ShantanuT01/DACTYL-Pretraining huggingface dataset:
Starting with the light-cone Hamiltonian for gravity, we perform a field redefinition that reveals a hidden symmetry in four dimensions, namely the Ehlers $SL(2,R)$ symmetry. The field redefinition, which is non-local in space but local in time, acts as a canonical transformation in the Hamiltonian formulation keeping the Poisson bracket relations unaltered. We discuss the electro-magnetic duality symmetry of gravity in the light-cone formalism, which forms the $SO(2)$ subgroup of the Ehlers symmetry. The helicity states in the original Hamiltonian are not in a representation of the enhanced symmetry group. In order to make the symmetry manifest, we make a change of variables in the path integral from the helicity states to new fields that transform linearly under the $SO(2)$ duality symmetry.
We conceive an all-optical representation of the dynamics of two distinct types of interacting bosons in a double well by an array of evanescently coupled photonic waveguides. Many-particle interference effects are probed for various interaction strengths by changing the relative abundance of the particle species and can be readily identified by monitoring the propagation of the light intensity across the waveguide array. In particular, we show that finite inter-particle interaction strengths reduce the many-particle interference contrast by dephasing. A general description of the many-particle dynamics for arbitrary initial states is given in terms of two coupled spins by generalising the Schwinger representation to two particle species.
We prepare metastable glassy states in a model glass-former made of Lennard-Jones particles by sampling biased ensembles of trajectories with low dynamical activity. These trajectories form an inactive dynamical phase whose `fast' vibrational degrees of freedom are maintained at thermal equilibrium by contact with a heat bath, while the `slow' structural degrees of freedom are located in deep valleys of the energy landscape. We examine the relaxation to equilibrium and the vibrational properties of these metastable states. The glassy states we prepare by our trajectory sampling method are very stable to thermal fluctuations and also more mechanically rigid than low-temperature equilibrated configurations.
Thermal fluctuations in time-dependent quantum processes are treated by a constant-temperature generalization of Wigner's formulation of quantum mechanics in phase space. To this end, quantum Nos\`e-Hoover dynamics is defined by generalizing the Moyal bracket. Computational applications of the formalism, together with further theoretical developments, are discussed.
LiDAR provides highly accurate 3D point clouds. However, data needs to be manually labelled in order to provide subsequent useful information. Manual annotation of such data is time consuming, tedious and error prone, and hence in this paper we present three automatic methods for annotating trees in LiDAR data. The first method requires high density point clouds and uses certain LiDAR data attributes for the purpose of tree identification, achieving almost 90% accuracy. The second method uses a voxel-based 3D Convolutional Neural Network on low density LiDAR datasets and is able to identify most large trees accurately but struggles with smaller ones due to the voxelisation process. The third method is a scaled version of the PointNet++ method and works directly on outdoor point clouds and achieves an F_score of 82.1% on the ISPRS benchmark dataset, comparable to the state-of-the-art methods but with increased efficiency.
At present, the fundamental solutions of the multidimensional elliptic equation with the several singular coefficients are known and they are expressed in terms of the Lauricella hypergeometric function of many variables. In this paper we study the Neumann problem for a multidimensional elliptic equation with several singular coefficients in the infinite domain. Using the method of the integral energy the uniqueness of solution has been proved. In the course of proving the existence of the explicit solution of the Neumann problem, a differentiation formula, some adjacent and limiting relations for the Lauricella hypergeometric functions and the values of some multidimensional improper integrals are used.
