ShantanuT01/DACTYL-Pretraining huggingface dataset:
Effective processing of video input is essential for the recognition of temporally varying events such as human actions. Motivated by the often distinctive temporal characteristics of actions in either horizontal or vertical direction, we introduce a novel convolution block for CNN architectures with video input. Our proposed Fractioned Adjacent Spatial and Temporal (FAST) 3D convolutions are a natural decomposition of a regular 3D convolution. Each convolution block consist of three sequential convolution operations: a 2D spatial convolution followed by spatio-temporal convolutions in the horizontal and vertical direction, respectively. Additionally, we introduce a FAST variant that treats horizontal and vertical motion in parallel. Experiments on benchmark action recognition datasets UCF-101 and HMDB-51 with ResNet architectures demonstrate consistent increased performance of FAST 3D convolution blocks over traditional 3D convolutions. The lower validation loss indicates better generalization, especially for deeper networks. We also evaluate the performance of CNN architectures with similar memory requirements, based either on Two-stream networks or with 3D convolution blocks. DenseNet-121 with FAST 3D convolutions was shown to perform best, giving further evidence of the merits of the decoupled spatio-temporal convolutions.
A weak scattering potential imposed on a $CuO_2$ layer of a cuprate superconductor modulates the local density of states $N(x,\omega)$. In recently reported experimental studies scanning-tunneling maps of $N(x,\omega)$ have been Fourier transformed to obtain a wave-vector power spectrum. Here, for the case of a weak scattering potential, we discuss the structure of this power spectrum and its relationship to the quasi-particle spectrum and the structure factor of the scattering potential. Examples of quasi-particle interferences in normal metals and $s$- and d-wave superconductors are discussed.
We consider generic properties of the moduli space of vacua in $N=2$ supersymmetric Yang--Mills theory recently studied by Seiberg and Witten. We find, on general grounds, Picard--Fuchs type of differential equations expressing the existence of a flat holomorphic connection, which for one parameter (i.e. for gauge group $G=SU(2)$), are second order equations. In the case of coupling to gravity (as in string theory), where also ``gravitational'' electric and magnetic monopoles are present, the electric--magnetic S duality, due to quantum corrections, does not seem any longer to be related to $Sl(2,\mathbb{Z})$ as for $N=4$ supersymmetric theory.
An SU(3)_L x U(1)_N gauge model, where E^{-i} (i=1,2,3) as heavy leptons are placed in the third member of lepton triplets, is shown to provide the large mixing angle (LMA) MSW solution to the solar neutrino problem. By introducing approximate conservation of L_e-L_mu-L_tau (\equiv L') into the model, we have estimated \Delta m_\odot^2 \sim \sqrt{2}\epsilon \Delta m_{atm}^2m_{E^1}/(m_{E^2}+m_{E^3}), where \epsilon represents L'-breaking effects and m_{E^i} is a mass of E^{-i}. Since \Delta m_{atm}^2 \sim 3 x 10^{-3} eV^2, the LMA solution is obtained for \epsilon\sim 0.01-0.1 in the case of m_{E^1} \sim m_{E^{2,3}}. This mechanism utilizes two-loop radiative mechanism, which contains a triplet version of the singly charged Zee boson, h^+, given by \xi = (\xi^{++}, {\bar \xi}^+, h^+)^T. Almost bimaximal mixing is dynamically realized by the approximate equality between the \xi-couplings of the first family to the second and third families.
The Gradient Ascent Pulse Engineering (GRAPE) is a celebrated control algorithm with excellent converging rates, owing to a piece-wise-constant ansatz for the control function that allows for cheap objective gradients. However, the computational effort involved in the exact simulation of quantum dynamics quickly becomes a bottleneck limiting the control of large systems. In this paper, we propose a modified version of GRAPE that uses Krylov approximations to deal efficiently with high-dimensional state spaces. Even though the number of parameters required by an arbitrary control task scales linearly with the dimension of the system, we find a constant elementary computational effort (the effort per parameter). Since the elementary effort of GRAPE is super-quadratic, this speed up allows us to reach dimensions far beyond. The performance of the K-GRAPE algorithm is benchmarked in the paradigmatic XXZ spin-chain model.
