ShantanuT01/DACTYL-Pretraining huggingface dataset:
The competition graph of a digraph $D$ is a (simple undirected) graph which has the same vertex set as $D$ and has an edge between two distinct vertices $x$ and $y$ if and only if there exists a vertex $v$ in $D$ such that $(x,v)$ and $(y,v)$ are arcs of $D$. For any graph $G$, $G$ together with sufficiently many isolated vertices is the competition graph of some acyclic digraph. The competition number $k(G)$ of a graph $G$ is the smallest number of such isolated vertices. Computing the competition number of a graph is an NP-hard problem in general and has been one of the important research problems in the study of competition graphs. Opsut [1982] showed that the competition number of a graph $G$ is related to the edge clique cover number $\theta_E(G)$ of the graph $G$ via $\theta_E(G)-|V(G)|+2 \leq k(G) \leq \theta_E(G)$. We first show that for any positive integer $m$ satisfying $2 \leq m \leq |V(G)|$, there exists a graph $G$ with $k(G)=\theta_E(G)-|V(G)|+m$ and characterize a graph $G$ satisfying $k(G)=\theta_E(G)$. We then focus on what we call \emph{competitively tight graphs} $G$ which satisfy the lower bound, i.e., $k(G)=\theta_E(G)-|V(G)|+2$. We completely characterize the competitively tight graphs having at most two triangles. In addition, we provide a new upper bound for the competition number of a graph from which we derive a sufficient condition and a necessary condition for a graph to be competitively tight.
The most common statistic used to analyze large-scale structure surveys is the correlation function, or power spectrum. Here, we show how `slicing' the correlation function on local density brings sensitivity to interesting non-Gaussian features in the large-scale structure, such as the expansion or contraction of baryon acoustic oscillations (BAO) according to the local density. The sliced correlation function measures the large-scale flows that smear out the BAO, instead of just correcting them as reconstruction algorithms do. Thus, we expect the sliced correlation function to be useful in constraining the growth factor, and modified gravity theories that involve the local density. Out of the studied cases, we find that the run of the BAO peak location with density is best revealed when slicing on a $\sim 40$ Mpc/$h$ filtered density. But slicing on a $\sim100$ Mpc/$h$ filtered density may be most useful in distinguishing between underdense and overdense regions, whose BAO peaks are separated by a substantial $\sim 5$ Mpc/$h$ at $z=0$. We also introduce `curtain plots' showing how local densities drive particle motions toward or away from each other over the course of an $N$-body simulation.
The exciton spin dynamics and polarization properties of the related emission are investigated in colloidal CdSe/CdS dot-in-rod (DiR) and spherical core/shell nanocrystal (NC) ensembles by magneto-optical photoluminescence (PL) spectroscopy in magnetic fields up to 15 T. It is shown that the degree of circular polarization (DCP) of the exciton emission induced by the magnetic field is affected by the NC geometry as well as the exciton fine structure and can provide information on nanorod orientation. A theory to describe the circular and linear polarization properties of the NC emission in magnetic field is developed. It takes into account phonon mediated coupling between the exciton fine structure states as well as the dielectric enhancement effect resulting from the anisotropic shell of DiR NCs. This theoretical approach is used to model the experimental results and allows us to explain most of the measured features. The spin dynamics of the dark excitons is investigated in magnetic fields by time-resolved photoluminescence. The results highlight the importance of confined acoustic phonons in the spin relaxation of dark excitons. The bare core surface as well as the core/shell interface give rise to an efficient spin relaxation channel, while the surface of core/shell NCs seems to play only a minor role.
One of the most important problems in regression-based error model is modeling the complex representation error caused by various corruptions and environment changes in images. For example, in robust face recognition, images are often affected by varying types and levels of corruptions, such as random pixel corruptions, block occlusions, or disguises. However, existing works are not robust enough to solve this problem due to they cannot model the complex corrupted errors very well. In this paper, we address this problem by a unified sparse weight learning and low-rank approximation regression model, which enables the random noises and contiguous occlusions in images to be treated simultaneously. For the random noise, we define a generalized correntropy (GC) function to match the error distribution. For the structured error caused by occlusions or disguises, we propose a GC function based rank approximation to measure the rank of error matrices. Since the proposed objective function is non-convex, an effective iterative optimization algorithm is developed to achieve the optimal weight learning and low-rank approximation. Extensive experimental results on three public face databases show that the proposed model can fit the error distribution and structure very well, thus obtain better recognition accuracies in comparison with the existing methods.
