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One way in which they often come close is when they discuss repeated
measures. See for example {{cite:52cb4f9c1e34e6868439905c92fb0f25af53db2f}},
{{cite:2f8c3d1ea245e1363a8fa43371db0fb9fd22541b}}, or {{cite:15432379e2531430763e3be37ee776bd327f67ce}},
{{cite:82ffd86ed9695a2d7a0f2bf2cc36893482744a99}}, and {{cite:e3dbb29e22db664358e02ead19f6545d7dacdc81}} for detailed
discussions of the concept in biosciences. `Repeated measures' consists of an
experimental setup very similar to the one used here and described in
sec. REF , i.e., measuring the same quantity on {{formula:602885dc-f00d-4300-b7a4-b877795cd68e}} systems and
repeating the experiment {{formula:5bc4fc08-1666-452f-928d-2d0bf1014c0a}} times, but it contains a fundamental difference:
it tackles measurements that are expected to change from repetition to
repetition [e.g., a time series, or table II of {{cite:200415c75e501cdfede6fec5e79a7b9f1f035f82}} discussed
in sec. REF ]. It is a key of our setup that we expect the
results of several repetitions to be the same. This is why it makes
sense for us to correct them, which would be unnatural in the
repeated-measures setup. Also, for repeated measures, it is not a requirement
that we are not interested in the absolute value but only in the inter-system
variation. In our case, this is essential.
| d | 4be8f4b42b28a5d6c1e6a7d2620eefbf |
The notation and terminology in this paper are standard in variational analysis and generalized differentiation; see, e.g., {{cite:227de480d6a7d26d8e4a27bdf89ea4d7cbe0e37e}}, {{cite:560f23b9ff377ff4a36c010b1fa1ac2229d9b2a4}}. For the reader's convenience and notational unification we use as a rule small Greek letters to signify scalar and extended-real-valued (i.e., with values in the extended real line {{formula:57dd3fe4-0962-4c09-9ab2-240d2fa436f5}} ) functions, small Latin letters for vectors and single-valued mappings, and capital letters for sets and set-valued mappings. For a nonempty subset {{formula:d14e0555-a249-4ee0-a436-a2f984ec7423}} of {{formula:8a05d0eb-77d3-413b-a73e-4c5aac707477}} , the symbols {{formula:0b8a068f-08ed-4589-a1c5-cd4f905d3195}} , {{formula:57301dbd-c8c3-42a4-86a7-e1c9d96b48ac}} , and {{formula:244925a2-f6ab-44c2-8670-2b5932ab58a1}} stand for the relative interior, closure, and polar of {{formula:b369adfc-a860-44ce-8d09-3ef1d455d737}} , respectively. We write {{formula:2012f0e3-d4a5-41cf-9a01-81b495db03dc}} to indicate that {{formula:034c0501-8de8-455f-8fe3-e3401651ee54}} with {{formula:12eb9d4a-25ee-42ba-911d-b498d7cc00d8}} . The distance between a point {{formula:816348f7-ccca-48f2-b387-160821e5cb9a}} and a set {{formula:1547a1f3-3841-45cb-8e8c-d9daacdfcf0c}} is denoted by {{formula:d5f812f2-9838-47cf-a374-13a7ab7e0e08}} . The indicator function of {{formula:0a450aef-313d-43f0-a88b-48756fd9cef9}} is defined by {{formula:30b603ad-bde3-4453-802d-383cfa7a68f9}} for {{formula:f4e8b687-9bcf-4035-bca9-82a28a3ed745}} and {{formula:ee3616b3-f680-4822-bf3b-c7d5a3d204a2}} otherwise. The notation {{formula:5fcebaad-afb0-4ce1-af3f-be63589cd274}} stands for the closed unit ball in the space in question, while {{formula:c3305caa-485c-4296-8388-b8ddfd954b8f}} mean the closed ball centered at {{formula:ac6cd567-f367-4f52-86f1-03eeacb5f437}} with radius {{formula:656440bc-8627-427c-905a-181f4da28895}} . The symbol {{formula:3045f14a-720f-4838-b17f-b5276a73cfef}} with {{formula:d93e764a-84df-4d84-9319-4d3b8428edda}} and {{formula:afdc7fc5-2c35-4b29-8df5-0b5d9934119c}} tells us that {{formula:5ad3e4a4-dfa3-4573-90f3-ef9dab8b22c3}} as {{formula:db30ce88-551d-4b50-a138-76b97a960693}} . Let us also mention that the notation {{formula:06cc894e-35c8-4805-9a25-686e07769913}} indicates the possibility of set values {{formula:34828d0f-2d0b-4087-9d1d-bc48e8e42139}} (including the empty set {{formula:ab3df762-6c79-400c-87e2-3eda9687b799}} ) of {{formula:70498e2c-94a8-4fc9-a506-2c5e0b065302}} for some {{formula:79186cdc-3244-49a3-8521-e180315658a2}} , in contrast to the standard notation {{formula:7b80d376-7cc1-44d9-9f56-cf11898c59da}} for single-valued mappings as well as extended-real-valued functions.
| d | 1d0c6dff452554e712d2657a40ee57b5 |
By {{cite:110f25432a84ce444bab291e2148bf79c052eb03}} Corollary 5.23, the stability of optimal transport maps implies that {{formula:450dbecb-e1a8-410b-8c70-c78afebe34a8}} is continuous; thus, we find that {{formula:4dbfd467-5674-4320-a069-20060c8320b8}} is precompact if {{formula:eb0b420e-5cb1-46e5-9ef3-c48b02d4569f}} is precompact. Note also that Brenier above gives us a corollary.
| r | 9bb7f56121add2b9472847acadbd3df3 |
The magnetic properties of systems with itinerant electrons have been studied extensively and partly understood through the Hubbard model and the self-consistent renormalization (SCR)
theory of spin fluctuations{{cite:b005c7fa856d355fa41ebdb60602c1bd69a4a9b1}}. The SCR theory excellently captures the dynamics of spin fluctuations
beyond the random phase approximation (RPA){{cite:a2f48badcef9051626b6d9f9c08a937d7055f174}} by renormalizing the ground state including the effects of electronic correlations. Such a renormalization was first introduced by T. Moriya and A. Kawabata {{cite:b9f011545ffe10f2f54db98f7e439bb3588f01f2}} and has been studied by various authors {{cite:496f44104a224423d49d6ca2563bb87291b1e363}}, {{cite:a8a672448b0a3cb17d55554bd8699aa3b330c8f2}}, {{cite:eb2a29e5970b2062346734bc94f72647fa4e8e0d}} for nearly ferromagnetic (FM) and paramagnetic (PM) metals. The SCR theory nicely takes in to account the influence of exchange-enhanced spin fluctuations on the thermodynamical quantities in a self-consistent manner. Gradually, this self-consistency has been proved essential for the theories of ferromagnetic {{cite:496f44104a224423d49d6ca2563bb87291b1e363}}, {{cite:60af7213cc11b25bd9c92633351c39c19f30c145}} and anti-ferromagnetic {{cite:6ae353de7a6720b6ab6eab71dc55af68fcc9b102}} materials. In this direction, a coupling theory of spin fluctuations in weakly ferromagnetic (FM) metals was developed later {{cite:581952f94aa8462594825396b31f7a228f87fdf4}}. The theory provides a mechanism, which explains the disagreement between the effective moment (obtained from the Curie constant) and the spontaneous moment of magnetic constituents {{cite:b005c7fa856d355fa41ebdb60602c1bd69a4a9b1}}. This theory can quantitatively explain the Curie Weiss (CW) susceptibility for Ferromagnetic and Paramagnetic metals.
Due to enhanced correlations in aforementioned systems ferromagnetic (FM) instabilities and {{cite:b1e755a1a89bc7c40e019371fbd0b570a1d7f89b}}, {{cite:af57b364872031e632a78dd2fee4b93a63f18ced}} and spin density wave (SDW) {{cite:1fd2027b087022f2bf3bbc3e981e08a363166e7e}}, {{cite:458568d06d2c31f15194d4370e5be0313e75df00}} instabilities arise. At absolute zero ordering the spin fluctuations{{cite:208f3dfd7f8dd1b5bb2a8fd3c4809939aecab644}}, {{cite:6ae45d4b13095b0236b0f27e92104d49116c077e}}, {{cite:768a9b6bc701de37da3d4cbb03b2836e2327e9a3}} with pronounced quantum character play an significant role in the measurement of quantities like magnetic susceptibility, specific heat, resistivity etc. Magnetic systems in this paramount edge can host a number fascinating phenomena like metal-to-insulator transition, non-Fermi-liquid to collective phases transition, superconductivity etc, and can be more clearly understood with the help of SCR theory {{cite:eb2a29e5970b2062346734bc94f72647fa4e8e0d}}.
| i | ab10c6f8e11ae670ba3620ae5ff2c255 |
It is likely that for many PQCs, further optimization would improve the circuit training. However, fully saturating the bound on the MSE value is hindered by poor fitting of the y-values close to {{formula:e69da71e-88e0-44be-9564-56467fc6f2ad}} . Improving the fit near these values can be achieved by incorporating post-processing of the measured value {{formula:ebed5cc7-2b2a-4914-a53b-8a4628780dec}} . In {{cite:a94fb71c8ac3141610fde68cfd19962cb9184631}} an additional constant was trained that re-scaled the output value {{formula:53c52384-2609-46ab-8c32-8facaf2ea198}} . Alternatively the training data could be re-scaled such that the predicted labels are constrained to a narrower range with zero mean {{formula:94c6dfb0-c234-4617-a1ae-0a8194de6f16}} .
| d | b0517d2b12962e2040b054369124a845 |
Under a correlated forcing in time, a numerical scheme for deterministic differential equations must be employed to obtain {{formula:1632615e-e0b1-4b86-afd7-62c760c6a978}} , since the external force is now continuous in time and space. For this reason, we generate the forcing with a numerical scheme for stochastic differential equations, and for the time evolution of the system, given the forcing, we use a fourth-order Runge-Kutta scheme.
The stochastic scheme for the forcing is the same as in the previous section, a first-order predictor-corrector algorithm {{cite:24541f0db5ebcf59e2cb2c02c90c497e82f94204}}.
A forcing with the specific correlation profile of Eq. (REF ) is provided by an Ornstein-Uhlenbeck process, defined by the solution of the following dynamics:
{{formula:93d2088d-0472-44c1-a065-e29b8497ae35}}
| r | 9a13bf0b04c8b69fe565720493207836 |
with {{formula:3a98384f-ed05-491c-960a-93861ba7ffcd}} {{cite:5836c32bfde2fde804c8868c2209d6ae809e925b}}, {{cite:f9852ac9a446f5ff2a5eb863da4b2589899cc35e}}, {{cite:96b334c6c2317778cc258b843a746dcb177e9575}}. By tuning the parameters such that {{formula:b1241280-c0c9-4501-92ed-80101c3f6a51}} , the propagator {{formula:83c9e57c-58da-4a4a-8e6d-e3b2241e8f47}} evolves the initial (separable) state {{formula:ae689ee8-86cf-4ea4-98d8-672ec921db85}} into the maximally entangled Bell state {{formula:78d3c309-352f-449e-8999-039ddfed6080}} .
| m | a83a12592151f3c82df56dfc07b72a5c |
Using the relativistic distribution function, we have derived a new form of the general relativistic virial relation for a spherical structure within an expanding universe based on an exact solution of Einstein equations without any ad hoc assumptions. The results are written in the familiar form known from Newtonian gravity. We then have applied it to the case of static spherically symmetric and asymptotically Minkowskian structure, and also within a static star calculating the mass-temperature relation for a relativistic gas model. To be as realistic as possible, we have also applied our virial relation to a structure within a cosmological expanding background (for the relevance and more exact formulation of such structures at large scales see {{cite:29f68a381df35c17dbfd2e81aa7793c0608c730d}}, {{cite:ad4c07c628e648eeadf5d45255508e2918b5292d}}, {{cite:b26a9161de0b72cda49eab273ce61b5224f52061}}). A new term due to the impact of the expansion of the universe on the structure arise which has been neglected so far in the literature.
| d | f6970f1830a17a6d9e776fddfc3b462e |
Given the above, as long as the noise in not low enough to allow for error correction {{cite:41d3437708c73e8f8eb5be76a73b217f4e7e3029}}, {{cite:8d737528dae0e83c50b729202a9bbc05e33718e6}}, {{cite:60136c85869338ec8f0a7888f2e3ff4e878095d0}}, to ensure that most of the output qubits have more signal than noise, we need the number of operations (i.e., depth of computation) to be bounded by some constant depending on the noise level.Here, we model NISQ devices as having a fixed amount of noise and a system that can scale to an arbitrary size. In current devices, the system size is relatively small compared to the noise level. If an output qubit is computed using a small number of gates, then its “light cone” will only involve nearby vertices.
In general, even for optimization problems on graphs, the topology {{formula:568191d0-1a02-445f-8469-4730b62d1d92}} of the device's architecture need not be the same as the input graph {{formula:c5b5b969-900b-4c05-b50e-a6ebe4640202}} .
However, natural optimization algorithms such as QAOA perform best when the two match as closely as possible {{cite:69cd90084af387682ae5e4d2d1672f6d5ebbbe4d}}. So, since our focus here is on the limitations of NISQ devices, it makes sense to consider the “best case scenario” where {{formula:5c0f41f5-f99d-4ee4-937c-df8303800b1f}} .
{{figure:1885e23c-eb0d-48cc-a58d-c4d7cba8725d}} | d | b6d8693abc5346c6ee6ac083e1efdecc |
it follows that the {{formula:9ff8c982-f424-488b-931d-3a476e2f9098}} -th Hecke eigenvalue of {{formula:6cdf852c-ec76-4b0e-8cf1-3ba44ea8475a}} is {{formula:202e5307-c3ec-45a5-a982-12f7ef94464c}} , where {{formula:b3c8f1f5-a005-4d04-8be1-3d066135a128}} is the Hecke operator on {{formula:58fdbc94-0e26-47e6-bf1a-93a60ffda757}} and {{formula:67a8788a-05a6-453a-878a-c24bf5d39729}} is the Hecke operator
on {{formula:5cf2e8c3-1557-40e6-bc1d-38bb60477510}} . By {{cite:c08be08c64ecd4bf88b17d2030caaa21f0c39c43}} we have
{{formula:8f89fb59-6451-445f-8480-4f9e225e43d6}}
| r | 388b8d1ecfb524a6fc0eedb2daea9497 |
Several experiments were next conducted to evaluate the effectiveness of REFINEment in the presence of domain gap. Table REF gives reconstruction accuracy for RerenderedShapeNet reconstructions, before and after REFINEment, of ShapeNet pretrained networks. Three methods representative of different reconstruction strategies are considered: OccNet {{cite:a5a5dedbfba735d90cbbd6a42ae88c7ac031bc8a}}, based on implicit functions, Pixel2Mesh {{cite:0ea7bd7b439f552ec8fec1df8b624a434e28eb58}}, which deforms an ellipsoid, and AtlasNet {{cite:7eb9fa38faf133541ab9c4c96e25311a3c2a2e94}}, based on surface atlas elements. A larger table with more REFINEd methods is presented in the supplementary. The results of Table REF are generally worse than those of Table REF ; while the methods perform well on the training domain, they struggle to generalize to out-of-distribution data. However, REFINEment significantly recovers much of the degraded performance for all networks. Average gains are particularly large under the Chamfer distance (-11.5 for OccNet, -14.9 for Pixel2Mesh, and -29.6 for AtlasNet) and increase with the network sensitivity to the domain gap (e.g. largest for AtlasNet, which has the weakest performance).
| r | 5e6d3824755b10d0a1867ce158e17c12 |
if {{formula:f4e7dd27-b5f8-4e56-8bdb-4c173d7f6860}} , and it is {{formula:4e98ea84-c036-4305-b1b8-a8ee55c95ace}} otherwise.
This refinement of the moments accountant has been already proposed in {{cite:475ddb9ae45e4ef0d4ade64a80af4737e5aa51e7}} using a fundamentally different approach (see also {{cite:5e8928f995f26c91519b8efbd7ed68440f72d232}}, {{cite:e130eb5d62460558cd938508e59c5b5a18d42234}} for different proofs).
We use this refined version of moments account, which is the latest version implemented in TensorFlow Privacy, in our numerical experiments (see the “Baselines” paragraph in Section ).
{{figure:08603b4b-8445-4e3d-a44c-18d68c0383a1}} | m | 03de8b7c128ea926d9c79a9d6a520d5b |
Autoencoder based capsule structure by Hinton et al. {{cite:cae2c8e76766645c0a74cb1e1a4aa910a4456f63}} required to give information about the augmentation in image. In the work of Sabour et al. {{cite:13bf4a6bc096bd072cfccff058c2193b6ed6c6ae}}, this problem appears to have been solved by using the margin loss and masking, but not specifically due to structuring of capsule. This is observable from the fact that when margin loss and mask is removed, the network starts to act as an autoencoder {{cite:47c13907a4fa2c3722073f995a1d68ad14dbbc88}}. The failure of stacked capsules {{cite:84c66ed51a8d416d464b44ed11abe6a6b38288bb}} can be used to interpret that capsules in the hidden layer are not learning the latent information of features. Possibly, this is because capsules require margin loss to force them to explore different paths and thus capsules require the special supervision of a loss directly.
| d | c71387a60155f3b8ff1f3892c7dc4866 |
In a similar vein, {{cite:484b7d2d9c55e83652e6652220742232ac9f07e7}}, {{cite:127d449fafade48951f284592ae3619e48fc9df9}} consider the multi-type variant of the classic housing market {{cite:67ec2b3db1053ec907440de439196bbf1d717b21}}, first proposed by {{cite:a44250dcef1b25287810f493f7d14818febf3248}}, and {{cite:fd24251a98326e553eb0a269c9a8c86f73f14bdd}} consider the variant where agents can receive multiple items.
