ShantanuT01/DACTYL-Pretraining huggingface dataset:
Video anomaly detection has proved to be a challenging task owing to its unsupervised training procedure and high spatio-temporal complexity existing in real-world scenarios. In the absence of anomalous training samples, state-of-the-art methods try to extract features that fully grasp normal behaviors in both space and time domains using different approaches such as autoencoders, or generative adversarial networks. However, these approaches completely ignore or, by using the ability of deep networks in the hierarchical modeling, poorly model the spatio-temporal interactions that exist between objects. To address this issue, we propose a novel yet efficient method named Ano-Graph for learning and modeling the interaction of normal objects. Towards this end, a Spatio-Temporal Graph (STG) is made by considering each node as an object's feature extracted from a real-time off-the-shelf object detector, and edges are made based on their interactions. After that, a self-supervised learning method is employed on the STG in such a way that encapsulates interactions in a semantic space. Our method is data-efficient, significantly more robust against common real-world variations such as illumination, and passes SOTA by a large margin on the challenging datasets ADOC and Street Scene while stays competitive on Avenue, ShanghaiTech, and UCSD.
The solar acoustic p-mode line profiles are asymmetric. Velocity spectra have more power on the low-frequency sides, whereas intensity profiles show the opposite sense of asymmetry. Numerical simulations of the upper convection zone have resonant p-modes with the same asymmetries and asymmetry reversal as the observed modes. The temperature and velocity power spectra at optical depth $\tau_{\rm cont} = 1$ have the opposite asymmetry as is observed for the intensity and velocity spectra. At a fixed geometrical depth, corresponding to $<\tau_{\rm cont}>=1$, however, the temperature and velocity spectra have the same asymmetry. This indicates that the asymmetry reversal is produced by radiative transfer effects and not by correlated noise.
We derive global consistency condition for strongly coupled heterotic string in the presence of M5-branes. Its elliptic genus is interpretable as generating functional of anomaly polynomials and so, on anomaly-free vacua, the genus is both holomorphic and modular invariant. In holomorphic basis, we identify the modular properties by calculating the phase. By interpreting the refinement parameters as background curvature of tangent and vector bundles, we identify the extended Bianchi identity for Kalb--Ramond field of heterotic M-theory in the presence of arbitrary numbers of M5-branes.
In this paper, we describe a way to construct cycles which represent the Todd class of a toric variety. Given a lattice with an inner product we assign a rational number m(s) to each rational polyhedral cone s in the lattice, such that for any toric variety X with fan S, the Todd class of X is the sum over all cones s in S of m(s)[V(s)]. This constitutes an improved answer to an old question of Danilov.   In a similar way, beginning with the choice of a complete flag in the lattice, we obtain the cycle Todd classes constructed by Morelli.   Our construction is based on an intersection product on cycles of a simplicial toric variety developed by the second-named author. Important properties of the construction are established by showing a connection to the canonical representation of the Todd class of a simplicial toric variety as a product of torus-invariant divisors developed by the first-named author.
The global effects of sudden changes in the interface growth dynamics are studied using models of the Edwards-Wilkinson (EW) and Kardar-Parisi-Zhang (KPZ) classes during their growth regimes in dimensions $d=1$ and $d=2$. Scaling arguments and simulation results are combined to predict the relaxation of the difference in the roughness of the perturbed and the unperturbed interfaces, $\Delta W^2 \sim s^c t^{-\gamma}$, where $s$ is the time of the change and $t>s$ is the observation time after that event. The previous analytical solution for the EW-EW changes is reviewed and numerically discussed in the context of lattice models, with possible decays with $\gamma=3/2$ and $\gamma=1/2$. Assuming the dominant contribution to $\Delta W^2$ to be predicted from a time shift in the final growth dynamics, the scaling of KPZ-KPZ changes with $\gamma = 1-2\beta$ and $c=2\beta$ is predicted, where $\beta$ is the growth exponent. Good agreement with simulation results in $d=1$ and $d=2$ is observed. A relation with the relaxation of a local autoresponse function in $d=1$ cannot be discarded, but very different exponents are shown in $d=2$. We also consider changes between different dynamics, with the KPZ-EW as a special case in which a faster growth, with dynamical exponent $z_i$, changes to a slower one, with exponent $z$. A scaling approach predicts a crossover time $t_c\sim s^{z/z_i}\gg s$ and $\Delta W^2 \sim s^c F\left( t/t_c\right)$, with the decay exponent $\gamma=1/2$ of the EW class. This rules out the simplified time shift hypothesis in $d=2$ dimensions. These results help to understand the remarkable differences in EW smoothing of correlated and uncorrelated surfaces, and the approach may be extended to sudden changes between other growth dynamics.