A spherically symmetric hydrodynamic stellar core collapse under gravity is time-dependent and may become unstable once disturbed. Specifically for a homologously collapse of stellar core characterized by a polytropic exponent \Gamma=4/3, we examine oscillations and/or instabilities of three dimensional (3D) general polytropic perturbations. For compressible 3D perturbations, the polytropic index \gamma of perturbations can differ from \Gamma=4/3 of the general polytropic hydrodynamic background flow. Our model formulation here is more general and allows the existence of internal gravity g(-)-modes and/or g(+)-modes. Eigenvalues and eigen-functions of various oscillatory and unstable perturbation modes are computed. As studied in several specialized cases of Goldreich & Weber and of Cao & Lou, we further confirm that acoustic p-modes and surface f-modes remain stable in the current more general situations. In comparison, g(-)-modes and sufficiently high radial order g(+)-modes are unstable, leading to inevitable convective motions within the collapsing stellar interior. Unstable growths of 3D g-mode disturbances are governed dominantly by the angular momentum conservation and modified by the gas pressure restoring force. We note in particular that unstable temporal growths of 3D vortical perturbations exist even when the specific entropy distribution becomes uniform and \gamma=\Gamma=4/3. Conceptually, unstable g-modes might bear conceivable physical consequences on supernova explosions, the initial kicks of nascent proto-neutron stars (PNSs) and break-ups of the collapsing core, while unstable growths of vortical perturbations can lead to fast spins of compact objects and other relevant results.
We use Chandra X-ray and Spitzer infrared observations to explore the AGN and starburst populations of XMMXCS J2215.9-1738 at z=1.46, one of the most distant spectroscopically confirmed galaxy clusters known. The high resolution X-ray imaging reveals that the cluster emission is contaminated by point sources that were not resolved in XMM observations of the system, and have the effect of hardening the spectrum, leading to the previously reported temperature for this system being overestimated. From a joint spectroscopic analysis of the Chandra and XMM data, the cluster is found to have temperature T=4.1_-0.9^+0.6 keV and luminosity L_X=(2.92_-0.35^+0.24)x10^44 erg/s extrapolated to a radius of 2 Mpc. As a result of this revised analysis, the cluster is found to lie on the sigma_v-T relation, but the cluster remains less luminous than would be expected from self-similar evolution of the local L_X-T relation. Two of the newly discovered X-ray AGN are cluster members, while a third object, which is also a prominent 24 micron source, is found to have properties consistent with it being a high redshift, highly obscured object in the background. We find a total of eight >5 sigma 24 micron sources associated with cluster members (four spectroscopically confirmed, and four selected using photometric redshifts), and one additional 24 micron source with two possible optical/near-IR counterparts that may be associated with the cluster. Examining the IRAC colors of these sources, we find one object is likely to be an AGN. Assuming that the other 24 micron sources are powered by star formation, their infrared luminosities imply star formation rates ~100 M_sun/yr. We find that three of these sources are located at projected distances of <250 kpc from the cluster center, suggesting that a large amount of star formation may be taking place in the cluster core, in contrast to clusters at low redshift.
This paper focuses on a comparison of the space densities of FRI and FRII sources at different epochs, with a particular focus on FRI sources. First, we present the concluding steps in constructing the Combined NVSS-FIRST Galaxy catalogue (CoNFIG), including new VLA observations, optical identifications and redshift estimates. The final catalogue consists of 859 sources over 4 samples (CoNFIG-1, 2, 3 and 4 with flux density limits of S_1.4GHz = 1.3, 0.8, 0.2 and 0.05 Jy respectively). It is 95.7% complete in radio morphology classification and 74.3% of the sources have redshift data. Combining CoNFIG with complementary samples, the distribution and evolution of FRI and FRII sources are investigated. We find that FRI sources undergo mild evolution and that, at the same radio luminosity, FRI and FRII sources show similar space density enhancements in various redshift ranges, possibly implying a common evolution.
