ShantanuT01/DACTYL-Pretraining huggingface dataset:
Hand segmentation for hand-object interaction is a necessary preprocessing step in many applications such as augmented reality, medical application, and human-robot interaction. However, typical methods are based on color information which is not robust to objects with skin color, skin pigment difference, and light condition variations. Thus, we propose hand segmentation method for hand-object interaction using only a depth map. It is challenging because of the small depth difference between a hand and objects during an interaction. To overcome this challenge, we propose the two-stage random decision forest (RDF) method consisting of detecting hands and segmenting hands. To validate the proposed method, we demonstrate results on the publicly available dataset of hand segmentation for hand-object interaction. The proposed method achieves high accuracy in short processing time comparing to the other state-of-the-art methods.
The shape of dark matter haloes plays a critical role in constraining cosmology with upcoming large-scale structure surveys. In this paper, we study the correlations between the triaxial shapes and formation histories in dark matter haloes in the MultiDark Planck 2 N-body cosmological simulation. We find that halo ellipticity is strongly correlated with halo properties that serve as proxies of halo formation history, such as halo concentration and the peak-centroid offset. In particular, the correlation between halo ellipticity and halo concentration is nearly independent of the halo density peak height. We present a simple model for the correlation between halo ellipticity and concentration using conditional abundance matching, and provide fitting formulae for the multi-dimensional distributions of triaxial halo shape as a function of halo peak height. We apply our halo shape model to gauge the effects of halo ellipticity and orientation bias on the excess surface mass density profiles in cluster-size halos. Our model should be useful for exploring the impact of triaxial halo shape on cosmological constraints in upcoming weak lensing surveys of galaxy clusters.
With the advancement in image capturing device, the image data been generated at high volume. If images are analyzed properly, they can reveal useful information to the human users. Content based image retrieval address the problem of retrieving images relevant to the user needs from image databases on the basis of low-level visual features that can be derived from the images. Grouping images into meaningful categories to reveal useful information is a challenging and important problem. Clustering is a data mining technique to group a set of unsupervised data based on the conceptual clustering principal: maximizing the intraclass similarity and minimizing the interclass similarity. Proposed framework focuses on color as feature. Color Moment and Block Truncation Coding (BTC) are used to extract features for image dataset. Experimental study using K-Means clustering algorithm is conducted to group the image dataset into various clusters.
Let X be an irreducible smooth complex projective curve of genus g at least 4. Let M(r,\Lambda) be the moduli space of stable vector bundles over X or rank r and fixed determinant \Lambda, of degree d. We give a new proof of the fact that the automorphism group of M(r,\Lambda) is generated by automorphisms of the curve X, tensorization with suitable line bundles, and, if r divides 2d, also dualization of vector bundles.
Spatiotemporal chaos arising from the competition between sine-Gordon-breather and kink-antikink-pair solitons by reshaping an ac force is demonstrated. After introducing soliton collective coordinates, Melnikov's method is applied to the resulting effective equation of motion to estimate the parameter-space regions of the ac force where homoclinic bifurcations are induced. The analysis reveals that the chaos-order threshold exhibits sensitivity to small changes in the force shape. Computer simulations of the sine-Gordon system show good agreement with these theoretical predictions.
We study positive solutions to the heat equation on graphs. We prove variants of the Li-Yau gradient estimate and the differential Harnack inequality. For some graphs, we can show the estimates to be sharp. We establish new computation rules for differential operators on discrete spaces and introduce a relaxation function that governs the time dependency in the differential Harnack estimate.
We prove various formulas which express exponential generating functions counting permutations by the peak number, valley number, double ascent number, and double descent number statistics in terms of the exponential generating function for Chebyshev polynomials, as well as cyclic analogues of these formulas for derangements. We give several applications of these results, including formulas for the $(-1)$-evaluation of some of these distributions. Our proofs are combinatorial and involve the use of monomino-domino tilings, the modified Foata-Strehl action (a.k.a. valley-hopping), and a cyclic analogue of this action due to Sun and Wang.