In this article we review a less known unperturbative and powerful many-body method in the framework of classical statistical mechanics and then we show how it works by means of explicit calculations for a nontrivial classical model. The formalism of two-time Green functions in classical statistical mechanics is presented in a form parallel to the well known quantum counterpart, focusing on the spectral properties which involve the important concept of spectral density. Furthermore, the general ingredients of the classical spectral density method (CSDM) are presented with insights for systematic nonperturbative approximations to study conveniently the macroscopic properties of a wide variety of classical many-body systems also involving phase transitions. The method is implemented by means of key ideas for exploring the spectrum of elementary excitations and the damping effects within a unified formalism. Then, the effectiveness of the CSDM is tested with explicit calculations for the classical $d$-dimensional spin-$S$ Heisenberg ferromagnetic model with long-range exchange interactions decaying as $r^{-p}$ ($p>d$) with distance $r$ between spins and in the presence of an external magnetic field. The analysis of the thermodynamic and critical properties, performed by means of the CSDM to the lowest order of approximation, shows clearly that nontrivial results can be obtained in a relatively simple manner already to this lower stage. The basic spectral density equations for the next higher order level are also presented and the damping of elementary spin excitations in the low temperature regime is studied. The results appear in reasonable agreement with available exact ones and Monte Carlo simulations and this supports the CSDM as a promising method of investigation in classical many-body theory.
This is not a research paper, but a survey submitted to a proceedings volume.
Accurate measurement of efficiency for thermoelectric generator (TEG) is of great importance for materials research and development. Approximately all the parameters of a material are temperature dependent, so we can't directly apply the $\eta_\text{max}$ formula for efficiency calculation in the large temperature range. To overcome that problem, we tried to calculate the efficiency of TEG by dividing large working temperature range into a number of small temperature difference. The aim is to make temperature dependent parameter to be constant for that small temperature range. Using maximum individual efficiency of each segment obtained by $\eta_\text{max}$ in the equation of $\eta_\text{overall}$, which gives overall efficiency. The $\eta_\text{overall}$ of TEG using $Bi_2Te_3$ and $TAGS$ as thermoelectric materials come out to be $7.1\%$ and $8.94\%$, respectively, which is close to experimental results. For the high-temperature region, we have used $SiGe$ material in TEG and found out $\eta_\text{overall}=3.5\%$. The cumulative efficiency obtained by keeping one end temperature fixed with another end varying can be applied in real life application, i.e. automobile sector. The present work provides a simple way for the design engineers to calculate the efficiency of TEG by using the temperature dependent materials parameters like thermal conductivity, electrical conductivity, and Seebeck coefficient on which $z\bar{T}$ depends.
We revisit the scaling theory of the Smoluchowski equation with special emphasis on the dimensional analysis to derive the scaling ansatz and to give an insightful foundation to it. It has long been argued that the homogeneity exponent $\lambda$ of the aggregation kernel divides the aggregation process into two regimes (i) $\lambda\leq 1$ nongelling and (ii) $\lambda>1$ gelling. However, our findings contradict with this result. In particular, we find that the Smoluchowski equation is valid if and only if $\lambda<1$. We show that beyond this limit i.e. at $\lambda\geq 1$, it breaks down and hence it fails to describe a gelation transition. This also happens to be accompanied by violation of scaling.
The Schiff moment, $\smij$, is a parity and time reversal violating fermion-fermion coupling. The nucleus-electron Schiff moment generically gives the most important contribution to the electric dipole moments of atoms and molecules with zero net intrinsic electronic spin and nuclear spin ${1 \over 2}$. Here, the electromagnetic contribution to the Schiff moment, $\emij$, is considered. For a nucleon, the leading chirally violating contribution to this interaction is calculable in the chiral limit in terms of the parity and time reversal violating pion-nucleon coupling. For the Schiff moment of heavy nuclei, this chiral contribution is somewhat smaller than the finite size effect discussed previously in the literature.
Interferences between different emitters in the multi-parton shower is the building block of QCD jet physics in vacuum. The presence of a hot medium made of quarks and gluons is expected to alter this interference pattern. To study such effects, we derive the gluon emission spectrum off an "asymptotic quark" traversing a hot and dense QCD medium at first order in the medium density. The resulting induced gluon distribution gets modified when the new interference terms between the initial and final quark are included. We comment on the possible phenomenological consequences of this new contribution for jet observables in heavy-ion collisions.
