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Multi-scale models are aimed at providing an efficient and more accurate representation of a complex system by coupling (sub)models that address different features/attributes at different levels of detail. However, the modeling of such systems is far from straightforward, not only because they are made up of dynamical systems of different characteristics, but also because of often intricate cross dependencies among the relevant physical processes at work {{cite:bd5b0f3d828b0336339cf9b6fc4ad0ff368efefc}}. As a consequence, the problem of tracking the evolution of a multi-scale dynamical system involves the prediction and estimation of several sets of variables that live in different state-spaces and evolve in different time scales. Moreover, the tracking of the variables of interest usually has to be performed from the observation of partial and noisy observations. Efficient recursive algorithms for this task are badly needed.
i
8e27216d0d263869f915a97ea5c2faf8
Query and Attend is a context-aware local feature processing layer. The key design choice of QnA is a convolution-like operation in which aggregation kernels vary according to the context of the processed local region. The heart of QnA is the attention mechanism, where overlapping windows are efficiently processed to maintain shift-invariance. Recall that three primary entities are deduced from the input features in self-attention: queries, keys, and values. The query-key dot product, which defines the attention weights, can be computationally pricey. To overcome this limitation, we detour from extracting the queries from the window itself but learn them instead (see subfig:overviewours). This process is conceptually similar to convolution kernels, as the learned queries determine how to aggregate token values, focusing on feature subspaces pre-defined by the network. We show that learning the queries maintains the expressive power of the self-attention mechanism and facilitates a novel efficient QnA implementation that uses only simple and fast operations. Finally, our layer can be extended to perform other functionalities (e.g., downsampling and upsampling), which are non-trivial in existing methods {{cite:bcda12a602bf4a5d3dd730638b460b9d0e997c84}}, {{cite:514a8461da519185b477cfc463cd2a386a8904be}}.
m
d0818e1e6b17a06e1def6343b2a9c05e
This can be established, along with the recursion relations: {{formula:16dfc466-1019-45c5-9bd7-ed11db4fc8c1}} , {{formula:d00248d7-6846-4146-8a6b-cebd4a83fbfd}} , and {{formula:b370e9e8-1df3-48ab-bd5d-6f06c34326ee}} (with {{formula:7fd7455d-e47f-4f9b-88c7-2de82e18573a}} ), by repeated application of Weber's second exponential integral for Bessel functions (Sec. 13.31 of Ref. {{cite:b3f64b6347b157cc0ecf885e67e9e9981b8f290d}} and 10.22.67 of Ref. {{cite:eeed57a117e991099cec248acf4d5ea6fdc3fafa}}), {{formula:c8c787e1-2d5b-4ef7-bd61-c61a285887a7}}
r
a96285fbe865d8a48dee3930a0245357
As stated in Section REF , the deep learning approach is based mainly on matrix-vector multiplications, which are highly well-tuned and execute on GPUs. Unfortunately, this is not the case with direct sparse solvers in the implicit finite element method, which are frequently the only robust solver technique, but to date, it fails to make full use of GPUs. For nonlinear high fidelity simulations with millions of degrees of freedom, it is realistic to predict that physics-informed neural networks using transfer learning on GPUs may outperform a traditional implicit finite element technique. Additionally, writing from scratch a physics-informed neural network to solve PDEs is much easier and quicker than writing a nonlinear finite element code. Finally, a combination of data-driven and physics-informed deep learning approaches has been used to solve incomplete and ill-posed problems in computational mechanics and other physics-based modeling disciplines, previously considered insolvable by the classical numerical methods {{cite:bd71a2660e7240c6dbf3d7ef9f2965dcc773c6c7}}.
d
512dd023d4ed40a0beddb87eb3116e86
A relativistic particle with a spin more than two is commonly known as a Higher spin particle. These particles are necessarily massive since it is not possible to construct interacting, unitary, Poincare invariant quantum field theory for massless higher spin particles To be more precise, it is possible to have a theory massless higher spin which is relevant at long distances/in the infrared.. Such particles don't play any role in the standard model of particle physics. However, there has been a lot of interest in understanding theories with higher spin particles in recent times. There are primarily two motivations. The first motivation comes from the theoretical quest to understand the structure of gravitational theories. The general relativity provides a consistent One can contest this claim in the strong gravity regime. Hawking-Penrose singularity theorem predicts singularity for generic initial conditions. However, in such cases, the singularity is inside a horizon and hence not observable, at least classically. dynamics for classical relativistic gravity. But is this theory unique, or is it one amongst many possible classical theories of gravity? One way to approach this question is to understand the allowed space of higher-derivative corrections to the Einstein gravity. Any higher derivative modification is dimension-full, and hence they become relevant only at (and above) a particular energy scale. There are at least two possibilities for choosing the energy scale: All the higher derivative corrections may become important at the Planck scale {{formula:89127b18-5b0b-48db-b308-7279c2b4d817}} . To understand this class of theories, it is equally important to understand quantum corrections. Considering Einstein gravity (and all its supersymmetric cousins) is non-renormalizableThough it is one-loop finite {{cite:4c762e22ea153ef7ab553980e3e9b71e309d1895}}. in 3+1 dimensions, it is not possible to understand them using our correct knowledge of Quantum field theory. Another possibility is that when the higher-derivative corrections become relevant at a scale (say {{formula:5857c9ea-6645-45c6-a856-ebad65868893}} ) which is parametrically smaller than {{formula:535b6339-7f48-44b1-a83a-b77f2fdbc9f6}} String theory is a model quantum gravity, and it falls into this category. But from the low energy considerations, there is no compelling reason for the existence of such a scale. One can only draw an analogy to the Fermi theory of beta decay. The theory is non-renormalizable, and the quantum corrections become extremely important at 300 GeV. This problem is resolved in the Electroweak theory, where new physics/higher derivative corrections become important around 80 GeV.. In such theories, it is possible to study perturbative corrections due to higher derivative operators. In {{cite:d4fb77dad02d4822f49c539dd560ed67ec2bfcec}}, the authors used the causality argument to show that any quadratic or cubic higher derivative correction to Einstein gravity must be accompanied by an infinite tower of higher spin particles. This result was further strengthened in {{cite:86dc2eea1115ad6f4a59204d2eaca28ca6fcb5fd}}, where the authors considered quartic corrections (= quartic contact interactions). The authors showed that there are no possible corrections graviton four-point contact interaction in {{formula:e5a332b7-beb8-4161-9e49-474eef9b627a}} . The question that one would like to understand is that what is the most general tree-level {{formula:c022f6e6-4291-4b73-99fe-971d60313ae3}} -matrix for four gravitons such that it is consistent with Causality, unitarity, and Lorentz invariance.
i
92bb8b965b443edd928f7fe811752bed
Perspective manipulation. Portraits taken by wide-angle cameras exhibit undesired foreshortening distortion due to the perspective projection  {{cite:9ea192e6a25628d23c2e2f12fd902723c7c4a958}}, {{cite:50b4ae525b2314aa0e862a666b7ba9479bf6857a}}. As our representation is 3D in nature, we can render a new image by virtually moving the camera closer (or further) from the subject and adjusting the focal length correspondingly to preserve the face area. We demonstrate perspective effect manipulation using portrait NeRF in Figure REF and the supplemental video. When the camera sets a longer focal length, the nose looks smaller, and the portrait looks more natural. Since our training views are taken from a single camera distance, the vanilla NeRF rendering {{cite:bd5cb063333fe95db04c3009cf76e0d6a72e8b0c}} requires inference on the world coordinates outside the training coordinates and leads to the artifacts when the camera is too far or too close, as shown in the supplemental materials. We address the artifacts by re-parameterizing the NeRF coordinates to infer on the training coordinates. {{figure:6efdf828-7b18-4ed3-b716-58b36231677c}}{{figure:e8874bab-1466-46ee-947a-a08d22f97298}}{{figure:5cd1d171-6423-4c74-aac2-618cee38fcf9}}{{table:415c246f-970c-4d9c-9245-f792e1ce5062}}{{table:cf8fe7e7-e483-4cef-8a6f-d03ce6f569f7}}
r
5a086806ea2c489f570fc24f70830c1a
i.e., a function of the resolvent {{formula:71bf1381-28e1-43fc-a035-8ab49b6bea3a}} . The resolvent is highly studied in random matrix theory (see for example {{cite:86549a1abc693a1a4a3b6767eed02601d33c942e}} and {{cite:cbd4bfbd9bb88acfecf9f9f0b05914ba933aeb19}}) and there are many techniques available to estimate it.
m
b704f3b613ee503d0292b42d9756a8a0
We evaluate the sample efficiency of our method in the competitive environments on the Multi-Agent Particle Environment {{cite:ed8b8554fe3b4fc6cd5cc5586d38dd29f6a24dab}}. Three scenarios are included, i.e., 1) Keep-away scenario with an agent, an adversary and two landmarks, 2) Physical deception scenario with two agents, an adversary, and two landmarks, and 3) Predator-prey scenario with a prey (agent) and three predators (adversaries).
r
818f0b9b62b727d40080d6207159c437
Speed comparisons of Different Devices: We have reviewed the computation speed of different devices, including V100 GPU and TPUv2/3, which were used in previous work {{cite:0847a9bdad36aef21d8b40189d1af7f2a3a0a17a}}, {{cite:dddfa3250574b94fee563a26f9885e3966590518}}, {{cite:2c88af3713b23b44c1157fa712bf3770bf84caa4}}, {{cite:a8035f5b0e602f2d9b2647352bf85962f745706d}}, {{cite:955ab40e115d1dab24fca944144737d639213f01}}, {{cite:4f2a3c8405daeb9398270ecfa72b7bb3c4c560b9}} or this paper. TPUv3 is {{formula:8e23bd23-103d-48e1-8d55-b5ce880ca99f}} faster than TPUv2See https://www.linleygroup.com/newsletters/newsletter_detail.php?num=6203year=2020tag=3.. The speed of a TPUv2 core is similar to that of one V100See page 24 in https://storage.googleapis.com/nexttpu/index.html.. Combining all of them, we can obtain the training speed ratios as {{formula:08f957d1-694c-4824-9052-b39d1972f939}} .
m
562748d0caf3936bc5452f7352d999c6
In this section, which broadly follows the lines of the proof of {{cite:8bcde616bab8f7af1cbdf780d4e2c00120cc9235}}, we set out the key elements of the proof of Theorem REF .
m
4d36cd64987596eaf731c052450ae63e
Computational and mathematical models are versatile tools, providing valuable insight into complex processes in the life sciences. Models can further our understanding of mechanisms and processes, facilitate development and testing of hypotheses, guide experimentation and data collection and aid design of targeted interventions {{cite:12075adcf3189de58764bcfbcbc98cf62bdc1693}}, {{cite:fa808c68b370bbbc31f3114a38aec137eb1c8016}}, {{cite:83eac4c2053831f5636032839c894ab5bb7f29e9}}, {{cite:1ea7102f6f5819d1da57babd87a79a42cb57ac59}}. However, there are considerable challenges associated with calibrating these models to data. For example, models need to be sufficiently sophisticated to adequately reflect the behaviour of the underlying system, while ideally admitting identifiable parameters that carry a physical interpretation, that can be estimated from available or obtainable data {{cite:b19cd62da3b627f08caa1e9ede1ecc142cfa7b9d}}, {{cite:38a4ce6864e2275c7c4d4c14a4dd693181e6a2a7}}. Further, available data can be limited and often is not collected for the express purpose of parameter estimation; data may be noisy, incomplete, or may not provide the level of detail or sample size required to obtain precise parameter estimates {{cite:7035e635d64959ab4cd477ef404244580bb5b564}}, {{cite:2ba822166b74104c797c9874ca2a7661658175f2}}, {{cite:7c77ef5f341e22ba8e87c38359db81a699496bec}}, {{cite:e5faa322cb8ba042ead54e23401a025be220f44f}}.
i
c2fc1ca5b64266e7bc3971b2703dbf73
The most significant anisotropy in the distribution of cosmic rays observed in the studies performed above 4 EeV is the large-scale dipolar modulation of the flux at energies above 8 EeV. The maximum of this modulation lies in Galactic coordinates at {{formula:121e87ed-9279-4834-9056-4200abfe27b4}} , with an uncertainty of about 15{{formula:da8d2912-fb61-4086-bea3-4dc95e93eb71}} . This is {{formula:0763baac-0e67-4ebc-8a52-fbebd84537d6}} away from the Galactic center direction, indicating an extragalactic origin for these ultrahigh-energy particles. As examples of the large-scale anisotropies expected from a Galactic CR component, we show in Fig. REF the direction of the dipole that would result for cosmic rays coming from sources distributed as the luminous matter in the Galaxy, taken as a bulge and an exponential disk modeled as in {{cite:ff7dd53d5ea2f6adc7eaacc6c5fcb4d8a02eb6ad}}. The CRs are propagated through the Galactic magnetic field, described with the models proposed in {{cite:f84f48a394a400ec2eeab8b052416c120abb08d2}} and {{cite:681210674a8eae22c18a35fd5d6e024986070a96}}, for different values of the CR rigidity, {{formula:2a9b5be4-ff20-447a-96fe-705d4099d4ef}} (with {{formula:495a046b-0cbe-4cec-9424-15c49c43eb90}} the charge of the CR nucleus). The results are obtained by actually backtracking the trajectories of antiparticles leaving the Earth {{cite:ac7419349fcd16abbfff00d29b9f52744c2061e6}} from a dense grid of equally spaced directions and obtaining the associated weight for each direction by integrating the matter density along their path through the Galaxy {{cite:f3bfda199451d921fe2be4ae481f1727cf3707fc}}. We obtain in this way an estimation of the flux that would arrive at the Earth from a continuous distribution of sources isotropically emitting cosmic rays and with a density proportional to that of the luminous matter. The points in the plot indicate the direction of the reconstructed dipolar component of the flux maps obtained. The direction of the resulting dipoles lie very close to the Galactic center for particles with the highest rigidities considered, and as the rigidity decreases they slowly move away from it towards increasing Galactic longitudes (closer to the direction of the inner spiral arm which is at {{formula:2a8ebd9b-4fdf-43a6-b17f-bbc7eb50bdfc}} ). Note that at 10 EeV the inferred average values of the CR charges is {{formula:d6d6b58a-b26c-4fe1-b171-99ac6c251960}} to 5, depending on the hadronic models adopted for the analysis, while in the lower energy bin the inferred charges are actually smaller {{cite:7769d21236fd5ce1f2ca5c4c1c7062208abfc68f}}, justifying the range of rigidities considered. The resulting dipole directions obtained in these Galactic scenarios are quite different from the dipole direction observed above 8 EeV, clearly showing that in a standard scenario the dominant contribution to the dipolar modulation at these energies cannot arise from a Galactic component. Besides the dipole direction, let us note that the amplitude of the dipole (and also the amplitudes of the quadrupole) turns out to be large in the models of purely Galactic cosmic rays depicted in the figure. In particular, we find that {{formula:d54af4f7-2f6e-49d5-aea5-713904d26dc0}} for all the rigidities considered, showing that the dominant component at these energies needs to be much more isotropic, and hence of likely extragalactic origin. {{figure:0222af30-1fd8-4f08-92c3-44cd95f57262}}
d
ceecc92e246800c2c3c230dc72acf810
The basic idea is to define two indices: allocation index and deterioration index. The allocation index is (to be derived) from the AI model of interest. Conceptually, AI models are abstracted as “resource allocators", such as predicting the probability of Intensive Care Unit admission. Note that the models themselves do not need to be particularly designed to allocate resources, for example, it could be risk prediction of cardiovascular disease (CVD) among people with diabetes {{cite:dbf8c07c8bc125ab5a5419ac4bf7155a5601e7d0}}. Essentially, a resource allocator is a computational model that takes patient data as input and outputs a (normalised) score between 0 and 1. We call this score the allocation index. Deterioration index is a score between 0 and 1 to measure the deterioration status of patients. It can be derived from an objective measurement for disease prognosis (i.e., a marker of prognosis in epidemiology terminology), such as extensively used comorbidity scores {{cite:89e046817762d9c453f2a2a89dee640ea17beb44}}, {{cite:fded608cfd436084706407cca084714369bcb282}} or biomarker measurements like those for CVDs {{cite:15df4c2745db99c116adb704aad6f2e2e6994792}}.