We develop the theory of equiangular lines in Euclidean spaces. Our focus is on the question of when a Seidel matrix having precisely three distinct eigenvalues has a regular graph in its switching class. We make some progress towards an answer to this question by finding some necessary conditions and some sufficient conditions. Furthermore, we show that the cardinality of an equiangular line system in $18$ dimensional Euclidean space is at most $60$.
The unsupervised depth estimation is the recent trend by utilizing the binocular stereo images to get rid of depth map ground truth. In unsupervised depth computation, the disparity images are generated by training the CNN with an image reconstruction loss. In this paper, a dual CNN based model is presented for unsupervised depth estimation with 6 losses (DNM6) with individual CNN for each view to generate the corresponding disparity map. The proposed dual CNN model is also extended with 12 losses (DNM12) by utilizing the cross disparities. The presented DNM6 and DNM12 models are experimented over KITTI driving and Cityscapes urban database and compared with the recent state-of-the-art result of unsupervised depth estimation. The code is available at: https://github.com/ishmav16/Dual-CNN-Models-for-Unsupervised-Monocular-Depth-Estimation.
We consider the relationship between the Laplacians on two sequences of planar graphs, one from the theory of self-similar groups and one from analysis on fractals. By establishing a spectral decimation map between these sequences we give an elementary calculation of the spectrum of the former, which was first computed by Grigorchuk and \v{S}uni\'{c}. Our method also gives a full description of the eigenfunctions.
Recent technological developments have made it increasingly easy to access the non-perturbative regimes of cavity quantum electrodynamics known as ultra or deep strong coupling, where the light-matter coupling becomes comparable to the bare modal frequencies. In this work, we address the adequacy of the broadly used single-mode cavity approximation to describe such regimes. We demonstrate that, in the non-perturbative light-matter coupling regimes, the single-mode models become unphysical, allowing for superluminal signalling. Moreover, considering the specific example of the quantum Rabi model, we show that the multi-mode description of the electromagnetic field, necessary to account for light propagation at finite speed, yields physical observables that differ radically from their single-mode counterparts already for moderate values of the coupling. Our multi-mode analysis also reveals phenomena of fundamental interest on the dynamics of the intracavity electric field, where a free photonic wavefront and a bound state of virtual photons are shown to coexist.
It is shown that for any translation invariant outer measure M, the M-measure of the intersection of any subset of R^n that is invariant under rational translations and which does not have full Lebesgue measure with an the closure of an open set of positive measure cannot be positive and finite. Analogues for $p$-adic fields and fields of formal power series over a finite field are established. The results are applied to some problems in metric Diophantine approximation.
We give an upper bound on the total variation distance between the linear eigenvalue statistic, properly scaled and centred, of a random matrix with a variance profile and the standard Gaussian random variable. The second order Poincar\'e inequality type result is used to establish the bound. Using this bound we prove Central limit theorem for linear eigenvalue statistics of random matrices with different kind of variance profiles. We re-establish some existing results on fluctuations of linear eigenvalue statistics of some well known random matrix ensembles by choosing appropriate variance profiles.
Let ${Z_n}_{n\ge 0}$ be a random walk with a negative drift and i.i.d. increments with heavy-tailed distribution and let $M=\sup_{n\ge 0}Z_n$ be its supremum. Asmussen & Kl{\"u}ppelberg (1996) considered the behavior of the random walk given that $M>x$, for $x$ large, and obtained a limit theorem, as $x\to\infty$, for the distribution of the quadruple that includes the time $\rtreg=\rtreg(x)$ to exceed level $x$, position $Z_{\rtreg}$ at this time, position $Z_{\rtreg-1}$ at the prior time, and the trajectory up to it (similar results were obtained for the Cram\'er-Lundberg insurance risk process). We obtain here several extensions of this result to various regenerative-type models and, in particular, to the case of a random walk with dependent increments. Particular attention is given to describing the limiting conditional behavior of $\tau$. The class of models include Markov-modulated models as particular cases. We also study fluid models, the Bj{\"o}rk-Grandell risk process, give examples where the order of $\tau$ is genuinely different from the random walk case, and discuss which growth rates are possible. Our proofs are purely probabilistic and are based on results and ideas from Asmussen, Schmidli & Schmidt (1999), Foss & Zachary (2002), and Foss, Konstantopoulos & Zachary (2007).
