d197a16de77ba3024e110f}}, {{cite:a1cfc87fd2a0a609996e3d8a612564ff6e5ab966}}, {{cite:ef50734cd2be8f3e7ccda0289a7bc76d5afe8fe7}}, {{cite:035805e8dec381eca54936a0ee9811fa9e034d13}}, the scalar fields are non-minimally coupled to gravity through a term {{formula:fe5a4a00-aaf6-4663-9cdc-f8359ff3acbf}} where {{formula:5701b25c-59a3-4ad3-ac4e-3dd854229ad3}} is some function of scalar fields {{formula:dd71520c-7aa1-4390-b2e9-18900639f78b}} and {{formula:13705513-734d-44af-bb63-0a808031958f}} is the Ricci scalar curvature. For example, the function {{formula:bd0358cf-b36e-4b83-9e8d-96dd1914ce08}} is proportional to {{formula:72d07324-cb7d-426c-a9b0-fdacef8f8c58}} in Jordan-Brans-Dicke theory {{cite:3afeb38f532ff36fbb56e5ede86d19d74b08aa81}}, {{cite:443ed6b2945cb25c04e94b071e432e262f35e780}} and Higgs inflation model {{cite:38ee105fcd29acce7d4309f86501e765ec0688b3}}. In modified gravity theories where only functions of {{formula:9f49d27e-5f9e-4428-94d9-580996eddd8b}} are introduced {{cite:fa8eb8f01224d0e6ac2cba62679fd232288d70d3}}, it is equivalent to treat as introducing a scalar field, for instance, {{formula:a76cd1ef-27a3-4b48-a9de-fb57ad660b39}} in the Starobinsky model {{cite:8d9665a7a7d42ffd0b21fd0620008b0b6ec12037}}.
| i | bac9c249ab544e50d156b166ca6e6e0f |
Driven by the rapid development of computation hardwares, the scale of deep neural networks (DNNs) is unstoppably increasing, where the amount of parameters has significantly exceeded the sample size by even thousands of times {{cite:c702464e9ce852b60e996fccad411e64f0da2652}}, {{cite:c4b4bea017f551331796d7a32482535226293fa4}}, {{cite:59a71e126136ec961c61f9b372a2c4b4c6f81231}}. These heavily overparameterized DNNs would stay in huge hypothesis weight spaces. On the one hand, this provides the power to fit very complex or even arbitrary functions {{cite:575276e895105c5f17f948702f8ced7cdfc142cc}}, on the other hand, it is challenging to seek optimal minima while resisting overfitting during training {{cite:4e602f6be070cacd3a73c07a050e015fec1d34fb}}. In general, minimizing only the empirical training loss yielded by the difference between true labels and predicted labels (such as the categorical cross-entropy loss) could not provide sufficient guarantee on acquiring minima with satisfactory generalization ability. Regularization techniques are in higher demand than ever for guiding the optimizers towards finding minima with better generalization ability.
| i | decb0b88d22240b8d626c4d302930f1c |
See {{cite:7323949ea7f62ddba20b6cc93c82658c5111a52a}} for more details.
| r | cd26dbf9fe36f99d134662ccdc87ecf4 |
We will also use the following lemma from {{cite:b974da5c99445c46b25c260c9063d32162edb6c6}}.
| r | 1743304c74db1f2f5bfd9175399e0d98 |
To establish that {{formula:a8ab5127-81ed-4765-b50e-c5596dde896d}} is GC, we will follow the methodologies developed in Section {{formula:fec0ca55-2162-4fb1-a751-8265f011f0ae}} of van der Vaart and Wellner {{formula:12a79375-9843-4181-b56a-dd5e992c3441}} {{cite:34b5fccb4fea991606dd7f65223f2eea3c37dd0c}} and Kosorok {{formula:9da397c0-9365-4df2-b8fc-fa39d36c9b2f}} {{cite:70841de4daf742f8fad9748031761514100f438b}}.
Let us observe the following facts under the assumption {{formula:eadc48bb-e10a-47b1-b360-a95ec3653066}} .
| r | f3953a261f29d7821f95c6b17d9f3719 |
Denote {{formula:3daa116b-6ef7-42e1-9f34-13f9bf692f33}} as the set including all the accumulation points of sequence {{formula:7a7c193a-7b14-4938-a1c5-1afa01921009}} . It follows from {{cite:aeb647202fb2c38b60c90a12d07dbd516cf5967d}} that
{{formula:a4db30bc-b03c-44dc-af65-83796ea9ec42}}
| m | 237d5143042e493294c18e1094821bba |
The characterization of {{formula:9c22164b-718f-45b4-9505-85f8b98660f6}} is distinct from the characterization using instrumental variables-type moment conditions in {{cite:09713f46bfdc8da67226658474d840992accd7ad}} and implicit in {{cite:6b4fe93f38301856fdc124d648b62a5b0f79b799}}. As we discuss below, when our assumptions hold and {{formula:b4961c29-d405-4fb3-a6cf-e50c6e793c80}} , our characterization provides additional restrictions that help identify {{formula:23791f97-8260-4c53-9fc2-2a616b284760}} .