m
b3391529ad4f35d6a3aae55bdba2dc2a
First, we investigated the gain-gain modes coupling that has not been paid attention to in previous studies. The mode evolution can be predicted by the phase diagram and exhibit the properties of PT-broken. This system can be used to improve the optical power of classical devices and the fidelity of quantum devices. The gain-gain coupling is expressed as red area in Fig. 1(b) of the full-parameter space phase diagram, and similarly exhibits very different properties in different phase spaces. Fig. 3 show the light intensities {{formula:e7e46081-a3f2-4de7-b7b6-261354a4da32}} , {{formula:6dee2a1c-23f4-40ec-8e18-dfa8da4aac42}} in two waveguides evolves with the propagation distance {{formula:7a75502d-c6d4-4a5b-9204-efcee03efb1a}} , the incident light are from channel 1 ((a) and (c)) and channel 2 ((b) and (d)) respectively. The red and blue curves represent light intensity in the above and below waveguide. Here, the coupling coefficient {{formula:db8950d6-99e4-4237-a147-54001897231f}} is always kept at {{formula:f7a7b17e-507f-4a28-ad8d-e32d6f6c819a}} cm{{formula:3c80bda5-18be-496e-9ffc-2b1a81a457dd}} . First in PT-symmetry phase, let both waveguides have the same degree of gain that {{formula:fb1a5e55-029b-45b7-8de3-f75818366049}} cm{{formula:7e1ade2d-4ada-4131-925b-377fa691db11}} , satisfying the condition {{formula:906265f0-8c75-43ac-b6f6-989d34999e74}} . The results are shown in Fig. 3(a) and (b). It can be seen that the waveguides experience gain as they exchange energy with each other, and the field intensity in both channels are of the same order, fitting the characteristics of PT-symmetry phase {{cite:3a6e72ba8f76c8499fe4a97392ed2e9b1dfa0d89}}, {{cite:f4885a2cb7e73d188878279ff9979c5049965315}}. While for the PT-broken phase, let the upper waveguide go through a higher gain rate ({{formula:b09acb22-8a19-47fc-b09e-516fee9573bb}} cm{{formula:7ad5939a-dfd1-4056-a81b-9cd1c3deee01}} ) than the lower one ({{formula:a713a121-b934-4549-8ea4-e55ddc82cc9d}} cm{{formula:19cfb3d1-7728-4f8d-92bd-b50b9e3b3cad}} ) and satisfy the PT-broken condition {{formula:30d67374-e4aa-4b7f-b3a7-72e6587ea007}} . From Fig. 3(c) and (d) we can see, regardless of which port the light comes in from, the field intensity of the top channel is about 3 times stronger than that of the bottom over a certain distance, showing most of the energy is concentrated in the waveguide with higher gain, fitting the characteristics of PT-broken phase {{cite:3a6e72ba8f76c8499fe4a97392ed2e9b1dfa0d89}}, {{cite:f4885a2cb7e73d188878279ff9979c5049965315}}. Therefore, the numerical results of gain-gain coupling are consistent with the theoretical expectation.
r
09eca715fa2a1ac38e65e6f0b6233e6a
Our main contribution in this paper is to extend the GM-PHD filter, initially proposed for the tracking problem {{cite:993f02e0e8e813c06528b4d44e07e21835bbc5da}}, to allow for search and tracking with a limited FOV robot. Our second contribution was to incorporate non-linear target prediction using GP regression. The current form is restricted to a 2D environment and a circular FOV but this can be extended to higher dimensional environments and any shape of sensing models by appropriately modifying Equation (REF ).
d
31cf2173ba6b012f26e0dd5d9c948968
Finally, even if one's initial intuition in data analysis could be that "more data is better", the addition of interaction network layers also brings additional degree of freedom {{cite:54219bdc7d437607cb7ddbd6d895cc14bb6b18d4}}. To evaluate the pertinence of the addition of multiplex networks or the addition of layers in a multilayer system, MultiXrank includes a systematic evaluation protocol based on Leave-One-Out-Cross-Validation and Link Prediction. Overall, our results show that adding networks data does not always increase the predictive power of the RWR, as already suggested by previous studies {{cite:edc39e8335b68568da31bf2fc10aea332e07f4e1}}. Our evaluation protocol can be used, for the first time to our knowledge, to evaluate in-depth the signal-to-noise of multilayer system combinations.
d
74bbcc87f5a524be2f388df06138d00f
where {{formula:f63cb1e9-4a5c-4ed8-ab4f-43dc01e6046e}} is a trade-off parameter between the loss function and the low rank regularization induced by one nuclear norm {{formula:4ffaf8b8-43b3-4f74-9bc1-c4347bb797c9}} . We will briefly introduce several nuclear norms including standard nuclear norm {{cite:a13d900bbc88cb0647f6ac3f9533b1a84d2a26e1}}, the weighted nuclear norm {{cite:a1608edd297572cb1a97e2efdc3e32cef42d6e66}}, Scappten {{formula:36e7b2ef-623c-418d-ae39-61ca7d84f374}} -norm {{cite:5671ef216626b9305f6f9efa35cd9f23116c4c53}} and the weighted Scappten {{formula:ab8f3733-7470-4030-8f50-f14f7178922a}} -norm {{cite:79331f3425a8dfe2b20e21935549c2021c5eecca}} in the next subsection.
m
386f21c3d11e88d8ae4e00f4e5c7a0da
Fundamentally, quantum randomness always comes from the unpredictability of state collapse induced by measurement. This unpredictability has previously been ensured with quantum features such as nonlocality, non-contextuality, state distinguishability, {{formula:3b6d16a7-2d4e-44a2-b2dd-5ec0e62b1c2d}} {{formula:fcfcee87-3690-4b41-9fca-aaf6dc8e1edc}}  {{cite:49048a49fe274fbb1ce66093b7104c4cc845b744}}, {{cite:6316f8b050368715d421b8530a0102aab072fdf7}}, {{cite:c9cc29500d52ba372446145ae4ffc89ae25903dc}}, {{cite:2a3753598fe9e3e9b54d8a8e352ef62549f4a972}}, {{cite:0232d85b9cadf039ceddbc7766633df58daa8650}}, {{cite:0c7a247579635452fedc7875dcb3c2598f0e2787}}, {{cite:b053c88220e929880610b7fc92193495786ac7ca}}, {{cite:e9c4c33ac2ec37b2e67e8eb84c9ab5c8d6805392}}, {{cite:56b4c09bad38658214c8e1a703df6741c3b5d9ea}}, {{cite:1cea23f2ab138c32eefa99ea56c85769dced14fa}}, {{cite:e39f3d1bbfa6cf08ef27a4f4132204eb44544325}}, {{cite:4e423ddfa50ca4074d8a04d3045e7e095426a212}}, {{cite:9282f3df026957d7d2133db20d4865a0c6d8815c}}, {{cite:c03f9231d84e9b869a748677c64211c3ddbb8277}}, and the demonstration of the properties often require additional assumptions on devices. In this paper, we have bridged in a direct way the two fundamental concepts, {{formula:a9804b84-c763-41d8-b86f-a5b926409516}} , randomness generation and the degree of state collapse, with a proposed a QRNG, where the state collapse is estimated with disturbance in measurement. The protocol enables us to estimate quantum randomness in the various scenarios, {{formula:b3a88e8e-aff4-4583-a778-6c1124874028}} , under classical adversary, in asymptotic limit under the classical and the quantum adversaries, respectively. The protocol employs trivial mathematics. Quantum randomness is verified once the disturbance is measured, and one does not need to take an optimization over the unknown parameters of devices. Our protocol also shows high efficiency and outperforms the protocol based on uncertainty relation. These merits are greatly beneficial for the real-time QRNGs. Therefore, we provide new insights on the estimation of quantum randomness and the practical design of QRNGs.
d
748480fe3be8ce420680f91eec953262
The existence of such currents in the early universe would break the homogeneity assumed in the cosmological principle, but inhomogeneities must occur to seed the formation of galaxies. In the literature, we find that the production of electric currents in the early universe has been discussed in the inflationary period {{cite:a3464052f96e95b06e89b34f1d2a9f74f2e57bb3}}, around the electroweak phase transition {{cite:63a9cdb04de2b941685a04889bb75e1ff9029859}}, {{cite:ad1be930e9b0ddf061dbc478de89a7f1af6d2d07}}, and around the QCD phase transition {{cite:c2f6ec47ee1ffd63241d9aec3084a5c16aafc517}}, {{cite:aaf0e04f61d29e03591640804788bc66e3860ab8}}, {{cite:63a9cdb04de2b941685a04889bb75e1ff9029859}}, {{cite:4eb2c3c41f2b87e8828b91bbe284c3b7af38c61c}}. These currents are expected to dampen rather quickly, compared to the Hubble time {{cite:aaf7e833889ef6bdafac8b89c44e136c740d670c}}, but their ability to locally polarize DM does not rely on long time scales.
d
9b29ff1e9206036cd7c370aac3bdb978
We benchmark our method with (i) uSARA (Algorithm REF ) solving the unconstrained problem (REF ), (ii) SARA {{cite:1d020f3b2e4c7ac29fc2aa8eb8e5cc111aaeb60e}}, {{cite:dc8eb73ba4d9e64853964bf44ec43e28cdef346b}}, solving the constrained problem (REF ), and the multiscale variant of CLEAN implemented in the WSClean software {{cite:12fc55ed9f89a0c039b2d383f7593b33368e5ac0}}.
m
6a27ad136a782a5128afdabdaec77f80
Robustness under AA. To further ensure that FGSM+NoiseAg do not benefit from gradient masking, following {{cite:fdbbf82bd403fc6d77b3e86a13a74f13b9f7ea89}}, Table REF report the robustness under AutoAttack (AA). We observe that FGSM+NoiseAug achieves superior robustness against AA.
r
9a5977084c21ca18128e04f2ab770cd3
Traditional 2D image and video quality assessment have attracted a lot of attention in recent years {{cite:80406c4179649e398b06c38c1962fcf9175196fe}}, {{cite:c227656c6e46819061dce103d870e4a55ecc5526}}. Some objective IQA metrics are well-established today, e.g., Peak Signal-to-Noise Ratio (PSNR), Structural Similarity (SSIM) {{cite:c88e7fd328255c8875b25490d6cfebaa2c943248}}, Multiscale Structural Similarity (MS-SSIM) {{cite:cb9e7ab73bda12f6c4db82aacc4c21554141a32d}}, Most Apparent Distortion (MAD) {{cite:80575ac27057f90cc3b5e4dade82f819958b5039}}, Feature Similarity (FSIM) {{cite:938ccb56970c275dd9d64f1673de9afa242d7bbd}}, Gradient Magnitude Similarity Deviation (GMSD) {{cite:83f44b2e6bcabd925e1f68dcbce196040a051753}}, and Haar wavelet-based Perceptual Similarity Index (HaarPSI) {{cite:d58855b31fb49fffd0036827d08c45047a5dac5c}}. Different from IQA metrics, VQA metrics must also take into consideration the temporal dimension and model the temporal aspects of the HVS. A straightforward and convenient approach to VQA is to use an IQA method on a frame-by-frame basis and then compute the global quality score by simple average of Minkowski summation. However, such approaches do not correctly model the temporal dimension.
m
2d7350421b95f8468c1db29e1965350b
In sec:single-crt we have described three perspectives on conditioning in randomization tests: conditioning on a set of treatment assignments, conditioning on a {{formula:8fe9b6a4-5b9c-44e4-af0c-13eb2b0cc0a7}} -algebra, and conditioning on a random variable. They are useful for different purposes: the first perspective is useful when the null hypothesis is partially sharp and one needs to construct a computable p-value; the second perspective is useful to describe the conditioning structure of multiple CRTs {{cite:2a7df00dcc4a0222cad4e3c05e1d881eda29a9f9}}; and the third perspective is the most interpretable and allows us to consider post-experimental randomization. We have collected some useful methods to construct CRTs in sec:practical-methods. In most of our development there, conditioning is presented as a technique to obtain computable randomization tests. But conditioning can improve power {{cite:a2f9cb96407e2c03e4ae1ce6da997a23394a53a5}} and obtain good frequentist properties {{cite:c59ada6564222d44cb0efe93b836aa33fe04ceb4}}. Theoretical guidance on choosing the conditioning event is an interesting direction for future work.
d
2f1e6aab2cd053edffc5c33f469b285c
Results on the UTD-MHAD dataset are shown in Table REF . We compare our approach to the baseline of the authors as well as a more recent approach {{cite:cdf4a8768f16d3e34e9622720644f01fcd9699c9}}, {{cite:1240bfb3c3752c3ad6d0e1497022b8a4c2bce227}}. While Zhao et al. {{cite:cdf4a8768f16d3e34e9622720644f01fcd9699c9}} perform better than our proposed approach we get slightly better results then Wang et al. {{cite:1240bfb3c3752c3ad6d0e1497022b8a4c2bce227}} and further have the benefit of being applicable on other sensor modalities. It is to note that the perfect accuracy of 100.0% in {{cite:26aab8d115a32818eae7747a0a6a830c83f8b80d}} was falsely reported on a similar named dataset. Fused experiments are executed by fusing skeleton estimates and inertial measurements {{formula:d5af509f-6d6f-4910-956e-2c24bb7d01f5}} . We improve the UTD-MHAD inertial baseline {{cite:66052b790273e7e58d333bba30436f97ef9d6610}} by +14.43% and the UTD-MHAD skeleton {{cite:cdf4a8768f16d3e34e9622720644f01fcd9699c9}} baseline by +1.13%. The proposed augmentation improved results by +2.19% for Skeletons, by +8.77% for IMU data and +10.37% for the fusion with the proposed augmentation methods. Fusion in our experiments did now have an overall positive effect. The inertial measurements seem to negatively bias the predicted action. Additional sensor confidence encoding could guide future research. The experiments we conducted on the ARIL dataset are compared to a 1D-ResNet CNN {{cite:2731d486e4275f6f607e9b70f8d8e8a59a801c4e}} architecture proposed by the datasets authors. Results are presented in Table REF . Our approach performs better by +3.12% and the additional proposed augmentation methods improved the baseline by +6.78%. Wi-Fi CSI fingerprints have the benefit of being separated by their 52 bands already. Signal reduction is therefore not necessary. The additional proposed augmentation methods increase the accuracy by another 3.66%.