Let $\Gamma=\Gamma(2n,q)$ be the dual polar graph of type $Sp(2n,q)$. Underlying this graph is a $2n$-dimensional vector space $V$ over a field ${\mathbb F}_q$ of odd order $q$, together with a symplectic (i.e. nondegenerate alternating bilinear) form $B:V\times V\to{\mathbb F}_q$. The vertex set of $\Gamma$ is the set ${\mathcal V}$ of all $n$-dimensional totally isotropic subspaces of $V$. If $q\equiv1$ mod 4, we obtain from $\Gamma$ a nontrivial two-graph $\Delta=\Delta(2n,q)$ on ${\mathcal V}$ invariant under $PSp(2n,q)$. This two-graph corresponds to a double cover $\widehat{\Gamma}\to\Gamma$ on which is naturally defined a $Q$-polynomial $(2n+1)$-class association scheme on $2|{\mathcal V}|$ vertices.
We show that there are effective three- and higher-body interactions generated by the two-body collisions of atoms confined in the lowest vibrational states of a 3D optical lattice. The collapse and revival dynamics of approximate coherent states loaded into a lattice are a particularly sensitive probe of these higher-body interactions; the visibility of interference fringes depend on both two-, three-, and higher-body energy scales, and these produce an initial dephasing that can help explain the surprisingly rapid decay of revivals seen in experiments. If inhomogeneities in the lattice system are sufficiently reduced, longer timescale partial and nearly full revivals will be visible. Using Feshbach resonances or control of the lattice potential it is possible to tune the effective higher-body interactions and simulate effective field theories in optical lattices.
We present a theory which can explain the micromaser as well as its optical counterpart, the microlaser, for appropriate values of dissipative parameters. We show that, in both the the cases, the cavity radiation fields can have sub-Poissonian photon statistics. We further analyse if it is possible to attain a Fock state of the radiation field. The microlaser is precluded for such analysics due to the damping of its lasing levels making transitions at optical frequencies. Hence, we focus our attention on the micromaser and our exact simulation of the dynamics shows that it is not possible to generate a Fock state of the cavity radiation field.
Using first principles calculations, we determined the epitaxial-strain dependence of the ground state of the 1:1 SrCrO$_3$/SrTiO$_3$ superlattice. The superlattice layering leads to significant changes in the electronic states near the Fermi level, derived from Cr $t_{2g}$ orbitals. An insulating phase is found when the tensile strain is greater than 2.2\% relative to unstrained cubic SrTiO$_3$. The insulating character is shown to arise from Cr $t_{2g}$ orbital ordering, which is produced by an in-plane polar distortion that couples to the superlattice d-bands and is stabilized by epitaxial strain. This effect can be used to engineer the band structure near the Fermi level in transition metal oxide superlattices.
We discuss the dynamics of a superparticle in a superspace whose isometry is generated by the superalgebra OSp(1|4) or its central-charge contraction. Extra coordinates of the superspace associated with tensorial central charges are shown to describe spin degrees of freedom of the superparticle, so quantum states form an infinite tower of (half)-integer helicities. A peculiar feature of the model is that it admits BPS states which preserve 3/4 of target-space supersymmetries.
Recently, anomaly detection and localization in multimedia data have received significant attention among the machine learning community. In real-world applications such as medical diagnosis and industrial defect detection, anomalies only present in a fraction of the images. To extend the reconstruction-based anomaly detection architecture to the localized anomalies, we propose a self-supervised learning approach through random masking and then restoring, named Self-Supervised Masking (SSM) for unsupervised anomaly detection and localization. SSM not only enhances the training of the inpainting network but also leads to great improvement in the efficiency of mask prediction at inference. Through random masking, each image is augmented into a diverse set of training triplets, thus enabling the autoencoder to learn to reconstruct with masks of various sizes and shapes during training. To improve the efficiency and effectiveness of anomaly detection and localization at inference, we propose a novel progressive mask refinement approach that progressively uncovers the normal regions and finally locates the anomalous regions. The proposed SSM method outperforms several state-of-the-arts for both anomaly detection and anomaly localization, achieving 98.3% AUC on Retinal-OCT and 93.9% AUC on MVTec AD, respectively.