| d | ff0f76f59a2048990358a54316368c98 |
Many calibration approaches disregard the role of refinement, leading to severe loss in the utility of DNNs thus trained. We successfully presented the case of declining refinement for a wide variety of approaches tested on many different datasets. The derived relationship in equation REF showed how improving refinement can help better calibrate the model. This provides justification for calibration observed for refinement approach of {{cite:19ccde3a27d7aa5d1e32c76ed2ea083ced2dc19b}}. In the appendix (REF ), we show that calibration is induced by the refinement technique proposed by {{cite:108f77aeb040ac7d77a67cbd193d10c6236b6643}}.
| d | b5b5160d7eab06f7b9087453d503e4e0 |
This phenomenon of regularization by noise is now well-studied in several situations. A lot of work has been devoted to the additive case {{formula:0b0748ba-b171-498c-bfd3-98a0cbb9ef82}} and for several kind of processes. One can think of the seminal work of {{cite:240930552a5f6a1fe7cacf1b23c82748bcd2aa9a}}, {{cite:2759c4f8dc023075ee309457c5599860289fd545}} for strong solutions of this equation when {{formula:ec0c765d-a17e-4304-aa81-7a2a4f16c39c}} is a Brownian motion. In this additive case and when {{formula:841c58b1-de1c-47ec-a7d2-94e60d116a8c}} is a Brownian motion, Davie {{cite:ac5c8624d1d75d9c87c693af04de799332cd3206}} exhibit a new and stronger notion of uniqueness and proved that the previous equation has a strong solution and enjoys "path-by-path" uniqueness whenever {{formula:642d75c2-c21e-4ddc-ae2a-636f9678c8ff}} , whereas standard theory and counterexample require {{formula:2edc0a40-524f-4cd9-b47d-50080a002cb0}} to be Lipschitz continuous. One can consult {{cite:95aa4eba80ec17cb048a6bd2de7a926be6c7a723}} for a deep discussion about notions of solutions in the additive case.
| i | 0d1a83978a2c58d9762c5dee31e61d29 |
Quantitative comparison results. We compare our method with three existing semi-supervised learning (SSL) methods: {{formula:d30b3762-e640-497e-bfd3-52cdd704b3eb}} -model {{cite:8871c8e6b7e9ef90f3f44f62bc1ecba67bc45603}}, temporal ensembling {{cite:8871c8e6b7e9ef90f3f44f62bc1ecba67bc45603}}, and mean teacher {{cite:50f39b130591e0b7eb7f7cad04a088eb1a3b1866}}. Regression MSE loss between predicted and GT BMDs is used on labeled images for all semi-supervised learning methods. {{formula:4a5dc768-5a90-4c87-be99-275465ca9a3b}} -model is trained to encourage consistent network output between two augmentations of the same input image.
Temporal ensembling produces pseudo labels via calculating the exponential moving average of predictions after every training epoch. Pseudo labels are then combined with labeled images to train the model. Instead of directly ensembling predictions, mean teacher uses an exponential moving average of model weights to produce pseudo labels for unlabeled images. For the proposed method and compared SSL methods, all models are fine-tuned from the weights pre-trained on labeled images.
{{table:fd2e5bd9-a6d7-423a-9933-a19289a6c91b}} | r | 9103a8f70f5376ae3be0a6891d011a86 |
Table REF demonstrates the results of wrong operator localization and repair. We report two accuracy metrics: localization accuracy and joint accuracy of localization and repair. We can find that compared with graph-structured baselines, Tree-Transformer achieves a significantly better performance, especially on the joint loc&rep accuracy. Our model gains an improvement of 7% on joint accuracy compared with the best-performing baseline GIN. This indicates that our bi-directional propagation enables the model to learn effective node representations for node-level prediction tasks.
The Transformer-based model {{cite:e0e1fa7b38ff26993955d32c798732e36c2ec6fd}} performs poorly on this task, its accuracies lower than all GNN baselines. This suggests that changing the original tree structures by converting arbitrary trees to N-ary trees is harmful for node-level prediction. In the wrong operator dataset, the branching factor of 10% syntax trees is larger than 15, so the structures of these trees are changed for this baseline.
{{table:b557e14e-0865-4350-aa79-60db77d9638c}} | r | f9e6d085d609b9ea66dcf69935920584 |
Furthermore , we can also exclude models of distant dusty absorbers that diminish the
UV by extinction and simultaneously diminish the X-rays by absorption.