r
519bb21772833e3aebccb2a828b03e88
In this paper, we propose a novel codim-n holography, called cone holography, which conjectures that a gravity theory in {{formula:0bf20f15-fff0-4158-8b26-37283fe7b7ec}} -dimensional conical spacetime is dual to a CFT on the {{formula:2dd748f6-e448-44ef-aacb-7b5afac8c346}} -dimensional defects. The cone holography can be derived by taking the suitable zero-volume limit of AdS/dCFT and it can be regarded as a holographic dual of the edge modes on the defects. For one class of exact solutions, we prove the cone holography by showing that it is equivalent to AdS/CFT with Einstein gravity. The proof is valid at least in the classical level for gravity, or equivalently, in large N limit for CFTs. We test cone holography by studying holographic Weyl anomaly, holographic Rényi entropy and correlation functions, and find good agreements with the results of CFTs. In particular, the c-theorem is obeyed by cone holography. These are strong supports for our proposal. In addition to the mixed boundary condition, we also discuss the cone holography with Neumann boundary conditions. We find that the end-of-world brane {{formula:26e61a3b-b526-4577-b7bd-29888a5fcee4}} intersects with the AdS boundary {{formula:31dd2ed8-1078-43c6-83a2-f44af379ba67}} at some specific angles for NBC. As a result, the effective Newton's constant is divergent and needs to be regularized. By performing the holographic renormalization, we get a well-defined Newton's constant, which is consistent with the c-theorem. Finally, we analyze the mass spectrum of cone holography and find that the larger the tension is, the more continuous the mass spectrum is. Due to the massive KK modes on the brane, in general, cone holography is different from AdS/CFT with Einstein gravity. When the tension {{formula:fc5ff14b-3fc2-44fc-8c26-a02c07aa54f0}} is small, since the massive modes are frozen at low energy, the effective theory on the brane is Einstein gravity. The cone holography is a generalization of wedge holography {{cite:19b16d812f833cb2ee6a9ed249ef751c385abf35}}, {{cite:43bbe3d1de9fea0579466f35d49d0c9cf748d41c}}, {{cite:3c11b24417d6ff3023c9c9f6dbfb25d478a5d9a3}}, and is closely related to brane-world holography {{cite:675e2b4e57c5d17b7508089ac274624be21940a8}}, {{cite:fbfa092b022089e95f011525a0e5e366ebe188a2}}, {{cite:fc035f33fb64f05828f64d43ae2564c356ba70e4}}, AdS/BCFT {{cite:d73eecb853d80ed71c1b0d8098fcf9e2638783fc}}, {{cite:1c5f82d94c163931d0f156780e73fdd4d0333317}}, {{cite:5bd38d41beb45a44b367275c341ed465c0b876ef}}, {{cite:da060557ed06c0cfb4bd03b353f029ff03d57063}}, {{cite:4ebadd5e63f0427b01f25c23f46b10139a3eed52}}, {{cite:0fbbb22659feba2e3757262185337d9bd8cea865}}, AdS/dCFT {{cite:8ed0a0fb6e8479652bc6caf074da3103f7e49f68}}, {{cite:9abd41c395c601bcb1e1235d2ee2b1368f9b5819}}, {{cite:406ca2f5604ec042b493ca81808f11cc54c91216}} and holographic Entanglement/Rényi entropy {{cite:406ca2f5604ec042b493ca81808f11cc54c91216}}, {{cite:6bb4920d4245639bd95cc3a80ddcf18d439cc82a}}, {{cite:93eda2b5055f85a9720ba31460871ea3d577ed5f}}, {{cite:d90a83a5c8606cd22ab3a44f0524e637367a19f9}}, {{cite:02cff63be0e1d04ccb1636cb3003399c441af4d3}}. Thus it is expected to have a wide ranges of applications.
d
adc6cf69e66e19cb718fa97a5b8de6c0
Relation to Multi-Hypothesis Models. Some recent works generate multiple plausible hypotheses {{cite:36568d12e53f8023d1bfad3083a631878660c13b}}, {{cite:cc2a36bee1c0a2b1f4872d259450a754e9588605}} and use extra information at test time to choose the best hypothesis. The techniques include training a set of models with dissimilar input gradients {{cite:cc2a36bee1c0a2b1f4872d259450a754e9588605}} and training multiple prediction heads that disagree on a target distribution {{cite:36568d12e53f8023d1bfad3083a631878660c13b}}. An interesting extension of *OccamNets could be making diverse predictions through the multiple exits and through CAMs that focus on different visual regions. This could help avoid discarding complex features in favor of simpler ones {{cite:2de57a3a9a263272eb5655c7608e00126ad127aa}}. This may also help with under-specified tasks, where there are equally viable ways of making the predictions {{cite:36568d12e53f8023d1bfad3083a631878660c13b}}.
d
211c62bf8bc58263266b744e487bad28
This framework on one hand allows to define many important decision problems. On the other hand, complexity classifications of the flavour of Schaefer's theorem {{cite:4fd79517d9f80a3014da66acd0b9ecd5fa0bd6de}} these problems tend to display are of theoretical interest. Directly relevant to this paper are temporal CSPs that are {{formula:137e7d31-1717-4528-a30d-9bb689d3eec4}} for {{formula:1b68ed28-8c7b-40d9-b0ce-898a18d9c44c}} with a first-order definition in {{formula:447e3295-695d-4358-b419-22c4fc9eff5c}} , called temporal (constraint) languages. In {{cite:ede3b28ea600cdc5fc4d005b7b4a5dc78e5e2196}}, nine large classes of tractable (solvable in polynomial time) temporal CSPs has been identified and it was proved that all other such problems are NP-complete. These nine tractable classes contain many decision problems studied previously and scattered across the literature, e.g., the Betweenness and the Cyclic Ordering Problem mentioned in {{cite:3da4214ca2b9a92f9c023b4441c382520bfddf96}}, and network satisfaction problem for Point Algebra {{cite:fcb20447d21335a80944b9bd4bb9ed3c3f733a7f}}. Furthermore, temporal {{formula:b1e8c474-24be-48c7-bc6b-25c63f2c16e6}} has been studied in the literature for so-called Ord-Horn languages {{cite:fba0eed14af6ffaaf47dbfbf93204af1bed47aa0}}, and AND/OR precedence constraints in scheduling {{cite:62ecd0bc991237fe405bee5d9aea938780131547}}.
i
bdbf747aae330ae35d6f8e2f1278e972
Transformer models. Four Transformer-based models are also implemented as benchmarks. ViLBERT {{cite:e0c2035869ce0745c3c20225199a2edc0345a827}} and UNITER {{cite:d8e67f7c86305c450e5e003fdb1adb1320ee3039}} are two Transformer-based approaches that take image object proposals from Faster-RCNN {{cite:ec816be44c501cd3a2e8e3a6d9e2571094da032b}} and question tokens as inputs. Specifically, ViLBERT learns the joint representation of the image content and the natural language content from image proposal regions and question tokens, while UNITER processes multimodal inputs simultaneously for joint visual and textual understanding. The last two benchmarks ViL {{cite:773722f2275b624e960851d10f6d6028f2688932}} and ViLT {{cite:17bad8b2ee4c332d52b35dc37f906eb0f7d9be4c}} are more recently proposed Transformer models that take image patch tokens instead of object proposals as inputs when representing the image.
m
2ce8fe9a894492a19673d916c9472aff
Emission obtained with the method described above is obtained self-consistently, and automatically accounts for magnetic field structures on small scales responsible for jitter emission. By performing such calculations for simulations with different parameters, we can investigate and compare the different regimes of jitter- and synchrotron-type emission {{cite:e45817f856d8f065629aea035e1c218b04715d51}}, {{cite:2e0751a09fe2824094da61eee0bb02ef05fa38fc}}. The feasibility of this approach has already been demonstrated {{cite:5f69d12b082758f68cccb7b648959d6c4cc84fea}}, {{cite:b2ce6a36c2b96dd2bff31f12f4cb081d86c744c8}}, and its implementation is straightforward. Thus, we should be able to address the low frequency GRB spectral index violation of the synchrotron spectrum line of death {{cite:2e0751a09fe2824094da61eee0bb02ef05fa38fc}}.
d
eaba23b77a32188978cc71910a45214f
The depolarizing channel {{formula:af612d17-eeba-4d57-b92b-be881328bb54}} is one of the most important and fundamental quantum channels {{cite:80557b31a5273aef3e8a5bcf06fe6e002f4a0ec0}}, {{cite:e0eeb2704bd952885d1b5fe248221371ec5c38ca}}, which is useful in modelling noise for quantum hardware such as the superconducting quantum processor {{cite:1094affa5fb1822265e4d712b19dcdb5c3bcd203}}. However, even for the qubit depolarizing channel, the quantum capacity remains unsolved despite substantial efforts {{cite:3795d4377163cb57f4ab3e857ceb4e715fa43a31}}, {{cite:2c7e85fd62854979a53b6cbd7bb244d719064b46}}, {{cite:3ee8640f84e2c0f1cfa5cb087a2269152f799a76}}, {{cite:08ccecea4d59ec873cff9c250a6fef6028adb307}}, {{cite:d3a0a0728f5f0f6d57e0c7d3ff222baee1a4bdd3}}, {{cite:0c743a66e2c5a994fcf1e87212897aae5189f03f}}, {{cite:30fe927f8d37e80829241a024f4c5eb44e912406}}. Recently, Fanizza et al. {{cite:30fe927f8d37e80829241a024f4c5eb44e912406}} considered the degradable extensions with non-orthogonal quantum flags and obtained an improved upper bound on the quantum capacity of qubit depolarizing channel in an intermediate regime of noise.
i
92c5f110abc6369033135550bd801240
where {{formula:10174097-7e71-462e-b1ee-77b8f5db62be}} is the total number of sites, and the summation is over all sites of the sample. Here the Green's function {{formula:191ab1c9-9562-4cb8-81c6-755866043682}} can be the dressed one {{formula:9b09085c-5899-4bd2-b9c2-dfb499467cc3}} defined above, or the bare one {{formula:5916c1eb-a975-4fac-8725-a84de9520b61}} , depending on whether one wants to include the effects from leads. With the LDOS normalized over the sample {{formula:f3071a09-380a-4099-8023-ad6359518342}} , the NPR can be defined as follows{{cite:2a6a5b8b802c39910056de1eb29d022df8c15a08}}, {{cite:ed0a28614fa1b3b53ab939ab1c584799327f4cc3}}, {{cite:4044dd8e04fc34d12a661d3ae6412685f6947299}} {{formula:abdc7bc7-30bf-4922-a11c-aa7fecef3c97}}
m
3279e8bf236870e6aecac0bb387e2695
where the second term denotes a white noise. Since {{formula:b5bbb114-b2cd-4702-85cc-6e4128d47c49}} is related to {{formula:d6193ad2-1243-47ed-99f0-ccdc311c99e9}} by Einsten's relation, the motion can be described by only one parameter {{formula:e27591e6-6f78-41cc-a608-352726ac237b}} . This formalism has been very successful in explaining the {{formula:df33d41f-8227-4bf1-be4e-13a394de1fca}} and {{formula:7414802b-a6f9-4929-9dc2-6b94600f7e08}} of {{formula:120aef70-c813-4ba5-ae29-9090da04e5aa}} mesons {{cite:8f22f708b35aa03320d8445b01ae36d323aa25bd}}. It is, however, difficult to calculate {{formula:b10d9fc2-5c62-4d8d-8e9a-1b6383c48fbb}} from thermal QCD: the leading order (LO) result {{cite:494e05c555b4e5a75e2b426e0e8620ccf4b67603}}, {{cite:ce9a25a59b0678566f567a54930ceaf8ce8de99e}} is far too small for phenomenology. Perturbation theory for this object is also quite ill-behaved: for temperatrues of interest, the next to leading order (NLO) result is an order of magnitude larger than LO {{cite:b41f854a5eaf9b7e27cfef92697410ce84fd322d}}. A nonperturbative estimation of the diffusion coefficient is therefore called for.
r
4404e20020cff3a66b26939289bd4053
We conclude our paper with two interesting issues worthy of further investigation. The first one is related to the Gubser-Mitra conjecture. As alluded to in the introduction section, Hollands and Wald proved the Gubser-Mitra conjecture for black branes in AdS spacetimes by resorting to the criterion they established for the dynamic and thermodynamic stability of the black holes{{cite:27cf25db1a4fbc0bdece4dfe941e5ca414aac1e9}}. Thus it is tempting to ask whether one can obtain the similar equivalence between the dynamic instability and the thermodynamic instability for the AdS planar star by the same token. On the other hand, new progress has recently been made towards the Lagrangian formulation of dissipative fluids and its various implications{{cite:89d29afc5ad4c6bf804d30a91b230f1e17b11417}}, {{cite:2134caad10b51e572e1200886af7977abae24a8f}}, {{cite:3e08844867aadb76aae72782a192c073be373821}}, {{cite:287fc1f7128d470b5f934e0a11e77b8ef4e1e8d3}}, {{cite:4f1a432862570ca8c11def5292dd0c098d857288}}, so it is also interesting to explore what new insights one can gain by applying the Wald formalism to it. We hope to report some progress along these two lanes in the future.
d
e028ce77460a4a5d80d927ee764dc994
The bridging between approximation techniques and high-performance computing finds numerous fields of applications in the industry as well as in academia: it is sufficient to think about heat transfer problems, electromagnetic problems, structural mechanics problems (linear/nonlinear elasticity), fluid problems, and acoustic problems. In all of these examples, the models are described using a system of partial differential equations (PDE) that usually depends on a given number of parameters that describe the geometrical configuration of the physical domain over which the problem is formulated or that describe some physical quantities (e.g., the Reynolds number for a fluid or the Lamé constants for a solid) or some boundary conditions. For all of these models, we usually focus on a particular quantity of interest, also called an output of interest, such as the maximum temperature of a system, a pressure drop, or a channel flowrate. Unfortunately, computing such an output for each new value of the parameter is a difficult task that is expensive both in terms of time computation and in terms of computer memory, even on modern HPC systems. With these premises in mind, it is clear why the Reduced Basis Method {{cite:7418077dac5517f49bb0b03e9fb80367e90ec814}}, {{cite:d18db98cd8e59d9f27f3a40f88fa9a71ee01154e}}, {{cite:749a6f8812ba94f0dc336c07ee1b87909475333b}}, {{cite:d048627bfbcfd6470178b72942a64d961e6f4205}}, {{cite:6541899027b674c9f99ba7f0cee2aeb7c4729789}}, {{cite:db5567f2ee322ce0f1a8dd097deef5f04b5c8533}}, {{cite:22518b1964e5d23fd90646c456a06f38763ccd9a}} (RBM) comes into play and shows a wide range of advantages: the idea at the core of the method is to simulate the behavior of the solution of our system of interest for some chosen values of the parameters in the PDE. This is usually performed using some well-established discretization technique, such as the Finite Element Method (FEM); another discretization method used, for example, in the compressible framework in computational fluid dynamics is the Finite Volume Method (FVM), and another possibility is the Cut Finite Element Method (CutFEM) (see for example {{cite:5d75c7156133257698c772a415f3e76d5d679c7f}}, {{cite:53e988e6c102afd94c30e221424e2050d171e8f7}}, {{cite:816243c45414286417b863b2e296da3d65996dc7}}). Once we compute these solutions, in an expensive offline phase, we can use them to build some other basis functions: with these new basis functions, in the inexpensive online phase, we can approximate the solution of the system for a new value of the parameter.
i
e2ee6b3a10d949c21c58d637c10535de
It is interesting to make a comparison of Theorem REF with what can be obtained by Gallager's method for nonlinear code ensembles over the erasure channel (see {{cite:dc57d76d163e239d9bf62237cca249c1de6709ca}}): consider the ensemble of all block codes of length {{formula:44d555c5-17f6-4550-90db-380597590846}} and rate {{formula:806b6eeb-830f-4e62-9dbc-2c526eb84e2e}} ({{formula:c557c4f6-f566-4bac-8eb6-3d9dbed37fc1}} ) over the erasure channel in which each letter of each codeword is selected independently as an element of {{formula:2272ab3f-6918-4a4b-9fbe-842de69e2076}} with equal probability {{formula:31f75330-a318-4fb9-9537-1f8091ccd920}} , then the average decoding error probability under list-decoding with list size {{formula:9a1dc3c4-f583-471a-8a9a-bc05ac41d2f8}} is upper bounded by {{formula:b9145ac1-0b48-484f-8756-d1fa8fdfd385}}
d
987a0dea6f78edb0f85977b4be37d027
The influence of QED vacuum effects from strong magnetic fields in the vicinities of magnetized stars has previously been studied by several authors. The combined QED vacuum and plasma medium is discussed in detail in the context of neutron stars in {{cite:74f096d55fc7232931d4398787fe67589b8a79ca}}. Vacuum effects have been found to dominate the polarization properties and transport of X-rays in the strong magnetic fields near neutron stars {{cite:024f3507bf59530a140d59134a41a40143049061}}, {{cite:6398143b41223ad0caa2f6c2d08144b08ea332f0}}, {{cite:a1aea12c759bfe780ad9ac6139a3718b21c1e352}}, {{cite:b775d6cd46d10cfb4ce25b9f0d7f281861c88474}}, {{cite:d68770365e7db42c4f10ae317a54dcfb6fa34782}}. Detailed consideration of magnetic vacuum effects is therefore critical to an understanding of emissions from highly magnetized stars.