We consider SUSY sine-Gordon theory in the framework of perturbed conformal field theory. Using an argument from Zamolodchikov, we obtain the vacuum structure and the kink adjacency diagram of the theory, which is cross-checked against the exact S matrix prediction, first-order perturbed conformal field theory (PCFT), the NLIE method and truncated conformal space approach. We provide evidence for consistency between the usual Lagrangian description and PCFT on the one hand, and between PCFT, NLIE and a massgap formula conjectured by Baseilhac and Fateev, on the other. In addition, we extend the NLIE description to all the vacua of the theory.
The observations of the Kepler space telescope revealed that fundamental-mode RR Lyrae stars may show various radial overtones. The presence of multiple radial modes may allow us to conduct nonlinear asteroseismology: comparison of mode amplitudes and frequency shifts between observations and models. Here we report the detection of three radial modes in the star RR Lyr, the eponym of the class, using the Kepler short cadence data: besides the fundamental mode, both the first and the ninth overtones can be derived from the data set. RR Lyrae shows period doubling, but switches occasionally to a state where a pattern of six pulsation cycles repeats instead of two. We found hydrodynamic models that show the same three modes and the period-six state, allowing for comparison with the observations.
A magnetic skyrmion isusually refers to a twisted spin texture surrounded by uniformly aligned out-of-plane spinsin the background of a uniformly magnetized state. The invariance of the magnetic skyrmion conserves its topological charge under any continuous transformations of the spin textures, leads to which represents the robustness of a magnetic skyrmion their texture against external perturbations, making it ideal to use skyrmions as . Such a behaviour is required for an ideal information carriers. To date, most magnetic skyrmion studies have been performedfocused on in perpendicularly magnetized systems, where the skyrmion topological number is determined by the relative orientation between the core and /outer perpendicular magnetization directions of the skyrmion is either up/down or down/up. Here we show that there also exists a new type of magnetic skyrmion with surrounding spins to be uniformly aligned to the in-plane direction. By continuous transformation and relaxation of the spin textures of out-of-plane skyrmions, we showed that an in-plane skyrmion, where the background magnetization is in the in-plane direction, is also possible. Different from the conventional perpendicular magnetic skyrmionsContrary to the skyrmions in a perpendicularly magnetized state, the in-plane magnetic skyrmions with opposite signs of topological charges can inherentlycharges can inherently coexist in the in-plane magnetization system coexist. Moreover, the iIn-plane skyrmions of opposite charge can move together by an electric current and exhibit with an opposite spin Hall effect. These findings showdemonstrate the inherent possibility of a double-bit transfer in a single magnetic wire that is not possible in a perpendicularly magnetized system.
We present medium resolution (1000) K-band spectra of 12 post-AGB candidates and related stars. For several objects in our sample, these spectra were obtained for the first time. The Br$\gamma$ line in emission is detected in seven objects indicating the onset of photo-ionization in these objects. Four objects show the presence of He i line. We detect H2 emission line in the spectra of IRAS 06556+1623, IRAS 22023+5249, IRAS 18062+2410 and IRAS 20462+3416. H2 emission line ratio 1-0 S(1)/2-1 S(1) indicate that H2 is radiatively excited due to the UV radiation of hot post-AGB central stars. When compared with the recent observations by other investigators, the Br$\gamma$ and H2 emission fluxes varied in some of the objects. The hot post-AGB stars IRAS 22495+5134, IRAS 22023+5249, IRAS 18062+2410 and IRAS 20462+3416 seem to be evolving rapidly to young low excitation planetary nebula phase. The spectra of the objects presented in this paper may be useful for future observers as some of these stars show spectral variation and since the post-AGB evolution of some of these stars is relatively rapid.