However, dust-free absorption, arising in the accretion-disk region for instance
in the form of a clumpy wind, is an efficient mechanism to cause X-ray spectral and flux
changes while leaving the broad-band UV unaffected. And our spectral fits of a
partial covering absorber consistently imply a decrease in covering factor
and column density as the source brightens in X-rays. Our fit parameters of
the ionization parameter, column density, and covering factor are consistent with predictions from models of clumpy disk winds {{cite:271ab3648ac76f2ce88888210b8fe4a73e4ee87e}}
that form via the Rayleigh-Taylor and radiation-hydrodynamic instability {{cite:1ec7de5ce5253956887afc629e43b90f8630eaaa}} and
which predict variability timescales on the order of weeks.
| d | e12322d0befc86910b6da4d3bebd27d6 |
Remark. Note that, in the formulation of constructing rank dataset, the selected perceptual metric is not constrained to a single one but can be any combination of multiple metrics. For example, perceptual index (PI) {{cite:677636954e7a563dbc3d27f15b702505432d22d3}} is a combination of NIQE {{cite:b8042971e79e6b4d59d486d08ed5130f3e5f5566}} and Ma {{cite:627984b3efa988935e4e5f7e1b29a06e0d93178b}}, which is formulated as {{formula:65608653-2039-4715-adf1-b2bfdec0aa40}} . In Sec. REF , experiments on PI and other metric combinations are conducted, showing that the proposed framework is capable of handling with combinations of different metrics.
| r | d728d1de4214d8750f3556f488458a68 |
The basic strategy of the proof of Theorem REF is to apply the fundamental ideas in {{cite:f6a358f84a46316b5c1929d38118f466ccbd2691}} to the case of group extensions, by using localization algebras, twisted Roe algebras, and a geometric version of
infinite dimensional Bott periodicity. We use the coarse embedding of the quotients {{formula:cb55fb16-95c6-434e-83a2-e2ca211f7144}} into a Hilbert space to
furnish the twisted Roe algebra of {{formula:7177bb8b-e57c-45f8-b3f6-ab7e3f085f96}} and its localization algebra with twisted coefficients, and then
apply cutting-and-pasting techniques to decompose these twisted algebras, so as to reduce the coarse Baum-Connes conjecture for
{{formula:e13613fd-21e1-41b1-9d07-5ab58039d023}} to the coarse Baum-Connes conjecture for {{formula:96817fd8-0247-4ae3-b054-ca7572cefee0}} .
At this point, it is natural to expect to complete the proof merely under the assumption that {{formula:2ad0c573-32c1-44e4-b5c6-d663a486c5f4}} coarsely embeds into
a Hilbert space.
However, there is a subtle issue about different completions of ideals inside the maximal twisted Roe algebras, for which we can not settle under this
assumption. Fortunately, this technical difficulty disappears under the assumption that the sequence
{{formula:1bb80cf2-1809-4aa9-9ba8-79d24f3ade0f}} has Property A.
| i | 0b82df143991c73520f59ee406585240 |
Therefore, one should evaluate the kernel centered in each training sample. If one relates the proposed LDU model to kernel ridge regression, the main distinction is that we do not evaluate it across the entire training set, but across a smaller set composed of the prototypes. Hence
{{formula:b1e202b1-1c59-4eaa-a2db-d5898988bf49}} with {{formula:9199e4aa-961c-4947-b658-6ee4e093b954}} , which is a composition of kernel positive definite functions.
In contrast with DUQ {{cite:68daccf20013e370fce312940e589647ac556108}} and similarly to SNGP {{cite:50f32e658cd52d39e12310cdb8aeffa95dd331bb}}
, we approximate the kernel ridge regression based on the prototype set which allows us to simplify the training.
However for SNGP, the authors choose to approximate the kernel differently, by relying on the random projection trick {{cite:22afe8713791ceed18d8dc370f572ddf43faae3e}}.
| m | 954f8623028d7877fb2bc07fbb74c4a3 |
To calculate the {{formula:44db7ee7-dc7b-44d5-8f9f-54e5997cc67e}} for stratified models such as this, one must calculate the so called next generation matrix {{cite:f462293921d7a0ea46c111f2170ec3e66ae8c906}} which has elements given by
{{formula:e7b46ac6-3ec9-4993-96d4-72d9fa1d8778}}
| r | 478c52742796a7c1f1b5a75496abddbf |
Neural machine translation {{cite:dbe3f57cf4660a72cbdc12e363c75f25f263d12e}}, {{cite:979e28ad02944eb2c0b36a5b0d625c425efefe19}} has established itself as the new state of the art at recent shared translation tasks {{cite:4ce954a9ad7f78d6ecfe0ea6bd66d721bd646d02}}, {{cite:eb258ec21899e7e09659970c9705a6cd8d81eda9}}.
In order to achieve good generalization accuracy, neural machine translation, like most other large machine learning systems, requires large amounts of training examples sampled from a distribution as close as possible to the distribution of the inputs seen during execution.
However, in many applications, only a small amount of parallel text is available for the specific application domain, and it is therefore desirable to leverage larger out-domain datasets.
| i | 4ee877cc0d458c3f7fccf73e15da98fa |
We have evaluated on both commonly used distance metrics: Euclidean ({{formula:5b1728c1-b141-46cc-b829-b40961da47aa}} ) and {{formula:ed359f10-349c-442b-ad9e-c0efe3eb13d1}} {{cite:bdef15fa31e448a75c3f9ef46169a1b9c6584aa2}}. Given the subtle differences or the continuous nature of disease progression {{formula:087478f2-c4dd-48f3-9b60-26032e709fde}} metric is more effective to our purpose (see Sec. ). The parameters are estimated via stochastic gradient descent (SGD) to minimise average negative log likelihood (see Eq. (REF )) of target label {{formula:663a4293-ae36-4632-9994-58aabe559c76}} for the query example ({{formula:69767bc2-ba3e-4a87-871a-04d48c0aa7cb}} ).