i
ce6419ae26f71688077ee5a2fe0c243b
For AwA2 {{cite:4cd7e531c69618704432218e1c743bce0aebe6c8}}, our GDAN  outperforms some recent methods like SP-AEN {{cite:fd6b933c8ead6f39de7e32739e97c69ac5225c3f}} and PSR-ZSL {{cite:e3f5c4131c48b29a53ff0440a353e02a93affaa0}} in both unseen class accuracy and harmonic mean accuracy. Although DEM {{cite:840b10ee81d852926b0d654d0c9279317b22ff86}} and RelationNet {{cite:27369f11da3500523f9809613b6f94c8d90e2691}} slightly outperforms our GDAN  in harmonic mean accuracy by less than 1%, GDAN  achieves a higher unseen class accuracy than them with a noticeable margin of 2.7%.
r
85dd0bf6fc2dbe15a99477f957eb5a72
Feedback is still a relatively poorly understood aspect of galaxy evolution, and it is particularly interesting to study if and how this phenomenon occurs in AGN in early phases of their life cycle, that is when they are "young". Carrying out such research at high redshift, when all sources were young, is not an easy task. An alternative approach is to focus on sources that are the low redshift analogs to the first quasars. Narrow-line Seyfert 1 (NLS1) galaxies are in this sense ideal laboratories to study the early phases of AGN feedback since, like high-redshift quasars, they are characterized by fast growing black holes with high Eddington ratios, and also by high metallicity, especially prominent Fe II multiplets {{cite:f7aa9dcb0ee7cc4d3c37cf612f92db76fdf0c827}}.
i
db9c8a73a7476a1cc0ecd5dfa1c55afc
We also reproduce some recent advanced algorithms  {{cite:c4217486a3c5b5f3664383e7b458868663b5a498}}, {{cite:aa39d35b9c111f5d5756671cb938cbefb2756901}}, {{cite:d0b95920795773fc6034113cb2b48c0f701d3f48}} to validate the effectiveness of our hubrid model on the dataset we created in Tab. REF . The performance of our method is far superior compared to methods that model only the appearance features.
m
3496737e4759a206c75ab15918968e30
Since the relative translation observations only contains the movement directions and not their scale, solving the viewing graph is the challenging step in the SfM process. To simplify the problem, almost all viewing graph solvers determine the rotations using only the rotation observations and then use them to compute the camera positions {{cite:8d7bcd70991ff2400c904c747f6b6ec1a590ba4e}}, {{cite:7fec8bf538a022d014a9fe2b94664924ffaa5a41}}, {{cite:a8adb9bd970372f48b5d79f82d73de6ac51cb2a2}}, {{cite:11d50721c2eb2d2da5690345e518e313d0018eb8}}. Obtaining a set of rotations from their relative observations is known as rotation averaging problem and has been studied in the computer vision community {{cite:3f4f2cc7131e92e940d86e5f68220e7b24223396}}, {{cite:8cbb5cbbf5453769edcd077718f25da7b19db512}}, {{cite:aa96d07f8ced33397b051e1e3ebd5724c0f3b129}}, {{cite:6369fc1b54e2b3d19a1932417b78c3d992572e53}}.
i
efceecde4413bcd2d16cb22094ff1dab
To achieve this, we first put back all the stride convolutions removed by DilatedFCN, while replacing all the dilated convolutions with regular convolution layers. As shown in Figure REF , the backbone of our method is the same as that of the original FCN, where the spatial resolutions of the five feature maps (Conv1{{formula:86bee6e3-73d4-4601-a087-55221658cf84}} Conv5) are gradually reduced by a factor of 2. To obtain a feature map similar to the final feature map of DilatedFCN, we propose a novel module named Joint Pyramid Upsampling (JPU), which takes the last three feature maps (Conv3{{formula:d882000c-cc24-463b-a813-c82f7de17f6a}} Conv5) as inputs. Then a multi-scale context module (PSP {{cite:95723330f0dbdb70d5306089616c139543934f29}}/ASPP {{cite:1ac32ae180d52b9a0676e1929ac046e1068f7f74}}) or a global context module (Encoding {{cite:a730666fba1073cd9873fdc87a25d4c2a345c4ad}}) is employed to produce the final predictions.
m
a9713dfcd1c2a074d134b4bc06504bc8
We now investigate our method to solve stiff systems with complex entries (i.e., advection problems). The second Dahlquist barrier states that the stable region of a multistep method for a stiff equation shrinks for accuracy orders higher than two (see, {{cite:cdebb1529fae1f1e6b82e2c22f1725bcaad94bfa}}). Our approach delivers the amplification matrix of (REF ), which requires solving {{formula:80cc23b1-1b23-439d-8ef5-da579157d071}} systems that are form identical to the second-order generalized-{{formula:5a17a783-e2ae-400a-a901-b11486e261ce}} method. Each block decouples from the others; therefore, their eigenvalues are independent as well. Thus, we solve {{formula:c9491669-c08c-4052-b55a-ee070882830a}} independent systems that lead to a high-order method with an invariant stability region. While, the analysis in REF supports our claims, herein, we consider a problem with complex eigenvalues, {{formula:5bd3d1ac-83a8-4334-81c0-5335beb613b2}} . Similarly, we consider the amplification matrix (REF ) to obtain the region of stability as: {{formula:d6de8c59-5ccc-4706-a6b8-410093e34b53}}
m
0bb0884d0ef233f7cca7aeac0ff0ab53
Active galactic nuclei (AGNs) are thought to be powered by supermassive black holes of {{formula:9848628d-26a4-466f-ace6-b66d177d85ef}} accreting the surrounding gas {{cite:a509a8bb2a151009ed209188afaa4c5c3f17c25c}}. They are also considered to be scaled-up versions of Galactic black hole binaries (BHBs, {{formula:e538cec2-fc75-4416-b470-8f474763eb05}} , {{cite:1300db516c7349a494331b6535e8254dc0f07eb0}} and references therein). The rapid X-ray variability is one example of the similarities between these two types of systems {{cite:3f452c0ed289fb7a3c225f7393cc35be1c3f0fd7}}. In Seyfert galaxies, variations of the X-ray continuum emission over a timescale from minutes to hours have been reported {{cite:6f004a8d93c3823e2826c66069e16c898f33ec99}}, {{cite:8d4605b98c4433a784f7764f27775961e123ae38}}, {{cite:22f9fdceffb57154060eb0c7f69a7670744f3732}}, however, persistent giant and rapid variability appears to be fairly rare and its origin is still poorly understood.
i
c5707acea70e513454114bf8001a63ac
In Figure REF , we provide the examples of frame-level video scene graphs generated by our model and RelDN {{cite:4d96a9345e6bbc7b0810893dff6e17ff9424417c}} in AG dataset {{cite:96237c4797fb1bf673ee58db1ac2b00d1719948c}}. In Figure REF , we provide the examples of frame-level video scene graph generation on frames sampled from the same video clip. {{figure:daa1d7cd-1b7c-4740-9e1e-7795c5fdc63b}}{{figure:7ce24403-95b7-4b5b-94b8-daea829a2108}}{{figure:6564cefa-be01-4cee-bdca-7c934bb97c1a}}{{figure:4a3628b3-52ac-4745-a506-6cfc01cfc6dd}}{{figure:5d37e2d3-6ef7-4838-8947-ec441583fba3}}
r
07cb7311f8ce2087bbe1254d15c807a9
In DA, data are assumed to be available in different domains. The domains share the same feature space, but the data might follow different distributions. In both domains, a learning task is to be solved, characterized by the same class structure. One distinguishes a source domain {{formula:bd6ad481-6b70-4405-90d5-a9053caa9c28}} , in which an abundance of training samples with known class labels is available, and a target domain {{formula:1ce283f3-cc29-4530-b18f-1c824f31ffd3}} . In semi-supervised DA, the scenario we are interested in, no labelled samples are available in {{formula:00bda799-8270-4446-9b20-4831a2946991}} {{cite:deb95bd0278e798d15cdaa438f1deecb8876b1e9}}. The main goal of DA is to use the information available in {{formula:5d373ca4-08c0-4937-b5da-79abc4aed6ff}} to find a better solution for the task in {{formula:ce78f0f2-db43-4d76-8edf-c38236255e99}} , which requires the domains to be related {{cite:2fa949489c9a6be94ce4d436efa262b4823cb6cb}}.
i
cdba148d78c54fc73b1d20460ff69a5b
Most grasp detection algorithms use some method for generating grasp proposals. A number of methods generate proposals exhaustively using a sliding window {{cite:f45dcb9d964f7b507e5517440e7f7be2f0051f9d}}, {{cite:7c8cc99078bd00c2e921f96cb451c7247774eca9}}, {{cite:b9bd77a7a0cd3a55f438b9b65bf16dae67b068f7}}, {{cite:75f780044d4ee4d552f957edc2afc5b6a1625d5c}}. {{cite:506242aafa3304feb862cb1e66d9846309c9c916}} cluster foreground pixels using background subtraction on the RGBD image. The sampling method from the literature most similar to ours method is perhaps that of {{cite:cb397b6b3a77ae96b064578c47550bd4fe8a777f}} (later adopted by {{cite:89d4b3c9625c2fe07b0e74ea17bd3f07328c9521}}). That method works by segmenting the object to be grasped from the rest of the point cloud and calculating the convex hull. For each face in the convex hull, a coordinate frame is created at the center of each face and oriented such that the {{formula:e52c1fbb-d884-4300-96a9-974ec425e8cf}} axis points outward (similar to {{formula:299d9da3-33af-464f-b5dd-d952b24057f7}} in our method as shown in Figure REF ). A one-dimensional grid search is performed over a set of angular displacements about the {{formula:2fc900d3-5406-4ca4-9b56-00f1531454b9}} axis and the hand is “pushed” toward the object (similar to what we do in Step 6 of Algorithm ).
m
cbebbff8998ae2972f9cc5427e3fd399
Safety is also often addressed by the higher-level planner. Grid/graph-based {{cite:9fcaf6acbaaaf8dce451644d511cab1d6d873144}}, and sampling-based {{cite:751234f6d4519ecf3cbf0faea3d092b24c1374b1}}, {{cite:14c2a893e44e621e94ef519c56f505ff0ac2ca1e}} planning algorithms can design paths to meet mission objectives while avoiding obstacles and unsafe states. In {{cite:c2f004cab58447473dbad6a4143b7a996997fc75}}, {{cite:cf3a067b7ab69b7443ce774f394df35c775dc425}}, the robot's dynamics are simplified to linear dynamics, and the provided safety guarantee assumes the nonlinear system can execute the trajectory generated by the linear dynamics. Alternatively, nonlinear Model Predictive Control (MPC) techniques have also been used, although guaranteeing convergence, stability and recursive feasibility of the solutions remains an open challenge {{cite:342838956178de6496c5f798846de6e399924966}}, {{cite:75c2f2be34a1035d98eb09c95b5a54c4d31efcf2}}. {{figure:7489a9e6-3cdd-4250-a02b-b20558ee7043}}
i
b8ec31e47b90b8e1f4661cc62210135e
To test the generality of N-BLS, we compare it against baselines on a labeled dataset. By assigning labels, the filtering algorithm can further reduce the search space prior to the search process. Because of this, labeled datasets are generally easier than unlabeled datasets. The degree to which labels make Subgraph Matching easier is hard to determine. For instance, if all the target graph nodes in the same global candidate set share the same label, then the additional label constraint provides little guidance to search. On the other extreme, if each query graph node has a unique label that matches only one target graph node, then the search becomes trivial. For example, Knowledge Graph (KG) reasoning {{cite:e5d242e00a3ff7b9a8e0a8b065215aeb94bffcab}}, {{cite:19182141fbf302e1471abc157a66669a7130feaf}} can also be viewed as matching a subgraph in a large KG, where a first-order logical query is represented as directed acyclic graph. However, since the KG can be incomplete with missing relations, exact Subgraph Matching may not be the most appropriate choice {{cite:e5d242e00a3ff7b9a8e0a8b065215aeb94bffcab}}.
r
94ed61bc2e3758183039ddf7e55c2456
Through the autoencoder structure described above, we obtain the information-compressed latent distribution {{formula:0c389af1-9790-48d9-ba9e-add45392af36}} of {{formula:95503e27-f6c1-48af-ba9c-3390f46cd2e0}} . Aligning embeddings or distributions in autoencoder's latent space is a generally used technology which has been proven effective in various fields {{cite:d11c18ceff4aec5985a2f1a97b13a024da971f2f}}. Thus we consider mapping the side information embedding {{formula:09c4ba1c-7fcd-4ee4-bb8c-c45be403d8de}} into the same latent space and aligning with {{formula:810cd20e-f005-4f84-923e-f233c8d56fa1}} . Specifically, Prior Encoder {{formula:e3563dcd-bad4-477a-9812-aa0cf61faea7}} maps {{formula:58bcaf42-ed73-48e9-a9db-2715a02ac4f4}} to {{formula:6c1dc623-a2f2-4c78-8e71-470f12076d00}} and a wasserstein loss {{cite:d2ca2323772b8218d4aa601ab24bcfd2fc9d8c73}}, {{cite:1cdda2a006414d5911bca29fb88b02ea98012b24}} function is applied to aligning distribution {{formula:417c9023-2503-45d4-823f-2c2e709ac06c}} with {{formula:f2808a19-7521-4434-87e9-30bf8eec7e87}} : {{formula:810b3fcf-cad3-482f-9b7d-7f5bf3b90280}}
m
8cd897a1826dd3be899fff2ffe30eac5
Image-to-image translation and image manipulation techniques attracted much attention {{cite:76765168f911b285f59b981bae8404d13f9068bb}}, {{cite:c9327aaef68079d5a03dcc4ed36366f0ba4f6d1a}}, {{cite:b7d1fa1ceec66d64242ab5cb6756994331005de9}}, {{cite:6940905b844127e00c3e38b887e5c7175c4d2653}}, {{cite:ea7ed5004ce3e9cf57827fdc0ba1531969fe978a}}, {{cite:397194a499e563e74e32d29d178ebf9bb053adc1}}, {{cite:b179d579811bc55fac50d4ad926fd964e1ba586f}}, {{cite:e06c0c5b407515ee8f64279fbe586ce8644ea6d0}}, {{cite:cb6512266edddda9a72cbd1c0e808a03fbaf0326}}, {{cite:ec53fe3c93edf7e7d3f22d467769ce2415b6f278}} recently as they can have a significant effect on many different tasks. Of particular interest is creating realistic synthetic training datasets to improve models' performance and generalization. One example that demonstrates the use of a synthetic dataset in the training of networks is presented in {{cite:ba48f0eb910d28dfa5ff4e77a370456f28605a20}} where the authors introduce a semi-supervised approach to generate datasets for semantic segmentation.