These works circumvent previous negative results on the existence of strategyproof and core-selecting mechanisms under the assumption of lexicographic extensions of CP-nets, and lexicographic preferences over bundles consisting of multiple items of a single type respectively. {{cite:8443ccb7abdaeda92e52d1fe27fd5d47548a9ed5}}, {{cite:69e24ea7b5154d0375e76161254f898e9352157e}} study MTRAs with divisible and indivisible items, and provide mechanisms that are fair and efficient under the notion of stochastic dominance by extending the famous probabilistic serial {{cite:55f07d06ec2ea63d9608ee178425820febbcbc79}} and random priority {{cite:1f9127fe55dbbfaae8eb5994858c5cb6df83b34d}} mechanisms, and show that while their mechanisms do not satisfy strategyproof in general, under the domain restriction of lexicographic preferences, strategyproofness is restored, and stronger notions of efficiency can be satisfied.
| d | 659f7cd7149c277fe3dab49fff1cdf97 |
We consider the following setting: Let {{formula:55b86683-b1a1-47f8-bbbe-cc24dddf9086}} be a {{formula:496f369f-d29e-4c7f-ab1c-b39f1162f260}} -finite measure space and let {{formula:9c419a15-4a81-4371-8e01-e0dc9cdb496b}} be a self-adjoint (possibly unbounded) operator on {{formula:e34dd088-51f9-448d-bab2-a50137e4635f}} . The Lebesgue spaces {{formula:648f25f5-e414-4ada-8d28-d038eba6b67e}} are compatible as {{formula:2bc632c7-a34a-4508-9608-47b522d108b7}} varies in {{formula:2b502b80-83cf-4c18-a913-7207e9d2368e}} , in the sense that {{formula:bcd0495b-2e00-4c18-80be-f4214a32c418}} is dense in both spaces in the intersection and complete with respect to the norm {{formula:74416b66-9ed0-42a3-9f66-6b0199b8b4e0}} (see {{cite:c3e2da8d988cbf9e492302cc6b569c36a177b66b}}). We fix {{formula:0c4d26d7-054e-4f8d-8c6f-8a361fb25079}} and assume that the resolvent operators {{formula:cc0911cb-3438-4343-95b6-11b420a881a7}} , {{formula:8e065f8e-6cb4-4e8e-b969-815a48ba71b2}} , have a consistent extension as bounded operators {{formula:5cea7ba7-7096-43ed-967f-5ab136521dce}} and {{formula:d74ea1fc-5368-4b6a-8d3d-400309c71989}} . Consistency means that {{formula:053e98ff-82ce-4ed7-9a9a-494bbdb3b4ab}} coincides with the {{formula:db235895-21d3-492f-8f1c-24fe03cd9f11}} -resolvent operator on the intersection {{formula:239321b9-d026-47b7-a874-0570014f2972}} (see {{cite:c3e2da8d988cbf9e492302cc6b569c36a177b66b}}). By the Stone-Weierstrass theorem this implies consistency of {{formula:50eaaa5c-9179-45ae-91c3-35182a807625}} for arbitrary bounded Borel functions {{formula:517abe47-d06e-49cd-b8b8-ecb84e4da867}} (see e.g. {{cite:ebc6a34243e0502031088a96d5199217674ee492}}). We will use the notation {{formula:3d11b1ba-0a6b-4432-8d6b-1e67ccd178d5}} for {{formula:b3406115-27a6-4bb8-b834-3a07b3f90e4f}} , {{formula:76c735d1-6362-4003-8e22-2bea468256dd}} .
| r | d94518748012fa92956cdbadb64d4461 |
We can also estimate an angular correlation length for the EM using the same method as {{cite:ddbf8e427af559d47b8d50760e4dec47d2b89539}}. {{cite:ddbf8e427af559d47b8d50760e4dec47d2b89539}} used a model for the CGM distribution and calculated the autocorrelation using the EM difference from that model. We instead compare to the median EM, as we have not generated a model for the two temperature case. This results in correlation lengths for the full northern hemisphere of {{formula:8fc627fa-b3ab-42ab-b9f0-81304232db19}} for the warm component and {{formula:d5595f5b-2b0e-404f-a848-e289f3738afa}} for the hot component. The correlation lengths for the full southern hemisphere are {{formula:a93e508a-7c46-4502-824e-66c30cd9f1d3}} and {{formula:0b732629-b8ce-4130-a46b-5a46f9b9479a}} for the warm and hot components, respectively. These correlation lengths are based on the full data set (including the NPS), and reflect the overall trend for EM seen in Figure 9. These errors are for the 90% confidence interval.
| d | fd98d9f85274f102d4b0b9fa74dd8e8f |
Equations (REF ) and (REF ) are solved using a
pseudo-spectral method in a periodic domain of size {{formula:dd60b78f-c516-4414-8a71-c266ffe8cb5c}} with {{formula:fefe5ac6-eabe-487e-95d7-749e4a853694}} grid points. The aspect ratio of the physical domain containing the plasma is {{formula:07987202-eff1-4339-8016-18771b476689}} . Spatial derivatives are evaluated
in Fourier space and multiplications are computed in physical space. To avoid aliasing errors, i.e., the production of small scales
due to nonlinear terms which are not resolved on the grid, the velocity and magnetic fields are dealiased at each time step by truncating
its Fourier coefficients using the 2/3 rule {{cite:cb5798afb75aae34fae229efc11da7aae162774e}}. Using the incompressibility condition of the fluid, the pressure term
can be eliminated by solving a Poisson equation. A semi-implicit time-advancing scheme of Adams-Bashforth type is used to solve the equations, with exact integration of the dissipative and magnetic
diffusion terms. Boundary conditions are imposed using a volume penalization method in order to build the cylindrical domain. Detailed description and validation
of the method can be found in {{cite:42001f39627d8e71133996a32a284602f9a4075d}}, and an application of the method to investigate RFPs in toroidal domains is
reported in previous work {{cite:93a2e2e7d046059a8cf5d1af77ab945f20c64bf7}}, {{cite:5f012302835b09092dce788cd7ffc7ee6122aaa4}}. We have verified by assessing the high-wavenumber range of the kinetic and magnetic energy spectra that the resolution for all simulations was sufficient to resolve all down to the smallest dynamical flow scales.
| m | 843c1ae5f68a0fb434c81b65d37ac39a |
Face attribute pairs: We generate the positive and negative pairs for face attribute editing by augmenting the negative source image with the attribute of interest from a source image. Fig. REF shows examples for all the attribute edits. For attributes such as hat, glasses, bald, bangs, beard, and eye-close, we use the segmentation mask from CelebAMask-HQ {{cite:7e1bccf43c0b3884346c17575dc450427e27cd1b}} dataset to perform a simple copy-paste operation for the region of interest. For pose, we flipped the source image for positive image creation and for age we use SAM {{cite:b3ad4ae945c40e13b36478798726e00dccc68524}} (state-of-the-art age editing framework) to create an aged face. We use the portrait relighting method {{cite:d7c845c9c233c2c4f90a18b8e7d095980585bdca}} to get the positive and negative image pairs for lighting.
| m | ca48b1e32a21e570a03ed9d6abe6484a |
Future work includes studying the effect of {{formula:ad717766-ed4f-4348-bd0f-7e3c19af7d93}} considering the trade-off between the performance and the sampling complexity. The naive idea is to increase {{formula:f8f8daae-a7b8-4a3e-a871-a276bf57c0bb}} for adjustment of the variance that affects the sampling complexity. However, as the author in {{cite:ac09f97d31ad2dfbd9f55c003249013cf5cea2c6}} described, the choice of {{formula:9a60b001-80c8-4a86-b1b5-71d23a6459d9}} does change the behavior of the resulting optimal control. Hence, depending on {{formula:bcd9b414-f955-4a6e-bdae-4ff33a9ed3e2}} , the optimal control can behave differently from the deterministic optimal control in terms of performance.
| d | 58dcc575eb0f09a390aef4300826ac45 |
Figure REF (a) shows the average out-of-sample error {{formula:adfb019a-ff0a-4b79-bb68-d6961c95e031}} (cf. (REF )) for various choices of the size {{formula:971e1ff6-cabc-4f1f-bcea-bea02124f8b2}} of the reduced-order basis {{formula:989d9ebb-7a03-4c8d-b3ad-b187f6e86c84}} and for three different tolerances {{formula:e23e57ec-2faf-4ccc-9b8f-d20bcbf71589}} for {{formula:78485243-82c1-4b99-83a2-f88cb5118bc8}} , the test space {{formula:be3f2cc0-52ec-48da-9eeb-c51421a38d19}} is chosen according to Algorithm REF with {{formula:0e01fa7e-659b-4897-89c0-bf547e9d2eaf}} . As for the linear problem, we observe that the ROM guarantees near-optimal performance with respect to the projection error, for sufficiently tight tolerances. Figure REF (b) shows the percentage {{formula:878862f9-2a75-433b-b4d6-dfd6ac92a727}} of sampled elements with respect to {{formula:ca7d253a-3ac2-4116-ae2d-b964bd65575a}} for various tolerances: for all test cases considered, {{formula:f1ab7dbb-26c5-4e3b-9e6e-3bec258b6782}} is less than {{formula:27b293c3-72ac-4b8a-ad51-2a195194ff24}} of the size {{formula:df984499-f421-4618-adc3-17cd9413e9c5}} of the complete mesh. As for the linear case, speedups of the hyper-reduced ROM compared to the ROM with HF quadrature scale with {{formula:c3a94550-15ff-4506-a16e-cf3ac043a9b9}} and thus range from {{formula:f69eb1a3-25ef-4b44-97ae-eaaca6c0a129}} to {{formula:1cdd1e1b-56c6-4807-8811-afdc0453a8fd}} for {{formula:ad9d475b-c843-42b1-bf22-bd4d0c8d08a9}} and {{formula:86664019-dbab-4a93-b973-f7bb33370f94}} .
In Figure REF , we replicate the results shown in Figure
REF for the linear problem. For the test in Figure REF (c), we consider various ROMs associated with {{formula:f4199762-9547-4e7b-8220-68813c9e2343}} and {{formula:ee7cc273-536e-4b13-bf26-5a73501bfb5b}} . We observe that the dual residual is highly-correlated with the {{formula:a1f2f237-0a51-412d-8069-31cf57355e3b}} relative error: this empirical finding motivates the use of the (approximate) dual residual estimator to drive greedy sampling methods (cf. {{cite:e58f82591b5bf07f61fa8250c3c8c06af51aa997}}).
{{figure:17ae72f2-d81a-4a5f-bcb5-ed389e2a5f47}}{{figure:4291383d-2260-4e18-8dd8-7461b10450a1}} | r | f4c168cf59abce035ea15ead57261f59 |
to weight features. A more informal but maybe more intuitive definition of mutual information is that
MI measures the information of {{formula:7b355d04-f45d-4690-a349-e2497c9c492f}} that is also in {{formula:06da9e33-60b0-4e29-88eb-eda0c83cfddb}} . If the features are independent no information
is shared so mutual information is zero. In the other end we have that one feature is an exact copy of
the other, all the information it contains is also shared by the other so the mutual information is the
same as the information conveyed by one of them, namely its entropy. A very popular feature weighting
method uses the idea of mutual information. It was proposed by {{cite:76597375f4cc3accbcce17e800ca73cdc2788175}}
and it is used in {{cite:843625e34341bd7499ae41e618169336a7b02fc7}} when splitting nodes in top down indutcion of
decision trees (TDIDT) best known as ID3. The term information gain (IG) in Eq. REF
is used there. Its intuitive interpretation would be: The more an feature reduces class entropy when
knowing its value, the more its weight. This is just another way to say: The more information is shared
between an feature and the class, the more its weight. So if we have a set of classes {{formula:f1fe03c7-9c43-42ab-b504-ddc6705f626e}} we can define
IG for the class knowing the value of a feature {{formula:565ea073-b952-4a65-b0cb-32bbf7b91e2a}} as shown in Eq. REF
{{formula:35aa27f0-fb7a-4914-a6a7-acc35af5356d}}
| m | 2ab1878f711bbd1044be46a249a2d6c1 |
We find that the proposed method trained with shape induction obtains both the highest classification accuracy and the best recall of TB examples. On the other hand, we find that the cycleGAN {{cite:2d584f92f76dc86395010de9d93fc11750126cbf}} CT offers less prediction value, with lower classification scores and lower TB recall rates. This is because cycleGAN {{cite:2d584f92f76dc86395010de9d93fc11750126cbf}} limits the expressiveness of X-rays, normalizing clinical abnormalities, and adds noise, see Figure REF .
{{figure:1a4dba78-57b1-4140-b626-90d3f12712e6}} | r | ced0315242f6771b42546fe9c3b4170c |
Further development of search technologies requires ever-increasing computational resources. Recent advances were achieved with cloud-based tensor processor unit pods with the power of over 100 petaflops and specialised chips designed to accelerate the training of neural networks. Albeit enough computing resources may be available today, the future demand for prodigious amounts of processing power is beyond traditional hardware. The adiabatic quantum algorithm {{cite:2c8da2650dacdf8f31907990a5dc5403624b6687}} and quantum stochastic walks {{cite:f347541658513ca5af003ab03b6ac8da0271212d}}, {{cite:6f22f944a67b6b2aed6aecbce972a617b996d228}} are considered as potential quantum analogues of the PageRank algorithm. Classical physical systems, such as crosspoint resistive memory arrays {{cite:e29aaacfa65340b31e290deb4d99eeeabf07605e}}, are proposed for emulating the original PageRank algorithm based on the power method. In another direction of novel computing, various unconventional physical systems are considered as simulators that can minimise spin Hamiltonians. Mapping a real-life optimisation problem into such Hamiltonian and its concomitant minimisation by the natural or guided evolution of the systems promises to solve hard optimisation tasks. The various platforms for such optimisation include optical parametric oscillators {{cite:d77b48e1ab050f079a8dd9d1a43043ea47af7df9}}, {{cite:5570df8d17be0872188d87df827f2969b6102ea0}}, electronic oscillators {{cite:aa41cb489fd108d4580efdbadffdd0822beebcb7}}, {{cite:e86cb8ebf47f2a46c6813f75e457453053eeb6f1}}, memristors {{cite:10271f86f7732d79cc30dae182841fafcd7e4857}}, lasers {{cite:fff13512e55c30edef24435676be92a30b1c71e7}}, {{cite:fcf9772ddf02456502e8a3c1c1e7917285fdab4d}}, {{cite:623adfd80ae42d1283c5df8dcd191dc139cec75b}}, {{cite:17b16df2b84ccfd3be755652525194085ada141d}}, photonic simulators {{cite:d855b6f56769d898c51c85c3a03c5663325ae6cf}}, {{cite:d088c3b7773eb335247b2bbb8e9d792a5a5c0c93}}, cold atoms {{cite:c93778c8c020eafaa26aff583de295397dbc24f8}}, {{cite:21857e8f0c6db173a37dfe0a055e2fd259199a35}}, trapped ions {{cite:ccc34f85c30fccc012bdad7cb8ec17ec43891fbf}}, polariton condensates {{cite:90258875c29618c4cb507d9ae451596254baeaaa}}, {{cite:4bfc448ff1128cc1b9d6b2a69fd3aadd661a9e20}}, photon condensates {{cite:7bbac07464683ea4fdea66dae204904978edfdba}}, QED {{cite:c6a937cecb2e548ca503c7fd67cd797640a121b1}}, {{cite:f0cecec0763e4cccd8482d151556edc5ab508ba3}}, and others {{cite:beb0a26f23bfb8718aa51cc31dcfd74481528ea9}}, {{cite:615adc5cbbecdbeabd6267c4613d299e10236a83}}, {{cite:71068b5d408b3d3a47559597c0a4b1162c1d7f25}}. While the demonstration of their ability to find the global minima of computationally hard problems faster than the classical von Neumann architecture remains elusive, many of these disparate physical systems can either efficiently perform matrix-vector multiplication {{cite:d855b6f56769d898c51c85c3a03c5663325ae6cf}}, {{cite:f7492b452d55affe316b4937e54f453c67c95fc8}}, {{cite:81cee0975488d08289873251c49fa5a0abe1ccf9}}, {{cite:272f5434f478598f0106c29ecb103bdd79ec8f21}}, {{cite:19309d2ce8567bf4bacfa537adcc8bea91073776}} or mimic the Hopfield neural networks {{cite:16543696fb44a4a85ae325c3a36dcfcb51de869d}}, {{cite:ee13a5ceae4cf99f2ccc275a1d22138c7c33917f}}, {{cite:10271f86f7732d79cc30dae182841fafcd7e4857}}. For a certain choice of parameters, the time evolution of such networks can be viewed as an eigenvalue maximisation problem {{cite:b41bd41273507af1ccb13c28f19e239cbb492c60}}, which results in finding the energy state dictated by signs of the eigenvector corresponding to the largest eigenvalue of the interaction matrix, i.e. principal eigenvector.
{{figure:de63a037-c878-4383-9b94-19cae9218f94}} | i | fb00046de1226da7b310bc5ead230f61 |
In recent years, considerable interest has been focused on the subject of higher curvature gravity theories, much of which has been motivated through the attempts to provide a quantum description for gravitational interaction. Indeed, the quest for unifying the principles of quantum mechanics with gravitation has a long history and the first attempts to apply the standard quantization techniques to the Einstein-Hilbert action indicated that GR is nonrenormalizable {{cite:8df088b02edc96836df33135a190525a5a802af7}}. However, GR action becomes renormalizable when it is modified by higher curvature terms {{cite:29f09244bf541266a49164117dfef1ab2b0ba4cf}}. Therefore, if our starting point is a higher curvature classical theory of gravity instead of GR, we can get a renormalizable theory in which such higher curvature corrections can be regarded as candidates for quantum gravity. On the other side, from historical point of view, many efforts have been carried out in order to unify gravitational interaction with other fundamental ones. An approach to investigating this issue is to examine theoretical frameworks based on higher dimensions, i.e., beyond our conventional four-dimensional spacetime. In this respect, higher-dimensional gravity theories are taken into account as important ingredients of contemporary theories of fundamental physics, such as Kaluza-Klein, string theory, supergravity {{cite:f493d390ff85893ea40df6ee3ddbb5435afe6dd2}}, as well as holography {{cite:a7586c9bed93902247ca927fceffe9c5eae06e6e}} and cosmological scenarios {{cite:36067eb6389fe0174b2a225915985ae9b77ebde9}}. Since the advent and development of these ideas, a great deal of effort has been expended to seek out physically reliable alternatives to GR theory. Of particular interest is Lovelock gravity, which is a natural generalization of GR to higher dimensions {{cite:6ff72534b32fb48cd230df9b6ba7092850cf604e}}. This theory is indeed the most general higher curvature gravity that possesses second-order equations of motion. The Lagrangian of Lovelock gravity is defined by a sum of dimensionally extended Euler densities so that in four dimensions all of the higher curvature correction terms appear as total derivatives, and thus, the theory reduces to GR. However, in higher dimensions, the new correction terms do make nontrivial contributions to the gravity sector of the action; see e.g. {{cite:e5dc88fd5ab401e0bf180f2f3c1e801bda960c2f}}, for recent reviews. Fortunately, in the framework of modified gravity theories the use of exotic matter can be avoided, thus providing opportunities for traversable wormholes, and, among these theories, Lovelock gravity is not an exception. In this manner, static traversable wormholes have been introduced in third-order Lovelock theory {{cite:6d9da58eeaa82970115ead48f679b624859a696e}}, where the presence of Lovelock terms helps the energy conditions to be satisfied near the wormhole throat. Static wormholes in vacuum in higher-dimensional Lovelock gravity have been reported in {{cite:2b32a4f86d478baf1c9129e2b528dbcd04752739}} and dynamic wormhole solutions in this framework with compact extra dimensions were analyzed in {{cite:9367a8e6dc1e4bf1a437a45bfa150d43ac9f300e}}. The occurrence of spacetime singularities has been also reported in the literature. In {{cite:de69805931d9208c9acb2078680e38c27bdbc517}}, exact radiating spacetimes filled with a null fluid have been found and application of these generalized Vaidya solutions in braneworld scenarios has been studied. Moreover, the gravitational collapse of a null dust fluid in Lovelock gravity has been studied in {{cite:11707a46a9cc100a9618586d976d7c88eede1f5a}} where it is shown that a naked singularity is formed whose nature and strength depend on spacetime dimensions or the power of the mass function. Also, in {{cite:f378cd645c4bdd4c7ac15b36682251bf9d344470}}, the formation of massive naked singularities and their properties in a spherically symmetric dust cloud collapse has been investigated within a class of Lemaitre-Tolman-Bondi (LTB) spacetimes.
| i | 67ca35d577b64be22a5dfcdba0ff58dd |
Data transformation. For fair comparison, we use the stochastic data transformation proposed by Chen {{cite:96e391f7fbe6f337ac638766e12ebdba54e88137}} for all methods. In the case of grayscale images, we only use the random cropping augmentation. For EBCLR, we also add small Gaussian noise {{formula:184fdc27-1451-4a77-88ea-98320934ff1d}} to stabilize training {{cite:96f7bd08c6dfa5c094c2802a44e9696897cb1a01}}, {{cite:dae7e25f4bde8bcdee6a73d3d36a97768360e3fb}}, {{cite:d3357e0c3924c110fce3433e9e478738f60aef48}}. We remark that Gaussian noise of standard deviation {{formula:e885e375-d06d-46db-a19b-1a51a87cddad}} is nearly invisible to the human eye.
| m | 209f7f116541265b1f92cd571bd9165b |
We introduce a novel milestone-based task tracker (M-Track) for vision-and-language navigation (VLN) and show that explicit milestone detection and checking significantly benefits long-horizon VLN tasks such as those in ALFRED {{cite:48a3d2578b948887f58811e264cf569337a32bd4}}. Our empirical results show the effectiveness of M-Track with two strong baseline models.