{{figure:2a5b99f4-6b63-4b9e-8fd4-0efb97e9176e}} | m | 9fb743a21dbd2fcee063c6fb1e3cadac |
Finally, Figure REF shows test accuracy achieved by our method as compared to the PGD approach (for {{formula:494e6322-a456-46ce-9ff9-219fe5a7b49e}} robustness) and adversarial smoothing (for {{formula:26028de9-0c19-4519-92e4-63faf8b56d99}} robustness) at various intervals (wall clock time) during the training process. In each case our method achieves significantly higher test accuracies. We acknowledge that recent and concurrent works have investigated fast algorithms for adversarial training {{cite:0e559049e5213e3bbd205f844199ac642c2ecb6a}}, {{cite:af9eb89736675efbebf0f266d5fe34f7685c8472}}. Our boosting based framework complements these approaches and in principle these methods can be used as base predictors in our general framework. We consider this as a direction for future work.
| r | 97c9d1247ac7bd4ca6307fc0f0e77aa9 |
Let {{formula:68004931-dd77-41ed-ae9c-d1da6592ec65}} with {{formula:f5a2200d-46d9-42c8-bce1-574ea90a8cf7}} . To prove that all points in {{formula:34d74ee6-515f-4c78-b7dd-43697f25dcf7}} have multiplicity one, consider the Jacobian matrix
{{formula:241929d0-0d1f-4e78-85bb-de83305d3ca2}}
The point {{formula:e10341a1-ce48-4ff3-b50d-ef4d133b480e}} has multiplicity one as a point of {{formula:53913d53-d337-4fab-b11b-9da9dd3c6d4f}} if and only if, when evaluated at {{formula:8e78f5d5-e3dd-4b40-b675-1c3440fc7a4e}} , {{formula:f2aa1579-d561-479e-8b49-1a3dfba33277}} has rank {{formula:4d6c62cf-cdd9-4c91-ba18-a66a11329ea2}} . Note that for {{formula:718f672b-e953-4c34-899a-6d36a8e1b3f4}} , {{formula:02a0ac40-1262-4bd9-a544-35c40eceb7ca}} ,
{{formula:95388da5-839c-4b66-89bd-c5e3224f04ab}}
Setting {{formula:6409e396-3ffb-4424-9c6e-3b3814a6b343}} we obtain the map
{{formula:436d6cb1-5578-4516-a98a-fadb8923b68f}}
where {{formula:e69e810b-e952-49d7-b543-fba9d73167a7}} sends {{formula:84db1988-03cf-49c0-8206-49d4cc046585}} , and analogously {{formula:ed337a04-4bae-44b6-9808-839a3c1a656b}} . We need to show that {{formula:c1c7a126-ecd5-474d-acd7-0c92190a16c4}} has rank {{formula:63d0c249-a556-4969-9109-e719a3dcc738}} .
Since
{{formula:2f3dc2c9-b701-4a5e-b259-d3e7f2ef3ece}}
it suffices to show that {{formula:c6b8a328-35de-4b16-9691-e7fbce057bbf}} has rank {{formula:c62252d7-f660-461f-82d5-c8fc641d4d85}} , {{formula:6fef2484-8ca5-4a7c-9b8c-9fd77a286ba2}} has rank {{formula:9edd122b-dd69-42d4-b0f9-997c96d2894c}} and {{formula:23d4d476-9f2a-4e0e-a0ac-fc2d2a82629d}} .