i
79b953d4a499f11ac3bb2700926a4d7e
To satisfy (REF ), using CountSketch {{cite:b8750ffe796f4220f4eab37b897e76f25e85da54}}, {{cite:bd4ca6cbb40fd7d520b9e121cbc426139f2937bf}}, we can obtain a sketching dimension of {{formula:614fc7aa-54d1-4ef1-aa37-1af297c5f48f}} for which the matrix {{formula:04255886-0d87-4aa9-ada9-0ee61f710c38}} can be computed in {{formula:cd3f0b03-ed9a-4743-9e7f-19dab3becfd8}} time, where {{formula:8d3d83bd-032f-43d6-97e9-33b4d6fb11c6}} denotes the number of nonzero entries in the matrix {{formula:86cb3f65-9802-4fdb-9b7d-753e31944008}} . Using OSNAP embeddings {{cite:3cbd9df9039cda59cc7f9b0e3d2600adca7e3f2b}}, {{cite:6c5503bd0abca86b7f536ea0d22208f80bd5dd9a}}, we can obtain a sketching dimension of {{formula:b5a60059-ae08-4ec4-8eb2-9bdb6cb62bb0}} for which the matrix {{formula:53cda38b-d9a5-4d8e-b693-70f23bee367c}} can be computed in time {{formula:b2026d5f-1d65-47bc-82a9-f539652dba81}} . For {{formula:409ecec8-b856-4fde-9740-2246599d5d9a}} , we have {{formula:d8f07ca9-3765-48bb-bc57-27d6023351f8}} with {{formula:62cbaadd-f4f9-4482-afdf-4ef00d68b6ee}} that can be computed in time {{formula:ae14ef7d-77cb-40f2-80fa-0a4b29d782b9}} . We can see that there is a tradeoff between CountSketch and OSNAP — one has a smaller sketching dimension while the other is faster to apply to a given matrix. If {{formula:07b11afa-8183-4100-8e61-21c8a27ad8c7}} is the time required to compute {{formula:32d0d65b-c31e-4982-a3d4-d6fbd70e371e}} , then {{formula:ab5e1a6f-fa85-4e8f-a3a4-c59122dcd70b}} in Theorem REF can be computed in time {{formula:ea6b6076-d7da-4a30-a2a4-391898094b9d}} where {{formula:47775926-5576-4502-8291-5508fb686d81}} is the matrix multiplication constant. Thus it is important to have both a small {{formula:c146da2d-957d-4e80-95c4-6e5aaf61926a}} and small {{formula:26106004-4772-4065-be88-42b2aff57900}} to obtain fast running times.
i
46895cfe0b420c7181edd74b54fc3780
We conduct experiments on landmark recognition datasets. We use Oxford {{cite:93f0d88c75c2554a067954129d48ab2c45a5671b}} and Babenko's Landmark dataset {{cite:500c9e33b3a01e63a704b6450d1c00372b7c1bfb}} to train our model. RParis {{cite:0efb0add896dd4137a4fea9b9e78c0fde56b857f}} is used to test the performance. Details of the dataset are described below.
r
a4932a9b0d0666f1e13240ae035aac92
Let {{formula:73905ee9-2997-4028-b68b-d4db237cfaba}} be as assumed above, and {{formula:005761e6-6dfa-45e1-955b-9bdda6e18ed9}} be the associated optimal plans in {{formula:878a7cce-82c1-43a6-a489-af638052f4da}} . Note {{formula:960abbcb-7cea-4807-b6ed-fb11abdcdc36}} (see Notation section). Since {{formula:bc402213-afb1-4f88-bc91-504c5ce885b3}} is weakly convergent it is tight, and {{cite:37cf7994b55fd0f84aebefdd6ad63ca8c1c07f61}} implies that {{formula:9de07f8a-4464-4c9d-98a5-e6da322bb80d}} is too, hence extracting (and relabelling) a sub-sequence {{formula:4a0307cc-1d2d-4d31-8db5-5d812fa1e172}} , we know that {{formula:bd2bad3d-54ac-4e9b-8c63-c9af489dc1cf}} . In fact {{formula:cd590f72-d370-42cf-a659-288bff08c81e}} since weak convergence of {{formula:5deb3175-f6cf-422f-990a-686416d24a4e}} implies weak convergence of its marginals (and we know {{formula:cbc09c0e-0028-4a51-91f6-176cae868211}} ). Now, the lower semi-continuity established in Lemmas REF and REF implies that {{formula:60ce7d76-d636-4676-b9ce-96be8282779d}}
r
28461a67c5dccf7020523a9b61767032
Synthesis-based HFR methods {{cite:a5bd25114b2670448c12dac9c746868badf696ce}}, {{cite:ff577d25608c171d1e45687d5b191c78d37495e4}} attempt to synthesize the source domain (VIS in most of the cases) from the target modality, after synthesizing the source images typical face recognition networks can be used to perform the biometric matching. Authors in {{cite:8494a1469807ece71b8c2a6d330f7c27c42d95e9}} proposed a patch-based synthesis approach to generate VIS to sketches and reverse using Multi-scale Markov Random Fields. The approach was evaluated using several face recognition methods such as Eigenfaces, Fisherfaces, dual space LDA, and so on. The work in {{cite:868d2f8b93e1a74032d5c57233eb155187261c0b}} used Locally Linear Embedding (LLE) to learn a pixel-level mapping between VIS images and viewed sketches. Authors in {{cite:dd3456d62e69a6e0b9539be64f5c03e8ab1b6190}} use CycleGAN {{cite:411c0c2c8c351b55a4ece9f8a1e7ea782ae1dfdf}} to transform images from the target domain to the source domain. Contrastive loss using a Siamese network is added during the training of CycleGAN to preserve the identity of faces. Moreover, the images are pre-processed before inputting to CycleGAN using {{cite:1cf2cfae0285db23ef0defc68f1f116c31bf8e01}} to reduce the domain gap further. Authors in {{cite:937d7f36ce8fc07e8b3d0f20c2eeb4e4aa845e15}}, proposed a Generative Adversarial Network-based Visible Face Synthesis (GAN-VFS) method to synthesize photo-realistic visible face images from polarimetric images. Identity loss was combined with a perceptual loss in the training process. The synthesized visible images were further used by a VGG network to extract the embeddings. Their method was evaluated on the Polathermal dataset and achieved an average Equal Error Rate of 34.58%. With the advancement in the development of stable methods to train GANs, several recent approaches have been proposed using GANs for the synthesis of VIS images from another modality. The work in {{cite:ff577d25608c171d1e45687d5b191c78d37495e4}} treated HFR as a dual generation problem and proposed a Dual Variational Generation (DVG-Face) framework. A Dual generator was designed to learn the joint distribution of heterogeneous pairs and to generate heterogeneous pairs to address the lack of adequate data to train the HFR model. A pairwise identity preserving loss on the generated images was employed to ensure identity consistency. The generated images are used to train the HFR network in a contrastive setting. This approach achieved state-of-the-art results in many challenging HFR benchmarks.
m
53d22ff23a6fa39f6edb1aa104c2831a
In our approach, we recover the BRDF parameters for every point of the scene with a differentiable renderer as a pre-processing step (Sect. REF ). We then learn the SH coefficients of the LIF using a network similar to DNR {{cite:b3a7b17a6e8afdd7e32e3b252050824461299494}}. The BRDF can then be independently modified to change the appearance of the scene. While generating new views, the SH projection {{formula:5d6beba1-c230-4959-b8dd-c38092123453}} of the modified BRDF is computed and the SH projection {{formula:533f4f55-47d5-4fbd-b41d-dd08f2f2590d}} of the LIF is generated using the learnt network. A dot product of the two as given in Eq. REF generates the final image (Sect. REF ). More details on the exact SH computations are given in the supplementary document. {{figure:ada78708-3dd0-4290-885d-9b3d7f05cb29}}{{figure:9ce18c7f-f2c5-468e-bde0-05e7c2b4007e}}
m
3d38e6c5e8e2e926d15f233b4202190f
The second motivation is due to the recent discovery of gravitational waves. There has a vast amount of work to understand the dynamics of two black holes or the scattering of gravitational waves from a black hole. Such physics can be understood by considering the spinning black holes as massive Higher spin particles {{cite:c317e36d46feb8b0ebb35233ccd1e78ded4b15fd}}, {{cite:df3314cad7f2150d88a1c1dedddcb478fe862ae6}}, {{cite:5b3ac794a1761162dddc18fab15981b11d235c1b}}, {{cite:9286cd7307cbcbbfb5089e7f57bc3689f41e5ed6}}. A simple way to understand this connection {{cite:eb5f8fe5a31ccb7375015cdebeb0e1dedbe27978}} is to note that the black holes in 3+1 dimensions are uniquely characterized mass, angular momentum, and charge (No-hair theorem). These are the same three quantum numbers that describe a quantum particle. A Kerr black hole can be considered a limit of highly spinning particle (to be more precise {{formula:9f0d4db4-bc99-46c8-95fd-0e5e5fa06ca0}} , {{formula:ddfb47ac-e450-4589-b92d-50cabc8c2bbb}} , keeping {{formula:01b3c055-afe8-472a-9136-33f78917bd92}} fixed). Given these connections, the scattering of Higher spin particles can be used to compute the effective dynamics of spinning black hole system(s) {{cite:d8899980cde34219f21e8596deef67544a29a9e6}}, {{cite:39d6a22b4e577e8587efe50ac481dd8a0b7a05a7}}, {{cite:eb5f8fe5a31ccb7375015cdebeb0e1dedbe27978}}, {{cite:a66e76df69e9ed61c810884db041a926f2259ffd}}, {{cite:877f4948c72d4f291d6f13e355220faf4ad6037f}}, {{cite:3249711df26b2cdb388180824717993a5df2f007}}, {{cite:46a668b350e498c07e8fa345402a5bf36c162bc6}}, {{cite:935b461ae21e52e37957f6b8505afe38061c55ba}}.
i
0b8f430d9ea4a5255db10e14f1df7cd6
The holographic {{formula:0d257645-2de7-4bfb-832b-5b05575ce16f}} -wave superconductors can be studied by condensation of a charged vector field in the bulk which is the dual of a vector order parameter in the boundary which can also be considered as the condensation of a 2-form field in the boundary. For this type of holographic superconductor, the formation of vector hair below the critical temperature is observed. Various models of holographic {{formula:c6fcf03e-8d53-4334-b8ae-7bca10e6e315}} -wave superconductors have been proposed. In {{cite:76e20ec012a4b7b7ec79d697abe1ec2ac3f8eb4a}} a {{formula:7ee4e7ac-45a4-4e0f-bc08-1fbe946e1224}} -wave superconductors proposed by using an SU(2) Yang-Mills field in the bulk and one of the gauge degrees of freedom which is dual to spin-1 order parameter in the field theory. Also, the {{formula:5c31b1aa-2c1f-4be0-a4a0-4fc5c6f3949d}} -wave type of superconductivity may arisen by the condensation of a 2-form field {{cite:c2a85a584def2c72d6607eee8b59401045c18cf0}} and a massive spin-1 vector in the bulk {{cite:8a3dc8b069da215faada0521e39ee8e41b697536}}, {{cite:fc130ce8f1c0faeed96541e78e13e8fc646a908e}}. The holographic {{formula:fd37f502-4e96-416e-bc5e-f6dbe456f447}} -wave superconductors have been widely investigated in the literatures (e.g.{{cite:d5fd511d5d1f332d2a92449a5f4894bf172da990}}, {{cite:9140ac5cef989391998693b177640c08915b5c29}}, {{cite:f6d4883e515d2033f60eab2b8756df4c1aa5f3ed}}, {{cite:d8c362363addcbc9f746a28ad02f44f1355d23ae}}, {{cite:6275b9c660e1a80944ac06800c7fd9cf0b97887f}}, {{cite:e1bd5e48d25a23c48d29176e431064dc0b14e678}}, {{cite:2bc4b49cb5a35c050aaf4c44502dbc373de524b1}} ).
i
077226c34b617af994f94da53aba4ef1
At this point, we need to clarify some aspects of the assumed setup. We consider a simplistic single user-system interaction scenario. But as a probabilistic building block, the setup can be reused in a more complex, collaborative recommender system. We ignore the position bias, i.e., the choice probability being dependent on the position of the option within the presentation {{cite:c46e8f3f7082d5cba2442f67726d47d95761b98a}}. We assume that the user is able to review the shortlisted alternatives and make a choice based on latent preferences. We ignore that the repeated and systematic exposure might actually change users' interests, leading to an echo chamber. We refer to {{cite:fb2ebd20df9c4538456e70c5dcb575389d956b4d}} for such an analysis, where sufficient conditions that lead to interest extremes are provided. It is worth noting that the Dirichlet-Luce model with the associated presentation mechanism at least matches two necessary conditions to avoid such degeneracy points, by naturally allowing a “growing pool of alternatives” and due to the randomization inherent in Thompson sampling. We assume that the user picks one of the presented options, although the model can be extended to include an artificial `browse' option corresponding to opting not to choose. We base this assumption on the “principle of least effort {{cite:fd3f416ae84a417f336211218645459fd5a11b3e}},” i.e., the user would conveniently pick from what is presented to her unless the presented alternatives were too unsatisfactory. Extensions to the model are conjectured to address some of the limitations as discussed above. The others are irrelevant to our concern, nevertheless, we mention them for clarity.
m
85d3f4a8354a5a92ff5d840728a3902e
However, all of these solutions require the agent to go through a learning cycle, where it naively explores a problem to learn from experience. This makes applying them to naturalistic problems challenging, where the irreversibility of death looms. In a predator-prey interaction, the prey cannot learn from a failed episode. AlphaGo {{cite:bb939c4f8a6e047a3bff9e924161f6acbd6dde4b}}, for example, played millions of games before being able to defeat Lee Sedol (world champion of Go at the time) in 2016. This was only possible because it was allowed to gain experience from won and lost games during that training. But this result would have never been possible if the agent had to erase all previous knowledge with every defeat. For these reasons, here we focus on a model-based method only. Agents start every episode with nothing gained via experiential learning, but two components of static knowledge: the location of the occlusions and boundaries (a cognitive map), and a generative model of the predator behavior as required for evaluating the decision trees.
d
37134610ae0802f1b5930a6419145751
The driving potential in {{formula:0ac3b368-482e-4cf1-a4a0-d1b6e95989b2}} can be transformed to an oscillating phase factor in the hopping amplitudes {{formula:4206f87a-8024-4607-b673-3e84733dd6af}}  {{cite:f3880f5520ce1a9c4cfe12a50e5433837fde9b0f}}. To do so, we consider the following unitary rotation {{formula:d5413751-3fcd-487c-b334-480fac093575}}
m
a06d54815c7580ccc6b393d525557deb
[leftmargin=*] CML, Collaborative Metric Learning {{cite:962a0d1feed2eeab35d53099268e970cf9271ccf}}, which learns a metric space to encode the user-item interactions and to implicitly capture the user-user and item-item similarities. LRML, Latent Relational Metric Learning {{cite:d58b93bdcddd46831cf92c82b3917d658ed2639e}}, which exploits an attention-based memory-augmented neural architecture to model the relationships between users and items. TransCF, Collaborative Translational Metric Learning {{cite:a3d1f89445af29a2e28aabcbbbe7038d493cd918}}, which employs the neighborhood of users and items to construct translation vectors capturing the intensity of user–item relations. SML, Symmetric Metric Learning with adaptive margin {{cite:f57774354d1fa68dcb165ce0bc86a8574d7c4b58}}, which measures the trilateral relationship from both the user- and item-centric perspectives and learns adaptive margins.