Accurate 3D reconstruction of the hand and object shape from a hand-object image is important for understanding human-object interaction as well as human daily activities. Different from bare hand pose estimation, hand-object interaction poses a strong constraint on both the hand and its manipulated object, which suggests that hand configuration may be crucial contextual information for the object, and vice versa. However, current approaches address this task by training a two-branch network to reconstruct the hand and object separately with little communication between the two branches. In this work, we propose to consider hand and object jointly in feature space and explore the reciprocity of the two branches. We extensively investigate cross-branch feature fusion architectures with MLP or LSTM units. Among the investigated architectures, a variant with LSTM units that enhances object feature with hand feature shows the best performance gain. Moreover, we employ an auxiliary depth estimation module to augment the input RGB image with the estimated depth map, which further improves the reconstruction accuracy. Experiments conducted on public datasets demonstrate that our approach significantly outperforms existing approaches in terms of the reconstruction accuracy of objects.
The aim of this paper is to construct regular Hayward thin-shell wormholes and analyze their stability. We adopt Israel formalism to calculate surface stresses of the shell and check the null and weak energy conditions for the constructed wormholes. It is found that the stress-energy tensor components violate the null and weak energy conditions leading to the presence of exotic matter at the throat. We analyze the attractive and repulsive characteristics of wormholes corresponding to $a^r>0$ and $a^r<0$, respectively. We also explore stability conditions for the existence of traversable thin-shell wormholes with arbitrarily small amount of fluids describing cosmic expansion. We find that the spacetime has non-physical regions which give rise to event horizon for $0<a_{0}<2.8$ and the wormhole becomes non-traversable producing a black hole. The non-physical region in the wormhole configuration decreases gradually and vanishes for the Hayward parameter $l=0.9$. It is concluded that the Hayward and Van der Waals quintessence parameters increase the stability of thin-shell wormholes.
Recently an unidentified emission line at 3.55 keV has been detected in X-ray spectra of clusters of galaxies. The line has been discussed as a possible decay signature of 7.1 keV sterile neutrinos, which have been proposed as a dark matter (DM) candidate. We aim to further constrain the line strength and its implied mixing angle under the assumption that all DM is made of sterile neutrinos. The X-ray observations of the Limiting Window (LW) towards the Galactic bulge (GB) offer a unique dataset for exploring DM lines. We characterize the systematic uncertainties of the observation and the fitted models with simulated X-ray spectra. In addition we discuss uncertainties of indirect DM column density constraints towards the GB to understand systematic uncertainties in the assumed DM mass in the field of view of the observation. We found tight constraints on the allowed flux for an additional line at 3.55 keV with a positive ($\mathrm{\sim1.5\sigma}$) best fit value $\mathrm{F_X^{3.55keV}\approx(4.5\pm3.5)\times10^{-7}~cts~cm^{-2}~s^{-1}}$. This would translate into a mixing angle of $\mathrm{sin^{2}(2\Theta)\approx(2.3\pm1.8)\times10^{-11}}$ which, while consistent with some recent results, is in tension with earlier detections. We used a very deep dataset with well understood systematics to derive tight constraints on the mixing angle of a 7.1 keV sterile neutrino DM. The results highlight that the inner Milky Way will be a good target for DM searches with upcoming missions like eROSITA, XRISM, and ATHENA.
In this article, we give evidence that computing Fourier coefficients of the Hecke eigenforms for composite indices is no easier than factoring integers. In particular, we show that the existence of a polynomial time algorithm that, given n, computes the n-th Fourier coefficient of a (fixed) Hecke eigenform implies that we can factor most RSA moduli (numbers that are products of two distinct primes) in polynomial time.