In summary, this work clearly demonstrates the importance of explicit progress monitoring (as opposed to, , resorting to a single policy network for both planning and implicit progress monitoring), especially for long-horizon tasks. To make the point, we propose one instantiation with reference to the conditions in ALFRED, and different (or more generic) instantiations for different conditions can be explored in the future. We note the following limitations of the current design that warrant further development:
| d | 7d9e92481bde3b07ed3fe6a1bcca188a |
We carried out the FCI and CCSD calculations using PySCF {{cite:80ee819100946542e8da39fce6f174818ba4e5a2}}, while the UCCSD computations were performed using the OpenFermion-PySCF {{cite:703fd34785c198bbfadffc84119965569f72bf73}} program. The one-body and two-body integrals, as can be seen from Eq. (REF ), are the main ingredients from a ClC to carry out many-body calculations on a quantum simulator. These integrals are obtained from the PySCF program {{cite:80ee819100946542e8da39fce6f174818ba4e5a2}}. In this program, Gaussian type orbitals {{cite:5989ea399377b4888f449c0f1e463e7966839e6d}}, specifically contracted versions of the minimal STO-3G and STO-6G basis {{cite:a5c57273d92701c62046a7c1a5216e601d35897c}}, as well as Pople's 3-21G basis and 6-31G basis {{cite:1ad95bce42a60c8cd0895eccb6598c3215602032}}, are employed. Since the number of qubits required for the computations is equal to the number of spin-orbitals (which is in turn decided by the choice of single-particle basis set), the qubit requirement for Be, Li{{formula:6c717152-6b7b-4206-9f0e-d2cb1ec93c69}} , and B{{formula:5a9c816b-89db-4366-bcce-a495ed0ae462}} is 10 for the STO-3G and STO-6G basis sets, while it is 18 for the 3-21G and 6-31G basis sets. We stress that we carry out all-electron calculations, that is, we do not freeze any of the occupied spin-orbitals. This factor, in combination with the chemically (and/ or physically motivated) UCCSD variational form, leads to the computations becoming expensive. As an example, Be in the 6-31G basis, which is a 18 qubit computation, demands for about 1900 gates even with the ‘heavy’ {{formula:b244377c-19e6-4a3b-a976-2e2766b80e3f}} with full entanglement strategy hardware efficient ansätz, but UCCSD demands for about 32000 gates. This scaling makes computations with more qubits challenging. In all of our calculations, we set the initial guess parameters for the variational form to zero. Also, we fixed the Trotter number to be one. We used a gradient-free approach, the COBYLA (Constrained Optimization BY Linear Approximation) optimizer, which is commonly used in literature {{cite:bfd6e641a582e8bd5f17bf3e6f7413fbc0de2d8a}}, {{cite:eda0416345a2d0ce919a77ce0ebffebdb33a206f}}, {{cite:e34017e0ca68df89a6da2d63bba489cd7c87568f}}, {{cite:4da4cc66e0641979f115fceeea53744bff214c80}}. For an optimization problem with {{formula:7668aa59-b517-405e-98f6-68e2ba55ef92}} design variables, a simplex of {{formula:de172952-31ab-409d-97ad-7a2607302bb2}} vertices is constructed. Hereafter, a linear polynomial approximation is used as an interpolation of the objective function and the inequality constraints of the problem. The algorithm controls the size of the trust region (simplex) and decreases it until a convergence is reached. The convergence for COBYLA optimizer is slower than the gradient based methods as it requires higher number of function evaluations to reach the optimum value. However, stability comes as a notable feature for this algorithm along with lesser number of parameters to be tuned for performing optimization {{cite:e83e163afb981f14fd34ef00b2ea9e5454180b60}}. We used the qiskit 0.15.0 package {{cite:cf49f161c320e1e5bcfe4794eb8ecce3731c252b}} to carry out quantum simulations using the VQE algorithm.
| m | cc439c058d8904b9630454439ff0c1fd |
Works particularly focus on the spectral energy of MHD flows started to emerge by the mid of the 20th century.
From the earliest of such works
the works of
Kraichnan {{cite:4b5119f58b5d3c6d6987b01a5836794ab2aac009}}, {{cite:c6cee68cd57b0478a69f4a99c743812e6f899453}} and Iroshnikov {{cite:88b822aca51e8d14ffc47cc5995eb9ffc2077ab6}} can be mentioned. Unlike Kolmogorov where the spectral energy decays proportional to {{formula:00553aef-eb61-4e30-9615-c47f2c45a796}} , Kraichnan and Iroshnikov concluded that
the spectral energy
of a fully developed MHD turbulent flow decays proportional to {{formula:82d92ca6-4719-4d34-a65c-ed286a905d7c}} , which
later on was supported by M. Dobrowolny, A. Mangeney and P. Veltri in {{cite:2fe3e51c6fa4a9ef0924bbe1096b7a22eded3d81}}.
Mahendra K. Verma in his review {{cite:1c92707ffa0901e64f3890903cf9a7057c9b8ece}} said that these works
are the first to establish phenomenological theory on MHD turbulence,
which he called
Kraichnan-Iroshnikov-Dobrowolny (KID) phenomenon.
| i | f7b2cecc478d53b4693aad13df5999fb |
While we were finishing this paper, Cueca and Mehta {{cite:2440c641b743a3ac8ef14801884e5bbb2f265988}} established
an isomorphism between the sheaf of functions on a graded symplectic manifold of degree 2 and the Keller-Waldmann algebra {{cite:121365d9a81aa97475ecc1d2cb1f1bed57055d20}} of cochains on a vector bundle {{formula:871d51cb-b4b4-4e1a-a55b-a9c83472ecdd}} , equipped with a non-degenerated symmetric bilinear form {{formula:0f265de6-e20f-4092-a9dc-edfdc11be008}} . In this algebra, the {{formula:14465a54-9473-4e1e-973c-3dbe1f3b79d7}} cochains coincide with the pre-Courant structures on {{formula:c863dfed-1316-4d22-8b8a-3236bd2ee591}} and in this case the one-to-one correspondence was already known (see {{cite:1c7e791288c40fc7ead38e1c712ec5aadb99a389}}). In the case where {{formula:db29b00f-cadc-440b-9f65-25f0c2a4c56e}} and {{formula:0bd69ba1-9ef2-4b03-b6a1-05a1531e7c65}} is equipped with the canonical pairing {{formula:9590dea4-185a-4ce7-8cb7-0fce9695ad5a}} , the map {{formula:6f44e67f-9c34-40d5-8df0-bcef2d1f57a3}} defined by equations (REF )-(REF ) can be recovered from the isomorphism defined in {{cite:2440c641b743a3ac8ef14801884e5bbb2f265988}}.
| i | 7faacfddd71cc38ee3049cfc0cce02c5 |
ii) Joint training. We can train a new task jointly with the previous and new training data. This method can achieve good performance. While as the number of translation tasks grows, storing and retraining on all training data becomes infeasible and cumbersome {{cite:c3125cdddab82e49cf7ed866bb538d3ad1c2d532}}. More seriously, in many cases, the training data for previously learned tasks is unavailable due to the data privacy and protection {{cite:3e5256c5d3f8f0f559ff0e2a4d0c30e5844138e3}}, {{cite:aabdd8f1e387524b97558e5aa2e8ff5a1f106889}}, and it is impossible to jointly train an MNMT model under this situation.
{{table:8998cae3-7585-4418-a815-d75466e5e1ed}} | i | 4ed996223d0c6ef0d8da86734e761316 |
Previous work has explored these features of genetic regulatory circuits, and much of it has become textbook material {{cite:33c6e05941992e53b8622c71e739cdb077d2d1df}}. In particular, simple autoregulatory circuit mechanisms are well-understood, as is one-dimensional Kramers escape from metastable states, both for cases where the dynamics are effectively diffusive and a Fokker-Planck description is adequate {{cite:4a84f9a675c1655d0c355f5d9a682329e2fd3721}}, and for those in which molecule numbers must be treated as integers, where one must solve a master equation {{cite:62f4b0fe3fa50d624dccb50a25749b86c46ff5e7}}, {{cite:df2a5af797a08a6e8ce7fd7594f1d4c9d035140b}}.
| i | 445f08b10eff2a57681d93edc76d4580 |
SC has been considered in the special setting where {{formula:8cc34d45-3716-4f71-a466-9d86a6477437}} is also assumed to be
monotone {{cite:d002e42c91c5cdb478083203fdff940e9a34e2d6}},
but to the best of our knowledge has never been considered in the
non-monotone setting. The topic of this paper is therefore to consider whether
approximation algorithms can be developed for this problem, and further whether
those algorithms can be made practical in the face of large data sets.
In particular, the streaming model is considered: {{formula:1b8c63f6-587b-499c-b49e-f4eb19900a3f}} is assumed to arrive
in an arbitrary order, and the goal is to solve SC so that very few passes are
made through the entire data set and in addition memory used at any point in time
is limited.
| i | 632d9ccd74dd6f4bfeef384fd44cc39b |
We assume
the expansion center of the SNR is at rest with respect to the LSR,
and so give it the median proper motion
of the stars when we compute the distance of stars from
the explosion center as a function of time. While certainly wrong at some level,
it is a better assumption than keeping it at rest in the
Gaia frame given that there are both large differences between the
Gaia frame and the LSR and that these differences have nothing
to do with any physics leading to the expansion center having
a motion relative to the LSR. Compared to {{cite:bf1afaf168861c8dbd79d912be48aef8bf675d78}}
we also used a maximum fractional distance of the closest
approach point from the expansion center of of {{formula:8983f411-896c-49e6-b77e-043e77060a58}} instead of {{formula:c5f81bde-2aa1-4920-8637-693924b66432}} .
| r | 5614e060c8c6f70dacce59f22db5690e |
The analysis of neural bandits has been enabled through the theory of neural tangent (NT) kernel {{cite:26cf969ef51cf5fcc518baf74d6fc8fba8a8f65c}} which approximates an overparameterized neural net with the kernel corresponding to its infinite width, and the bounds on the approximation error (e.g., see, {{cite:7fc8760b83c4990091ee4f8bdd5d575101391702}}). {{cite:f19ec8f88f002ed8277224db3e0aa66f4d787a78}}, {{cite:32b2b8143e029777842c9076b1a703fd3f9efcf3}}, {{cite:914d4e82a5880df269bae3a80f36953bcdf6464d}} proved {{formula:547c2015-3209-40c4-999e-ac79657daa35}}The notations {{formula:1120c300-b142-467c-b38f-689e33befefd}} and {{formula:f31ef3b6-79dd-42ab-8303-8e08c508dcf0}} are used for mathematical order and that up to logarithmic factors, respectively. bounds on cumulative regret, where {{formula:ad54bc0d-e492-4e26-a136-59de09ef1c63}} is the number of steps and {{formula:6ba73b54-2887-4087-917e-e552efb7e0db}} is a complexity term determined by the neural tangent kernel {{formula:719c6b2d-a0d2-4eab-a1ff-768431f6a8f2}} associated with the particular neural network. Specifically, {{formula:5812b6d6-b0bc-4240-a756-16e18b654937}} is the information gain corresponding to {{formula:d2b1d0e3-f5e6-4937-b1bf-da0e4992ac6e}} for datasets of size {{formula:79c62bbc-b811-4703-a995-31ac2709aca7}} . For the ReLU neural nets on {{formula:54c728b8-aced-41a7-be67-b9e1da482be7}} -dimensional domains considered in {{cite:f19ec8f88f002ed8277224db3e0aa66f4d787a78}}, {{cite:32b2b8143e029777842c9076b1a703fd3f9efcf3}}, {{cite:914d4e82a5880df269bae3a80f36953bcdf6464d}}, {{formula:35dcffb5-0143-4342-862b-1e9a08cfa5f1}} is the best upper bound known for the information gain {{cite:8407393fc27166737eb347bf029c1ac35b4ad09a}}, {{cite:0cb230bfa05907327a21d40b36be861a3c4d7ba7}}. Inserting this bound on {{formula:21b872fb-f3a1-4aa1-8c81-22da55da0852}} , the aforementioned regret bounds become trivial (superlinear) generally when {{formula:fdbe6938-6b5e-4169-a1c2-b89bb18985c1}} , unless further restrictive assumptions are made on the contexts. {{cite:8407393fc27166737eb347bf029c1ac35b4ad09a}} addressed this issue by considering the Sup variant of NeuralUCB (referred to as SupNeuralUCB). The Sup variant is an adoption of SupLinUCB, which was initially introduced in {{cite:e5eb8f6226e90fd87e5974c5e3d8af28c8b176d1}} for linear contextual bandits, to the neural setting. {{cite:8407393fc27166737eb347bf029c1ac35b4ad09a}} proved an {{formula:623e758f-7d7e-4421-99ad-50e07c61e3c4}} regret bound for SupNeuralUCB in the case of ReLU neural nets, which solved the issue of superlinear regret bound (non-diminishing instantaneous regret).
| r | fe2c81f43cd3652209ff6e73504cb936 |
Previous works demonstrated vulnerability of DNNs when the input is either an image {{cite:d4a92cb39b61075b7093c628f5c6da6cb4e3ad95}}, {{cite:7baa61b0d82776b9575f8005f7ea161c2c7918f5}} or a point cloud {{cite:c0a6606631255e1643fd2c12637e06b38d01055d}}, {{cite:757f43e85657267e7dce0cc7b9391fcacd51589f}}. Most point cloud attacks, simply alter or add individual points to the point cloud, and are not physically realizable due to properties of LiDAR sensors. More recently, a physically realizable adversarial attack on point clouds was made using a perturbed mesh that is placed in the 3D scene and rendered differentiably by simulating a LiDAR {{cite:03c7f7627948556bf6a18cd4a544e92f2f0a3301}}, {{cite:edd56d02e5488d8c7c05a2a049f02103b6594b23}}. Existing attacks either target a single modality or are not physically realizable, limiting their applicability to real world scenarios.
| i | a655c3ad7ea15761475d8d93cb889d74 |
This research proposes an object detection model based on the YOLO v3 classifier for Smart Surveillance System (3s). Yolo v3 was utilized for this research because of its superior speed compared to other stable versions following recent updates. Compared with some newer versions {{cite:d9712015f7229106e29c9331606855049adf8923}}, Version 3 is a preferred choice that trades off a bit of accuracy for speed and is ideal for real-time detection in Smart Surveillance Systems (3s). Newer versions, despite their advantages, have some considerable drawbacks that this research takes into account. This research proposes a two-phased Smart Surveillance System (3s) model: the detection phase and the Analysis phase. These phases encompass pre-training and post-training processes, as described in Fig. 7 below.
{{figure:0231cee8-c2c7-4074-8fb4-96551836450b}} | m | 009637ce08c679295df05a6e0b1db0c1 |
Relativistic fluid dynamics has been proved to be a successful theory for ultra-relativistic heavy-ion collisions {{cite:fbfdb24849b824167088beba9a5bc2d8f200346a}}, {{cite:2dcafc79ab1aa0d1f8d17aab64715567690ec34b}}, {{cite:a2a9b92296abc1bc5db2fd7b394accdde8f753b8}}, {{cite:8fc765fe9eddc0cc126b01f2981124612324bf85}}. Spin polarization measurements of {{formula:00373a06-5008-4c1c-9e3d-526c6bbc867c}} hyperons done recently indicated that the we should include space-time evolution of spin in the framework of relativistic fluid dynamics {{cite:3b98c219699536a124b6c86445bf4fb9446adc90}}, {{cite:74ffe8efc67d0208a7f32bc13f29dbfb6df94a94}}, {{cite:6ce8784c5fa2822b85cfdf10e90bc1c83cec7f33}}, {{cite:e6e1240912aa8c173a6c936e864cff7188785598}}, {{cite:1c7937534f8ec428243c009a6819573779a230ea}}, {{cite:434214cd62f514f29ebe4e1df04cc65a9e11b0a1}}.