We have measured the scattering timescale, $\tau$, and the scattering spectral index, $\alpha$, for 84 single-component pulsars. Observations were carried out with the MeerKAT telescope as part of the Thousand-Pulsar-Array programme in the MeerTime project at frequencies between 0.895 and 1.670 GHz. Our results give a distribution of values for $\alpha$ (defined in terms of $\tau$ and frequency $\nu$ as $\tau\propto\nu^{-\alpha}$) for which, upon fitting a Gaussian, we obtain a mean and standard deviation of $\langle\alpha\rangle = 4.0 \pm 0.6$. This is due to our identification of possible causes of inaccurate measurement of $\tau$, which, if not filtered out of modelling results, tend to lead to underestimation of $\alpha$. The pulsars in our sample have large dispersion measures and are therefore likely to be distant. We find that a model using an isotropic scatter broadening function is consistent with the data, likely due to the averaging effect of multiple scattering screens along the line of sight. Our sample of scattering parameters provides a strong data set upon which we can build to test more complex and time-dependent scattering phenomena, such as extreme scattering events.
We report on mid-IR observations of the central region in the Trifid nebula, carried out with ISOCAM in several broad-band infrared filters and in the low resolution spectroscopic mode provided by the circular variable filter. Analysis of the emission indicates the presence of a hot dust component (500 to 1000 K) and a warm dust component at lower temperatures (150-200 K) around several members of the cluster exciting the HII region, and other stars undetected at optical wavelengths. Complementary VLA observations suggest that the mid-IR emission could arise from a dust cocoon or a circumstellar disk, evaporated under the ionization of the central source and the exciting star of the nebula. In several sources the $9.7\mu m$ silicate band is seen in emission. One young stellar source shows indications of crystalline silicates in the circumstellar dust.
In this work we present the homogenization of a reaction-diffusion model that includes an evolving microstructure. Such type of problems model, for example, mineral dissolution and precipitation in a porous medium. Hence, we are dealing with a multi-scale problem with free boundaries on the pore scale. In the initial state the microscopic geometry is given by a periodically perforated domain, including spherical solid grains. The radius of each grain is of order $\epsilon$ and depends on the unknown (the solute concentration) at its surface. Therefore the radii of the grains change in time, leading to a nonlinear, free boundary problem. In a first step, we transform the evolving micro domain to a fixed, periodically domain. Using the Rothe-method we prove the existence of a weak solution and obtain a priori estimates that are uniform with respect to $\epsilon$. Finally, letting $\epsilon \to 0$, we derive a macroscopic model, the solution of which approximates the micro-scale solution. For this, we use the method of two-scale convergence, and obtain strong compactness results enabling to pass to the limit in the nonlinear terms.
We exhibit an analogy between the problem of pushing forward measurable sets under measure preserving maps and linear relaxations in combinatorialoptimization. We show how invariance of hyperfiniteness of graphings under local isomorphism can be reformulated as an infinite version of a natural combinatorial optimization problem, and how one can prove it by extending well-known proof techniques (linear relaxation, greedy algorithm, linear programming duality) from the finite case to the infinite.
We present the results of the first joint search for gravitational-wave bursts by the LIGO and GEO600 detectors. We search for bursts with characteristic central frequencies in the band 768 to 2048 Hz in the data acquired between the 22nd of February and the 23rd of March, 2005 (fourth LSC Science Run - S4). We discuss the inclusion of the GEO600 data in the Waveburst-CorrPower pipeline that first searches for coincident excess power events without taking into account differences in the antenna responses or strain sensitivities of the various detectors. We compare the performance of this pipeline to that of the coherent Waveburst pipeline based on the maximum likelihood statistic. This likelihood statistic is derived from a coherent sum of the detector data streams that takes into account the antenna patterns and sensitivities of the different detectors in the network. We find that the coherentWaveburst pipeline is sensitive to signals of amplitude 30 - 50% smaller than the Waveburst-CorrPower pipeline. We perform a search for gravitational-wave bursts using both pipelines and find no detection candidates in the S4 data set when all four instruments were operating stably.