m
c9079ebcfa8d22095d7ec58ab6ebc6c2
In this paper, we have defined a family of 14 constructive modal logics both proof-theoretically and semantically motivated, corresponding each to a different classical modal logic. On the one hand, the logics correspond to the single-succedent restriction of standard sequent calculi for classical modal logics. On the other hand, the same logics are obtained by considering over intuitionistic Kripke models a natural generalisation of the classical satisfaction clauses for modal formulas in the neighbourhood semantics. The main result of this paper is that, despite being mutually independent, for the considered logics the two approaches return exactly the same systems. In addition, we have provided some preliminary analysis of W-logics. First, we have shown how W-logics are related to the corresponding classical modal logics from the point of view of the axiomatic systems: each classical modal logic considered in this paper can be obtained by extending the corresponding W-logic with both excluded middle {{formula:113dd297-3599-4a55-94a7-57967e8634bd}} and disjunctive duality {{formula:e2fbfc94-5d49-4496-8c16-b9ff38a30f79}} . Moreover, basing on their sequent calculi we have proved some fundamental properties of W-logics, such as the disjunction property, decidability and Craig interpolation. Simpson {{cite:52ffa56fb487616576527e2f77243ef537ee207c}} listed some requirements that one expects to be satisfied by any intuitionistic modal logic: they must be conservative over {{formula:409b6967-989a-4368-b601-7d4fdfff33ea}} ; they must contain all axioms of {{formula:d6b37c05-cd2e-40cc-b5b8-fd87748df94f}} (over the whole language) and be closed under modus ponens; they must satisfy the disjunction property; the modalities must be independent; the addition of the axiom {{formula:49a4ff57-6753-48f3-9277-f133c07fd563}} must yield a standard classical modal logic. Basing on the results presented in this paper, it is easy to verify that all W-logics satisfy the first four requirements, by contrast they do not satisfy the last one.This requirement has been sometimes criticised as being too strong, see {{cite:a03dd1f807d62d994105002d5aa333dd52c1514d}} for an argument against this requirement based on negative translations. However, it comes natural to ask whether there could be some modal principle, additional to excluded middle, that distinguishes between constructive and classical modalities. As a matter of fact, it is easy to identify such a principle for W-logics: as we observed above this principle is precisely {{formula:81d727ab-b66b-4fd2-94c3-4dcafa968f85}} . This relation between classical and W-logics is not entirely trivial. For instance, the same relation does not hold between {{formula:2c5bcb91-1997-43b3-9c3a-56170fa225b8}} and {{formula:0e06b70e-3bea-47bf-ae02-f58f82fdd247}} , in particular {{formula:32e38012-c4ed-4a19-b98a-a67d80a3f90c}} must be extended also with {{formula:e4d75438-dda3-4a3b-81c6-9b29d401c8e4}} (or equivalently with {{formula:3b5adeea-bde6-470b-a0ff-57c95d7bfb90}} ) in order to obtain classical {{formula:c4d9d27d-4fd6-4bcb-bddd-d325e3214f1f}} . Moreover, we believe that failure of {{formula:78707282-0069-4990-b9fb-0998a95596ed}} is justifiable from a constructive perspective, as it can be seen as a modalised form of excluded middle. Concerning the semantics of W-logics, the choice of considering neighbourhood models is motivated by the possibility to uniformly cover all considered logics, which include both normal and non-normal systems. However, {{formula:ef31fe30-93a5-4ebf-abfc-b8dea2cabce5}} , {{formula:56612ccd-fbfe-4a9e-8d62-beab0368e137}} and {{formula:f93a9645-e9b0-4102-96b5-f6aad831bd4f}} have an equivalent characterisation in terms of constructive bi-relational models {{cite:9acefa250af3fe64d0f0506dbc0408f54c7c8d24}}, and we conjecture that an analogous characterisation can be given for {{formula:61af2cc9-d386-4eee-b332-59349edaa44c}} and its extensions in terms of relational models with non-normal worlds (cf. e.g. {{cite:5617258af60062e390a053c2592415677dd47252}}). As a byproduct of this work, we have provided a new semantics for {{formula:4169015c-f40a-46bb-adfd-161a5d5020d9}} alternative to its original relational semantics {{cite:9acefa250af3fe64d0f0506dbc0408f54c7c8d24}} and to the neighbourhood semantics in {{cite:62e8cc418322b240938eb189202913e905c3f5cc}}, {{cite:5327a51d385134ea24dd1b0eba88f7281ca05c10}}. The possibility to define constructive counterparts of both normal and non-normal classical logics can be seen as providing additional justification for the present approach. To make a comparison, it is not obvious how to extend the family of intuitionistic modal logics ({{formula:aa71d6f9-ad08-420f-97a2-17b3616334eb}} and extensions) to non-normal systems, given that their definition ultimately relies on the standard translation of modal formulas into first-order sentences, which in turn is based on the relational semantics. Interestingly, the constructive counterparts of non-normal logics that we have obtained are not entirely new. In particular, {{formula:a78fa065-8598-4aa9-91b2-73d93ee1fb78}} and {{formula:a18d689c-410b-4b78-852a-d1714e93f410}} coincide with the logics {{formula:3e51a89c-8d0e-412a-90d6-c84552c48fd8}} and {{formula:ee01e4b6-81f8-476b-a831-2b3d2dce661a}} introduced in {{cite:5327a51d385134ea24dd1b0eba88f7281ca05c10}}, where they are given an alternative semantics with distinct neighbourhood functions for {{formula:706cf72b-1fdd-4ccf-904c-da3623f5eeb4}} and {{formula:beb92dec-fb06-4968-b65a-8a5b4c5a121a}} . By contrast, {{formula:1bf1464b-29c7-473d-ac6b-b620515585cd}} is not equivalent to {{formula:743e7148-7530-41db-a851-90fb1ecd10a9}} in {{cite:5327a51d385134ea24dd1b0eba88f7281ca05c10}}, since {{formula:5cc5eddf-1345-452f-a2ad-7fdb8e42f5bc}} contains {{formula:a4aecea2-8501-4700-98c2-900250a071d8}} which is not a theorem of {{formula:1167c7bb-2d14-4218-8aa9-af2ca283c003}} . The results presented in this paper can be extended in several directions. In future work we plan to study the complexity of W-logics, possibly extending some optimal calculi for {{formula:6c07cdce-7f39-4a5f-b8a2-508d52eb65e8}} (G3-style calculi are not adequate to establish good complexity bounds for constructive logics). Moreover, we would like to study whether Iemhoff's proof-theoretical method for proving uniform interpolation {{cite:bc90d97fbda51d4aa4bc2f5f103e20700160931e}} can be adapted to W-logics. We would also like to define calculi for W-logics that allow for a direct extraction of countermodels from failed proofs, along the lines of {{cite:0ae1480b68183ef568fe89813cda3259748e18fe}}, {{cite:1873c3f1b0d514d2c239ef890e836e3faa0eda42}}, {{cite:2727451126fbce014a2d80befc00d2d99afd151b}}. Furthermore, one can extend the present analysis to further classical modal logics in order to enrich the family of W-logics, but also to inspect the limits of our approach. An obvious limit concerns the logics for which no standard cut-free Gentzen calculi exist, such as {{formula:c64f46d7-0e30-4e1e-b520-a8190375aba3}} . For these logics one can study whether a similar analysis could be based on alternative kinds of calculi, like hyper- or nested sequent calculi. At the same time, it is known that incorporating hereditariness into the satisfaction clauses is not sufficient to provide a semantics for some constructive systems, this is the case for instance of the logics with axiom 4 {{cite:fdc420c53bc48ca401b542174b85490222198807}}. Concerning instead weaker systems, it seems that for non-normal logic {{formula:f2de3a9d-0978-45e1-aad3-2730ac2f6d44}} {{cite:77983d6919fa871b74669623cde0549b51df7272}} this approach returns a very weak form of duality analogous to the one of {{formula:70b2d422-dbb2-4f70-a339-e750feca566e}} in {{cite:5327a51d385134ea24dd1b0eba88f7281ca05c10}}, but this requires further study.
d
304570b6b8b9d2cfb29f7e75e50ee1ce
We have devised a Bayesian hierarchical framework for the emulation and calibration of dynamically evolving spatiotemporal mechanistic systems. Our approach is broadly applicable across a variety of application areas as demonstrated through a series of examples. Building upon the rich literature on state-space extensions to nonlinear systems {{cite:0375ad9108e2e43b980c13594223f98c17ba8883}} can yield deliver full Bayesian inference using more accurate and flexible emulators. Additionally, the applicability of our model to network-like structures suggests that our methodology could also be applied for calibration of agent-based models evolving over space. Further scalability of our model by making use of spatial partitioning {{cite:a00f34f6081ba144a25ac100eed0550dcf1e119c}}. Our dynamic spatiotemporal approach is likely to work well in calibrating computer models with low to medium-dimensional parameter input spaces. For high-dimensional computer simulations, inference of Gaussian process hyperparameters becomes cumbersome due to the Metropolis-Hastings steps required. Therefore, a sequential screening procedure may be employed to identify the most influential parameters {{cite:991c88ff40248c5e52363feb3ea1e49f464ad5e8}}, {{cite:51d0e90e4a5933bc40445f311d37a55d3d94cfb6}}. Extensions to generalized dynamic linear models {{cite:9a7d211bf813feb5a82f9f048d9b9bc7de53122e}} will enable analysis of non-Gaussian data. Lastly, the burgeoning field of sequential Monte Carlo analysis is applicable to build more general statistical emulators within this framework {{cite:7a63d773ecf329930aae8440a5edde9c4586bd59}}. We developed our methods in C++ with functions available in R by way of the Rcpp package {{cite:e24f00e4bc5102f16a20ab18cc4bc023b7751e3b}}.
d
4d51e22c68c91ba6e3a339396874c40b
Brain dynamics is often inherently variable and unstable, consisting of sequences of transient spatiotemporal patterns{{cite:4ff91aa257e9d54dbd3ce3c92d6a002b8e3560e1}}, {{cite:705b07b9e270af35a6ce3c5b4d03aad847386d72}}. These sequences of transients are a hallmark of metastable dynamics that are neither entirely stable nor completely unstable. The neuronal noise of brain dynamics, given by synaptic connections and channel noise, must play a role in the observed multistable dynamics. Here we present the first attempt to raise the question and find two types of coexisting firing patterns.Our results pave a possible way to uncover the underlying mechanisms of noise-driven coexisting firing patterns, such as metastable dynamics, that may mediate perception and cognition.
d
32aa3e4f73d24be51c7855a955eecd5f
Image down-sampling during a segmentation task presents the problem of feature map reduction, followed by a strong spatial information loss. This problem has been addressed in v-net {{cite:aaa9837068e1aaf1b8b7751b36d91b059b2f6d29}}, {{cite:04f441883e5ec9c2937ffbaf25b5599a2fb58ef0}} by adding skips layers between down-sampling and up-sampling layers in order to fuse low-level features within high level features.
m
1a6a05d4d58282bfd8fdefb1582a01be
Gradient-based approaches optimize the objective function by assuming smooth, continuous topology over the probability density where setting the derivatives to zero will yield local optima. If a closed form solution is not available, it is often possible to estimate gradient directions in a given point. Optimization can then proceed by updating the parameters towards the desired direction along the gradient, gradually improving the objective function value in subsequent gradient ascent steps. So-called quasi-Newton methods use function values and gradients to characterize the optimized manifold, and to optimize the parameters along the approximated gradients. An appropriate step length is identified automatically based on the curvature of the objection function surface. The Broyden-Fletcher-Goldfarb-Shanno (BFGS) {{cite:954e1e72c8b802b239649d32fc5094dda3b983d8}}, {{cite:4aa1612d572c898ea882cf3fcede78c712404caf}}, {{cite:ad48eefb40e2eeaf4b7782018a6850b6397e9940}}, {{cite:9bc7b5dd54f207a2436606fc4c964169928fead2}} method is a quasi-Newton approach used for standard optimization tasks in this thesis.
m
1764ec1d4965096cc3993cd05050e815
After a TUC has been properly defined, the next step is to consider which IML methods might be appropriate. This does assume that IML methods are necessary, that is the team should have demonstrated that the TUC presents challenges to more “trivial” or conventional diagnostics. For example, {{cite:8f3ced5fef01851e17e9310a7454baa21a12c267}} found model confidence to be a competitive baseline against dedicated interpretability approaches for AI-human decision making teams.
m
025c608b429bb5ddf302e51feb28f08a
In addition to corrupted domains, we also plot adversarial domains, in Fig. REF , crafted by PGD {{cite:0761cb4d761377adee0f4a8c46ef0fec1bf5356d}} attacks in the input as well as the representation space (see Appendix REF ). The large gap between the certified loss and the empirical loss indicates the existence of distributions beyond corruptions and adversarial examples, which could degrade the performance of the models. Since the worst-case distribution computed by Cert-DG can contain points distorted by different amounts, its loss can be higher than the loss incurred by a PGD attack which constrains the distortion of every point to be the same {{cite:0761cb4d761377adee0f4a8c46ef0fec1bf5356d}}, {{cite:0a7e2db496841f5e320b26af1a32a84b0296411a}}. This highlights that Cert-DG considers a more general worst-case distribution than the adversarial distribution with a fixed perturbation budget. As shown in Sec. , our certification framework is compatible with various loss functions. Here we demonstrate the certification performance of DG methods with the cross-entropy and modified hinge loss. As seen from Fig. REF , the certification produces similar results when using different loss functions although we found that the modified hinge loss makes the inner maximization better behaved (see Appendix REF ).
m
365c44556690b5ae1037af52042da536
In this work, we use petar to carry out numerical simulations {{cite:09e783606cff7eee284f612374bdfcf872bdf140}}. petar is a hybrid {{formula:d2f705c5-0c06-4cb9-8739-d86a4b2b822b}} -body code that combines three integration methods:
m
3828949a3aa8491eea76d28fa5499300
In the field of asset management, the problem of portfolio allocation has gained unprecedented popularity over the past few years. Constructing a good portfolio combines the art and science of balancing between trade-offs and the aim to meet long-term financial goals. The simple core of any portfolio optimization is to assign optimal weights to each portfolio's component in order to minimize investment's risk and maximize the return. In 1952, Markowitz {{cite:9977a825e3dd1a3f3c649a060012efa4d17425d6}} demonstrated that, by assuming risk to be quantifiable by the variance of the portfolio's returns, the optimal weights which minimize portfolio's variance at a given average portfolio's return can be computed with a simple and exact formula. However, the Markowitz's theoretical maximum is attained only in-sample, on the train dataset, whereas off-sample, on the test set where investment is made, performances of the Markowitz's portfolio can be largely sub-optimal.
i
8ad241a4fbbb05b9a53f3d8f6773ce08
Intersection homology was introduced by Goresky and MacPherson to restore Poincaré duality for some singular spaces called pseudomanifolds. They first defined it for PL-pseudomanifolds in {{cite:a7a475099a7e14b43a6f58c5c8d08e56212595a0}} and extended it to topological pseudomanifolds in {{cite:abd05f50c627661af5a46d229333575ad5942576}} by using a derived category of complexes of sheaves. A presentation of intersection homology directly from the singular chain complex of a filtered space and its concordance with the initial definition is made by H. King in {{cite:9f12688c8480b0835ec0c619170d7a219909b232}} for CS sets (Definition REF ). The starting point is a selection of some specific singular simplexes, called {{formula:fb9f9b2c-7c46-43a7-ba94-e9f640e9639c}} -allowable, from a perversity introduced as a sequence of integers {{formula:f2486f66-c13c-4cdc-81c5-33f819a63030}} (cf. Definition REF ) or as a map {{formula:4c06da2f-cd34-4228-8f77-4ce1b8898ea0}} , defined on the set of strata of {{formula:f0b1dc7e-cb86-4ba9-8644-b4cd6cd0007e}} and taking the value 0 on the regular strata (cf. Definition REF ). Before stating it formally in Definition REF , let's contemplate the key formula for a stratum {{formula:e94c8bb5-2003-4f3a-8d55-995aab929429}} and a simplex {{formula:ee60f330-9a3b-489d-9ebd-9758089a7697}} , {{formula:f6abad8e-4c61-442d-b474-f3be6e3ea35b}}
i
546a8e11de1082450be38ea33eb91f9c
In the case of the unit disk, comparing the results of this study to those of a previous study {{cite:141f4c45f7957948b722f0b1850746123522636a}} demonstrated that the optimums reported here are consistently an improvement on previous work. This is due to the use of a more accurate asymptotic expression {{cite:8dc133fe72be4e5edd203eb9a90bbebf8a07aebe}}, as well as removing the constraint that all traps be located on rings within the domain.
d
e07c67baa57bdca55229ce0bf717708e
In this sense, the one-step model is a better candidate, even though it has only been developed for the description of the energetics of the photoemission process and not its dynamics. In fact, it is difficult to tell which process among photon absorption, electron virtual transition and actual photoelectron emission might occur in a finite time. Indeed the influence of the time evolution of the {{formula:9682ef41-c3c3-4099-aaf7-33da933246f3}} field on the phase shifts is under debate {{cite:867cab0c403cdd6a014feef343f2950e4d487dfd}}, {{cite:6ed0d106aec952c4a026abd2d69b225e7f7f81dc}}, {{cite:66f55fe65f04063aaead7ff338aac899fd8cc90a}} and there might exist a time-threshold for light absorption. A finite decoherence time required by the wavefunction to be formed in the final state might also be an issue to consider {{cite:da97c195a1da09823ddb95704de47cc2a5de6178}}. Lastly, once the final state wavefunction is formed above the vacuum level the electron could spend a finite "sticking" time before reaching the free-particle state. In other words, the final state wavefunction will evolve in time such that the density of probability will move from the absorber site towards the outside of the crystal (in analogy with the tunneling process, where the particle wavefunction is already present on both sides of a potential barrier). The last part seems to be the one that better matches the half-scattering picture, but this separation is only artificial, since the process takes place as a whole.