Small 3He-rich solar energetic particle (SEP) events with their anomalous abundances, markedly different from solar system, provide evidence for a unique acceleration mechanism that operates routinely near solar active regions. Although the events are sometimes accompanied by coronal mass ejections (CMEs) it is believed that mass and isotopic fractionation is produced directly in the flare sites on the Sun. We report on a large-scale extreme ultraviolet (EUV) coronal wave observed in association with 3He-rich SEP events. In the two examples discussed, the observed waves were triggered by minor flares and appeared concurrently with EUV jets and type III radio bursts but without CMEs. The energy spectra from one event are consistent with so-called class-1 (characterized by power laws) while the other with class-2 (characterized by rounded 3He and Fe spectra) 3He-rich SEP events, suggesting different acceleration mechanisms in the two. The observation of EUV waves suggests that large-scale disturbances, in addition to more commonly associated jets, may be responsible for the production of 3He-rich SEP events.
Using GALEX, UVOT and optical photometry, we explore the prevalence and strength of the UV-upturn in the spectra of quiescent early type galaxies in several nearby clusters. Even for galaxies with completely passive optical colours, there is a large spread in vacuum UV colour consistent with almost all having some UV upturn component. Combining GALEX and UVOT data below 3000\AA, we generate for the first time comparatively detailed UV SEDs for Coma cluster galaxies. Fitting the UV upturn component with a blackbody, twenty six of these show a range of characteristic temperatures (10000--21000K) for the UV upturn population. Assuming a single temperature to explain GALEX-optical colours could underestimate the fraction of galaxies with UV upturns and mis-classify some as systems with residual star formation. The UV upturn phenomenon is not an exclusive feature found only in giant galaxies; we identify galaxies with similar (or even bluer) $FUV-V$ colours to the giants with upturns over a range of fainter luminosities. The temperature and strength of the UV upturn are correlated with galaxy mass. Under the plausible hypothesis that the sources of the UV upturn are blue horizontal branch stars, the most likely mechanism for this is the presence of a substantial (between 4\% and 20\%) Helium rich ($Y > 0.3$) population of stars in these galaxies, potentially formed at $z\sim 4$ and certainly at $z>2$; this plausibly sets a lower limit of $\sim {\rm 0.3 - 0.8} \times 10^{10}$ $M_{\odot}$ to the {\it in situ} stellar mass of $\sim L^*$ galaxies at this redshift.
Motivated by recent numerical results, we study the phase diagram of the Kane-Mele-Hubbard (KHM) model, especially the nature of its quantum critical points. The phase diagram of the Kane-Mele-Hubbard model can be understood by breaking the SO(4) symmetry of our previous work down to U(1)_spin x U(1)_charge x PH symmetry. The vortices of the inplane Neel phase carry charge, and the proliferation of the charged magnetic vortex drives the transition between the inplane Neel phase and the QSH insulator phase; this transition belongs to the 3d XY universality class. The transition between the liquid phase and the inplane Neel phase is an anisotropic O(4) transition, which eventually becomes first order due to quantum fluctuation. The liquid-QSH transition is predicted to be first order based on a 1/N calculation.
Incoherent photoproduction of pions on the deuteron in the first resonance region is investigated with special emphasis on single-spin asymmetries. For the elementary pion production operator an effective Lagrangian model which includes the standard pseudovector Born terms and a resonance contribution from the $\Delta$(1232)-excitation is used. Single-spin asymmetries, both for charged and neutral pion photoproduction on the deuteron, are analyzed and calculated for the first time in the first resonance region. The linear photon asymmetry $\Sigma$, vector target asymmetry $T_{11}$ and tensor target asymmetries $T_{20}$, $T_{21}$, and $T_{22}$ for the reaction $d(\gamma,\pi)NN$ are predicted for forthcoming experiments.