Formulation of such a spin fluid dynamics formalism was studied first in Ref. {{cite:55aa84aa66be2952dd79ac5993d451a688d9f2d4}}, which gave rise to many studies {{cite:ee0e3891034e2646a1687e936f1ddc08537dedf0}}, {{cite:ffabd45850961444c8de9298da4eebedb7cb44c8}}, {{cite:348baa86790c039eb230943479ab506f99065b87}}, {{cite:8df713ac41e9771861a5d328780d2a5684d0d4f6}}, {{cite:1f6036b93345b66a39dcb74ebae73a877d61659c}}, {{cite:a5bbd9bd877c4360e953c04fde8583a614ca9f41}}, {{cite:82f0352a36e7c55d473870f5371cdeccd812f6c0}}, {{cite:ab9a73daf447f926f9ed1348d5322b209e792d6d}}, {{cite:b3e6dc62322bd3d46291d7d91e3240b85890bd71}}, {{cite:4212d88fbeea86b02acb5a9ecefea7cfb80fb8af}}, {{cite:c3a14940556545a712b8a3e89705306fc379f25e}}. Contrary to theoretical studies done on spin which considered spin-vorticity coupling to be the reason for the spin polarization at freeze-out {{cite:4fc723f8e6579fd4bf566ced6023ac62ce5dd27c}}, {{cite:3c109b0ce1822d5bd277b80927edc63d8ad2d587}}, {{cite:e0b9f1024ac6ecddb5a491440921ed884be54ae2}}, {{cite:98010898ea9e7f06baa2bcd3f3c44eca8b66b6ea}}, {{cite:b5d1a8f41d580c2d99ae65e4c51e58b0033e439e}}, {{cite:29a22d0d8255049ea3310100000cded3b0bb9cda}}, {{cite:f1996cafe4bc7f6b1061b1a44db975e4531568ae}}, {{cite:5cb0070dddc0782ff7d03cd186aa9ef74338e5ee}}, {{cite:70f86ffb1f235484934081f5b28907c9718a9dd5}}, {{cite:91cfd9d1d457931d0f3538e8bf07a2a02caa9a7b}}, {{cite:b08e398131c2a77cb2c3f06649a52e1777f23d1e}}, {{cite:be85635b1080eb2a250845d0166f2084bc0f5437}}, {{cite:7e4a0d3dc4a1e3f8906a03b3e72411ed00aa74b3}}, {{cite:0778b3a832c4436d194e1d016c49e6e27e298e06}}, {{cite:41c4234f4cb436a3542d98a41b6c1f564f23b07b}}, {{cite:b3cda3d6001f430802fb1341c3988be73a8da4ed}}, {{cite:f4ab73112f9e9683dec260abc561ef46431bf65b}}, {{cite:7cceb13e32fc0249eb55a045e0d82eb330e660fc}}, {{cite:9324549ff14bf3c6f8f5d91cdef8cd52deb63afa}}, {{cite:86f0a6b850746552c95492ab304403e541e4b17a}}, {{cite:10fc86a3a9e885f261dbbfde430b659ec760b831}}, {{cite:1039d66162aa7d9c8cd2ffa61b7e264fc8d40bba}}, {{cite:5d40a814fbcd1d8e493d8f348a7dde28d14197c6}}, {{cite:ac97c60e9d11806011f56ff9a98041f3fa70ab9a}}, {{cite:787a9126b3c30f89e25ff5d2974187dfa1cd6b06}}, {{cite:d641ed720d5836028ff0fab56201de186e8fd800}}, {{cite:ca45cbc36a7b9640a4fc717873caf6df1495c6f3}}, {{cite:0c34e6327f8d1f5f954a3228acbda1fedf35ac8a}}, {{cite:2ccdc1baba4311c7f889908a725c07abaf88d190}}, {{cite:d40c0ae75ddeb514b94c825e0d9269e2196bd486}}, {{cite:25c05cdbcf543cfb981c1a27909985fedcc73424}}, {{cite:c7fdf1bf405b1be2e3cb7d30634c25911253f275}}, {{cite:379c2a771cc1da0bb89465a8ed318e978e11c981}}, {{cite:f8a9dacc12b500878eb542b37be85bcc5a9e0b2a}}, {{cite:f735f0df2190ab8b94f4b913ceb43bc2cde3cf0c}}, {{cite:7e745dbcb1ea7f577c588bee101ea053dbd4624b}}, {{cite:50aab1c0dc646e2fb418e76a170243dd8ea9abd5}}, {{cite:5a3d6dc9c2474d53427156bd13b6d5967c8b0324}}, {{cite:0ae9fd0f200b2f735d70e2556e98e4c2a60d3086}}, {{cite:25e6d5fb0431682fbadf6e3c9d84f92917845480}}, {{cite:c35294ed38e0fe6b4755f6c6bc5b76024a7703ac}}, {{cite:51e6d5d25170f8f36eae9ecbb7bdbf421f909d4c}}, {{cite:7ef650f92f3f4bcffe5ba5bacca5eaeb52cd2614}}, {{cite:4a6dfc65c34a685afe444786efc1e633cbb14eed}}, {{cite:e636d6010b2d1ad89f4d4b53dba6c7f61e4ea4c3}},
the spin hydrodynamic formalism has been developed on the basis on conservation laws and local thermodynamic equilibrium, introducing new dynamic quantity namely spin polarization tensor. In this work, we use the Gubser symmetry {{cite:44c0b73481bbeba1807e45f6f33438b0aff249eb}}, {{cite:9ddfd0657bb186e61ed1f73a254d19484da73213}}, {{cite:2ac5eaf784538fcf263843f3e120cc1f2e2e66bc}} arguments to find the conformal transformations and criteria for conformal invariance of the conservation laws which are used in the spin hydrodynamics framework {{cite:4212d88fbeea86b02acb5a9ecefea7cfb80fb8af}}, {{cite:a5bbd9bd877c4360e953c04fde8583a614ca9f41}}, {{cite:f66279f4954a0a5e39a0af298f23aafd83b7ea9a}}. Throughout the article we use natural units, i.e., {{formula:725fe4df-cea9-4d36-bc2e-d7dac3d68f63}} .
| i | 1993284e2a3e38f6aed070bfbca6cdf7 |
This leads us to a conclusion, that we have detected a dark remnant candidate.
Based on the masses we obtained the lens could be a candidate white dwarf, neutron star or a black hole.
If the hypothesis of the dark remnant is correct, the mass of the object along with uncertainties lands within the mass-gap {{cite:82c287845549198149e2863165be1b357bdf0308}}, {{cite:5ffda4598c703a558e5ad8601f02d0205ebc149c}}.
This could be another case that supports the hypothesis that there is in fact no mass-gap {{cite:5d515dec8b21ee3702a4d5ef7377ba0486ecff9f}} along with recently observed mass-gap objects {{cite:d883270320bb801822b2f3e923e86b1a1835c8d9}}, {{cite:1d260381b6cbf119dff625757df360bd362962cf}}, {{cite:4d91c8fbaa6e7f50056ba8dc6547a4004b2f3617}}.
| d | fa8ba5e4c092856534364e6bdc7b2978 |
[noitemsep,topsep=0pt]
(i)
Neutrino oscillations: Two-dimensional NH and IH {{formula:b74dd2f2-6d4a-408c-983a-b158931daf8a}} tables for {{formula:6c9ea194-f359-4703-a21d-5a4aaa46676c}} and {{formula:c5f32e08-5348-44ac-abcf-9808512ee9a2}} from NuFit 4.1 {{cite:6749e165d35e7fbde82f0fa3f30d491d1b72e87e}}. These come from fits to the data from solar (Homestake chlorine {{cite:0dcedfa6caa804cc22a6ac818973be2731cc133a}}, Gallex/GNO {{cite:66eb077de49ede7f7151b0999152f61d4e652cf0}}, SAGE {{cite:50f42c93a37e291cb23c2c732916e5ae1be0e381}}, SNO {{cite:26fa4df69a47250414e7de470b7ed89ee3cbb02d}}, four phases of Super-Kamiokande {{cite:845b95a62cad964a9519fb8a9f276e7b9d5190a0}}, {{cite:1f006f864b515344e0e99dd077e16151cdfd0051}}, {{cite:3930f6b3b86699908d255a7da00102b6a280d54b}}, {{cite:7c2d82335327eb9cde93227e6145ff4766d49e79}}, two phases of Borexino {{cite:a97dc6e4d4b113c70ca37890b0bb3e37a94806ad}}, {{cite:1b790e9ba84f5864f23f903e0bfffef3277028af}}, {{cite:b91a44b0998ab1036f3abb6258905b7c594be14d}}), atmospheric (IceCube/DeepCore {{cite:79f70f924a4715e1f4c3e1389fd7825e1ecca35c}}, Super-Kamiokande {{cite:d45b1c97734c7f87ef800eff05c8df39d15479cb}}), reactor (KamLAND {{cite:499e609f26a6a870ce407bbc3465acb2d4e4fb18}}, Double Chooz {{cite:d5dd0a1ad37602a14d87c310c9c02485dbd93752}}, Daya Bay {{cite:0277fddede1f254a50cf3f47fa15240382874047}}, {{cite:b7dfcb11a83c053649228007bf986179ac8de378}}, Reno {{cite:b1bcd7849c0e18364a75f31b22c8ad681070f4a3}}), and accelerator experiments (MINOS {{cite:c08fe1146443043689695905f6019d5a7ae6af7c}}, {{cite:4faf13c4f7504b729d0855bef667c212ff94cd53}}, T2K {{cite:4973687b123fb6b0a5e0d646b3357615f8292e04}}, {{cite:efbc808fc37139c64a4ac120e115812d81ccfeaa}}, NO{{formula:d0d6da6a-d739-4617-ab43-4a1c9a5f5781}} A {{cite:2a083aa5cc15a2719a1646216446a61e3b8451e2}}, {{cite:bd58a85965bf786a87b85949ad75801134a52750}}). The other oscillation parameters (mixing angles {{formula:c94229bb-989a-41dd-97fc-f693a748d0cf}} and CP phase {{formula:48e565d4-be24-4a80-901b-adf2bbf66001}} ) have no bearing on neutrino mass studies and do not enter our analysis. Updates contained in NuFit 5.0 {{cite:dd1ecd71150ac9d8685571524e4d95d87c9519f1}} released when this article was in the final stages of preparation include only small improvements to the likelihoods for {{formula:5f293bb7-231d-4d7a-b0d9-119998989da8}} and {{formula:2ff130cd-8442-4687-82be-3d657850a593}} , so they have minimal impact on the results we show here.
(ii)
BBN: Primordial abundances of {{formula:1e52dc73-ce9a-419c-8da7-49b5acb00bd5}} He, {{formula:de585073-5aba-4e28-8b6a-a2d41e68fdc5}} {{cite:28c0f9d3cc691047fa2bfc079d364c6688d7aa11}} and deuterium, {{formula:e17524fd-5921-4019-88c7-7b9e10a7b7f2}} {{cite:92fadfdcf98d570d2023a9b29f2329d88be365f0}}.
(iii)
CMB: Planck 2018 baseline likelihoods consisting of high-{{formula:43601aab-6576-44fc-97fa-f00892baa19d}} and low-{{formula:c8ee25e0-c267-482a-8dd1-a1659867aa7a}} temperature and polarization data, plus CMB lensing {{cite:030796be2de7f330ad9e001e146dbd42fb673f58}}.
(iv)
Supernovae Type Ia (SN Ia): 1048 SN Ia included in the Pantheon compilation {{cite:f1b72045e0cc25a131a1ec5850ad8686739506d7}}.
(v)
BAO scale: Measurements of the transverse comoving distance {{formula:7b330b05-b7ff-4bd6-ba46-4e62520fe7f2}} and the Hubble parameter {{formula:2851e2e6-b6a6-42bf-aeab-cf0d3eb28751}} from the BOSS DR12 anisotropic consensus {{cite:4afa33745642a2efca8b9a6a5b7737d27c3cd255}}, {{formula:1fcce344-cbe0-4467-84a7-155c80efb07d}} from DES Y1 {{cite:f8949949796701fc86b6c6b9ad06fbbba6e38717}}, and the volume-averaged distance {{formula:d4c8cdeb-7354-434e-8b84-329d38fbfe6b}} from the combined 6dF and MGS galaxy surveys {{cite:9804029390dc4459f4b00f798f1a54362d26af1b}}, {{cite:6d32e1b713f27036bab8c7b64d996fbd067d6206}}, {{cite:4bad2b2a4c9e668f794eb5f49e0c2db2273b536a}} and the eBOSS DR14 lumious red galaxy (LRG) and quasi-stellar objects (QSO) samples {{cite:30c7b3e82ec90897db7c2606362d2163212dbde1}}, {{cite:a72b83fdd3c183dd8c3f11a5301db3ddfd4b4ef9}}. All measurements are relative to {{formula:302b8fea-1ed4-4388-a476-5c760ba259e2}} , the radius of the sound horizon at the baryon-drag epoch.
| m | 0935c19a55ab6c2610acfec4dcaf6218 |
There are several disadvantages of spectrogram based MSS methods. First, spectrogram based MSS systems only predict the spectrogram {{formula:3910df63-8040-441a-911d-39009ec1a566}} of sources, but do not estimate the phases of separated sources. Therefore, the performance of those MSS systems are limited. Recently, several works have investigated estimating the phases of sources for MSS {{cite:b8c7448c86fd650589da1c2e5b28363d2a905b68}}. Secondly, spectrogram may not be an optimal representation for a time-domain signal. For example, STFT performs well in analysing stationary signals in a short time window, while signals are not always stationary. Time-domain MSS systems have been proposed to address those problems. Both the input and output of time-domain systems are waveforms instead of spectrograms. Those time-domain systems have the advantage of not needing to estimate phases for MSS, such as WavUNet {{cite:bfa052456b455863706924836fcd4f1ce32d6bf4}}, Conv-TasNet {{cite:83b6f339bcb6c07ee9acc26bd4f1e4cad557ee9d}}, and Demucs {{cite:d24b3de60f3662b2dde45472f78f60d6f034acda}}. Similar to the spectrogram based MSS systems, we build a mapping {{formula:e1a2261a-fe30-4bcd-89cb-8d8296f103f1}} from the mixture signal {{formula:46083e13-330f-45f8-aaaf-724317496d7a}} to separate source {{formula:3787e63d-900c-4cf1-902f-c38a0940b995}} :
{{formula:6a3e2746-eb16-41de-b8e9-3e49503c48cf}}
| m | a6a21ea6bfb74dfc42ae6776473c30f5 |
In order to assess the performances of our system, we report the standard as well as the BCubedUnlike the classic version, the BCubed version of precision, recall and F1 score favors solutions that (i) make errors in clusters with already many errors (ii) make errors in a large clusters rather than in small ones. {{cite:772b0fdcbf7f034c6f8e5a8df5bff2c79cba0a1f}} precision, recall and F1 score.
We evaluate our system for two tasks: monolingual and multilingual news clustering.
| r | e846c4fc469cc12b0d0a7db1b288c5ad |
where {{formula:19c0ac3d-78fe-492c-9ef1-5fcba67a56ae}} is the `grey-body coefficient'. Notice that {{formula:5941da1f-4cad-43c4-996b-1677743b88b6}} is the reversible limit, when only an infinitesimal amount of radiation escapes, while {{formula:e2d2ce7f-14d7-4949-9157-f4b67c95d23d}} is the case with a trivial grey-body factor (no reflections). Since {{formula:c02231b6-51a8-4b8e-ac2f-d1ca6ad89d90}} , the rate of change of the total thermodynamic entropy is always {{formula:3ab59d8d-ad64-47e3-b302-31a92029c49b}} which is a statement of the generalized second law for black hole evaporation {{cite:702fbf0e17cc653afc76c968915036f471f0c240}}, {{cite:f5497a09793616e446f12c292c3cb07f5ee9bd78}}.
| i | 8eb6f897abe16b533d7173fd12dd242f |
A first-principles band-structure calculation for 3-ML-thick Fe on Au(111) was carried out by adjusting the lattice constant to Au. At the initial growth stage of Fe on Au(111), this assumption is plausible through the proximity in the ultrathin layer case before the lattice relaxation to stabilize the bulk bcc structure. DFT calculations were performed using the Vienna {{formula:08e92220-e0fc-4211-8d63-bc68de59eab2}} {{formula:3c89e94b-eb1b-4898-b6b5-9adca5598c39}} simulation package {{cite:653b1d1c29439075db0a95a245c9f19f5e0deaf0}} with the projector augmented wave potential {{cite:725dfc5ae77c27a50105f43a2a12966b2e5658cf}}, including spin-orbit interaction and the spin-polarized generalized gradient approximation for the exchange and correlation term {{cite:25a28a2ab058f372d378c96b3e81e6c03e8fc017}}. The Fe/Au(111) slab was constructed with 19 atomic layers of Au and three atomic layers of Fe with an in-plane lattice constant of 4.078/{{formula:ebd53e6a-ba1d-4b6e-9990-fa4516c2a62f}} ({{formula:2edb1c89-f008-4aed-83de-cd4680a6f92a}} ) of the hexagonal unit cell. A plane-wave cut-off energy of 400 eV for the wave function and {{formula:ca99ba39-18b9-4929-8af4-0b504ce1112a}} {{formula:5e463466-5901-4bde-acb5-ad8a8c80a18e}} -points in the first Brillouin zone. Figure 5 shows the orbital-resolved band dispersions of the Fe 3{{formula:e1d52164-89ca-4d28-923f-03f72c557d38}} states with Au valence bands along the {{formula:94a79887-f2b6-4115-a1aa-22bf31f020fc}} -{{formula:31ae1f06-10dc-4a6a-a978-0a5f36f0d050}} symmetric line in the two-dimensional hexagonal Brillouin zone. The Au(111) band dispersions with Rashba-type surface state splitting were clearly observed. The dispersive features derived from Fe are typical for dispersions in strained fcc structures.
The 3{{formula:c5ee153f-6c71-4159-8467-18c04fbb0fee}} orbitals at the {{formula:1cfb88c7-f350-4413-990e-e7d0a9257dbe}} point are evident for the {{formula:8c6fc874-da54-4ae5-ab50-1add6cb0f1b0}} -{{formula:f4e87aec-3a57-4a6a-9c73-d5198672e23a}} hybridization along the out-of-plane direction. In the vicinity of {{formula:3df37108-e38c-498a-96e6-4d758c56f64d}} , the in-plane orbitals are dominant, which favors the out-of-plane orbital magnetic moment.
In the case of bcc Fe, the band dispersion features were quite different {{cite:d6400943b887c403b3a87121856fd6964752443a}}. Therefore, the Fe layer facing on the Au is essential for the PMA from the viewpoint of DFT calculations.
| r | 76261d851af38038285e645a15e5893e |
As shown in Table REF , our method outperforms all the other methods under most metrics.
Particularly, our method improves the F-score by more than {{formula:47bf1983-4901-4abb-8aaf-8b36cc4322e5}} , while advances CD a large step.
Surprisingly, our method even outperforms PU-Net in NUC, although it is not trained with the repulsion loss {{cite:b53c5507d42ec5308cbcc7ca1315dcaa6b641255}}, which forces the generated point cloud uniform.
We attribute this to the effect of our adversarial loss.
As for MLS, it performs well in Deviation but has the lowest NUC scores.