To see that {{formula:ed56a47d-1ffc-4c72-9d36-50893f9aff55}} , note that {{formula:9c1103d5-f16f-4d4b-a7b0-ed934afe1200}} if and only if {{formula:98c6533a-bfb2-4e11-a2d7-06eb7ba709eb}} . It is clear that {{formula:4c6fb88f-f6b1-4d81-8dbc-9047ac2df8ef}} . Suppose {{formula:9d5f8d97-0ea3-4f9c-8486-20a591f936b1}} for some {{formula:4a5d4b06-6637-4d01-96b8-15da790bbf3c}} . Then
{{formula:0f3877f4-f2e8-497b-8f64-6d56471cb697}}
But by bilinearity of the tensor product this would imply that {{formula:f23130e3-6227-4757-ba97-285275740fbd}} for all {{formula:574cdc83-96d8-41d6-a0a8-350d98a28dac}} j = 1, ,..., s{{formula:357a9ba1-2d94-436a-95df-097418b2ebde}} VX(I){{formula:cc62a8d2-506c-4e8f-a767-00d1dff6d378}} A1 = spani){{formula:edc42d5a-4916-45b3-bb1a-3a34e1684e3b}} rank(A1) = m{{formula:74732d40-fd8e-4f55-9796-c5e089728aa3}} rank(A2) = n{{formula:1a3bc5c2-ce9a-4433-9d8f-c933516633ff}} The next step is to show that {{formula:f9cade9d-19c4-4ba9-899d-2067937181dd}} .This can only make sense if {{formula:4785aa6f-e30e-46bc-87de-1600813d58e4}} . Note that, having established that {{formula:2a5507fb-344d-41e3-a843-0c167dafce4e}} consists of finitely many points, we indeed have this inequality. If {{formula:542d6a3d-01e1-4a45-8851-54483320a577}} , we need to show that {{formula:e18d83c8-4578-42d2-b0f8-bdb39e30a8fe}} and {{formula:3e53852a-5c60-4966-af55-a9bb85771f8e}} . We have
{{formula:acb25409-b74d-4c60-a406-5359534a5e3b}}
As an immediate consequence, there are unique coefficients {{formula:4edd468b-8c82-4d1c-9048-417ead695d1a}} a1 = = ar = 0{{formula:fb06af39-60e1-4f34-b607-7807ac35f09e}} v spani) = A1{{formula:393942fb-b802-4e51-b1f9-ae8041f05ebb}} w spani) = A2{{formula:fbf36311-b296-4934-8a18-8460e8136123}} ai{{formula:216109ec-07ca-43a0-a4c7-40e8318ed4b0}} v{{formula:80e7fa9a-e668-4330-9af2-1c5d8f42e8dd}} w{{formula:899ab619-0c37-4244-97ff-a33cee2ce19e}} |a1| + + |ar| = 1{{formula:23e79c8c-e058-41e3-95e1-8d2bd2816d2e}} fj{{formula:615ad758-80f4-45d1-b747-4d1276058dd3}} ai = 1{{formula:87cc78a4-2a18-4151-b197-d4d33cf03ec7}} ak = 0{{formula:b556706f-1dec-47d1-8401-41306974884d}} k i{{formula:3fc64513-9eb1-4f4d-a25a-d2d98094af15}} v spani) = A1{{formula:3d5269bc-c162-4fc5-a534-bd6a52d2e68d}} w spani) = A2{{formula:e5eb892e-06ad-4eb8-8e09-e45c1d92f7d5}} ai 1{{formula:42468d36-2099-467d-bce5-3a93c399e177}}{{formula:1de7c4b4-a14a-47fd-97de-466b45982d16}}{{formula:56a5ef2e-c2ce-4c83-a5e0-d5fd13eed224}} (ai i + (ai - 1)w) A2 = spani){{formula:65c0a770-3a73-4111-a0cc-3a0847213182}} w spani) = A2{{formula:a6183cba-cc2d-45ed-a90e-cc87a2e899b0}} v A1{{formula:1008f316-6686-425b-8d02-32c818af9f6b}} A1(v) = A2(w){{formula:1f7d6edc-411c-499b-aef3-7d7d8ae82158}} v A1{{formula:916733c1-d2bd-4659-a32f-fe4720c8f72c}} w A2{{formula:5cddc57c-f19f-49b4-8a78-3cabb273f67f}} imA1 imA2 = {0}{{formula:1ddfff08-4080-47ab-bc51-2ac23342e0a6}}
For two ideals {{formula:c8b58bc7-d52f-4ccb-b1ed-62cde830347d}} , we write
{{formula:7c921273-1516-4156-8325-932491e5d91c}} The next result follows from lem:zerodim.
Corollary 1.1
Under assum:vanishingideal, we have the identity {{formula:931861c5-c052-4a98-87b3-0743be7a93d4}} , where {{formula:efb6918d-1742-45aa-88cc-6773bb3461e5}} , {{formula:d09c384d-f9a8-427f-a469-78e011cb586e}} is the vanishing ideal
{{formula:74e103f2-b017-48b2-ad58-8d187d0b52bf}}
and {{formula:367cbc54-9d44-40ef-a6fb-3b2130ebf533}} is the irrelevant ideal of {{formula:421c60c9-3fbb-4a3e-88d2-56023badac4b}} .
By Lemma REF , the modules {{formula:3d288fd6-8d7c-4890-8e45-2048f0d0596c}} and {{formula:74e0b965-9597-41e0-9181-c0b4cfe548a5}} define the same subscheme of {{formula:0f5c40a4-8e80-4e6c-878b-8be698f4539f}} consisting of {{formula:a7802b62-65ad-4a8a-b4fc-8ff9dbd59d28}} simple points. It follows that {{formula:39e2cee4-f099-4729-aa56-568d96134219}} for large enough {{formula:092b35c0-a7b1-4406-9299-bb13e437645a}} . See for instance {{cite:5cf2ed9e4627d8cc400db05758c11936e48c3ae8}}.