The magnetic field--driven transition in the spin-Peierls system CuGeO_3 associated with the closing of the spin gap is investigated numerically. The field dependence of the spin dynamical structure factor (seen by inelastic neutron scattering) and of the momentum dependent static susceptibility are calculated. In the dimerized phase (H<H_c), we suggest that the strong field dependence of the transverse susceptibility could be experimentally seen from the low temperature spin-echo relaxation rate 1/T_{2G} or the second moment of the NMR spectrum. Above H_c low energy spin excitations appear at incommensurate wave vectors where the longitudinal susceptibility chi_{zz}(q) peaks.
I describe here the attempt to introduce spin-charge separation in Schrodinger equation. The construction we present here gives a decomposed Schrodinger spinor that has one problem: Its absolute value can only have value between 0 and ${1}{2}$. The problem we solve is to expand and generalize this construction so that one can have a Schrodinger spinor with absolute value that are arbitrary non-negative numbers. It may be that one has to introduce a set of different decompositions to cover all nonnegative values, that is to introduce patches over $\mathbb{R}_{+}^{3}$ so that in each patch one has a different representation. It seems that the decomposition has a direct relation to so called entangled states that have been discussed very much in connection of e.g. quantum computing, and we would like to find this relation and discuss it in detail.
In this paper we revisit the thermocouple model, as a linear irreversible thermodynamic energy converter. As is well known, the linear model of the thermocuple is one of the classics in this branch. In this model we note two types of phenomenological coefficients: the first comes from some microscopic models, such as the coefficient associated with the electric conductivity, and the second comes from experimental facts such as the coefficient associated with the thermoelectric power. We show that in the last case, these coefficients can be related to the operation modes of the converter. These relationships allow us to propose a generalization of the first and second Thomson's relations. For this purpose we develop the ideas of non-isothermal linear converters, operated directly (heat engine) and indirect (refrigerator). In addition to this development we analyze the energy described by these converters.
Using density functional theory calculations, many researchers have predicted that various tungsten-nitride compounds WN$_x$ ($x$ > 1) will be "ultra-compressible" or "superhard", $i.e.$ as hard as or harder than diamond. These compounds are predicted to have large bulk and shear moduli (> 200 GPa) and to be elastically and vibrationally stable.   Compounds with such desirable properties must be energetically stable against decomposition into other compounds. This stability can only be found after the determination of the convex hull for W$_x$N$_1$$_-$$_x$ lines which connect the lowest enthalpy structures as a function of composition. The phase diagram of the W-N structure is uncertain, both experimentally and computationally. Complex van der Waals forces play a significant role in determining the structure of solid N$_2$.   Here we use high-throughput calculations to map out the convex hull and other low energy structures for the W-N system. We find that the ground state of the system is the NbO structure, and that the WN$_2$ structures found by Wang $et$ $al$. are also stable when the van der Waals forces are neglected. Other proposed structures are above the convex hull of the W-N system. We show how the choice of density functional influences the shape of the curve and the structures that form the hull. In nitrogen-rich compounds, the choice of functional can dramatically change the structural parameters and mechanical behavior. Using any of the functionals, the bulk and shear moduli of the NbO phase are comparable to the WN$_x$ compounds that have been claimed to be ultra-compressible for superhard.
We report an experimental determination of the phase boundary between a quantum paramagnetic state and the proposed spin Bose-Einstein condensate of triplons in the spin gap compound BaCuSi2O6. The ordering temperature is related to the proximity to a quantum critical point at the lower critical magnetic field H_c1 = 23.52 +/- 0.03T by a power law parameterized by critical exponent nu. We obtain an experimental estimate of nu = 0.63 +/- 0.03 which is in good agreement with the mean field prediction of nu = 2/3 for the 3D XY model, used to describe the Bose condensation of a 3D dilute interacting Bose gas.