A discussion on the contribution of Peshkov, Bertin, Ginelli and Chate, arxiv:1404.3275v1, in this special issue.
We study the statistics, in stationary conditions, of the work $W_\tau$ done by the active force in different systems of self-propelled particles in a time $\tau$. We show the existence of a critical value $W_\tau ^\dag$ such that fluctuations with $W_\tau >W_\tau ^\dag$ correspond to configurations where interaction between particles plays a minor role whereas those with $W_\tau < W_\tau ^\dag$ represent states with single particles dragged by clusters. This two-fold behavior is fully mirrored by the probability distribution $P(W_\tau)$ of the work, which does not obey the large-deviation principle for $W_\tau <W_\tau ^\dag$. This pattern of behavior can be interpreted as due to a phase transition occurring at the level of fluctuating quantities and an order parameter is correspondingly identified.
We show that each entanglement witness detecting given bipartite entangled state provides an estimation of its concurrence. We illustrate our result with several well known examples of entanglement witnesses and compare the corresponding estimation of concurrence with other estimations provided by the trace norm of partial transposition and realignment.
We show how the periodicity of 180^{o} domains as a function of crystal thickness scales with the thickness of the domain walls both for ferroelectric and for ferromagnetic materials. We derive an analytical expression for the universal scaling factor and use this to calculate domain wall thickness and gradient coefficients (exchange constants) in some ferroic materials. We then use these to discuss some of the wider implications for the physics of ferroelectric nano-devices and periodically poled photonic crystals.
In this PhD thesis, we introduced a new strategy to investigate the kinematical and physical predictions of self dual Loop Quantum Gravity (LQG) and by-passed the old problem of implementing quantum mechanically the so called reality conditions inherent to the self dual Ashtekar's phase space.   We first review the loop quantization of the spherically isolated horizon and the computation of its micro-canonical entropy. Then we present the so called gas of punctures model for the quantum horizon, discussing its results in the canonical and grand-canonical ensembles and its limits.   The fourth chapter is devoted to studying to what extend the loop quantization based on the self dual variables could cure those problems. We introduce a new strategy, based on an analytic continuation of the degeneracy from $\gamma \in R$ to $\gamma = \pm i$. We review in details the construction of the procedure, and present the results. At the leading term, we recover exactly the Bekenstein-Hawking area law.   The fifth chapter is devoted to understanding more precisely the interplay between the status of the Immirzi parameter. In order to do this, we introduce from a new toy model describing $2+1$ gravity which depends explicitly on the Immirzi parameter.   Finally, the sixth chapter is devoted to applying our procedure to the simplest Loop Quantum Cosmology model. By first constructing the LQC dynamics for any arbitrary spin j and then implementing our analytic continuation, we show that our procedure preserves the key features of the LQC models, i.e. we obtain a bouncing universe which admits the right semi classical limit after the bounce.
Reflection and implantation of low energy helium (He) ions by tungsten (W) substrate are studied using molecular dynamics (MD) simulations. Motivated by the ITER divertor design, our study considers a range of W substrate temperatures (300 K, 1000 K, 1500 K), a range of He atom incidence energies ($\le$100 eV) and a range of angles of incidence ($0^{\circ}$-$75^{\circ}$) with respect to substrate normal. The MD simulations quantify the reflection and implantation function, the integrated moments such as the particle/energy reflection coefficients and average implantation depths. Distributions of implantation depths, reflected energy, polar and azimuthal angles of reflection are obtained, as functions of simulation parameters, such as W substrate temperature, polar angle of incidence, the energy of incident He, and the type of W substrate surface. Comparison between the MD simulation results, the results obtained using SRIM simulation package, and the existing experimental and theoretical results is provided.