The reason is that MLS tends to produce new points close to the points in the input point cloud, which leads to a non-uniformly distributed point cloud, resulting in poor performance on NUC metric.
However, the mean deviation to the ground truth is small.
Similar results are obtained on SHREC15 as shown in Table REF , which shows the generalization ability of our method on the unseen dataset.
As for NUC and Deviation, our method outperforms the baseline methods by a large margin.
| m | 4a58e8138a9573adeb0cdf5be059950e |
As mentioned above, the proposal of our analysis is to study the
vanishing viscosity limit for the compressible Navier-Stokes system
with density dependent viscosity. The strategy adopted in order to
prove the convergence relies to the issue of weak-strong uniqueness by
using relative energy estimates. In particular, we introduce a
relative energy functional “measuring" the distance between the weak
solution of the compressible Navier-Stokes system and the strong
solution of the compressible Euler system. Consequently, we derive a
relative energy inequality satisfied by the weak solution of the
Navier-Stokes equations. As the weak formulation, the relative energy
inequality involves some test functions that have to satisfy the
no-slip conditions, which are not satisfied by the solution of the
Euler equations. For this reasons, we will introduce a “correction"
based on the Kato's “fake" boundary layer in order to work with test
functions satisfying the no-slip conditions at the boundaries.
However, different from the construction of Feireisl et
al. {{cite:4c2c840aa7af001971e5255617706c8c688681cb}}, {{cite:3e6598e488544476a46b0b0b1d892ab1ecdf9cc6}}, our relative energy inequality
is derived from an “augmented version" of the compressible
Navier-Stokes system (see Bresch et al. {{cite:3a12f18743f6437ffd57f1c6113f6666cea5c8d2}}, {{cite:966b640cc3db13fc952b269705d4990f52390f99}},
{{cite:a9ca05252e885c6bb875972f6dca8eb9d99bde39}}; see also {{cite:edd653bfa0434a2b2fb8d98fc9e43b659ff1eea1}},{{cite:02a62b3eec2c3935c8da19ddcd8ee18f94719afc}},{{cite:99dd46902952bf6af4d01351e8608b7719f28dce}} for recent
applications). The reason for that stands in the fact that a {{formula:5cb74c24-4eca-4a10-9212-291c8b0920cf}}
bound for the velocity is no longer available because of the density
dependent viscosity. Consequently, standard application of the Korn’s
inequality in the weak-strong uniqueness context is not possible (see,
for example, Feireisl et al. {{cite:3e6598e488544476a46b0b0b1d892ab1ecdf9cc6}}). We would like to
mention that, as far as the authors are aware, this is the first
result in this direction. A recent result of similar type has been
proved by Geng et al. {{cite:65cecf9b2ad25b7c09e35d364c24e15742b6bf91}} where the authors establish the
convergence in the vanishing viscosity limit of the Navier-Stokes
equations to the Euler equations for three-dimensional compressible
isentropic flow in the whole space {{formula:de327d22-f391-4e75-87f0-5c8c1cc07af1}} when the viscosity
coefficients are given as constant multiples of the density’s
power. Moreover, a convergence to dissipative solution of compressible
Euler equations has been analyzed in {{cite:3a12f18743f6437ffd57f1c6113f6666cea5c8d2}} in the
three-dimensional torus {{formula:1e7cf2d4-52c9-4990-bc1f-142e047bb68f}} .
| i | bff3b5fcddbb5ee9ca0b8a73e2e0e8e5 |
A wide range of estimators based on convex relaxations, spectral methods, and non-convex approaches have been proposed for specific instances of GLMs, such as sparse linear regression {{cite:3ea37714e83e6eb5bbc00c1b3eb4339c23349caf}}, {{cite:d7c091c2a08e1c5e4d131c67edbeaaae5bc9d0e4}}, {{cite:66a8ccdfb915325d9d9081e21e0e9f9222bb51df}}, phase retrieval {{cite:943e0bea735d6dbc1dfc8f779be7031f381a91d9}}, {{cite:8cb210e0eacb0c056c410482aae743fb295e7117}}, {{cite:2560c6680ebfabe30194d837ad1297c36dac3442}}, {{cite:996b795e1b500f147dffbadd0312706da4dd12cc}}, {{cite:38fe92192320a7060c5a8941612fcc8af66c9770}}, {{cite:64906ce557096282b079f02ee70ddc600b06c0f0}} and one-bit compressed sensing {{cite:e674109a7e3ef99ddfed43ffe4cb1270d7bfd73a}}, {{cite:b1a74a1c7315a4e47ad23c958d55f796f6679e08}}, {{cite:33fcc118dc55cb048023a29041b9cfd877f078ee}}. Most of these techniques are generic and can incorporate certain constraints like sparsity, but they are not well-equipped to exploit specific information about {{formula:4ef4c316-d30d-455b-a7d1-8c27d557db76}} , e.g., a known signal prior.
| i | 14aaffff2d5c610048b7841e22e48e39 |
We have described methods for valid inference two common downstream targets of
inference: the label prevalence {{formula:0fdbde7f-7d44-4bd1-9a1c-e99ec22e5db5}} and class-conditional feature means {{formula:074a899b-89f1-4fc1-a460-43fafeef632b}} .
Inspired by our motivating example from TIRF microscopy, we focus on the case where
the classifier used for automatic labeling is trained on data that differs in
distribution from the new, unlabeled data. As this dataset shift may
prevent classifiers from generalizing to the new data, and therefore prevent valid
statistical inference, we rely on identification of a subset of features that
enable construction of a generalizable classifier. These features can be designed from
training data, and a variety of methods exist to construct features which
satisfy the covariate shift assumption {{cite:cbd39f3a71ca495fefdee9e4586c9b591d42af49}}, {{cite:f32488f80d92a7b1ede116bdb5d6635f3ac28071}}, {{cite:2be71e66552733f6cfc9e1cc39066e40b893b3a1}}, {{cite:fb54d677e9fff8bff09f142ded1fe9c50e40a141}}, {{cite:50935c91363e4fecb0088428b0ab905f87d94a35}}. In our TIRF microscopy case study, a label shift
assumption is more appropriate than covariate shift, and we show that
exploratory data analysis and careful feature engineering can construct
generalizable covariates.
| d | 34797848e72f3ae168f3892c04b2023c |
Although the average length of Line of Code (LoC) is 47 in all PyTorrent packages, we investigate it with more precision on a portion of the PyTorrent dataset for 66,528 sample raw Python scripts. The sample data includes 9,951,811 LoC, and the average number of LoC in each script includes 149. In this sample dataset, we observe the length of LoC with an average of 44.92 (which is very close to the whole dataset with the length of 47). Interestingly, we observe that selecting a length of 50 and 70 covers 61,854 (%86) and 65,656 (%99) of all sample records without truncation, respectively. The detail of percentile coverage is shown in Figure REF . Therefore, base on the statistic results we recommend that researchers safely truncate a LoC Python programming language with a much smaller length (i.e., 70) in comparison to natural language models (i.e., 512). Selecting a smaller size allows the researcher to generate a smaller tokenizer and less LoC encoder size to save computation resources and much speedy processing on both fine-tuning and inferring from a BERT-based language model {{cite:0086944bb9ade33dbcb3e1e76e851ca37e73d103}}.
{{figure:d87fc134-90c2-4043-ba22-73583deb558a}} | m | 70eb89e06c951e73d10158aa7104ad75 |
We also note that the operator size distribution is a more refined description of the time-evolved operators than the averaged OTOC that we have presented here. It remains a question as to how and when the size distribution discussed here compares with the usual notion of the operator size {{cite:d82b91ad95f9316e66da199a3a0b320659b9931d}}, and to those amenable in experiments {{cite:3612450413315f4bc76fc264db5ce0ba4fe2d3d2}}. It is argued in {{cite:f6e7dbf4fb40a807ecab98fdff0f3fb2ef3a73b7}}, {{cite:c8993d8ae6155f8819786eceda6d1c22fe623b97}}, {{cite:5f93498bb3e0809436f667d30c5a3b51779f52bc}}, {{cite:b0f47de0635de529a347976e2b4ecbc1b1de65fb}}, that the rate of change of momentum of the particle falling in to the bulk spacetime is dual to the complexity of the dual operator at the boundary. This complexity basically measures the growth of the size of the operator under time evolution. Some recent progress has been made towards understanding complexity for the dual field theory {{cite:ea51a2a75986970b347d75f93e565dc45537411b}}, {{cite:79b640b92afe5c9650b8f8f32b85c13400096fed}}, {{cite:5462dba851334a4e8a4c7fe14235473e0cccc6c8}}, {{cite:5103d93663200bca1cf4b8c549d9033070566d5a}}, {{cite:6dcb21dbeebc903a59c1ec54f500ed4f0b902ee2}}, {{cite:b8090575847fee7e3dcadadcfd926025fe035e13}}, {{cite:7e9c12969f9525842690d863e2fa2f33166a3e75}}, {{cite:08f2e9ab886b0fe147c9b837e80f3d31d31bd648}}, {{cite:1b723f9e5dfb60abd182fa005f2a23aa4ba855c5}}, {{cite:90ae1d2567a846bd1640a331420979aedad04101}}, {{cite:c0d4df651eba8a3113eb8a40e0a253bf30984e16}}, {{cite:22cc2f93958b004c561dcec571cd62762c00b7bb}}, {{cite:1837ec9ebb2af05388a5bbf3dc7db9c49c0197d6}}, {{cite:948119422af8ef222d77a73daa11ba57fa6b2247}}, see {{cite:85c0d1b167a397a5f641cdadd39a2e54afeb4eeb}} for a recent review. However, it is in its early stage of development. An interesting direction will be to develop this idea of operator growth using complexity as a possible diagnostic. This will not only enable us to make connection with certain predictions coming from holography but will also help us to compare with other diagnostics which are measurable via experiments. Another important theoretical direction is to explore the finite temperature generalizations of the many-body teleportation in the spirit similar to {{cite:4cd23fb3cfbd4e85bb6b09978ef42b095d3e935f}}, {{cite:339646947fe28e673bca86c0c90deefa5aebcefd}}, {{cite:0794daec9d98973a6f4ddb16b0212e83bd0d3a49}}. In recent times, several toy models based on tensor network construction for holography has been proposed {{cite:6e870a2d21768c77f9796d7a2ea018997047b6f6}}, {{cite:5048f080c49d602de433c6bf1913867633c749cf}}, {{cite:4936b4bd3db00b420361fb7e6eb806e23b033db5}}, {{cite:768de3bd3402164a58016b1c0fe77fc6b9e6d93f}}, {{cite:157e86183bbe7a85151aa99bfaa24d6f9fa7c6c0}}, {{cite:3429a6ac532eeb224811d2fd3764df0e5c4e7534}}, {{cite:eb970ae03ad78e02bbd1b146dcb7a9cc8b6b96f6}}, {{cite:08d2d24249484013cc6d2d5bd8cd062cdefb2c04}}. In this context, it will be interesting to realize the thermofield double state and the teleportation protocol. Perhaps {{cite:e09d825837f6f999d9bb06416436ae68e411c499}} will provide a good starting point. This will pave the way forward to some of the predictions coming from holography using interesting quantum many-body systems.
| d | 62cdca8091aa6b35de817171fe2cc0da |
Benefits of CAPD: A CAPD points out the most likely class. If a semantic space embedding vector of a class and the CAPD of the image lies close to each other, there is a strong confidence for that class. One important contribution of this paper is the derivation of the CAPD for each unseen class. Conventional ZSL approaches in this vein of thought essentially calculate one principal direction {{cite:90c24ff4bb3d46834227ce7463360beae7f3b490}}, {{cite:b6a14c102aa217eb6ce2e896c03374ea0a6f7a18}}, {{cite:4458da9c87e34600966c81e3c17b80413d6cc950}}, {{cite:59902cf82143ee04d7a51c6561e95edc32e29a37}}, {{cite:11ff591ea3c2a54a89c9a15aea7764497f4e2e96}}. Generalizing all seen-unseen classes with only one principal direction cannot capture the differences among classes effectively. In our work, each CAPD is obtained with the help of bilinear mapping (matrix multiplication). One can extend this by incorporating latent variables, in line with the work Xian et al. {{cite:4458da9c87e34600966c81e3c17b80413d6cc950}} where a collection of bilinear maps along with a selection criterion is used.
| d | 37d2facf65f2140431cca04a803c7d48 |
Cross-modal/multi-modal pre-training methods have been proposed: OpenL3{{cite:a51f0983d9ec4c148853b9eecb0423b0e35ba5df}} was pre-trained by using audio-visual correspondence as training signal. Wang et al. {{cite:9e366ee68fb34d1e617b2f6d5d566df2a33b46e0}} was pre-trained by using correspondence between video, spectrograms, and raw waveforms to learn general-purpose audio representations.
COALA{{cite:8a03f6442ac05ff92c1ecd0cfc0a884315fa2115}} was pre-trained by aligning the learned latent representations of audio and associated tags and evaluated on SER and music tasks.
| m | b52194e21b797a82d9e96552ae14f753 |
The Evaluation of Data Augmentation Methods. The quantity and diversity of training data are of great importance to model's generalization ability. However, since there is no unified metrics, how to evaluate the synthesized image quality is an open problem {{cite:9403f58574f626ec86393ec03cb2867e11dea39e}}. At this stage, researchers evaluate the quality of the synthetic data in several following ways.
First, the synthetic data are usually evaluated by human eyes, which is time-consuming, labor-intensive, and subjective. Amazon Mechanical Turk (AMT) is often used to evaluate the realism of outputs. AMT evaluates the quality and authenticity of the generated images by asking participants to vote for various images synthesized with different methods.
Second, some studies combine the evaluation with specific tasks, which is to evaluate data augmentation methods according to their effect on the tasks metrics with and without data augmentation, such as classification tasks with classification accuracy and semantic segmentation with IOU of masks.
However, there is no evaluation index only for the synthetic data itself.
Generally, the evaluation metrics are based on diversity of individual data and consistency of overall data distribution regardless of what task is. Data quality analysis can help design evaluation metrics .
| d | 2c09494b4a863275ee4287b466e4d810 |
The first attempt to classify all the multi-affine partial difference equations defined on the quad graph and possessing CAC was carried out
in {{cite:be993bfad5357685a12da3fb81bfe2a2086db431}}. There the equation on the quad graph was treated as a geometric object not embedded in any {{formula:8eb9e437-25f0-4307-a09d-ebd26857284a}} -lattice, as displayed in Fig. REF . The quad-equation is an expression of the form
{{formula:59830812-18a6-4ba9-954f-5b2e711b142e}}
| i | c650730fdbdc72079e5414f83c794fc2 |
where {{formula:b00ef2d5-a545-4ae1-9f8b-ad7074b37cb0}} and {{formula:f1ee8360-708a-45ed-b1ce-e3b1fad77d80}} are the measured and theoretically predicted quantities respectively. For the BAO data from {{cite:b08f7cfb7b5170b2f5712fce8ab638b951bd0c27}}, the covariance matrix C is given in eq. (19) of {{cite:0edeb3e0a02ea6491cdbe34f21843bb3e75669a1}} and the covarience matrix for the {{cite:72e5b76e49e3e0c021d32768eb7b478396eea737}} data is
{{formula:90c52a0f-4882-4834-a6a6-ede9cfa7809a}}
| m | 99ad53fd144376646412f22679a47a4e |
Let indeed {{formula:d9861cef-0f78-490a-8ab9-82f1694ac35b}} , where {{formula:95250d9a-96f8-4132-99a7-c68036ca4023}} are the Pareto-optimal strategy profiles and {{formula:94f07395-0582-41ac-ad6c-18f2789b83c5}} , {{formula:0bcccc29-94ab-4fff-96dc-9f3c25ae0548}} . We consider the program PLAY-PARETO specified informally as followsAs in {{cite:b2b88f4775e51d6fddc6756489e65ca3b815c247}}, we will neglect issues related to representing real numbers in programs. That is, we will be working in a model of real computation. Such computation models are found in other areas of theoretical computer science: The most well-known is the BSS-model {{cite:29089397907b24c68052b63ba3385d7d242c7588}}.: Agents synchronously sample an index {{formula:c47bef14-7086-4eb1-b13a-42a708f9a1ac}} , value {{formula:27ca2bff-5c93-4cd0-b231-0a1681235d9e}} appearing with with probability {{formula:db8d2557-8674-4a6b-afb6-2f4e38a13e9b}} .
Then each agent {{formula:6cb7e35c-f995-40b8-9d94-3dca8d16867f}} performs {{formula:708c3a1b-cd4c-49ad-a08b-20c7156e5889}} . Since the random sampling is synchronized, when agent {{formula:b24c5ef7-aa9b-468d-abb6-432c680605a6}} plays {{formula:cfa3ba7e-dfbe-4290-8423-d58c6e64d1b6}} all other agents {{formula:6ccd8e2e-acb5-42ee-8384-237272784eab}} play {{formula:18d6b649-3a05-45cc-bae9-328348bbfd5d}} . Thus PLAY-PARETO implements {{formula:8dfc43f6-f3e7-4954-bac8-86a8ed4c82de}} . Formally:
| r | 54b860dd243493db7622023a6ab05efa |
All baselines and methods are clearly worse in predicting humanness than
animacy.Performance for `humanness' is lower overall, with the F-Score of our best-performing method decreasing from 0.79 to 0.63. Due to space limitations, we could not include the evaluation on humanness annotations in this paper, but it can be found on our Github repository: https://github.com/Living-with-machines/AtypicalAnimacy. In the case of the supervised baselines, this is possibly due in part to the very limited amount of annotated data for this concept (81 instances of animacy with humanness, 120 instances of animacy without humanness). Besides, the lower agreement between annotators in detecting humanness (Krippendorff {{formula:09ec5f8c-7185-4420-b2fb-23393e12f571}} of 0.50) suggests that the task is more subjective.
Table REF reports the top predicted tokens by the pre-1850 BERT model in sentences where animated machines are attributed or negated humanness. This experiment shows how language models can hint a social bias embedding in nineteenth-century discourse.Contextualized word embeddings have been used in the past to identify cultural and social biases that permeate language {{cite:afea2138f34c68cd21a020e830796fa4e61f8d77}}. While `man' remains the most predicted token replacing machine (and `woman' is not far behind), the appearance of `slave(s)' and `savage' in contexts of negated humanness reflects the nineteenth-century tendency to use these words in discourses that confer diminished human qualities on those people.
{{table:021f3581-2aa5-4248-883d-71b8fb7127d8}} | d | 407d977efdee108689c890e18968fd1a |
The lens equation at the leading order in the strong deflection limit
coincides with the conventional one,
if the deflection angle {{formula:329f0b8d-394a-4a2d-905d-66da8a949729}} is replaced
by the offset deflection {{formula:83077cd9-d9fa-4916-b244-9c8c968c2893}}
{{cite:e45c6d00b676357f24c578e7c33163b401c36540}}.