We give a new and representation theoretic construction of $p$-adic interpolation series for central values of self-dual Rankin-Selberg $L$-functions for $\operatorname{GL}_2$ in dihedral towers of CM fields, using expressions of these central values as automorphic periods. The main novelty of this construction, apart from the level of generality in which it works, is that it is completely local. We give the construction here for a cuspidal automorphic representation of $\operatorname{GL}_2$ over a totally real field corresponding to a $\mathfrak{p}$-ordinary Hilbert modular forms of parallel weight two and trivial character, although a similar approach can be taken in any setting where the underlying $\operatorname{GL}_2$-representation can be chosen to take values in a discrete valuation ring. A certain choice of vectors allows us to establish a precise interpolation formula thanks to theorems of Martin-Whitehouse and File-Martin-Pitale. Such interpolation formulae had been conjectured by Bertolini-Darmon in antecedent works. Our construction also gives a conceptual framework for the nonvanishing theorems of Cornut-Vatsal in that it describes the underlying theta elements. To highlight this latter point, we describe how the construction extends in the parallel weight two setting to give a $p$-adic interpolation series for central derivative values when the root number is generically equal to $-1$, in which case the formula of Yuan-Zhang-Zhang can be used to give an interpolation formula in terms of heights of CM points on quaternionic Shimura curves.
Optical absorption spectra of Cr$^{3+}$-Cr$^{2+}$ pair center in KZnF$_{3}$:Cr$^{3+}$,Cr$^{2+}$ crystal were investigated in wide temperature range. Broad band at 30800 cm$^{-1}$ is attributed to cation-cation (e_g)-electron transfer transition. Narrow lines with maxima at 16720 cm$^{-1}$ and 19880 cm$^{-1}$ have been assigned to purely electronic exchange-induced electric-dipole transitions from the ground (Cr$^{3+}$,(^4A_{2g});Cr$^{2+}$,(^5E_g)) state to excited (Cr$^{3+}$,(^4A_{2g});Cr$^{2+}$,(^3E_g^a)) and (Cr$^{3+}$,(^4A_{2g});Cr$^{2+}$,(^3E_g^b)) states, respectively. It's vibronic satellites corresponding to (a_{1g}) local mode of Cr$^{3+}$ fluorine octahedron of the pair are also observed. Energy of the local mode for the ground and mentioned excited states are 580, 540 and 530 cm$^{-1}$. Instead of expected double exchange for mixed valence pair ferromagnetic superexchange for Cr$^{3+}$-Cr$^{2+}$ pair in KZnF$_{3}$ crystal is realized. Exchange integral (J=-14.9\pm0.4) cm$^{-1}$ and Jahn-Teller splitting (\Delta_{JT}=340\pm40) cm$^{-1}$ for the ground state of the pair were obtained by analysis of the temperature dependence of absorption lines. Important features of the crossover double exchange - ferromagnetic superexchange are discussed.
Softmax-based losses have achieved state-of-the-art performances on various tasks such as face recognition and re-identification. However, these methods highly relied on clean datasets with global labels, which limits their usage in many real-world applications. An important reason is that merging and organizing datasets from various temporal and spatial scenarios is usually not realistic, as noisy labels can be introduced and exponential-increasing resources are required. To address this issue, we propose a novel mining-during-training strategy called Basket-based Softmax (BBS) as well as its parallel version to effectively train models on multiple datasets in an end-to-end fashion. Specifically, for each training sample, we simultaneously adopt similarity scores as the clue to mining negative classes from other datasets, and dynamically add them to assist the learning of discriminative features. Experimentally, we demonstrate the efficiency and superiority of the BBS on the tasks of face recognition and re-identification, with both simulated and real-world datasets.
From the underlying non-linear realisation we compute the complete E11 invariant equations of motion in eleven dimensions, at the linearised level, up to and including level four in the fields. Thus we include the metric, the three and six forms, the dual graviton and three fields at level four. The fields are linked by a set of duality equations, which are first order in derivatives and transform into each other under the E11 symmetries. From these duality relations we deduce second order equations of motion, including those for the usual supergravity fields. As a result the on-shell degrees of freedom are those of the eleven dimensional supergravity. We also show that the level four fields provide an eleven dimensional origin of Romans theory and lead to a novel duality relation.