Light fields can be amplified by measuring the field amplitude reflected at a beam splitter of reflectivity R and adding a coherent amplitude proportional to the measurement result to the transmitted field. By applying the quantum optical realization of this amplification scheme to single photon inputs, it is possible to clone the polarization states of photons. We show that optimal cloning of single photon polarization is possible when the gain factor of the amplification is equal to the inverse squareroot of 1-R.
We obtain several new regularity results for solutions of scalar conservation laws satisfying the genuine nonlinearity condition. We prove that the solutions are continuous outside of the jump set, which is codimension one rectifiable. We show that the entropy dissipation vanishes away from the closure of the jump set. We prove that the solution decays algebraically in $L^\infty$ as $t \to \infty$ and we compute the presumably optimal decay rate. All these results are based on a local oscillation estimate which is obtained properly adapting some ideas of De Giorgi from the context of elliptic equations.
We employ the chiral nucleon-nucleon potential derived using the method of unitary transformation up to next-to-next-to-leading order (NNLO) to study bound and scattering states in the two-nucleon system. The predicted partial wave phase shifts and mixing parameters for higher energies and higher angular momenta beyond the ones which are fitted are mostly well described for energies below 300 MeV. Various deuteron properties are discussed. We also apply the next-to-leading order (NLO) potential to 3N and 4N systems. The resulting 3N and 4N binding energies are in the same range what is found using standard NN potentials. Experimental low-energy 3N scattering observables are also very well reproduced like for standard NN forces. Surprisingly the long standing Ay-puzzle is resolved at NLO. The cut-off dependence of the scattering observables is rather mild.
We study the temperature of rotating probe D7-branes, dual to the temperature of flavored quarks, in the Kuperstein--Sonnenschein holographic model including the effects of spontaneous breakdown of the conformal and chiral flavor symmetry. The model embeds probe D7-branes into the Klebanov-Witten gravity dual of conformal gauge theory, with the embedding parameter, given by the minimal radial extension of the probe, setting the IR scale of conformal and chiral flavor symmetry breakdown. We show that when the minimal extension is positive definite and additional spin is turned on, the induced world volume metrics on the probe admit thermal horizons and Hawking temperatures despite the absence of black holes in the bulk. We find the scale and behavior of the temperature in flavored quarks are determined notably by the IR scale of symmetry breaking, and by the strength and sort of external fields. We also derive the energy--stress tensor of the rotating probe and study its backreaction and energy dissipation. We show that at the IR scale the backreaction is non-negligible and find the energy can flow from the probe to the bulk, dual to the energy dissipation from the flavor sector into the gauge theory.
We present new three-dimensional (3D) interstellar dust reddening maps of the Galactic plane in three colours, E(G-Ks), E(Bp-Rp) and E(H-Ks). The maps have a spatial angular resolution of 6 arcmin and covers over 7000 deg$^2$ of the Galactic plane for Galactic longitude 0 deg $<$ $l$ $<$ 360 deg and latitude $|b|$ $<$ $10$ deg. The maps are constructed from robust parallax estimates from the Gaia Data Release 2 (Gaia DR2) combined with the high-quality optical photometry from the Gaia DR2 and the infrared photometry from the 2MASS and WISE surveys. We estimate the colour excesses, E(G-Ks), E(Bp-Rp) and E(H-Ks), of over 56 million stars with the machine learning algorithm Random Forest regression, using a training data set constructed from the large-scale spectroscopic surveys LAMOST, SEGUE and APOGEE. The results reveal the large-scale dust distribution in the Galactic disk, showing a number of features consistent with the earlier studies. The Galactic dust disk is clearly warped and show complex structures possibly spatially associated with the Sagittarius, Local and Perseus arms. We also provide the empirical extinction coefficients for the Gaia photometry that can be used to convert the colour excesses presented here to the line-of-sight extinction values in the Gaia photometric bands.