This follows from the fact that all {{formula:88ec7fdf-22de-42b7-b556-6256d047f945}} satisfying {{formula:fb22ccb1-8f22-4a48-baf2-9e61d4d5b22b}} lie on a hyperplane {{formula:8d919cae-d878-4825-b98c-63ceaea629d7}} through the origin in the {{formula:67cefd6f-a1da-4222-b3df-85cfa3857936}} S(d',e'){{formula:3ddfd61e-d5dc-4d42-8975-41d5cb1887ae}} h0{{formula:746d2ce6-0d31-4bcc-8a62-ae08d66f6507}} H1 Hr{{formula:b8ee0386-f1ec-456c-8936-e8f7dc299ed4}} h0(i) 0, i = 1, ..., r{{formula:74d0bb8c-c4ea-4444-a6ea-1c0642ea26ef}}
Let {{formula:f5c205d3-a1d7-460d-8071-318e6d975750}} be the saturation of {{formula:75972576-7131-4a58-b96d-4b897abfcb22}} with respect to the irrelevant ideal {{formula:7f7fd2cb-dc79-460c-b71b-81f6b8afb8b7}} (see cor:satisvan). First, it follows from {{cite:401f1cd218670ee7bed8664fedad5a348ce81055}} that there exists {{formula:0dc2a448-a1c8-417d-a346-eb56bbb911f2}} such that {{formula:d4f6c729-3c98-452b-a460-bd57b24a7ec8}} for all {{formula:a9d28f23-31df-413c-af1e-76c1d8aa64a4}} . Secondly, we show that there exists {{formula:d8ac5f4c-eae7-48af-8975-f38c47bb0846}} such that {{formula:55c7c8c4-eb35-401b-9170-4aff78049243}} for all {{formula:769a0d6c-b079-4321-8f3b-6b49b65293a8}} . To see this, note that {{formula:772cc673-b99f-4603-b593-0a51cbc3c249}} for some {{formula:ebd39dc4-a012-4a8d-ac58-9a38deba202b}} (see e.g. {{cite:4d7b2c131578caa7bb7e23a456733783d8db49ae}}) and {{formula:eb2f6cd7-2cee-4e20-8724-808dcf1dd1b4}} . For a finite set of homogeneous generators {{formula:1a1b0c2b-8be8-423a-82ed-5e97e875dace}} of {{formula:6b18c471-a432-421e-ade0-a4671d03aaca}} , choose {{formula:5957f5e0-a506-438a-ac08-6409d28a8cc1}} such that entry-wise, {{formula:ab69515a-d9c4-4c28-9a27-4dfc89257386}} . Take {{formula:9d83dfb7-ead1-489d-828e-fc8e7a247b2a}} such that {{formula:2dee9e4f-4879-44cf-852c-224843ef28b2}} and {{formula:8b81cbc5-218a-40f5-b157-f82a0d59c360}} .
Under the assumptions of the theorem, {{formula:030b184b-84cc-49ec-bc36-1aee2f7cfa13}} is a regularity pair for the ideal {{formula:a7744154-cefe-4b00-aaca-2537b83505ba}} , defining the same set of points {{formula:b8b37bf1-d337-46e2-b034-3639fe9aa7cd}} (see Corollary REF ). The statement now follows from {{cite:63731d40d84257e4b09f0ca6b308514a491a3988}}.
We prove the case {{formula:8bead954-1c82-4413-8a9c-ef7ce65edfc4}} in item (3) of the theorem. It suffices to show that for some configuration {{formula:666aba57-2576-4cc1-bcb9-48a23dc2176a}} , the matrix
{{formula:3e5ff495-76e1-42f0-924c-412521d0b9e1}}
has full rank. We set {{formula:ae8072d0-fe15-413a-9396-a9196273d7ee}} , such that {{formula:05cd37eb-583d-413b-86ac-de9e50285640}} is the identity matrix. The condition (REF ) ensures that {{formula:0f08e816-997d-436f-a3b4-54c99b36638f}} has more rows than columns, so it suffices to show that {{formula:534b4abf-7232-4ec5-a2f4-64ac54f6f4a9}} . Suppose {{formula:93076d1e-0a8b-48a0-8aa1-c47cd5130a4d}} , then {{formula:518b3d08-7ad0-4797-8a8b-997a11e3f150}} can be split into {{formula:3a308977-8424-450d-bbb0-f73fa7ae17ad}} such that {{formula:aecd2d51-8b26-4fe2-ba04-6d383cfa6fa1}} . If {{formula:33701f63-6e82-4141-91f4-addd6a55d0c0}} , it is clear that this implies {{formula:9653fcdc-bf9f-4cbf-afca-b4b964b7503a}} for generic {{formula:d1529470-9c66-4a68-9f1e-2f89d78d0a8e}} . Therefore, we assume {{formula:f29ec042-cc51-4067-aa72-a504bf3ea162}} and make the following choice for {{formula:65575063-ed98-4d75-8404-81aaac2aeecf}} :
{{formula:cabc90fc-7900-4960-81d4-794f341b99b9}}
where {{formula:26272462-74f0-4212-9e9c-cdbb409eb162}} is the submatrix of {{formula:81ac2ba8-b8cc-43fc-a3d9-4f7a6686e974}} consisting of its last {{formula:4e032de2-a803-42aa-8de3-6cde2d2f6c8b}} columns. We have that {{formula:a9906845-757f-466d-b9b4-707e363e97be}} implies {{formula:5f4ee4ea-735b-4ccc-b897-506f043b183f}} for some {{formula:2b2bea63-016e-42cd-be36-a6373bc81f0e}} and {{formula:090446c1-bce5-4d56-ae8a-acbd1ca81d0f}} . Hence {{formula:a6963377-8f09-41b4-bbbd-3ca997533a8a}} is equivalent to