Human activity recognition and analysis has always been one of the most active areas of pattern recognition and machine intelligence, with applications in various fields, including but not limited to exertion games, surveillance, sports analytics and healthcare. Especially in Human-Robot Interaction, human activity understanding plays a crucial role as household robotic assistants are a trend of the near future. However, state-of-the-art infrastructures that can support complex machine intelligence tasks are not always available, and may not be for the average consumer, as robotic hardware is expensive. In this paper we propose a novel action sequence encoding scheme which efficiently transforms spatio-temporal action sequences into compact representations, using Mahalanobis distance-based shape features and the Radon transform. This representation can be used as input for a lightweight convolutional neural network. Experiments show that the proposed pipeline, when based on state-of-the-art human pose estimation techniques, can provide a robust end-to-end online action recognition scheme, deployable on hardware lacking extreme computing capabilities.
By using the Grothendieck-Riemann-Roch theorem we derive cycle relations modulo algebraic equivalence in the Jacobian of a curve. The relations generalize the relations found by Colombo and van Geemen and are analogous to but simpler than the relations recently found by Herbaut. In an appendix due to Zagier it is shown that these sets of relations are equivalent.
Gravitational collapse of a massless scalar field with the periodic boundary condition in a cubic box is reported. This system can be regarded as a lattice universe model. We construct the initial data for a Gaussian like profile of the scalar field taking the integrability condition associated with the periodic boundary condition into account. For a large initial amplitude, a black hole is formed after a certain period of time. While the scalar field spreads out in the whole region for a small initial amplitude. It is shown that the expansion law in a late time approaches to that of the radiation dominated universe and the matter dominated universe for the small and large initial amplitude cases, respectively. For the large initial amplitude case, the horizon is initially a past outer trapping horizon, whose area decreases with time, and after a certain period of time, it turns to a future outer trapping horizon with the increasing area.
An ideal quantum walk transitions from one vertex to another with perfect fidelity, but in physical systems, the particle may be hindered by potential energy barriers. Then the particle has some amplitude of tunneling through the barriers, and some amplitude of staying put. We investigate the algorithmic consequence of such barriers for the quantum walk formulation of Grover's algorithm. We prove that the failure amplitude must scale as $O(1/\sqrt{N})$ for search to retain its quantum $O(\sqrt{N})$ runtime; otherwise, it searches in classical $O(N)$ time. Thus searching larger "databases" requires increasingly reliable hop operations or error correction. This condition holds for both discrete- and continuous-time quantum walks.
Two-qubit Bell-diagonal states can be depicted as a tetrahedron in three dimensions. We investigate the structure of quantum resources, including coherence and quantum discord, in the tetrahedron. The ordering of different resources measures is a common problem in resource theories, and which measure should be chosen to investigate the structure of resources is still an open question. We consider the structure of quantum resources which is not affected by the choice of measure. Our work provides a complete structure of coherence and quantum discord for Bell-diagonal states. The pictorial approach also indicates how to explore the structure of resources even when we don't have consistent measure of a concrete quantum resource.
In this paper, we study a dissipative dynamical system non linear of second order $ \ddot{x}(t)+\lambda(t)\, \dot{x}(t)+\nabla \Phi (x(t))=0,$ with the non-negative friction coefficient $\lambda \in \mathcal{C}([0,+\infty[)$ and the internal constraint $\Phi \in \mathcal{C}^2$.
We give a simple algorithm that enables us to determine whether a subgroup of finite index of the Hecke group is normal.
We prove global Sobolev regularity and pointwise upper bounds for the gradient of transition densities associated with second order differential operators in $\mathbb{R}^d$ with unbounded diffusion, drift and potential terms.
In this article, we describe a geometric method to study cusp forms, which relies on heat kernel and Bergman kernel analysis. This new approach of applying techniques coming from analytic geometry is based on the micro-local analysis of the heat kernel and the Bergman kernel in \cite{bouche} and \cite{berman}, respectively, using which we derive sup-norm bounds for cusp forms of integral weight, half-integral weight, and real weight associated to a Fuchsian subgroup of first kind.