We show that the diversity in the density slope of the dense wind due to non-steady mass loss can be one way to explain the spectral diversity of Type II luminous supernovae (LSNe). The interaction of SN ejecta and wind surrounding it is considered to be a power source to illuminate LSNe because many LSNe show the wind signature in their spectra (Type IIn LSNe). However, there also exist LSNe without the spectral features caused by the wind (Type IIL LSNe). We show that, even if LSNe are illuminated by the interaction, it is possible that they do not show the narrow spectra from the wind if we take into account of non-steady mass loss of their progenitors. When the shock breakout takes place in the dense wind with the density structure \rho\propto r^{-w}, the ratio of the diffusion timescale in the optically thick region of the wind (td) and the shock propagation timescale of the entire wind after the shock breakout (ts) strongly depends on w. For the case w<~1, both timescales are comparable (td/ts \simeq 1) and td/ts gets smaller as w gets larger. For the case td/ts\simeq 1, the shock goes through the entire wind just after the light curve (LC) peak and narrow spectral lines from the wind cannot be observed after the LC peak (Type IIL LSNe). If td/ts is much smaller, the shock wave continues to propagate in the wind after the LC peak and unshocked wind remains (Type IIn LSNe). This difference can be obtained only through a careful treatment of the shock breakout condition in a dense wind. The lack of narrow Lorentzian line profiles in Type IIL LSNe before the LC peak can also be explained by the difference in the density slope. Furthermore, we apply our model to Type IIn LSN 2006gy and Type IIL LSN 2008es and find that our model is consistent with the observations.
We present a general analytical formalism to calculate accurately several statistics related to underdense regions in the Universe. The statistics are computed for dark matter halo and galaxy distributions both in real space and redshift space at any redshift. Using this formalism, we found that void statistics for galaxy distributions can be obtained, to a very good approximation, assuming galaxies to have the same clustering properties as halos above a certain mass. We deducted a relationship between this mass and that of halos with the same accumulated number density as the galaxies. We also found that the dependence of void statistics on redshift is small. For instance, the number of voids larger than 13 Mpc/h (defined to not contain galaxies brighter than M_r=-20.4 +5logh change less than 20% between z=1 and z=0. However, the dependence of void statistics on sigma_8 and Omega_m h is considerably larger, making them appropriate to develop tests to measure these parameters. We have shown how to efficiently construct several of these tests and discussed in detail the treatment of several observational effects. The formalism presented here along with the observed statistics extracted from current and future large galaxy redshift surveys will provide an independent measurement of the relevant cosmological parameters. Combining these measurements with those found using other methods will contribute to reduce their uncertainties.
We analyse the fluctuations of the ground-state/funnel solutions proposed to describe M2-M5 systems in the level-k mass-deformed/pure Chern-Simons-matter ABJM theory of multiple membranes. We show that in the large N limit the fluctuations approach the space of functions on the 2-sphere rather than the naively expected 3-sphere. This is a novel realisation of the fuzzy 2-sphere in the context of Matrix Theories, which uses bifundamental instead of adjoint scalars. Starting from the multiple M2-brane action, a U(1) Yang-Mills theory on R^{2,1} x S^2 is recovered at large N, which is consistent with a single D4-brane interpretation in Type IIA string theory. This is as expected at large k, where the semiclassical analysis is valid. Several aspects of the fluctuation analysis, the ground-state/funnel solutions and the mass-deformed/pure ABJM equations can be understood in terms of a discrete noncommutative realisation of the Hopf fibration. We discuss the implications for the possibility of finding an M2-brane worldvolume derivation of the classical S^3 geometry of the M2-M5 system. Using a rewriting of the equations of the SO(4)-covariant fuzzy 3-sphere construction, we also directly compare this fuzzy 3-sphere against the ABJM ground-state/funnel solutions and show them to be different.
In this paper, we prove a semistable reduction type theorem for multi-filtered vector spaces (or known as multi-weighted vector spaces).
Given a prime $p\ge5$ and an integer $s\ge1$, we show that there exists an integer $M$ such that for any quadratic polynomial $f$ with coefficients in the ring of integers modulo $p^s$, such that $f$ is not a square, if a sequence $(f(1),\dots,f(N))$ is a sequence of squares, then $N$ is at most $M$. We obtain this result by reducing to the case where $f$ has an invertible dominant coefficient.