{{formula:128da027-b5db-4953-b606-5dec11cf675c}}
The condition (REF ) implies {{formula:97d90d92-fd40-4d1e-9250-2699af947552}} , so that the coefficient matrix in this equation has more rows than columns. Upon closer inspection, we see that
{{formula:059f986c-ff39-4498-a826-144baa1e0313}}
In order to make rows {{formula:ebb84536-cd93-4ff4-b914-782f6cf72258}} equal to zero in {{formula:472ae2e9-c37f-4916-8534-696b1d703f0f}} , we set {{formula:942fe771-629b-4e5a-9664-cc7533c98b0e}} . All other {{formula:d9e72149-c0ab-4191-be03-9da1e1c7b5fc}} -coordinates are chosen ad random, such that all entries of {{formula:96831cee-eef5-4b19-aff2-c27d9c27fe48}} , except those in the rows {{formula:d59f22df-7ac4-4d2f-8875-d0afdd1b1ee0}} of {{formula:2b721a87-63ea-41e8-8ad8-397c386a823c}} , are of the form {{formula:bdb2713f-5d9b-4033-8cd6-3531609af765}} , with {{formula:ee036cae-a72b-436f-a6f0-a621a0508f01}} some non-zero complex number. Then,
{{formula:dadb9889-b024-4176-9c71-c50d7d5f5109}}
where {{formula:8a884e81-b67b-46d1-8052-e0cb4d6190b4}} and {{formula:6ee982d8-98e9-4167-a6d0-b8bf5822f43d}} . The minor corresponding to the first {{formula:390f9b3d-06eb-47a7-8a5d-87c2eb96db44}} rows is {{formula:4196d3b0-2202-4514-87aa-e723492f5285}} . This is a product of two nonzero polynomials in the parameters {{formula:109e9f92-f934-40ff-a75b-ddb27645b42f}} , {{formula:49bd1afb-bd12-4c20-a632-d29fa6858aae}} . For generic choices of the parameters, this minor is non-zero, hence {{formula:fe2c6bee-a902-465e-a67d-6974bdb14d18}} , and thus {{formula:c7e56103-027f-488f-b3eb-d2a64a3e421b}} and {{formula:27dbb9ca-e97e-4f69-a4a0-30cfe3896e37}} .
| r | 2b8ba001304512770f495722add5e15b |
In the experiments, an episode terminates when the agents receives a non-zero reward or the maximum number of steps allowed in one episode is exceeded. This maximum number of steps per episode is 1000, whereas the maximum number of total training steps is 500,000.
Furthermore, we set the Jensen-Shannon divergence threshold {{formula:79dd4e4d-2140-45fd-922f-35e526b4e965}} of Section REF to {{formula:fb11c92e-441e-41be-8075-e7423e9190cd}} , and Algorithm REF selects a random action with probability {{formula:6f71387a-5b24-43cd-bd33-25928522e2f6}} .
Our implementation utilizes the RC2 SAT solver {{cite:ebc8002d668131ddb5a649638e14872e310a2879}} from the PySAT library {{cite:2470f63d79c528ca4646a191c95344e036f40472}}. All experiments were conducted on a Lenovo laptop with 2.70-GHz Intel i7 CPU and 8-GB RAM.
| r | 6a70163e5372f49f9b09fbd4c6994b9f |
More specifically, we refer to knowledge distillation {{cite:e3c2a7c37eb007febecd90aa5d198ab27cb0eb9b}}, i.e. the process of transferring knowledge from a large neural network to a smaller one that may be appropriate for deployment on a device with limited computational resources. Another area of interest includes the techniques, widely known under the term regularization {{cite:18639a651a8b5278657243de436cde50c2946054}}, which aim to lower the complexity of neural networks, in order to show better performance during inference time, when they process data that are not in the training data set (avoid data overfitting). Moreover, neural network models in systems or programs with learning-enabled components {{cite:ac0dd7d3db020de595fd73f4319ace35ccd67cc8}} may have to be updated for a number of reasons {{cite:f2d6b7bdd89e38ea2b397f0cbab04c4adcca378a}}; for example, security concerns such as the need to withstand data perturbations (e.g. adversarial examples), or possibly incomplete coverage of the neural network's input domain.
| i | 0aaf0908d2ede587ee3b7ede5b2d0407 |
Since our method is in principle applicable to any gated RNNs, we further validate the fast gate on another popular gated RNN, GRU {{cite:8170bfa1909b6c72ac1cd90f8da5411c22d1ab95}}.