= - DLSDS N .
By solving this equation at the leading order in the offset angle,
we find
N = B e-C (- N0) DSDLS ,
which agrees with Eq. (81) of Reference {{cite:e45c6d00b676357f24c578e7c33163b401c36540}}.
See e.g. Section IV of Reference {{cite:e45c6d00b676357f24c578e7c33163b401c36540}} for more detail.
| m | ffe7d1faccae78be2830a28b8fe6b163 |
HVPR {{cite:f4c84dd73a8922b1389194b6f1e9f2bf0b3b98c3}} is a single-stage detector. It has two feature encoder streams extracting point-wise and voxel-wise features. Extracted features are integrated together and scattered into a pseudo image as hybrid features. An attentive convolutional middle module is performed on the hybrid feature map, followed by a single-stage detection head. STD {{cite:4ddc91bdbbbdad83a5bcce87108a99c2eb7b604d}} is a two-stage detector that uses PointNet to extract point-wise features. A point-based proposal generation module with spherical anchors is designed to achieve high recall. Then a PointsPool module voxelizes each proposal, followed by a VFE layer. In the box refinement module, CNNs are applied on those voxels for final prediction. PV-RCNN {{cite:55cdf89e37a210d66e7a995156ba40aabd90d1fc}} uses the 3D sparse convolution for voxel feature extraction. A Voxel Set Abstraction (Voxel-SA) module is added to each convolutional layer to encode voxel features into a small set of key points, which are sampled by farthest point sampling. Key point features are then re-weighted by foreground segmentation score. Finally, they are used to enhance the ROI grid points for refinement. H{{formula:9efdefc7-6b5d-4ccd-9d9c-b462dc15802b}} 3D R-CNN {{cite:fa953bb2da46f99e096745b81b6d9022775703ed}} extracts point-wise features from multi-view projection. It projects the point cloud to a bird's eye view under Cartesian coordinates and a perspective view under the cylindrical coordinates, separately. BEV feature and point-voxel (PV) features are concatenated together for proposal generation in BEV and fused together as point-wise hollow-3D (H3D) features. Then voxelization is performed on the 3D space, and point-wise H3D features are aggregated as voxel-wise H3D features for the refinement process.
| m | bc5a8bd198c0de4c0d7eb6a2446c5aac |
A further point to discuss is whether the radical detected in this work could be an important intermediate to forming larger molecules. Although dedicated studies on the reactivity of CH{{formula:5b778fde-e0dc-4280-9599-0595951861e6}} C{{formula:137b3e46-ea84-42e8-99b2-0f804be3562a}} N are needed, our radical could play a role in the synthesis of large organic N-bearing molecules, such as nitrogen heterocycles. For example, benzonitrile ({{formula:7738da1c-068c-43cb-9296-b46016383f36}} -C{{formula:64602411-6fc2-473b-a171-352392bf1d2b}} H{{formula:7fbc9eab-77b5-48c5-a67e-9211440b0ca3}} CN), known to be present in TMC-1 and other molecular clouds {{cite:6ba281f09e2b3e41551662aef4d908dd1cca6f62}}, {{cite:1ee48303d41495b855d6948766b6954575b859d4}} and thought to be formed through the reaction of benzene with CN {{cite:ace1f9970f45ca7054f143044f75ffe9d0930bab}}, could be formed through the reaction of CH{{formula:3c91272c-9019-4e54-94cb-76ec2e6aff4a}} C{{formula:91ed8a2d-eb97-4e80-9f98-7b933193722b}} N with allene (CH{{formula:7605d090-b489-45b1-88a6-66ae875bbee6}} CCH{{formula:d7f79292-0ace-4652-8a8d-67f3ef9cda69}} ), which is suspected to be abundant in TMC-1 {{cite:aca994694ed197b81af7b172705504c28bfc984d}}, {{cite:6b774ba105d45e7e4ab5f33e2bc1cba1af8b0777}}, {{cite:6b9514a859016396c42389612f44f0fde5608a2d}}.
| d | 4a7878a9358c46efa65af9c892e0ae01 |
The whole architecture of the proposed DACM framework is illustrated in Fig. REF . Given the input support and query images, multi-level deep features are first extracted by the fixed backbone network pre-trained on ImageNet {{cite:213c7bd7c43a9a963b3e70fee3398d9b172b8f8a}}. Three levels of deep features with different spatial resolutions form a pyramidal design. For each level, average pooling is used to aggregate multiple features into a single one. Then, three different GP models are trained for computing the covariance matrices (4D cost volume) for each level. Next, the proposed Deformable 4D Transformer Aggregator (DTA) is combined with the weight-sparsified 4D convolution for cost volume aggregation. Finally, a decoder is used to predict the final segmentation result for the input query image.
| m | a257ca9667a58e2eea6897d01a6852c5 |
Several interesting results observed when mapping overlapping links between the cortical thickness and functional networks by lobar divisions need further attention. First, the approach adopted here was to compare the networks at a single value of network density. The advantage of this approach is that is maps only the most pronounced correlations within the both networks. This means that the correlations statistically not different from zero were not considered in the analysis. However, the obtained topologies may include different numbers of correlations for a larger study-group size. Thus, the calculation of the maps of overlapping correlations across a range of networks densities (based also on a larger study group) may reveal some of the cortical interactions that did not pass statistical significance test in this study. Second, the definition of conventional lobar divisions used in this study was based on the Desikan-Kelliany cortical parcellation. Although well established, there exist alternative approaches for the cortical segmentation by using different brain templates {{cite:c9ef402bf240d820c37126de0451d23c091ab02e}}. Since adoption of different brain templates may have influence on the patterns of network correlations, further studies could validate these results using different anatomical (or functional) classifications. Finally, a study combining structural, functional and diffusion-weighted MRI data could test to what extent variations and strengths of positive and negative correlations can be inferred from underlying direct axonal links or synchronous/asynchronous functional links. These future studies could also resolve problems of estimating networks individually for each subject.
| d | e16111fd26a11e9b2e46669de957507c |
The test accuracy results are reported in tabel:graph-res. Note that the last two rows are reported results from {{cite:725d2e1283b99f1ebf33c66518ff7c613c98d3a3}}, thus do not have standard deviations. All the other models are trained in an end-to-end manner. Because of the highly imbalanced label distribution in the Friendster dataset, we reweight the test accuracy by the label proportion as in {{cite:6ae1da028f84bf7fb8bcb930c2488adedf6da1e2}}. We see that for the Friendster and PubMed datasets, single-hop node classification using Set Twister achieves the best results, while in Cora and Citeseer, Set Twister performs the worst. One reason for this is that as seen in tabel:stat, the Cora and Citeseer graphs have small degrees, and, thus, there are almost no higher-order dependencies to capture in the node neighborhoods. In the Arxiv dataset, which is large and dense, with similar architectures, DeepSets and Set Twister outperform most GNN and collective inference methods.
We note that for the GCN and Arxiv dataset, we obtain performance results that are worse than those reported in {{cite:b46f549aef6b4d7a83e8c016542de9a410a04062}}, and choose instead to present our results.
| r | 6eb5f2914ad24fc6cd2bfa9cf0d43b30 |
Quantum walks have been a successful tool used in many algorithmic applications, specially in search algorithms {{cite:4eb0512c7cb9bac45092e262b4a4853b2ee32daf}}. Another related problem is the task of performing quantum state transfer {{cite:6354fbfa9ee40dc1ed32bb3c39455936a2ec900e}} between two vertices of a graph, often called sender and receiver. In this problem, we want to transfer with high probability a state localized initially on the sender vertex to the receiver vertex.
| i | 461d77cf6165b1cd3b44f5d76c6241e9 |
A saliency map is a representative of what the network has learnt and it is not guaranteed that the explanations match human intuition. However, it is observed that a network with a higher classification accuracy generally produces more intuitive maps{{cite:5ee506d4c156fc0c62e072be677d67d2b7793441}}. A desirable property of every explanation map is that it is non-random and highlights only the relevant regions in the image and no more. Many of the methods use a qualitative assessment based on human inspection to evaluate and compare different maps. To evaluate the Grad-CAM maps, the authors conduct user surveys to find which maps and models they find reliable. Although human measurements on the quality of these maps are useful, they are time-consuming, could introduce bias and inaccurate evaluations{{cite:a10eb88057bec200a68e7e842f15062ff898e8a5}}.
Another way to compare the generated explanation/saliency maps is to use different metrics proposed in the long-term research on the prediction of visual attention in images and video {{cite:f7066e2915ec43ed919cb16af97007ac1cc73337}}.
For FEM{{cite:f0769ddf8108baf1331cdf3e77f117f8de9a4363}} the authors compare the saliency maps obtained by FEM with gradient-based methods. They show that the most similar explanations in terms of usual metrics of comparison of saliency maps such as Pearson Correlation Coefficient, {{formula:eca377e7-eff6-4236-8f69-116576fce7e7}} -Similarity are given by Grad-CAM method we presented in Sec. REF .
| d | 6f795e7ea02bce5c65f77efddc62bac9 |
Fig. REF shows the pareto frontier of HAO with respect to accuracy and latency. MobileNetV2 {{cite:1b4150b51e805284c48ec36ebfc2928a376c17f8}} is a popular neural architecture manually designed for efficient inference. The original MobileNetV2 is in floating-point format. To achieve a fair comparison, we quantize MobileNetV2 to 8-bit weights and 8-bit activations, and then run it on FPGA with a {1x1 convolution, 3x3 depthwise convolution, 1x1 convolution} subgraph. We follow {{cite:1b4150b51e805284c48ec36ebfc2928a376c17f8}} to change the channel width multiplier (selected from {{formula:181a00ef-0422-44b9-9bdd-2c9e015a4011}} ) and input resolution (selected from {{formula:365f1ae8-ff4c-49ec-bb81-4d6f080228ab}} ) of MobileNetV2, in order to trade-off latency and accuracy. In comparison, the neural architecture (including input resolution) and quantization bitwidth setting are automatically selected in HAO. As can be seen, HAO outperforms MobileNetV2 on a wide range of latency values. HAO can achieve 72.5% top-1 accuracy with 20ms latency (50 fps), which is more than 1% higher accuracy than MobileNetV2 while running 15% faster. In the cases with a more strict latency constraint (for example autonomous vehicles), HAO can still preserve 66% accuracy with only 8ms latency (125 fps). This is significantly higher than the 63% of MobileNetV2 while being faster. Furthermore, we compare with results from MnasNet {{cite:f9d288f8bcf5dc642423b7aaa23d79ecb4fa83ad}}, which is a hardware-aware neural architecture search method. As in Fig. REF , HAO also outperforms MnasNet by a large marginPart of the MnasNet pareto curve is out of the latency range in Fig. REF . We present these extra results in Table REF ..
{{figure:ae1f9e56-a51e-45e8-bd3a-f787df0e7fb6}}{{table:e67b0884-b351-4339-9cdb-0cb1f06f86a3}}{{figure:697859fd-c873-4180-b053-aec1daf4c3c1}} | r | 10460772cc930236d8cda6ba0c4a01fa |
Adding richness to the data collected in statistical learning tasks removes researcher degrees of freedom when trying to fit current models or theories that may be of insufficient specificity {{cite:b5e6ae080333f3c93250f41181b7859b3bf96875}}, {{cite:345dd6da89c64cf8c16896fe7183784775af831e}}. Our task directly collects priors and current beliefs without the need to infer them from sequential participant actions. In order to fit a Bayesian model, for example, to our belief measurements, one must fit model parameters without freely setting a prior or decision rule to describe participant actions. In other words, we force ourselves to fit models of beliefs to literal measures of belief (initial and concurrent), rather than inferring the belief driving observed actions through the adoption of un-tested assumptions.
| i | aba2d7c3093ea42044446cca5bfca1bc |
This symbolic approach to the modelling and analysis of cryptographic protocols is called the Dolev-Yao model {{cite:523be4d8c1047bd89d31246faf7ee0b506d5e481}}. In this approach, messages are modelled as terms in an algebra. The intruder controls the network, and can see, block, inject, and redirect messages, as well as derive new terms from old according to set rules (but cannot break cryptography). Various extensions to the basic Dolev-Yao model have been proposed, and automated tools have been developed based on them {{cite:08114e4d5e939b748ea723014c26cec77b066abc}}, {{cite:d2a66025e49a6ca9b8f9c27b584ef17dd9732328}}, {{cite:2d054bee206b24bea7a08df5d2a677f721dfee7a}}, {{cite:919b047b82ded037f26b1a8651739e353dfbe503}}, {{cite:52450840c6365afaf7708d24d2341c26ddb7ae4f}}.
| i | f299a034861c562a958e5083b25dd13a |
This operator and approximation properties are needed, e.g., to handle terms involving {{formula:5fbfa504-dc96-4785-a33d-8c005a9ac560}} . We mention that a similar goal of approximating non-smooth functions is applied in the context of a-posteriori error estimates; see, e.g. ({{cite:4ca17dce9c4e919c5ca5084ee02256cb512ddfdc}} page 71).
| r | 14ffaa83a64dece98fc815a115adaf40 |
Robot navigation problems were solved by generating optimal trajectories from robot dynamics model. The trajectory optimization modules are based on dynamic programming, specifically differential dynamic programming and iterative linear quadratic regulator ({{cite:3c675236200dec807a2a1721b98bac2eb9c05d3c}}, {{cite:9f4d4c43a87efcaad4d42e8cdd65bc70795de3e0}}, {{cite:f76100061d1270d0954af63740c304ed8afa0bec}}). These methods are essentially an open loop control and thus susceptible to model errors or disturbances in deployment. To address these problems, model predictive control (MPC) ({{cite:26e731b8d698ffb9cf74fe2fc982cbc2dc0c20f8}}) generates controls given the systems current state by repeatedly solving the optimal control problem over a prediction horizon and only the first optimal control is executed leading to a closed-loop control form.
| m | 4eecba50cb644575874a2050bf4c4ee8 |
The first method for computing the CEI-1 is to take the series expansion of variable {{formula:ec7bcfbe-65fb-4095-95d3-fde2389fd481}} . Actually, with the help of the generalized Newton's binomial theorem, we have {{cite:92af9628976c1aeba65ec5422bbedcf713887836}}
{{formula:3b9f0baf-ab38-476d-ab54-3e382c4d3d50}}
| m | 06d9b22d66615561dc5616506700fb71 |
The roadmap to build the fully-fledged Qinternet has been envisioned in {{cite:035c9cff270d069dc1c0acd92e7d4f06b6832106}}. According to its functionality, six stages lie ahead. At the time of writing, the first three stages are in the experimental phase, and the trusted-repeater networks concept has the potential of extending the network to large areas. It forms an important stepping stone towards the Qinternet {{cite:035c9cff270d069dc1c0acd92e7d4f06b6832106}}, although it does not provide end-to-end security. Prepare-and-measure networks provide links for directly-linked nodes, while entanglement-distribution networks link up nodes connected to a common intermediate node, where the qubits received from the other two nodes are measured using the measurement-device-independent technique of {{cite:180a5bb185833a166b85c5c1c7b5c61916d03d30}}. Thus, the scale of quantum networks classified as prepare-and-measure networks and entanglement-distribution networks remain limited. Satellite-based repeaters are capable of increasing the distance between the directly connected nodes, but they remain limited to 3 nodes, so they are also at the entanglement-distribution network stage.
| i | a5df2b4806b101fea519d450bba91b2f |
[leftmargin=*]
One possible extension of the results we presented here are explicit formulas for the maximum number of faces of any dimensions or also for the number of bounded faces. Explicit formulas for lower-dimensional faces are of particular importance for the combinatorial complexity of tropical varieties {{cite:7a996131c265e39f46988c2044ed080ad2938ffe}}, which are intersections of tropical hypersurfaces, and consequently also for the complexity of many algorithms in tropical geometry.
Further refining the bounds for deep networks is also an interesting endeavor for future work. Even the case of ReLU networks is still the subject of intense investigation.
Another interesting avenue is the explicit number of faces for specific families of non-simple arrangements, for example those that one might obtain in convolutional networks or graph and simplicial networks, which have been recently studied in the ReLU case {{cite:5ce0fe1cafc9225c4f07d1156fefe7b8c708b4e0}}, {{cite:a8eee815b450a5ab511d3660655f33d3f204269a}}.
An interesting open problem is the estimation of the expected number of faces for a given probability distribution over the parameters of shallow and deep maxout networks. The case of ReLU networks was recently studied in {{cite:f7798bbd89f2a9a773fa568a68ea57b202bea26b}}, {{cite:3aaf196f2985930c608edbf6ee1e83dfbc9f67c9}}.
In shallow ReLU networks, any generic parameter gives rise to the maximum number of regions (the number of regions of a generic hyperplane arrangement or equivalently the number of upper vertices of a zonotope).
In contrast, for shallow maxout networks, generic choices of parameters can result in different numbers of regions.
The expected number of regions of a single maxout unit with Gaussian weights corresponds to the number of (upper) vertices of a Gaussian polytope, which has been studied in the literature {{cite:6600951622abb87fd4f159ac03694a05ee63e496}}. However, for a maxout layer one would need to consider Minkowski sums of random polytopes, which to our knowledge have not yet been studied.
A further aspect of interest is the development of parameter initialization strategies that would allow for faster optimization or better algorithmic biases when training maxout networks.
We have presented ways to select parameters that lead to the maximum number of regions for shallow maxout networks and to asymptotically maximal number of regions for deep maxout networks.
Other properties of the initialization that can be considered include the normalization of the activation values across layers and the distribution of linear regions over the space of inputs.
Related aspects for the case of ReLU networks have been studied in {{cite:dadff6743621b32064b00326657b10d0239fce52}}, {{cite:2b7c2ffb6c493b766749fbceb236f0e484e38cfd}}, {{cite:5b3c9d7677406d1955bf168e363ed2e75286d025}}, {{cite:ec8d13a164c2caa7f699977349c27a3e84dbfdec}}, {{cite:b5aa4b1b593096c30b46a5e90619f008b5701a9c}}.
| d | 9e4f8cb6de225c3ab073e6511989555d |
We simulated an idealized HCI system with static phase and amplitude wavefront aberrations generated by an out-of-plane phase aberration.
The system was operating at 1550 nm, consisting of a clear aperture, an idealized DM (e.g., no actuator cross-talk or quantization errors), with a 40{{formula:2e5c5adc-1ef9-4ded-b6d1-6ce1726f25a6}} 40 square grid located in the pupil plane, a charge 2 vortex coronagraph, a (PE)SCC Lyot stop, and a polarizing beamsplitter and detector.