d
5a8aecb882b0a01ea65d18b0a35db85a
The above procedure can be generalized to the case of sectorial {{formula:f7de211b-7f4e-4268-9ce3-3f50cd70584c}} by application of the results of {{cite:483b67d2838645162868ae0d332e2e90f98d50d5}} and {{cite:9bf2c4068b0854a202dc0d2259abdf7ee9267103}}.
d
3c359aa0da022798e1a94ede671863f5
RoBERTa {{cite:db32fd4a57e440cd6c51dc10ef1cc3e85b1b56f9}} (Robustly Optimized BERT Pre-training Approach) improves on BERT {{cite:cff81dfe61a666f394cdd77909437ed34b543f95}} by modifying and optimizing its architecture and training procedure. It makes some key changes to BERT including the removal of Next Sentence Prediction (NSP) objective. RoBERTa also dynamically changes the masking pattern by duplicating the training data and masking it 10 times, each time with a different strategy. It uses larger mini batches for training which improves perplexity on masked language modelling objective and also makes it easier to parallelize via distributed data parallel training.
m
39f35290bbb061fc2ff78570af1ee5aa
But what about the legacy to use Perelman's thermodynamics for Ricci flows when such a theory was rigorously formulated and applied to prove the Poincarè-Thorston conjecture for geometric flows of Riemannian metrics {{cite:64d58a90d98e1c86e2fadba71a3b86314b911c72}}? There are substantial difficulties to formulate and prove certain nonassociative/ noncommutative analogs of the Poincarè conjecture in certain general forms – see discussions and references in {{cite:b9827955ce1fd0cc39355efda16f31b14322d806}}, {{cite:ebe59ae44ccde399459f6ebfda2c7faf85b58cf6}}, {{cite:d98a3720b0bac93dd8406cd66ba01963e38715a9}}, {{cite:db2e1ae8275da1634a16200e372a234142fe3d25}}. One could formulate a number of such topological and geometric models which depend on the type of nonassociative/noncommutative configurations studied, as in {{cite:2636f012ca68cc00617be6cd91c8114b2807981c}}, {{cite:a3e6123b443fd22d6b5918f6dfcc7b2a92c1ede6}}, {{cite:51c02506ad0c7f3ddcaad7a5cc028773de35a0ca}}, {{cite:99302c21658e4409bc3dca6f0498ec6acf8bcd37}}, {{cite:e3493f4f20b5c0eef9e5354b110fe498315bed56}}, {{cite:a060896f19c7769fe6fc93b974eb9a64aa7a91ad}}, {{cite:f860b3129f6dea5fea47edf38cab66364fcc27ab}}, {{cite:1f0302f3cb9d7ca07c6f665e7ac6760e812a612a}}, {{cite:9c59531dd862e62a50d2efaf98838d3d13a8f557}}. Various nonassociative theories are different from those with {{formula:4681f117-e679-4dd4-a1ea-0c232ce36bbe}} -products and R-fluxes considered in this work. So, it is not clear how to formulate a general mathematical framework involving fundamental topology and geometric analysis, and applications, for all models of nonassociative and noncommutative spaces. Nevertheless, self-consistent generalizations of the statistic and geometric thermodynamics using G. Perelmans F- and W-functionals are possible if one considered respective nonholonomic deformations with functionals of type (REF ). They encode nonassociative data in {{formula:79f055a0-00f1-4c31-b4ea-71980e8ef782}} –parametric form and result in a Ricci soliton, i.e. modified vacuum Einstein equations, of type (REF ). Applying the AFCDM, such systems of nonlinear PDEs can be decoupled and integrated in very general form (as we prove in section REF , see details in {{cite:8fe6e0232211cfbdaaf4c86b9410006e2e4a012d}}). We can associate and compute for such generic off-diagonal solutions respective Perelman like thermodynamic variables (REF ). Thus, such modified gravity and thermodynamic theories can be elaborated in self-consistent relativistic and causal geometric and physical forms even if there is not a rigorous mathematical version of nonassociative Poincarè hypothesis. It should be noted also that if we can attribute physical significance to generalized classes of solutions encoding nonassociative data then even the concept of Bekenstein-Hawking entropy is not applicable. However, the W-entropy and related statistical Perelman thermodynamics can be considered for very general classes of modified theories and solutions.
d
9246967077bab7252310774436450409
While both methods are capable of generating more realistic results than those approaches that solely rely on pixel-wise loss, they have some inherent shortcomings. The first paradigm typically trains the generator from scratch using a combined objective function consisting of an adversarial loss and a fidelity loss. In this setting, the generator is responsible for both capturing natural image characteristics and maintaining fidelity to the ground truth. This inevitably limits the capability of approximating the natural image manifold. As a result, these methods often produce artifacts, such as unnatural textures and colors. As shown in Fig. REF (b), while ESRGAN {{cite:977327b42ccae78cce24f4d6474529ebee04a565}} faithfully recovers the structures (e.g., pose, ear shape) of the cat, it struggles to produce realistic textures.
i
17fea8b6b27cce0bdafafd249ed28603
In existing works, unbiased random walks (e.g., PPR {{cite:455bf8f0ec5bdf209ef278929ff00738d33ac651}} and unweighted DeepWalk {{cite:ea4d0d405db2c789a27ea561173cd7c056ec44ce}}) adopt NAIVE sampling. In contrast, biased random walks (e.g., weighted DeepWalk {{cite:75bfacee488ced8e066a6525afe8c37ac43a8e07}}, {{cite:cae2c92c63a52cef6c2c9e72b1b89f1a14bc4309}}, Node2Vec {{cite:97337c6a77575c7106309a124b60ca99f9f611c5}} and MetaPath {{cite:0fe73204546e709605d6cbe2f2c147f9b84c5eb8}}, {{cite:f08bcc5b9c3150db21fc0ba8f9d745a30c2f0a73}}) use ALIAS sampling because the time complexity of the generation phase is {{formula:d6be24d3-7104-49b4-b919-1bc4b509dd92}} . C-SAW adopts ITS to utilize the parallel computation capability of GPUs to calculate the prefix sum. KnightKing {{cite:e6a070d7d3a8e73e060aef1fdd0bb3979e607204}} uses O-REJ to avoid scanning neighbors of {{formula:f164f9e3-e933-4757-8d5d-a94bd75b9a56}} to reduce the network communication cost.
m
9016de3208902f0ac1353bc9d0d85668
DeepWalk (DW) {{cite:ae7493ab293cb8dd1d841d96697c276fbf317caa}} is network embedding method, which is based on the Skip-gram language model. It cannot distinguish positive and negative edges, so the sign information was discarded during the random walk in sign prediction. LINE {{cite:ac67e352ae9d3e1334ad81057988ef1ddf6431a5}} is a network embedding method, which considers first- and second-order proximity. It cannot distinguish between positive and negative edges, and the preprocessing of sign prediction is similar to that of DeepWalk. SIDE {{cite:c215e108793bc34f51bdb6969d2a99074a8c410e}} is a signed network embedding method based on random walks. It aggregates signs and directions along a path according to balance theory. Graph factorization {{cite:b40c54286660a882ab339778664c6e1b558b586d}} is a framework for large-scale graph decomposition and inference. SEAL {{cite:9ffa41a0b884fe56317dc2dd8a5fa67385da3111}} learns from local enclosing subgraphs, embeddings, and attributes based on graph neural networks. Beside_tri {{cite:a1bcdf8044a401fa6c5c649a5310b72ac873b78f}} incorporates the balance and status social-psychology theories to model triangle edges in a complementary manner. The triangle edge set {{formula:5def55fd-f6d1-44c0-9427-49e50302ffd2}} consists of edges whose adjacent nodes share at least one common neighbor. Beside {{cite:a1bcdf8044a401fa6c5c649a5310b72ac873b78f}} incorporates the balance and status theories to model both triangle and bridge edges in a complementary manner. The bridge edge set {{formula:d980b3d2-f5f9-4247-85c8-c74c58d572a9}} consists of edges whose adjacent nodes share no common neighbors, {{formula:9b06de23-4203-4886-b536-22bfbb5e7dca}} {{formula:53f9f75e-9d57-4637-9e1c-24c035b0b981}} Like the integration model, Logistic and ANN can also be adopted to train the node features generated by Node2vec. ANN includes three hidden layers and uses a dropout function to solve the problem of overfitting. Hidden layer parameters have uniformly distributed initialization. The number of neurons in each layer is 128, 32, 4, the dropout rate is 0.3, Adam is used as an optimizer, and the learning rate is 0.01.
m
62bcb630f1dd6eac4db7009e795dcc18
The motivation behind our approach is two-fold. On one hand, game-theoretic matching (GTM) {{cite:6eb194676f1a1f7ef460bab9bb6d0315605b44e9}} has been developed as a powerful technique for establishing single-consistency correspondence even in the presence of elastic deformation  {{cite:25b7ecfec49534a7606417e1a4d8618635873e78}}; however, it has not been extended to multiple consistencies to the best of our knowledge. The conventional framework of GTM is inappropriate for multi-consistency feature matching because the inliers associated with different moving objects are incompatible, which violates the fundamental assumption with a global geometric compatibility between feature correspondences. To overcome this limitation, we propose a novel payoff function that considers both geometric and descriptive compatibility in the definition of payoff function. With newly defined payoff function, we can play multiple local games simultaneously by following the classical evolutionary stable strategy (ESS) algorithm {{cite:2bbcf1dceaa1d2f08dc72d693f17f18cc29d5d21}}.
i
996ed069b15fde8267e369973e180800
We briefly discuss the idea for the proof of Theorem REF here; the complete proof is provided in Appendix . A key step in our analysis is to establish an error contraction inequality to characterize the estimation error of {{formula:112b59ed-5d6b-44f4-b1e3-b7184a1ae3cb}} based on the one of {{formula:75d7fbc5-7d1c-41f4-a9c1-113208cb7861}} . Since the proposed non-convex gradient descent is performed on {{formula:f3420ff7-e873-48cb-9078-ae66719cb122}} jointly in lieu of {{formula:fc1c35af-594b-4fdd-a33e-fd3ef41c34fb}} directly, it becomes technically difficult to develop a direct link between {{formula:892eeb20-bd67-4fd1-a237-8129e3e3473e}} and {{formula:b1d51b36-4ad0-40bc-ad6a-919212606453}} . To overcome this difficulty, a “lifting” scheme was proposed and widely used in the recent literature on low-rank asymmetric matrix optimization {{cite:6b2881f5135d184528d42b9214f48e880128e63e}}, {{cite:3786f40b5bad92cbadff643eb44349051ac283f7}}, {{cite:63dd8236d954b0e543fb56ae590865f50a357244}}: one can factorize any rank-{{formula:76fb3b49-93fb-4972-9fa9-fc2c5677c417}} matrix estimator {{formula:6278563d-deb6-477c-80fa-f2238d7615e6}} and the target matrix parameter {{formula:69eb2718-95a3-488d-b4de-75ba15e3b333}} into {{formula:75a7f7d5-e7e7-4047-901f-11b03b513057}} , where {{formula:a9a8ea77-589f-459a-9dc0-71f7a2878e02}} (or {{formula:1f133c00-4878-499e-8863-1946a89b608b}} ) both have {{formula:41655d16-2639-44b4-bec5-8bc90d6fd259}} columns and share the same singular values. Then, one can stack them into one matrix {{formula:99420a4e-2538-431f-ab34-a9d55b55a604}}
r
477e0bf9c4c01c0ab24118de72f2b007
Although discourse unit segmentation and connective detection are crucial for higher level shallow and deep discourse parsing tasks, recent years have seen more progress in work on the latter tasks than on predicting underlying segments, such as Elementary Discourse Units (EDUs). As the most recent overview on parsing in the framework of Rhetorical Structure Theory (RST, {{cite:aafacd70b03c684531a6f5a1f11ea25b45c318f6}}) points out {{cite:09d8a9ee01cb8c41def3a3bbedf098207e37f79f}} “all the parsers in our sample except [two] predict binary trees over manually segmented EDUs”. Recent discourse parsing papers (e.g. {{cite:cf2030a1e3da40b3f051d02a2d3f44ac92f0b97e}}, {{cite:dea8e38bd9f582d54b787d3f0190d504986d72c5}}) have focused on complex discourse unit span accuracy above the level of EDUs, attachment accuracy, and relation classification accuracy. This is due in part to the difficulty in comparing systems when the underlying segmentation is not identical (see {{cite:df52b2f749435282fe86782f81ee69794e2c0e1d}}), but also because of a relatively stable SOA accuracy of EDU segmentation as evaluated on the largest RST corpus, the English RST Discourse Treebank (RST-DT, {{cite:539ec7807cc14e2a15a452c8c3411bd70efb5e0a}}), which already exceeded 90% accuracy in 2010 {{cite:009a7150226311ada43fb30e0b2c786dbccb0c11}}.
i
0c1bb413262c04afe8df9483ade576c7
The curves for which we determine the cubic points are exactly those {{formula:60fb509c-e0c1-41d7-a052-6292a7a3d6c3}} of genus {{formula:507a4bb4-7f64-4d56-8780-23f0cc507eca}} that have infinite Mordell–Weil group and for which the Chabauty condition on the rank holds true. Only two of these curves also satisfy the rank condition for quartic points: {{formula:b29fb97c-c294-4d60-8524-91d3e6c48ef9}} and {{formula:eeb4a636-1afd-42cb-95ad-b6015515f6b7}} . However, a genus 5 curve admits infinitely many degree four maps to {{formula:a99d723a-29be-475a-ae93-949662c5bb91}} (see §REF ). This prevents us from determining the quartic points on {{formula:cb68fb87-9e04-4e4e-bd2b-f96b7abde88b}} . For {{formula:f3b0d824-909a-43fa-83a6-3eb93ea52bb5}} on the other hand, we are in luck. All degree four maps to {{formula:8617039f-e8a9-446f-b043-dbfe07120b84}} defined over {{formula:d401bf83-1522-4c15-ba91-243affdedd38}} factor through the elliptic curve {{formula:d1808ef6-9720-46c4-a952-82b62c4342fe}} . Applying our partial relative Chabauty method with respect to this quotient, we determine all of the isolated quartic points on {{formula:2a49ff28-1496-4520-acc7-b21833ee4466}} . The Magma {{cite:be4d4d1ed77405a34435d6f89b31f815bff94d70}} code to verify all computations made in this paper can be found at {{formula:ad84edd7-34ec-4095-a289-2b607ea4f307}}
i
8197a69d663c29ba859f8798f7bff918
In this section we discuss how the use of alternative conditions impacts our understanding of the behavior of Polyak's Heavy-Ball method {{cite:0c208a8e56a62a18780adf744b58e54528e42ed0}}: {{formula:6d2dc40e-6b61-42b2-854b-362b79c9c34e}}
d
1890c96330535e89f1ca13ae0132aa98
In order to get a better understanding of which strategy was working best, we tested the performance of both recommender strategies and, additionally, we compared them against a baseline recommender which made random recommendations. Given that the aim of the work in this regard was descriptive, not prescriptive, an A/B/C testing, a well-established evaluation approach in this context, was performed. This methodology was recently used by {{cite:8882c63e80fbd0653216e94603038354ce62a93f}} to evaluate their recommender algorithm in Taobao display advertising platform in production, and so was used by {{cite:b016b6459d026e04dbd228371a56fcecaee76841}} to evaluate theirs on a large scale online test on an online video portal.