The Diels-Alder surface modified top epitaxial graphene layer, with newly created pair of sp3 carbon centres, results in abrupt minimization of interlayer van der Waals interactions between two stacked graphene planes, and escapes the wafer during post-reaction manipulation stage, leaving the layer under it almost pristine-like. Above picture shows Diels-Alder functionalized sp2/sp3 graphene adduct leaves the parent wafer. In this communication we systematically address several fundamental questions in graphene surface chemistry, which are of extreme importance for device fabrication, and in successful implementation of covalently modified graphene in electronics industry.
Negative differential resistance in electronic conduction has been extensively studied, but it is not the case for its thermal counterpart, namely, negative differential thermal resistance (NDTR). We present a classical Landauer formula in which the nonlinearity is incorporated by the self-consistent phonon theory in order to study the heat flux across a chain consisting of two weakly coupled lattices. Two typical nonlinear models of hard and soft on-site potentials are discussed, respectively. It is shown that the nonlinearity has strong impacts on the occurring of NDTR. As a result, a transition from the absence to the presence of NDTR is observed. The origin of NDTR consists in the competition between the temperature difference, which acts as an external field, and the temperature-dependent thermal boundary conductance. Finally, the onset of the transition is clearly illustrated for this model. Our analytical calculation agrees reasonably well with numerical simulations.
In this paper, we conduct a large-scale study of font statistics in book covers and online advertisements. Through the statistical study, we try to understand how graphic designers relate fonts and content genres and identify the relationship between font styles, colors, and genres. We propose an automatic approach to extract font information from graphic designs by applying a sequence of character detection, style classification, and clustering techniques to the graphic designs. The extracted font information is accumulated together with genre information, such as romance or business, for further trend analysis. Through our unique empirical study, we show that the collected font statistics reveal interesting trends in terms of how typographic design represents the impression and the atmosphere of the content genres.
The crossover among two or more types of diffusive processes represents a vibrant theme in nonequilibrium statistical physics. In this work we propose two models to generate crossovers among different L\'evy processes: in the first model we change gradually the order of the derivative in the Laplacian term of the diffusion equation, whereas in the second one we consider a combination of fractional-derivative diffusive terms characterized by coefficients that change in time.   The proposals are illustrated by considering semi-analytical (i.e., analytical together with numerical) procedures to follow the time-dependent solutions. We find changes between two different regimes and it is shown that, far from the crossover regime, both models yield qualitatively similar results, although these changes may occur in different forms for the two models. The models introduced herein are expected to be useful for describing crossovers among distinct diffusive regimes that occur frequently in complex systems.
We introduce the notion of microlocal versal deformation of a plane curve. We construct equisingular versal deformations of Legendrian curves that are the conormal of a semi-quasi-homogeneous branch.
We use observational measurements of thermal and kinetic Sunyaev-Zel'dovich effects, as well as soft X-ray emission associated with galaxy groups to constrain the gas density and temperature in the circumgalactic medium (CGM) for dark matter halos with masses above $10^{12.5}M_{\odot}$. A number of generic models are used together with a Bayesian scheme to make model inferences. We find that gas with a single temperature component cannot provide a consistent model to match the observational data. A simple two-phase model assuming a hot component and an ionized warm component can accommodate all the three observations. The total amount of the gas in individual halos is inferred to be comparable to the universal baryon fraction corresponding to the halo mass. The inferred temperature of the hot component is comparable to the halo virial temperature. The fraction of the hot component increases from $(15-40)\%$ for $10^{12.5}{M}_\odot$ halos to $(40-60)\%$ for $10^{14.5}{M}_\odot$ halos, where the ranges reflect uncertainties in the assumed gas density profile. Our results suggest that a significant fraction of the halo gas is in a non-thermalized component with temperature much lower than the virial temperature.