We found that the PESCC has {{formula:e956b894-11c1-4650-9997-e3ff4d27039d}} 16 times more photons available than the SCC (this includes the 50% throughput of the RH polarizer and polarizing beamsplitter).
This was confirmed with additional simulations where we studied the sensitivity of the wavefront sensing with photon noise, as the PESCC reached a sensitivity {{formula:dcabf1dc-a63b-4912-aec1-661b664f4683}} times higher than that of the SCC.
This can either be used to increase the loop speed of the WFC or reach higher sensitivities in the wavefront sensing.
The RH being closer the pupil also relaxes the focal-plane sampling and spectral resolutions constraints with regard to the SCC by a factor 2 and 3.5, respectively, to 2 pixels per {{formula:0336f39e-4efa-42cd-9d61-1ab400e98323}} (which is a factor four gain in number of pixels) and {{formula:efe0304b-673f-4d9b-a27e-bf555ad28cb1}} for an infinitely small RH.
The latter was confirmed with numerical simulations.
Another advantage is that the PESCC automatically estimates the RH PSF, enabling CDI post-processing for all science frames.
Through idealized simulations, we have shown that CDI after WFC can reach a {{formula:96b821b4-19ac-4af3-b361-029994322a29}} raw contrast of {{formula:5b880c11-f883-43de-b61f-73b7890fd42f}} between 1 and 18 {{formula:0c9903e1-3448-4ce6-bb45-54b7954e2c77}} .
However, we found in the analytical and numerical studies that instrumental polarization and differential aberrations need to be tightly controlled for the PESCC to operate successfully.
We have shown that it is possible to measure the degree of instrumental polarization in the OTFs of the two channels when the differential aberrations are not dominant, and this can subsequently be used to correct the images.
If the differential aberrations dominate, then it is preferable to use an instrumental polarization model to predict {{formula:6aad3188-45a2-4c69-8534-9f0acd2b9160}} {{cite:8248856b9a95d4913b5a134a110a73d3ea02a14c}}.
Leakage from the RH polarizer was found not to affect the wavefront sensing significantly, but it does pollute the dark hole in the other channel.
| d | 1b7cab4f39aba177017ab743c3c27660 |
On OTB2015 {{cite:1c59cfda7aef92c1b93e35e804158df1c923191c}}, we first compare prior methods designed for dense task only.
Table REF shows that
ConST-CL outperforms the evaluated methods by a large margin.
Specifically, compared to VFS {{cite:adb095ddf72828849d9e6490ee54082618698c85}}, ConST-CL achieves {{formula:c1a25eab-5abd-4225-917d-9fd35c5e1411}} ({{formula:9844cc5a-57e0-42bb-ae99-d167e6de395c}} ) in precision score and {{formula:74b7b68f-e6d6-4270-b58d-505065d0b28d}} ({{formula:1186d5f0-3076-4159-a933-adfe330db82f}} ) in success score.
To rule out the effect of architecture difference (2D network vs. 3D network), we inflate the 2D ResNet into 3D and load the VFS pre-trained checkpoint, denoted as VFS-inflated in the table.
Compared to the numbers reported in {{cite:adb095ddf72828849d9e6490ee54082618698c85}}, VFS-inflated performs similarly to its 2D counterpart, which indicates the effect of this architecture difference on the tracking task is insignificant.
Further, comparing to the CVRL pre-trained model, CVRL outperforms the VFS-inflated model.
Since the CVRL can be seen as the extension of VFS on clip-level pretraining, the improvement likely comes from a more homogeneous experiment setup.
When compared with CVRL, ConST-CL achieves clear performance gain for single object tracking on the OTB2015 benchmark.
With the backbone model learned by ConST-CL, our tracker achieves the state-of-the-art results in terms of precision and success scores on the OTB2015 {{cite:1c59cfda7aef92c1b93e35e804158df1c923191c}} dataset.
| r | 1d08f87c738b83d8897896ce6449a42e |
We explore the results of running CHAMP on community structures found in various network data sets. In Section REF , we consider a network of NCAA Division I-A college football teams from the 2000 season {{cite:e44d99944958d0f5b1ed65f51db89c385813e231}}, {{cite:cea8f0ad7c897c0abb190544bce8572c1306f907}}. We then look at results of applying CHAMP to a Human Protein Reactome (Section REF ) and a Caltech Facebook network {{cite:43040bc75555ea055eb3ddffc304ecb28c876cc7}} (Section REF ). All three of these undirected networks are studied using the Newman-Girvan null model with a resolution parameter as in Equation (REF ). Finally, in Section REF we apply CHAMP to communities found using the multilayer generalization of modularity in the multilayer network of roll call similarities across time, where each layer is a different two-year Congress {{cite:b94b1b14853ba435f1889420bd044dd96fc7c986}}.
| r | 25ae8b70b6d5f12a59d79c874b6af279 |
Regarding (REF ), the first named author {{cite:90ac46c4394cec0d5c56ec81f4ed21943d7a4e88}} showed that (REF ) holds for star-shaped domains with {{formula:e99ed747-51b9-4579-91a7-d08def1ea5ac}} -mean convex ({{formula:8799c698-27f0-44c7-b2b4-82d033c96f12}} ) boundary, by using the smooth solution to the inverse anisotropic mean curvature flow, in the same spirit of Guan-Li {{cite:695b76d96cd106886a8c7fe84b095fa51bff5545}}.
Della Pietra, Gavitone and the first named author {{cite:e79227cf022eda2a883cd6f273290dccd8458a5e}} has considered the level set formulation of the inverse anisotropic mean curvature flow, in the spirit of Huisken-Ilmanen {{cite:4fbff57ac99ebe918f511adeee838126bcceaaa5}}, and proved the existence of the weak solutions by using {{formula:2612ff29-8668-4967-bb50-d501447fce42}} -type approximation. However, such approximation seems not sufficient to prove (REF ) for outward {{formula:36b22067-6731-4685-b47a-fcc182c3dd39}} -minimising sets.
| i | 415085d4e7f02e9b7274296fe01be68b |
In CM2-W1, only {{formula:70e662cf-4bdd-4017-8ffe-58b2bf295844}} features with {{formula:d2bfdcf4-9db8-41bd-b7e7-e6ec034b6ac0}} {{formula:2509ecea-cdc0-4bf9-b7c0-dbaf938d9432}} km s{{formula:fa483419-e519-4a36-89a5-3773d0aec420}} were detected in the early epochs, before and at the onset of the accretion burst. In CM2-W2, the masers were initially only features in the range of {{formula:79478ff5-ed01-4769-aa69-93a30de6f5d2}} km s{{formula:a9c10fb6-5fb5-475a-bb82-8b781290d2f9}} {{formula:ace4a824-2678-4204-99cd-bbda34ae32ee}} km s{{formula:ae200829-8080-4b6a-b2b3-bd90140b27a9}} , and the size of the bow shock traced by the water masers was {{formula:288c7912-04d0-4f4a-bf15-384e115925dc}} AU. In the later epochs, highly blue-shifted features with {{formula:4ca79542-9fdb-4184-ba56-ca4322a0cb17}} {{formula:7ffb6c41-41cc-46e9-8592-75f7c9d2e8cd}} km s{{formula:8a0ea211-c2d7-4671-ac4a-c6b78a8a4d13}} were detected at the northern part of the bow structure. The masers also traced a more well-defined bow shape with a size of {{formula:0eafc931-7b85-45e8-9638-17d9eff03791}} AU in later epochs. This is seen in the top of Figure REF , where the maser spots become a straight line over time. CM2-W2 was the region containing the brightest masers, and also the masers which had the most significant flares due to the accretion burst {{cite:4a5621bef88a77a3082c594aaa556de4e45f127c}}. In the epochs 2014.7 {{formula:b952b6e1-d4de-47af-a835-f93769e60f7d}} 2015.3, the masers in MM1-W1 form a linear structure on a milliarcsecond scale with a size of {{formula:b022b3bd-7973-46ff-a318-f17bdba4c15e}} AU and velocity range {{formula:098b43b1-338d-40cf-a61c-8af99d425983}} km s{{formula:20243a41-02e1-43fb-9906-d3a1540a773f}} {{formula:401cfd6a-7f68-4e41-a71b-1e2d24fcedc3}} km s{{formula:f6dadc3b-b732-4ab2-adfc-9c1db32aed18}} . After epoch 2015.3, the masers in MM1-W1 are displaced and the maser spots have a smaller linear structure, with size {{formula:43e0305e-20bb-4f26-9e42-c8a2db86fec5}} AU. The velocity range stayed the same.
| r | 40fa9e216aaf9a967368a4a6bf2ece0c |
Solitons, fascinating nonlinear wavepackets localized in space and time, can form in nonlinear media and propagate over long distances without distortion {{cite:e9481dc4a1452b65f378e33b003c0a0be598951a}}. The underlying physical mechanics for the formation and stability of solitons in conservative nonlinear systems is the exact balance between nonlinearity and dispersion (and/or diffraction).
Among various solitons studied so far, optical solitons have attracted much attention and have been investigated extensively because of their important applications in optical information processing and transmission {{cite:6378103cab80bffb595c519bdac127befc1c6f8d}}.
| i | 753c349d38a61485a3688f20a4a3b87b |
Filter methods employ some measure of dependence between a feature and the event class to rank the features, and retain only the top ranked features. As the measure of dependence, various statistical tests, including one-way analysis of variance F-value test, sure independence screening, mutual information, Pearson correlation, and Kendall correlation have been used in literature {{cite:ac9b30ba4cad7e9817c47942a4f1a3671a8d97ed}}. Given that we are focusing on a classification setting, we are interested in determining the correlation between numerical features and a categorical target variable. To this end, we use F-value test (F){{cite:9cd1029d35aa2c01753efdb48027ed62c6f7f057}}, sure independence screening (S){{cite:643af4d158fd86bcb26ba012fab7932b8654cbc8}}, and mutual information (M) {{cite:0dc30b10942296f371225cdb412a8ee23a366d22}} to quantify the correlation between features and the target variable. We use the off-the-shelf packages in Python to estimate the mutual information between discrete and continuous variables based on the nearest neighbor method (see {{cite:0dc30b10942296f371225cdb412a8ee23a366d22}} for more details).
| m | c3bb11d0787c2602f9015cf0cae762b9 |
The last two decades has witnessed the rapid development in the field of
quantum information and strengthened the notion that entanglement is not
only one of the fundamental concepts of quantum theory but also a key
concept for transmitting and processing quantum information {{cite:52c5a77c19efce71b349800d936b9a7828cc498c}}.
Entanglement between spatially separated parties is used as a potential
source for quantum teleportation of unknown states {{cite:b6180b925a2e7d1eecf161b6f8fd114feaf9fd2e}}, quantum
key distribution {{cite:1f7dbde6b40303adee293aa989fe49108dca96e0}}, quantum cryptography {{cite:d28d6cdf74e9e2f46d6161dc0a15f4587c90e7ec}} and
quantum computation {{cite:8274a5de581893a2bba6ebe80f613eaceb865c5b}}, {{cite:14b312050f34b95a69764678516a3f002dca701f}}. However, the behavior of
entanglement between various systems is still not fully known and efforts
are on the line to understand its dynamics deeper under various setups. The
study of entanglement in a bipartite system has recently been extended to
the relativistic setup and its behavior for various fields has been examined
{{cite:b7178902709cd41d4ba0fb737e16d569b929f0ad}}, {{cite:c41108848ac9508d528e49f1a5bbb784b95d2d20}}, {{cite:322fbac7d4d8c439fff7436756d9fc1444ec16b5}}, {{cite:0be1385f0584c2e244b8779a797d1809c1eef97b}}, {{cite:ee204efaab0dbf4c78d98848d688c54458641005}}, {{cite:47cd350ee2f43b2d0cabf626bce0b7efee93cfab}}. However, these
investigations on entanglement are limited to closed quantum systems.
Practically, quantum systems are influenced by its environment that may
results in non-unitary dynamics of the system. For most accurate and
practical results in quantum processing, the effect of environment on the
entanglement between spatially separated systems needs to be necessarily
investigated. The environmental effect on a quantum system gives rise to the
phenomenon of decoherence that causes an irreversible transfer of
information from the system to the environment {{cite:205be74c0deb625901a03cab097faf0dc58e07bc}}, {{cite:080ccf705205bff315d9f7f38544403028b2551a}}, {{cite:dac3d4c12608866b4bb3e0ce0243d000a0934e63}}.
| i | 97cc33683ec5679a9b58b41fdbb0f464 |
eXtreme Experiments.
We now present our empirical results on eXtreme multi-label datasets. Our experiments are performed under simulated bandit feedback using real-world eXtreme multi-label classification datasets {{cite:817428a99366e240f1c8a2bcf602510e00c11b92}}. This experiment startegy is widely used in the literature {{cite:386115bc52cd33756ecba8bb2572420e810ba033}}, {{cite:be36a859a2d4468b70b4df362b2b38fd68d0a8be}} with non-eXtreme multi-class datasets (see Appendix for more details). Our implementation uses a hierarchical linear function class inspired by {{cite:1d176d3aaf2c38e8af648174494ccd9620a080c2}}. The hyper-parameters in all the algorithms are tuned on the eurlex-4k datasets and then held fixed. This is in line with {{cite:be36a859a2d4468b70b4df362b2b38fd68d0a8be}}, where the parameters are tuned on a set of datasets and then held fixed.
| r | 5cf8d872929a10b013b48b396e22c774 |
Equations (REF )–() are solved numerically following a high-order spectral approach
which is outlined here. More details on its implementation and validation can be found in {{cite:320bf98527fa2797b73936b5afccf7373f66fdc0}}, {{cite:b6c05f03001c57a3b5e4f54189a2b7ff34f65b8e}}, {{cite:e6cca12c8c1a61852f33cec5dc874c5c6fc2bf80}}.
Discretization in space is accomplished via a pseudo-spectral method based on the fast Fourier transform.
The computational domain spans the interval {{formula:e1de9613-4788-4bab-a460-95c9dbe8ce78}} with periodic boundary conditions
and is divided into a regular grid of {{formula:c444c3f2-857d-4df6-9175-6b067c032a61}} collocation points.
Applications of spatial derivatives or Fourier multipliers are performed in the Fourier space,
while nonlinear products are calculated in the physical space.
For example, if we wish to apply the zeroth-order operator {{formula:a5973737-1d5a-4566-96c8-0a45b55217b5}} to a function {{formula:a71643bb-40b6-4509-b362-738e8ea58ae2}} in the physical space,
we first transform {{formula:65df8d81-8314-473c-97b4-9671cded6a47}} to the Fourier space, multiply the diagonal operator {{formula:65222fad-7633-4973-9b99-d2a7156126d0}} with the Fourier coefficients of {{formula:fbe0b200-1f73-4393-9325-10294be04414}} ,
and then transform back to the physical space.
| m | 908cbe589fbd634972e27f0df6ac21da |
Quantum computation has been evidently demonstrated to be surpassing classical supercomputers in the near future {{cite:c36230b07f4e66de7a12c7766c5d520f2819a7e9}}. Towards large-scale and distributed quantum information processing (QIP) {{cite:50d306361da733dcc3088f859df8f7eb7d823bf6}}, the efficient control of networked quantum systems is highly demanding {{cite:2c34e65793d868251a6b87ecb0f7902b5a9d3044}}. In the past decades, the control of “standing" components (namely the nodes, e.g., atoms or resonators {{cite:06ee47489c1f9135ca39120fa75d1c9aae26ba2a}}) for on-site QIP had been extensively studied {{cite:8cd84239369a4b135614cee8808f6a34509956cc}}, {{cite:883bdac5f9318656b7a62956a9b3c6c49cb1c5de}}, {{cite:e82f4efce343324fdb08d8112a514f9cd1902670}}, {{cite:a814a4c2166f64a75c90441d89865fbde27d041a}}, {{cite:59ccb829451683527ec45a4a997e7ea7b7e181cd}}, {{cite:e81371894efdd20113eb75654ae86fb440474425}}. However, the control of “flying" components for information transmission, as are often called flying qubits, has received much less attention {{cite:2cc04327963887e3db08200991c695d99c521098}}.
| i | 58033c8e9c6b20fea6320451e2b4cc2c |
We have made some simplifications in our simulations, and there are some caveats.
We have assumed that the jets are uniform on the emitting surfaces and
have sharp edges.
To compare the simulations and the observations further, more sophisticated
modeling is required {{cite:af9f3551ec6d852b5cde5e5a31c56b16ce2989c8}}, {{cite:cba2366c8e5182ba8501be23c79e221c334723d6}}.
| d | 16d70b75a5a08d8be1c393108fd4b96e |
To address these issues in the context of this work, in this section we generate a suite of mock dust emission models to quantify the accuracy to which we expect the dust properties to be recovered from our fits. Again, we assume that dust emission in galaxies is isothermal and optically thin, and it can be described by simple modified black bodies with dust temperature {{formula:ca92a21f-656f-42c3-a37d-7523846bf0e1}} and emissivity index {{formula:696cd3e3-6a1d-411e-8e21-0a335fc4dcd5}} (eq. REF ). We generate a library of {{formula:eaaee73b-13be-423e-8457-4d6f4000c813}} models with dust temperatures uniformly distributed between 15 and 80 K, {{formula:f7eeafef-f00e-456c-9e5a-e3853c3b20dd}} between 1 and 3, dust luminosity {{formula:031e1b97-ac34-4359-bfc7-fc61069903ca}} between 11.3 and 13.5 (a luminosity range similar to that of our SMGs; {{cite:d5b928f5beba9bfadb8dcc540d853d0192bdd3c0}}). To simulate our observables, we place these models at different redshifts using a Gaussian distribution centered at {{formula:aeb0c19f-6389-4488-92f6-e676fba2edc7}} , similar to the redshift distribution of our ALESS sources {{cite:edb090434feca93c69cef3fabe3b363c39c558fe}}, {{cite:d5b928f5beba9bfadb8dcc540d853d0192bdd3c0}}. For each model, we randomly draw a set of {{formula:6446240a-ea22-44b6-9590-97a0bfe0edc2}} , {{formula:fa55574d-9958-47af-9ee0-c1adb1f34606}} , {{formula:02437663-35fd-477c-bce6-90e2b09add49}} and {{formula:3b40c113-46c8-490d-93c2-a3ce2101e714}} from these distributions, and we compute the predicted (`observed') flux of each model in the same bands as for our observations, i.e., the Herschel/SPIRE bands, and ALMA Band 7 at 870µm and Band 4 at 2mm. We include the effects of the CMB in the observed fluxes as prescribed in {{cite:bdaa3c71b7dd35e9021c66f072e64bacc0ce9d51}}. We then perturb these observed fluxes by {{formula:03b26c2a-802d-4263-8db6-27162fe0024d}} to mimic our typical observational errors, and assign observational uncertainties to each flux that are similar to those of our real observed galaxies. That is, we assume: (i) a random signal-to-noise ratio drawn between 4 and 6 in the SPIRE 500- and 350-µm bands, and between 4 and 10 in the 250-µm band {{cite:3f7833c56f5c5d56cdf2c83fd7953a4bd3158ac5}}; (ii) a random signal-to-noise ratio drawn between 3 and 15 in ALMA Band 4, and
(iii) an ALMA Band 7 signal-to-noise that is correlated with the band 4 S/N in the same way as our observations (which yields a distribution between 4 and 40).We note that, strictly speaking, the signal-to-noise should correlate with the actual model fluxes however, we choose to set our simulation up this way because it allows us to perform the test with realistic errors but at the same time without limiting the parameter space of our models. We then fit our mock observations in the same way as we fit the actual observations in Section REF .