We derive the group structure for cyclotomic function fields obtained by applying the Carlitz action for extensions of an initial constant field. The tame and wild structures are isolated to describe the Galois action on differentials. We show that the associated invariant rings are not polynomial.
We consider the problem of efficient simulation estimation of the density function at the tails, and the probability of large deviations for a sum of independent, identically distributed, light-tailed and non-lattice random vectors. The latter problem besides being of independent interest, also forms a building block for more complex rare event problems that arise, for instance, in queueing and financial credit risk modelling. It has been extensively studied in literature where state independent exponential twisting based importance sampling has been shown to be asymptotically efficient and a more nuanced state dependent exponential twisting has been shown to have a stronger bounded relative error property. We exploit the saddle-point based representations that exist for these rare quantities, which rely on inverting the characteristic functions of the underlying random vectors. These representations reduce the rare event estimation problem to evaluating certain integrals, which may via importance sampling be represented as expectations. Further, it is easy to identify and approximate the zero-variance importance sampling distribution to estimate these integrals. We identify such importance sampling measures and show that they possess the asymptotically vanishing relative error property that is stronger than the bounded relative error property. To illustrate the broader applicability of the proposed methodology, we extend it to similarly efficiently estimate the practically important expected overshoot of sums of iid random variables.
The exact form of quantum propagator of a quantum oscillator interacting with a bosonic bath consisting of $N$ distinguished quantum oscillators with different frequencies is obtained in the Heisenberg picture. Reduced density matrix for oscillator is obtained. The kernel or Green's function connecting the initial density matrix of the oscillator to the density matrix in an arbitrary time is obtained and its connection to Feynman-Vernon influence functional is discussed. Weak coupling regime and squared mean values for position, momentum and energy of the oscillator are obtained in equilibrium.
A detailed Dirac's canonical analysis for a topological four dimensional $BF$-like theory with a compact dimension is developed. By performing the compactification process we find out the relevant symmetries of the theory, namely, the full structure of the constraints and the extended action. We show that the extended Hamiltonian is a linear combination of first class constraints, which means that the general covariance of the theory is not affected by the compactification process. Furthermore, in order to carry out the correct counting of physical degrees of freedom, we show that must be taken into account reducibility conditions among the first class constraints associated to the excited KK modes. Moreover, we perform the Hamiltonian analysis of Maxwell theory written as a $BF$-like theory with a compact dimension, we analyze the constraints of the theory and we calculate the fundamental Dirac's brackets, finally the results obtained are compared with those found in the literature.
We study a one dimensional nonequilibrium lattice model with competing features of particle attraction and non-local hops. The system is similar to a zero range process (ZRP) with attractive particles but the particles can make both local and non-local hops. The length of the non-local hop is dependent on the occupancy of the chosen site and its probability is given by the parameter $p$. Our numerical results show that the system undergoes a phase transition from a condensate phase to a homogeneous density phase as $p$ is increased beyond a critical value $p_c$. A mean-field approximation does not predict a phase transition and describes only the condensate phase. We provide heuristic arguments for understanding the numerical results.
Interfaces play an essential role in phonon-mediated heat conduction in solids, impacting applications ranging from thermoelectric waste heat recovery to heat dissipation in electronics. From the microscopic perspective, interfacial phonon transport is described by transmission coefficients that link vibrational modes in the materials composing the interface. However, direct experimental determination of these coefficients is challenging because most experiments provide a mode-averaged interface conductance that obscures the microscopic detail. Here, we report a metrology to extract thermal phonon transmission coefficients at solid interfaces using ab-initio phonon transport modeling and a thermal characterization technique, time-domain thermoreflectance. In combination with transmission electron microscopy characterization of the interface, our approach allows us to link the atomic structure of an interface to the spectral content of the heat crossing it. Our work provides a useful perspective on the microscopic processes governing interfacial heat conduction.