Additionally, we evaluate the fast gate combined with the gate initialization technique, called uniform initialization {{cite:6abe7f5310004a56552a365f7049a1f4704f4482}}.
| m | 680df8450dfb2cd1887d15b8985dcfb3 |
Single crystals were grown by chemical vapor deposition {{cite:f9a2ca3a8fde356b3af8e252a3d6f0a40ac5a85e}}, {{cite:dacda3a67cda024ab010e2a3a11d6922e401f512}}. Their orientation was checked at room temperature using a Laue diffractometer. Oriented plates were prepared using an electrical-spark cutter. 15-{{formula:59f39481-723c-49ff-821b-46c6bbf5e50a}} m gold wires have been spot-welded along the larger dimension of each sample. Samples measured with an electrical current {{formula:4b714c93-7851-46e7-8257-62636f2068c0}} had dimensions of approximately 1-2 mm along {{formula:17169487-e10c-4014-92de-14f1b4fef716}} , 0.3-0.5 mm along {{formula:2f6b1ffc-8f90-40d1-9ea9-070b7e1f38b1}} and 0.1-0.3 mm along {{formula:2fbf79ff-7d02-494f-92ed-dd987f507373}} . Samples measured with an electrical current {{formula:bbf3da29-60e5-4af0-95b7-ed1893e7ac8d}} had dimensions of approximately 1-2 mm along {{formula:21d8d585-4340-491c-84ae-fe6234d71dee}} , 0.5 mm along {{formula:0ca12217-45b7-4d3f-a4d8-795a4137c9f8}} and 0.1-0.3 mm along {{formula:a1faa08a-d511-446f-a7d7-018ca4e4dd02}} . Electrical-resistivity measurements have been performed using 70-T pulsed-field magnets at the Laboratoire National des Champs Magnétiques Intenses in Toulouse. A 6-MJ generator was used to generate pulses of 30-ms-rise and 150-ms-fall durations. Temperature and magnetic-field variations of the resistivity are presented for the up-sweep and the variations of the quadratic coefficient {{formula:2e4192b6-b655-4f5a-a4b4-7d8d2bdd5f9a}} are presented for both up- and down-sweeps (more data from up- and down-sweeps are shown in the Supplemental Material {{cite:e8ff391f8ed895412df030381723ed9317c0d1d1}}). Pulsed-field experiments were performed at constant temperatures from 1.4 to 80 K using a {{formula:272cca90-b077-4a4f-8ea8-9938f2796196}} He cryostat. Resistivity was measured by the four-point technique, with electrical currents at frequencies between 20-40 kHz and a digital lock-in analysis. For each current direction, measurements under magnetic field directions {{formula:6cc4073f-6698-47fd-beb1-58f232496360}} , {{formula:725c056d-45e5-4d7f-a1dd-92ad9bde4fd5}} , and {{formula:8f61beb6-88b0-42e2-8a19-d1faf83e0d92}} were made on three samples simultaneously (samples {{formula:bf6d7606-703f-4d1a-b6db-ff850aa07ab8}} , {{formula:72d8e57a-9e2e-4453-86af-e20607498e5b}} , and {{formula:dc2e74dd-5292-4154-9f08-a0551e60d313}} with {{formula:1b178882-217e-4775-862d-a6a01a200681}} and samples {{formula:76fcb083-20ec-46aa-8b06-6b65e964d4ed}} , {{formula:f97db7a1-e3d6-4c66-84c5-50495a2c39a1}} , and {{formula:a97db211-32e9-4525-9b6a-0a78d4b3cb48}} with {{formula:44441d48-614f-4fa1-bb9f-31f1f07c8d66}} ). The resistivity data were normalized to absolute values following measurements made at the CEA-Grenoble on samples with well-defined geometrical shapes {{cite:ab2d3988ea1a5f5d6a2c3882654139bfc3c83f32}}. The resistivity data of samples with {{formula:630e3e92-b66f-4421-b0ca-2c231165edd2}} , initially published in [Knafo2019], have been reanalyzed using a geometric factor consistent with data published in [Knafo2021a].
| m | 11f2e0af324d4ec2f655f9636972039b |
We show more results on a variety of model architectures.
In particular, we choose two CNN-based models RepVGG {{cite:bc5c0d5bb7996d0d7e16abc57cfa9e903032cf26}} and ResNet-50d {{cite:605a423ce945d7ee92058d0e85bba3e612a2db7f}} and two transformer-based
models Swin Transformer {{cite:19667ecba2d7384dc87a3689f4195be341db7c65}} and DeiT {{cite:7f890593a0bc53637c78395b890c03eea634b2e5}}.
Their average AUROCs and average FPR95s over the four OOD datasets are listed in tab:other.
It is shown that ViM is robust to model architecture changes.
The detailed experiment setting and results are in the supplementary materials.
| r | 033032b0ec1569d30eb746513e6444b3 |
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