The volume cut off by a hyperplane from a bounded body with smooth boundary in $R^{2k}$ never is an algebraic function on the space of hyperplanes: for k=1 it is the famous lemma XXVIII from Newton's Principia. Following an analogy of these volume functions with the solutions of hyperbolic PDE's, we study the local version of the same problem: can such a volume function coincide with an algebraic one at least in some domains of the space of hyperplanes, intersecting the body? We prove some homological and geometric obstructions to this integrability property. Based on these restrictions, we find a family of examples of such "locally integrable" bodies in Euclidean spaces
The paper presents the results of three-dimensional (3D) modelling of the structure and the emission of accretion columns formed above the surface of accreting strongly magnetized neutron stars under the circumstances when a pressure of the photons generated in the column base is enough to determine the dynamics of the plasma flow. On the foundation of numerical radiation hydrodynamic simulations, several 3D models of accretion column are constructed. The first group of the models contains spatially 3D columns. The corresponding calculations lead to the distributions of the radiation flux over the sidewalls of the columns which are not characterized by axial symmetry. The second group includes the self-consistent modelling of spectral radiative transfer and two-dimensional spatial structure of the column, with both thermal and bulk Comptonization taken into account. The changes in the structure of the column and the shape of X-ray continuum are investigated depending on physical parameters of the model.
We obtain the solution for non-extremal charged rotating black holes in seven-dimensional gauged supergravity, in the case where the three rotation parameters are set equal. There are two independent charges, corresponding to gauge fields in the U(1)xU(1) abelian subgroup of the SO(5) gauge group. A new feature in these solutions, not seen previously in lower-dimensional examples, is that the first-order "odd-dimensional self-duality" equation for the 4-form field strength plays a non-trivial role. We also study the BPS limit of our solutions where the black holes become supersymmetric. Our results are of significance for the AdS_7/CFT_6 correspondence in M-theory.
We consider an initial value problem for a Hamilton--Jacobi equation with a quadratic and degenerate Hamiltonian. Our Hamiltonian comes from the dynamics of $N$-peakon in the Camassa--Holm equation. It is given by a quadratic form with a singular positive semi-definite matrix. Such a problem does not fall into the standard theory of viscosity solutions. Also viability related results, sometimes used to deal with degenerate Hamiltonians, do not seem applicable in our case. We prove the global existence of a viscosity solution by looking at the associated optimal control problem and showing that the value function is a viscosity solution. The most complicated part is the continuity of a viscosity solution which is obtained in the two-peakon case only. The source of the difficulties is the non-uniqueness of solutions to the state equation in the optimal control problem. We prove that the viscosity solution is Lipschitz continuous and unique on some short time interval if the initial condition is Lipschitz continuous. We end the paper with an example showing the loss of Lipschitz continuity of a viscosity solution in the one-dimensional case.
In the last few years multiwavelength observations have boosted our understanding of Ultraluminous X-ray Sources (ULXs). Yet, the most fundamental questions on ULXs still remain to be definitively answered: do they contain stellar or intermediate mass black holes? How do they form? We investigate the possibility that the black holes hosted in ULXs originate from massive (40-120 $M_\odot$) stars in low metallicity natal environments. Such black holes have a typical mass in the range $\sim 30-90 M_\odot$ and may account for the properties of bright (above $\sim 10^{40}$ erg s$^{-1}$) ULXs. More than $\sim 10^5$ massive black holes might have been generated in this way in the metal poor Cartwheel galaxy during the last $10^7$ years and might power most of the ULXs observed in it. Support to our interpretation comes from NGC 1313 X-2, the first ULX with a tentative identification of the orbital period in the optical band, for which binary evolution calculations show that the system is most likely made by a massive donor dumping matter on a $50-100 M_\odot$ black hole.
The non-minimal coupling of a scalar field is considered in the framework of Ashtekar's new variables formulation of gravity. A first order action functional for this system is derived in which the field variables are a tetrad field, and an SL(2,C) connection, together with the scalar field. The tetrad field and the SL(2,C) connection are related to the Ashtekar variables for the vacuum case by a conformal transformation. A canonical analysis shows that for this coupling the equations of Ashtekar's formulation of canonical gravity are non-polynomial in the scalar field. (to be published in Phys. Rev. D)
In this work we study the connection between anisotropic flows and lumpy initial conditions for Au+Au collisions at 200GeV. We present comparisons between anisotropic flow coefficients and eccentricities up to sixth order, and between initial condition reference angles and azimuthal particle distribution angles. We also present a toy model to justify the lack of connection between flow coefficients and eccentricities for individual events.