{{figure:c661de7f-56d1-427b-8baa-69c3b8978b14}} | m | 8a81116ef6a7053b50b47e573cbdb4e1 |
Instabilities of Si6 are measured via direct beat over a noise-cancelled optical fiber {{cite:b184e11c2a1864d8f982ba9c5dcb600f6576264b}} with Si3, a 21 cm long silicon cavity with dielectric coatings operated at 124 K {{cite:93294d69fb8534fbdc38f871ed990588a9d5eabe}}, {{cite:cd80d3ac9c390fa808e406d67896ece067f2acf8}}. Knowledge of the reference laser's noise spectrum is crucial and the instability of the latter system is verified to be thermal noise limited with fractional frequency noise power spectral density {{formula:a046d50f-346f-45c4-b569-1f2b1f736c91}} and fractional instability {{formula:cc611516-5bf5-45e6-8637-7fabbcdf5165}} from 1-1000 seconds {{cite:93294d69fb8534fbdc38f871ed990588a9d5eabe}}. The frequency noise of Si6 is calculated by measuring the combined fractional frequency instability of a Si3-Si6 optical heterodyne beatnote on a zero dead-time lambda-type counter. The Si3 instability contribution is then subtracted off in quadrature.
| m | e25b309a7aae022285d8aded13446544 |
We now evaluate the effect of correlated/i.i.d channels under traditional/generalized fading with phase errors on the performance in the investigated scenario, as well as the goodness of the proposed approximation for the equivalent channel in RIS-aided system. For all plots, we consider a RIS network geometry as in {{cite:9af481214834711f2a0c561554fee58fe1ef9b0d}}, where the fixed system parameters are setting as {{formula:f52f0761-e333-43e2-b13d-335877ab0d46}} dB, which corresponds to transmitting 30 dBm over 10 MHz of bandwidth with 10 dB noise figure, and a carrier frequency of 3 GHz, so the size of a single RIS element will be {{formula:6d6bb88f-1ba8-4480-8421-f7017256b1dd}} mts. The phase errors {{formula:61144d30-40c8-447d-8a37-9bdd0306a2cd}} are modeled as zero-mean Von Mises RVs with concentration parameter {{formula:c5794653-1ef7-40b1-9b50-d569d234b6c2}} , which captures the accuracy of the phase estimation at the RIS elements (i.e., a smaller {{formula:7fab1b74-b765-48d7-8686-28aad011ea77}} means a larger phase error). For the sake of comparison, the approaches in {{cite:8aba144a34e8b806b467cfa2ecb97de7e428b375}} and {{cite:004fb8d978ebf48e07e7e78274d7e379604f94d7}} for modeling correlated Rayleigh and i.i.d. generalized RIS channels, respectively, are included as a reference in the OP analysis. For informative purposes, to estimate the mixture model parameters in (REF ) with the EM algorithm's aid, {{formula:e2fc44fd-c08e-4b41-b5ff-7254a897f622}} realizations are generated for the training set in (REF ) for all instances. Monte Carlo (MC) simulations for the true channels are provided to validate the accuracy of the proposed framework.
{{figure:8a64d4db-8e9a-453f-8f34-657147ff8c01}} | r | eacc922d9f11f3fe063105671094ae5c |
The newly emerging coronavirus, severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), has spread rapidly over the world {{cite:9d7f1842e62a4c6cdf7a334e670a6ab27eeb05d3}}, {{cite:c5ab76b0c43b4d126056c4dea13ee59b001b5405}}, with more than 22,000,000 cases of coronavirus disease 2019 (COVID-19) and 790,000 deaths as of August 21, 2020 {{cite:733a909c5de000f15466001a52574920cb20348c}}. This pandemic outbreak has drastically changed our society, and has compelled us to stay alert to the continuous risk of SARS-CoV-2 infection {{cite:d043faeea6c2e656a1c6dba6249a1221173403a7}}. To overcome this dire situation, the development of novel drugs or vaccines is still an urgent global challenge. During the therapeutic development process, the elucidation of cellular mechanisms is essential for the discovery of potential targets; the fundamental question to be solved is how SARS-CoV-2 influences host cells and causes COVID-19 at the molecular level. However, these cellular mechanisms for COVID-19 are poorly understood.
| i | 073efea409915d7fc81339b1ff278a3b |
We remark that RCD methods have been shown to exhibit linear convergence rates in the strongly convex regime {{cite:86ca4695b04b7498887cd5240febcd5816cf09d3}}. Such fast convergence is, however, not to be expected in the presence of linear constraints. While strong convexity of the primal objective ensures smoothness of the Lagrangian dual function, but not its strong concavity. Hence, in general, we do not expect to see linear convergence rates by only assuming strong convexity in the primal. However, we note that {{cite:404e164b02030021f76b9c904002ad2841b6f66c}} obtain linear convergence rates in the well-posed scenario if there is one block variable that is independent of all others in the objective (but coupled in the linear constraint) and also the corresponding component function is smooth.
| m | 4637581c37fd5b40eb04ada85cf79e22 |
Depression prediction.
We find that among all combinations, the FW combination—representing the combination of the individual - physical health and individual - well-being (W) edge types—is the most accurate in terms of all evaluation measures (Figure REF and Supplementary Figure S7). In more detail, the FW combination is significantly (p-value{{formula:e73553aa-66d7-47c8-ae08-3d4721ddb647}} 0.05) more accurate than the rest of combinations, including the combination of all five non-target edge types (“All”), in terms of all evaluation measures (Figure REF and Supplementary Figure S7). Potential reasons why the FW combination is more accurate than the “All” combination are as follows. First, DMF is an MRMF method (Section REF ). MRMF typically contains a large number of parameters and may be prone to overfitting, meaning that MRMF may fit well on the training data but not predict well on the testing data {{cite:db19a3978689265519ab60742297c61257349a6f}}. The complexity (the number of parameters) of the “All” combination is higher than the complexity of the FW combination. Thus, the higher number of parameters of the former may cause its overfitting, which in turn may cause its lower prediction performance. Second, some edge types in the “All” combination may be less informative than the individual - physical health (F) and individual - well-being (W) edge types in the FW combination when predicting depression. Using edge types that may be suboptimally informative may lower the prediction performance compared to using only edge types that are optimally informative. In other words, it might not be surprising that using some subset of all data types might be more informative/accurate than using all data types. Specifically, in our evaluation, since each of the F and W edge types alone is more accurate than any one of S, I, and P edge types alone (Figure REF ), it might not be surprising that the FW edge combination is more accurate than the All combination. Importantly, it is the case that the other edge types alone, namely S and I (although not P), are performing significantly better than at random (Figure REF ), meaning that they do contain some predictive power. So, it is the subject of our future work to understand how to significantly improve upon the FW combination while incorporating the S and I (and possibly even P) edge types, i.e., how to get a truly synergistic, multiplicative effect when integrating the different data types. In Section , we discuss a possible direction towards achieving this goal.
{{figure:76fdc015-70fe-4f91-9825-6938ebca90c8}} | r | af13488dc062104c8af6664865ac910f |
Its spectrum is depicted in Fig. 3a of the main text; due to the no-crossing theorem {{cite:51fb03f0df7fa99403a4bd4e3cb38130a6015f67}}, it only shows avoided crossings. On the other hand, the half-filled odd CP symmetric sector only has one basis element, namely
{{formula:2e51fdec-41e1-4383-a0b2-079408c7ad0f}}
| m | 5bb3c4d1e025b7cb690d58572b63a128 |
The entangled pair source {{cite:7baa19224f5ee6ad844ceb7f79c594407ca12793}} is displayed in Fig. REF (a). A Ti:Sapphire laser emits a beam of pump pulses with wavelength 775 nm at a repetition rate of 80 MHz. A small fraction of the beam is picked off and sent to a fast photodiode (FPD) which sends an electronic synchronization pulse to both Alice and Bob once every 960 laser pulses. The remainder of the pump beam is sent through a single-mode fiber to clean up its spatial mode. After exiting the fiber, the beam is gently focused and prepared in the diagonal polarization state before it is equally split into two paths by a polarizing beam displacer (BD1). In each path, photon pairs are produced via type-II spontaneous parametric downconversion in a 20 mm-long periodically poled potassium titanyl phosphate crystal placed at the pump beam's focus. Polarizing beam displacers BD2 and BD3 and a series of half waveplates are used to recombine the beams into two paths (with one photon in each path). A silicon window filters out the pump beam, then each photon is coupled into single-mode fiber over which it is sent to Alice's or Bob's measurement station. By controlling the polarization rotation that occurs inside each fiber, we ensure that the pair arriving at Alice's and Bob's measurement stations is in the maximally entangled singlet state {{formula:ee08fe04-afec-4395-abf4-6a83e9b51ebe}} , where {{formula:77528edf-c2ae-41f8-8b7b-0092932298b6}} ({{formula:ee124ce7-32b2-43e5-a01d-239da69874e0}} ) denotes horizontal (vertical) polarization.
| m | cd7ea887a218f5ef09aea9fd7c08d435 |
Traditional voice conversion (VC) aims to modify one's voice to sound like that of another while keeping linguistic content and emotional style unchanged {{cite:1da4d347052c9130d728dafa3f10456f6eef131b}}. VC is an enabling technology for various tasks, such as conversational assistants, cross-lingual speech synthesis {{cite:6ff589b68831fb743055e494573175ccca2e0eee}}, and speaker verification {{cite:e1274e104393527da87b3ddfbbbff7cc8e0c36a3}}. In this paper, we formulate a new research topic denoted as Expressive Voice Conversion, and propose a solution that jointly performs speaker identity and emotional style transfer for emotional speakers.
| i | 8b52497cbecdaf5bedd148b15bf74f51 |
The quark and lepton sectors of the Standard Model (SM) are interestingly similar, motivating one to hypothesize a fundamental symmetry between the two sectors. Such a symmetry can be found in many grand unified theories, such as grand unified SU(5), Pati-Salam models based on SU(4) or R-parity violating (RPV) supersymmetry (SUSY) models. These models naturally predict a new class of bosons carrying both lepton and baryon number, called leptoquarks (LQs). LQs are hypothetical colour triplet bosons, which couple directly to a quark and a lepton. They can be of either scalar or vector nature and they carry fractional electromagnetic charge. Recently, LQs have gained more attention as they could provide an attractive explanation to the recent hint of lepton flavour universality violation from the observed B decay anomalies in BaBar {{cite:2bb9ffd364766f50523f3c829e364b9ebc8341f0}}, Belle {{cite:a25469c63ec687d2b2cf8ec155fdd9ab8029df11}} and LHCb {{cite:00da0dbeb8d3fedf315f33e8f4838522f030dbb5}} {{cite:cdfc474bf2c27fbe009655349fdbd5ce18cb9dc5}} {{cite:0ed3e61b9f22c13a49c25200949dd48b9f785a4a}}. If their mass were near the TeV scale, leptoquarks could be produced at the Large Hadron Collider {{cite:e2a4ee0270f91d9cf3b6b893c68c8a311d43436a}}.
| i | f9e2da867e2a379a49ff55bba6116203 |
The new interactions between the SM fermions and the physical states arising from the introduction of a second Higgs doublet imply a richer phenomenology than the SM. This is further enhanced by the new free parameters and couplings in the general two Higgs doublet model (GTHDM), also known as type-III 2HDM {{cite:91995ab3506bc751c095955754e4d4bc08a85df4}}. Physical effects such as CP violation, scalar mixing and flavour changing transitions are expected {{cite:f223cda6f5721bfe30654af97aad058587525b5a}},
allowing for signatures to be observed in particle colliders. One of the most interesting experimental consequences of the flavour changing currents present in the GTHDM is lepton flavour universality (LFU) violation. Experimental measurements of LFU violation come from flavour changing charged currents (FCCCs), such as those in {{formula:7bc804d6-33a8-4fa1-8d98-d64c6a5c0dbd}} meson decays, and flavour changing neutral currents (FCNCs), for instance in kaon decays. The observed deviations from the SM in the measurements of FCCCs (around {{formula:c9ec9b15-4a22-4c7d-be06-7aa12b6f68b7}} from the SM {{cite:dd03fa76c5fc51d53c8f6a40617d560e6908e8e0}}) and FCNCs (close to a combined {{formula:9aaf8ea9-491d-467a-bcb6-a333df832e43}} deviation, see for example {{cite:6f2633be9ae5d05714f3c296a687d6cc494d9d79}}, {{cite:cbb2544314e886ed2718452625f4fe5afc305c63}}, {{cite:2d1a5821dcc78ca4c892d57a2b86cee094896c67}}), hint at the existence of new physics (NP) contributions and thus serve as a clear motivation for the study of NP models capable of explaining the anomalies.
| i | b33c30ea0e7923e146ef0b77c3afd6c5 |
The primary contribution of this paper has been to develop a sample-optimal paradigm that simultaneously overcomes the curse of multiple agents and optimizes the horizon dependency when solving two-player zero-sum Markov games. This goal was not accomplished in any of the previous works, regardless of the sampling mechanism in use.
The adoption of the adversarial learning subroutine helps break the curse of multiple agents compared to the prior model-based approach {{cite:944f3e68be7ce1eed0c81e1310d8c54da628c3af}}, {{cite:7f477cdd3f6bcc698548c346c48c2756ff809884}},
whereas the availability of the generative model in conjunction with the variance-aware bonus design enables sharpened horizon dependency compared to {{cite:6ac9a09aa6a4bf8dd025ee1dc34544a9f2c003aa}}, {{cite:761dfbb5e6a24e494b89e6cc2f53218433037c27}}.
Our work opens further questions surrounding sample efficiency in solving Markov games.
For instance, how to attain minimax-optimal sample complexity if we only have access to less idealistic sampling protocol (e.g., local access models {{cite:0bbe94424c1461095892519f4ba9f9e2c3d2bae8}}, {{cite:bae2439a9e0fce9202630e862ee4583e4e82f835}}, and online sampling protocols {{cite:9a7cd8aca2ae62057e4662572e6f570fe0a55e01}}, {{cite:bcb725c891d17d4830cada04b6e32a664cbf9820}}) as opposed to the flexible generative model? How can we optimize the horizon dependency when computing (coarse) correlated equilibria in multi-agent general-sum scenarios {{cite:5ce41f4aef37cb1fa3545a34160a4722602be6da}}, {{cite:761dfbb5e6a24e494b89e6cc2f53218433037c27}}, {{cite:3575ac85fbddc763645b1e8c80db4ebad6252135}} without compromising the dependency on the size of the action spaces. In addition, our refined regret bound for FTRL (based on variance-type quantities) only covers the full-information case;
it would be of interest to generalize it to the bandit-feedback setting (where only partial entries of the loss vectors are observable each time).
| d | 2345265f8299492eb877459d9cedc077 |
E.g., in the Newtonian singularity case, i.e., for a point-like
static mass source, many types of higher derivative terms remove
singularity in the modified Newtonian potential. This occurs
starting from the simplest fourth-derivative theory with the action
composed by (REF ) and (REF ) terms {{cite:8cf317d917aa6f62379207e2c9ebf1ec11a13f8c}}.
The same is true for the local (see, e.g., {{cite:a00f4bc9c7bd67b42c5095b12925407a697efbec}}, {{cite:f104d61cf38554d4f897a17bf2ca0a693d262558}}) and
nonlocal {{cite:cedc638b7a2277dd1b334a53131d5afb7a08be43}} higher derivative models. It is worthwhile
to note that the detailed analysis of the Newtonian and especially
black hole cases is more complicated (see, e.g., {{cite:18b57641ec21b34d34f26cfe1ef0c6682a5043e0}},
{{cite:b6205b2e2fa54c22201acc2030e0ea686ee261fc}} and further references therein).
| d | d8313c6a0d038dd6ca0e0fda495cc27b |
Han et al. 2020 {{cite:6ffeb5d58fba8458cd0516a61dbc6adb5bc1bc51}} Conv Rate 69.40 512 2.048 1.43 729.77 5.42 8.07
| m | f123ad9fa4c1ed16b07989d7034eddee |
In our analysis, we assumed the Clifford circuit in the classical shadow part is noise-free. If there are noise in the Clifford circuit part, it can be mitigated if the noise is independent of the Clifford gates, as in {{cite:72a6fbb5d297fdcb4c66c986bd67346ad54bb18e}}, {{cite:9a9fe7c783b85a64e56fd6a6d5ace4932a843870}}, {{cite:247df2ca868cb1ebd9c532eae8d623037294bf91}}, where similar idea was used for randomized benchmarking {{cite:869f0903760b5e2ef0b7a8a34c406cf514afa80c}}, {{cite:58eda2806b6f7e3f74985f5c1bc80502bd268817}}.
| d | 2ee02dcc306a9080a9b64360fa5c00e7 |
The mean field game theory examines systems of identical players those interacts via some external media. It was proposed independently by Lasry, Lions {{cite:3847037d271ccc239e98a9c9038c0b9a46a5051a}}, {{cite:b45956d2e5a2d0d27720fc1f52005399f4c5be17}} and Huang, Caines, Malhamé {{cite:9ec7751e531bb667efb90f03728c3f8af0a91665}}, {{cite:e201ea256246f3010e2c9761c27df55ea52a1c39}}. In the paper, we study the continuous-time finite state mean field games that is the infinite player dynamic game under assumptions that the players are similar, when the dynamics of each players is given by a continuous-time finite state Markov chain with transition probabilities depending on distribution of all players and player's actions. The finite state mean field games find various application in the analysis of socio-econimic systems and modeling of cybersecurity {{cite:bbde1bbd949a716424db9b7d2a3ce7410baed11a}}, {{cite:e4ba647d46950020d0ce5cf9c4e7fea21e572a32}}, {{cite:95ca235cb661a1096ed4ae4abd1ac0915fd9a5ab}}, {{cite:43b6823ec39bf5319d3df735cd1fe3b7b650db17}}, {{cite:c41d810e1695a94891b635619bff70183b6ebadb}}.
| i | f03f18c63c04e03f466bc90d85d7b751 |
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