We derive exact results for the rate of change of thermodynamic quantities, in particular the configurational specific heat at constant volume, $C_V$, along configurational adiabats (curves of constant excess entropy $S_{\textrm{ex}}$). Such curves are designated isomorphs for so-called Roskilde liquids, in view of the invariance of various structural and dynamical quantities along them. Their slope in a double logarithmic representation of the density-temperature phase diagram, $\gamma$ can be interpreted as one third of an effective inverse power-law potential exponent. We show that in liquids where $\gamma$ increases (decreases) with density, the contours of $C_V$ have smaller (larger) slope than configurational adiabats. We clarify also the connection between $\gamma$ and the pair potential. A fluctuation formula for the slope of the $C_V$-contours is derived. The theoretical results are supported with data from computer simulations of two systems, the Lennard-Jones fluid and the Girifalco fluid. The sign of $d\gamma/d\rho$ is thus a third key parameter in characterizing Roskilde liquids, after $\gamma$ and the virial-potential energy correlation coefficient $R$. To go beyond isomorph theory we compare invariance of a dynamical quantity, the self-diffusion coefficient along adiabats and $C_V$-contours, finding it more invariant along adiabats.
In this paper we study the Gevrey smoothing effect of solutions to the non-cutoff spatially homogeneous and inhomogeneous Boltzmann equation for soft potential. We consider the mild singularity case $s<1/2$ as we did in the previous work for spatially homogeneous case (J. Diff. Equ. 253(4) (2012), 1172-1190. DOI: 10.1016/j.jde.2012.04.023) and for spatially inhomogeneous case (arXiv:1304.2971), and try to extend the range of $\gamma$. We derive a new coercivity estimate for collision operator, using which we can obtain the Gevrey regularity for $\gamma \in (-5/2,0)$ improving the previous assumption $\gamma \in (-1-2s,0)$. Besides, we consider $\gamma$ and $s$ separately instead of viewing $\gamma+2s$ as one untied quantity.
In this paper, we consider the Schr\"odinger equation with a mass-supercritical focusing nonlinearity, in the exterior of a smooth, compact, convex obstacle of $\R^{d}$ with Dirichlet boundary conditions. We prove that solutions with negative energy blow up in finite time. Assuming furthermore that the nonlinearity is energy-subcritical, we also prove (under additional symmetry conditions) blow-up with the same optimal ground-state criterion than in the work of Holmer and Roudenko on $\R^{d}$. The classical proof of Glassey, based on the concavity of the variance, fails in the exterior of an obstacle because of the appearance of boundary terms with an unfavorable sign in the second derivative of the variance. The main idea of our proof is to introduce a new modified variance which is bounded from below and strictly concave for the solutions that we consider.
It is shown that chiral perturbation theory (in its original form by Weinberg) can describe NN scattering with positive as well as negative effective range. Some issues connected with unnaturally large NN ^1S_0 scattering length are discussed.
We derive the spectrum of Kaluza-Klein descendants of string excitations on AdS_5 x S^5. String states are organized in long multiplets of the AdS supergroup SU(2,2|4,R) with a rich pattern of shortenings at the higher spin enhancement point \lambda=0. The string states holographically dual to the higher spin currents of SYM theory in the strict zero coupling limit are identified together with the corresponding Goldstone particles responsible for the Higgsing of the higher spin symmetry at \lambda\neq 0. Exploiting higher spin symmetry we propose a very simple yet effective mass formula and establish a one-to-one correspondence between the complete spectrum of \Delta_0 <= 4 string states and relevant/marginal single-trace deformations in N=4 SYM theory at large N. To this end, we describe how to efficiently enumerate scaling operators in `free' YM theory, with the inclusion of fermionic `letters', by resorting to Polya theory. Comparison between the spectra of 1/4-BPS states is also presented. Finally, we discuss how to organize the spectrum of N=4 SYM theory in SU(2,2|4,R) supermultiplets by means of some kind of `Eratostenes's sieve'.