m
11d7d31b3d7704284b2bc90b4c9d33e8
Graph-based methods: DialogurGCN {{cite:bf9ca1861b324097a99af31224378632f985a091}}, KET {{cite:2255024f5b30f2b7c64ff76ce98f17dda104abb5}}, DialogXL {{cite:b61fdc2c6b8196bbe41fa1e604e98eb164312770}} and RGAT {{cite:98742394d636f72075ca11649250db60d904b12e}}.
m
96b113e4515d99949b6e46d45023516c
The conditions include action labels, textual descriptions, or even empty conditions. Specifically, given an input condition {{formula:acddc536-79b8-49f1-a837-91e9f9f34776}} , such as a sentence {{formula:6f48f60c-1907-48b6-b81c-7b59dc0e995b}} describing a motion  {{cite:99382585f09199f2bee8fb5966db2dc4e01adc74}}, a action label {{formula:fcef65e9-142a-40fc-8ac7-cbdf99a79683}} from the predefined action categories set {{formula:fd9bda1c-a3f2-4bc7-8e49-68c1dbc48d1c}}  {{cite:fcf7020c1c0e8891582a3f9bf7d74e26ffe5d219}} or even a empty condition {{formula:f9770ea6-016f-4a84-affc-a2a0c84260c9}}  {{cite:6d1700b83823012907bceb19d5f85df80e6d0b99}}, {{cite:0f9e135e2f75fcdc84deaf02f54aef16574ed4b3}}, our MLD aims to generate a human motion {{formula:433c741f-e3d9-4786-8ea5-bddf8b49829f}} in a non-deterministic way, where L denotes the motion length or frame number. Here, we employ the motion representation in {{cite:8259c75945f84efb8e4b1e4cd59b666ab62cd7af}}: a combination of 3D joint rotations, positions, velocities, and foot contact. In addition, we propose the motion encoder {{formula:2c711cbd-efc2-4e48-b1c9-6ec1904cf387}} to encode the motion sequences, {{formula:d51f4aea-d1dc-40f7-b3ca-38bfdea5cc35}} , into a latent {{formula:3c570921-0860-4207-8471-8b1edd333ca8}} , and decode {{formula:ac71662d-ec2d-4974-906f-0182f271499e}} into the motion sequences using a motion decoder {{formula:8b204ebc-b015-44b0-851d-9304324504c1}} , that is {{formula:fe39ddb5-6c1a-4183-8386-31ccf7ff8b7e}} .
m
ef31dc4bc84e6651ad7d91e6ed51bfab
Thus, our analysis demonstrates that all experimentally detected features i), ii) and iii) can be reproduced within a microscopic model describing topologically trivial SNS junctions with {{formula:acb8c8d4-49ff-458f-91eb-8fc379067ea3}} -periodic CPR, cf., e.g., the results presented in Figs. REF and REF of this work and those in Fig. 2 of Ref. Gre. None of these features actually requires {{formula:51a29c9b-f844-49da-8db0-e6b83c894bc4}} -periodic CPR which never pops up in our calculation. In addition, we point out that missing integer Shapiro steps at {{formula:6d087313-178e-4708-9e75-d9b432e5ae0a}} – along with well pronounced fractional ones – were recently observed in topologically trivial Josephson junctions based on InAs quantum wells {{cite:e7e93faed2e17be59feebe5d82759d86accc8e19}}. It is also well known that Shapiro steps with odd {{formula:3675a30d-e10e-4ea2-bc61-99ab8e89ecca}} can be significantly reduced (as compared to ones with even {{formula:6393fe1c-3934-480c-bd3e-ba7f3b5fdf04}} ) or even vanish completely due to size effects {{cite:a32a1a4f77d2ed6634ef2ff62e16355aa3257118}}. Hence, caution is needed while unambiguously interpreting experimental results for superconducting weak links in terms of Majorana physics.
d
be437e5bd0f50fc5f24518cd59b42bee
The nonmagnetic impurities are assumed to be quenched at their lattice positions, i.e. their positions are fixed. The magnon-magnon interaction, which gives rise to short-wavelength spin waves, is neglected, i.e. the system is in the low temperature limit {{cite:3670b36e301ed557a93be3639cbff0bbac1e85de}}, {{cite:581307097476347ec4032d33d0c7a1731c6b4138}}. The Heisenberg model is constructed in a Bravais lattice with nearest-neighbor interaction in the presence of an external magnetic field. Our method is applicable to a regime where the nonmagnetic impurity concentration is below the critical percolation concentration {{formula:d97a0a66-d28e-4fc3-9c4a-fc55fe7c8139}} , i.e. {{formula:29b51051-823e-4d06-842a-78b5dd5c05e4}} , where for the simple cubic lattice {{formula:8598ff07-26e2-4033-aa37-19fbba901492}} .
m
774da49729eaa5dc04961c2bd6bf1464
In this paper we discussed a natural scenario to solve the strong CP problem in the framework of the higher dimensional gauge theory. It has a similarity to the well-known Peccei-Quinn {{cite:5cf73f3807b696756a552d45d29e3a1d5430ebf5}} or invisible axion {{cite:db06013299081923f813c4e35d5ad61bfa0ed110}}, {{cite:5ddb05cff03d86180961aa4798b216632bf80d3d}} solutions of the strong CP problem. Axion-like particle {{formula:7dd4e686-53c8-42ab-9cd5-2024c3207eb7}} has been built-in as the extra-space component of the higher dimensional gauge field. Though {{formula:6781f627-1a29-4991-8b75-e77ed0caafb3}} is not a NG boson associated with a global symmetry, it has a shift symmetry associated with higher dimensional local gauge symmetry. The coupling of the axion-like particle {{formula:0ceedce4-040a-471d-beb5-978a63a4739a}} with gluons is attributed to the “Chern-Simons" (CS) term, which is radiatively induced. We adopted a toy model to calculate the CS term with some unknown gauge symmetry U(1){{formula:9ffe878e-9d90-4e74-91cd-598171a04568}} . The CS term was obtained in two ways: first by a concrete 1-loop calculation and next by use of the Fujikawa's method {{cite:3d3aab3c037faf1b8507c1765f082844d2cd9f6b}} to deal with the chiral anomaly in 4D space-time. The obtained results are identical. We argued that this means that the radiative correction to the CS term is “1-loop exact", since the result obtained by the latter method should be exact, valid in all orders of the perturbation. The Wilson coefficient of the resultant CS term is also free from UV-divergence even though the theory itself is non-renormalizable higher dimensional theory.
d
d094c22ab2b3423d598d6724570abe96
It might seem surprising that NLM is able to compete with a pretrained deep denoiser for image regularization; after all, the denoising quality of DnCNN is generally a few dBs better than NLM. In this regard, we note that the exact relation between denoising capacity and the final restoration quality (within the PnP framework) is not well understood. For example, although DnCNN is more powerful than BM3D {{cite:78c393c2783fde5a6f029ea9a6938cbc97c4049d}}, it is known that plugging BM3D denoiser within a PnP algorithm can produce better results than DnCNN {{cite:9a72ce3e4cb47cd3c5352410dccaf2ddef429324}}, {{cite:37c7c011f1036fd8182720bc0c9631e9c1a551e1}}. Similarly, NLM has been shown to outperform BM3D (which is more powerful than NLM) for some applications {{cite:e207587f15cab4b37e94477246554266317a1dd3}}, {{cite:246e81f029b52a637c46115f405a9de2788a0603}}. {{figure:92b07906-1782-4c1d-b32a-0f29da4e204f}}{{table:b1fb09b9-b1dd-40dc-8fef-ede7f6d78cfd}}{{table:004822f1-a014-421c-9139-4848195e98c2}}
d
bf8cbce26aa691d6bee8f337f51e04e5
To test whether selecting systems that have experienced spontaneous transitions could bias the analysis towards false positive detection of early warning signals, (the Prosecutor's Fallacy) we selected replicates conditional on having collapsed in the simulations. We then selected a window around each system that ended just before the collapse, while the population values were still above the Allee threshold. For each replicate, we calculated the most common early warning indicators, variance and autocorrelation {{cite:16adcf2d8a40ad2deaa95d6d4a16a9f432bb7fa3}}, {{cite:ea79813082b84d12ca4c06ce9321e877c47aeca5}}, {{cite:1d65f749a2dd0f4afdb317ed2530d97f378f8a46}}, around a moving window equal to half the length of that time series.
m
f3ea1f1e86fb06f3887c3f8398760e03
During construction of the GREW benchmark, privacy and bias problems are our first concern. To protect privacy, only silhouettes, flow and human poses would be utilized and released, which do not reveal any personal visual information. We will provide strict access for applicants who sign the license, and try our best to guarantee it for research purposes only. For dataset bias, the GREW has balanced gender distribution, while some attributes (race, age group, dressing) are inevitably biased due to capture location and time. Since our dataset is large-scale and diverse, one can sample balanced data to train models with less bias. Besides, recent de-bias researches in the biometrics community {{cite:09f470dc3cbac125345dd0767906a89b6db3d3d0}}, {{cite:e98c42ffd6c9381cb9e2f98f2e19950dbf97bbc8}}, {{cite:51937ba5284b650359ad970173e501d9eb935e54}} may also alleviate this problem.
d
8cfbd2cc99ae441eacbf1bf49820294c
Synthetic preference feedback proved more effective than feedback provided by humans. It could be expected that human feedback has the advantage in the exploration-heavy games, where the human can shape the reward to encourage promising exploration strategies. Analysis of the labels shows that the human annotator prefers clips where the agent seems to be exploring in particular directions. However, instead of encouraging exploration, this feedback produces `reward pits' that trap the agent into repetitive and fruitless behaviors. This effect is not novel; {{cite:cd591875bdcce91f775639f6203ddc194f778e93}} have previously argued that humans are bad at shaping reward. However, our results show that demonstrations can provide consistent exploration guidance.
d
582b0390c64954056e0cc0068f311b43
paragraph4 .5em plus1ex minus.2ex-.5emFrozenBN exists in previous works that fine-tune a pre-trained classifier for downstream tasks such as object detection {{cite:6b35a8e250fd6366cce787d9e44cda8a0f150343}}, {{cite:fe9fe4815d54d66f4af9bf4f8241dc8f0b91a16a}}, {{cite:1c559f9ae1bda916c633d4d81da62f0f224c5b6c}}, metrics learning {{cite:67184d98c48f6e728868c7ffec3e545cc37be516}}. When applied in fine-tuning, it's common to freeze both normalization statistics and the subsequent affine transform, so that they can be fused into a single affine transform However, during fine-tuning it is not a good idea to fuse the affine transform with other adjacent layers (e.g. convolution), although this is a standard optimization for deployment. See Appendix REF .. This variant of FrozenBN is computationally efficient and often performs similarly well.
d
c491fd7a5fc079d5267cf4ca6da815b5
where {{formula:423f6d67-1020-4288-bc2e-62c73f9046d3}} controls the decay rate of {{formula:184de1bb-5fd5-47ac-86d4-c5ce46af8d15}} . We use the ADAM optimizer {{cite:a3548931c5b8bae5a732d8c3bd2b7d1a90b52889}} with learning rate {{formula:0c16ab85-7667-42ce-b319-58be621e7ed8}} for all the experiments. The network architectures and the hyperparameters chosen are summarized in Table REF . We consider {{formula:31921339-038e-46b5-ada5-45fce31696a8}} dB for the AWGN channel. For the BN channel, we use the same SNR range as the AWGN channel for the low noise state and set {{formula:a0b588ad-2492-422e-968f-66c2df63dd2b}} for the high noise state. We consider {{formula:2616a109-2ff2-4b73-ab6b-4f13a923a86c}} to see the effect of changing the high noise state probability. {{figure:2d24f3c5-2a68-43e7-95e5-edb30dfd18f4}}{{figure:225ca006-a6e1-4c88-9bde-4aec9c0abafc}}{{figure:1cf536fc-2c59-4a50-9e16-0b24ce41d0c9}}
r
5c458ec0141282a7fcd5229b34632d4f
To alleviate this issue, few-shot object detection (FSOD) methods {{cite:9d6adf924d39415faada48810109cd974ea7e994}}, {{cite:cf6329a85cddc8730c4e5257e99d36e7c7e0c892}}, {{cite:6fde9232a8c7df607ea43c9d05fabfc05850cad2}}, {{cite:c7c40d6167d180eb1047c97f60c7ff75fd504bca}}, {{cite:9772b477cb41cb744d0abc6cd35f94e8c5486e68}}, {{cite:a0108a55f0c0f51b8b3cac375b06668c8c5dac25}}, {{cite:50c0854d32c88ce7b7c5374a205da0fe4c2b5a44}}, {{cite:6e0c2758c60497cd75f50ae9524ca3613d13dbb7}}, {{cite:52a074729baa2d5d54031429d0b63ccebcea7156}}, {{cite:ed802c64993edfa9f5ca3adb5cdd09be5598bab7}} are developed to reduce the data dependence of the CNN models. FSOD aims to train the detector based on few samples. Various approaches have presented significant improvements in FSOD problem. However, these methods hold a closed-set assumption, where the training and testing sets share the same classes. In the open-world situations, there are countless unknown classes, not included in the training set. These unknown objects can easily disrupt the rhythm of the close-set models, causing them to identify the unknown classes as known ones with a high confidence score {{cite:3c81e26a73bc4955ba1f866f06d59b08edebff84}}. {{figure:6ae54a1f-fcd2-45e0-9642-ca23943e8485}}
i
5c2571adf710f7d0c25f93a5c102de21
We report the results of UCF-101 in tab:ucf101space and tab:ucf101time, following similar convention as in tab:spatialsampler and tab:temporalsampler. We reproduce the results of TSN {{cite:eced9c0c801a73d57395d99bcecbbfd2f12f057f}} on split-1 of the dataset using our hardware for more comparable results. Behaviors similar to EPIC-KITCHENS are observed in this dataset, , the both spatial and temporal samplers can reduce complexity while maintaining comparable accuracy. {{formula:086530e8-6aea-4a26-bb34-4edaa9b0d69e}} has the highest speed-up with only 0.82 loss of top-1 accuracy and {{formula:3b9ca95b-4d4a-40f9-99f0-c83583917764}} has the best accuracy with 1.37x speed-up.
r
b3a69ab1c94e377c4ef1dfc983dc955a
Note that these also correspond to Breit-Wigner parameters determined experimentally from {{formula:cc3b419d-9d8b-4130-9f97-ffe02f082208}} reactions. The deviation to other reactions can be of the order of {{formula:35ca0ec9-842f-4a22-87fd-e2f0a3b7935c}} . We observe rather good agreement for {{formula:867d1593-e806-4acc-b230-d4c7db00f241}} , while our value for the width is slightly too low. This is also visible in Figure REF , where we plot the experimental phase shifts from Ref. {{cite:6f1fc89e115ce810ddd5bd8f90134e948e8a79de}} and compare them to the phase shift curve we obtain using the final values from Eq. (REF ) and then again assuming the Breit-Wigner form from Eq. (REF ).
d
b7f67bce6dad417513db8d1e0daaed96
The proposed framework is built based upon the inner product based formulation {{cite:acb4a83705605ca81a4ccce4a42b66789425ed75}}, {{cite:337d8f213576d79addb1e3a11f528c81ad079469}}, {{cite:e01d0bee83539aaf16ae9e1115e81d4cb51ec035}}, {{cite:c7639ff15a45a451c8ab0637744cb573611a7ee6}}, {{cite:01c2ba739f78a8619c152689ddb02ab9767e9111}}. The key ingredient is to map data points into binary codes, the inner product of which can well approximate the similarity matrix {{formula:e74872e0-7e41-4f08-9a3b-a15db7bd6ecd}} where {{formula:35d68a68-7047-495a-97da-d7457e74da73}} , if {{formula:26dbf3e9-78de-4070-bf10-ed3e2a353fb3}} , and {{formula:ff8f9864-7ab4-449f-afb9-3915e4319ba9}} otherwise. More precisely, the goal of inner product based methods is to minimize the following objective function: {{formula:b0d4690b-15e4-4dc7-9427-60fcfcd56b6b}}
m
258a6a04758e457f62e39d4711f5b94f