In this paper we study the relationship between two different compactifications of the space of vector bundle quotients of an arbitrary vector bundle on a curve. One is Grothendieck's Quot scheme, while the other is a moduli space of stable maps to the relative Grassmannian.   We establish an essentially optimal upper bound on the dimension of the two compactifications. Based on that, we prove that for an arbitrary vector bundle, the Quot schemes of quotients of large degree are irreducible and generically smooth. We precisely describe all the vector bundles for which the same thing holds in the case of the moduli spaces of stable maps. We show that there are in general no natural morphisms between the two compactifications. Finally, as an application, we obtain new cases of a conjecture on effective base point freeness for pluritheta linear series on moduli spaces of vector bundles.
We show that $L_{3,\infty}$-solutions to the three-dimensional Navier-Stokes equations near a flat part of the boundary are smooth.
Given positive integers $p$ and $q$, a $(p,q)$-coloring of the complete graph $K_n$ is an edge-coloring in which every $p$-clique receives at least $q$ colors. Erd\H{o}s and Shelah posed the question of determining $f(n,p,q)$, the minimum number of colors needed for a $(p,q)$-coloring of $K_n$. In this paper, we expand on the color energy technique introduced by Pohoata and Sheffer to prove new lower bounds on this function, making explicit the connection between bounds on extremal numbers and $f(n,p,q)$. Using results on the extremal numbers of subdivided complete graphs, theta graphs, and subdivided complete bipartite graphs, we generalize results of Fish, Pohoata, and Sheffer, giving the first nontrivial lower bounds on $f(n,p,q)$ for some pairs $(p,q)$ and improving previous lower bounds for other pairs.
In this work, we consider a probability representation of quantum dynamics for finite-dimensional quantum systems with the use of pseudostochastic maps acting on true probability distributions. These probability distributions are obtained via symmetric informationally complete positive operator-valued measure (SIC-POVM) and can be directly accessible in an experiment. We provide SIC-POVM probability representations both for unitary evolution of the density matrix governed by the von Neumann equation and dissipative evolution governed by Markovian master equation. In particular, we discuss whereas the quantum dynamics can be simulated via classical random processes in terms of the conditions for the master equation generator in the SIC-POVM probability representation. We construct practical measures of nonclassicality non-Markovianity of quantum processes and apply them for studying experimental realization of quantum circuits realized with the IBM cloud quantum processor.
Using highly correlational quantum chemistry we compute from first principles the contributions of the electric dipoles and quadupoles, and magnetic dipoles to the nonlinear optics of NiO. The material is modeled as a doubly embedded cluster and all magnetic intragap d-character states are calculated, thus explaining the experimental results.
I characterize the structure of the master field for $F^{0}_{z \bar z}$ in $SU(\infty)$-$YM_4$ on a product of two Riemann surfaces $Z \times W$ in the gauge $F^{ch}_{z \bar z}=0$ as the sum of a `bulk' constant term and of delta-like `contact' terms.\\ The contact terms may occur because the localization of the functional integral at $N=\infty$ on a master orbit of a constant connection under the action of singular gauge transformations is still compatible with the large-$N$ factorization and translational invariance.\\ In addition I argue that if the gauge group is unbroken and there is a mass gap, that is if the theory confines, the functional measure at $N=\infty$, in the gauge $F^{ch}_{z \bar z}=0$, must be localized on the moduli space of flat connections with punctures on $Z \times W$.
RGB-D salient object detection (SOD) has been in the spotlight recently because it is an important preprocessing operation for various vision tasks. However, despite advances in deep learning-based methods, RGB-D SOD is still challenging due to the large domain gap between an RGB image and the depth map and low-quality depth maps. To solve this problem, we propose a novel superpixel prototype sampling network (SPSN) architecture. The proposed model splits the input RGB image and depth map into component superpixels to generate component prototypes. We design a prototype sampling network so that the network only samples prototypes corresponding to salient objects. In addition, we propose a reliance selection module to recognize the quality of each RGB and depth feature map and adaptively weight them in proportion to their reliability. The proposed method makes the model robust to inconsistencies between RGB images and depth maps and eliminates the influence of non-salient objects. Our method is evaluated on five popular datasets, achieving state-of-the-art performance. We prove the effectiveness of the proposed method through comparative experiments.