We propose a novel hierarchical approach for text-to-image synthesis by inferring semantic layout. Instead of learning a direct mapping from text to image, our algorithm decomposes the generation process into multiple steps, in which it first constructs a semantic layout from the text by the layout generator and converts the layout to an image by the image generator. The proposed layout generator progressively constructs a semantic layout in a coarse-to-fine manner by generating object bounding boxes and refining each box by estimating object shapes inside the box. The image generator synthesizes an image conditioned on the inferred semantic layout, which provides a useful semantic structure of an image matching with the text description. Our model not only generates semantically more meaningful images, but also allows automatic annotation of generated images and user-controlled generation process by modifying the generated scene layout. We demonstrate the capability of the proposed model on challenging MS-COCO dataset and show that the model can substantially improve the image quality, interpretability of output and semantic alignment to input text over existing approaches.
We prove two conjectures in spectral extremal graph theory involving the linear combinations of graph eigenvalues. Let $\lambda_1(G)$ be the largest eigenvalue of the adjacency matrix of a graph $G$, and $\bar{G}$ be the complement of $G$. A nice conjecture states that the graph on $n$ vertices maximizing $\lambda_1(G) + \lambda_1(\bar{G})$ is the join of a clique and an independent set, with $\lfloor n/3\rfloor$ and $\lceil 2n/3\rceil$ (also $\lceil n/3\rceil$ and $\lfloor 2n/3\rfloor$ if $n \equiv 2 \pmod{3}$) vertices, respectively. We resolve this conjecture for sufficiently large $n$ using analytic methods. Our second result concerns the $Q$-spread $s_Q(G)$ of a graph $G$, which is defined as the difference between the largest eigenvalue and least eigenvalue of the signless Laplacian of $G$. It was conjectured by Cvetkovi\'c, Rowlinson and Simi\'c in $2007$ that the unique $n$-vertex connected graph of maximum $Q$-spread is the graph formed by adding a pendant edge to $K_{n-1}$. We confirm this conjecture for sufficiently large $n$.
In this paper we propose a novel sparse optical flow (SOF)-based line feature tracking method for the camera pose estimation problem. This method is inspired by the point-based SOF algorithm and developed based on an observation that two adjacent images in time-varying image sequences satisfy brightness invariant. Based on this observation, we re-define the goal of line feature tracking: track two endpoints of a line feature instead of the entire line based on gray value matching instead of descriptor matching. To achieve this goal, an efficient two endpoint tracking (TET) method is presented: first, describe a given line feature with its two endpoints; next, track the two endpoints based on SOF to obtain two new tracked endpoints by minimizing a pixel-level grayscale residual function; finally, connect the two tracked endpoints to generate a new line feature. The correspondence is established between the given and the new line feature. Compared with current descriptor-based methods, our TET method needs not to compute descriptors and detect line features repeatedly. Naturally, it has an obvious advantage over computation. Experiments in several public benchmark datasets show our method yields highly competitive accuracy with an obvious advantage over speed.
First we show that any group of automorphisms of null-entropy of a projective hyperk\"ahler manifold $M$ is almost abelian of rank at most $\rho(M) - 2$. We then characterize automorphisms of a K3 surface with null-entropy and those with positive entropy in algebro-geometric terms. We also give an example of a group of automorphisms which is not almost abelian in each dimension.
We present near--infrared J and K observations of giant stars in five metal-poor Galactic Globular Clusters (namely M3, M5, M10, M13 and M92) obtained at the Telescopio Nazionale Galileo (TNG). This database has been used to determine the main photometric properties of the red giant branch (RGB) from the (K,J-K) and, once combined with the optical data, in the (K,V-K) Color Magnitude Diagrams. A set of photometric indices (the RGB colors at fixed magnitudes) and the major RGB evolutionary features (slope, bump, tip) have been measured. The results have been compared with the relations obtained by Ferraro et al. 2000 and with the theoretical expectations, showing a very good agreement.