ShantanuT01/DACTYL-Pretraining huggingface dataset:
V. Golyshev conjectured that for any smooth polytope P of dimension at most five, the roots $z\in\C$ of the Ehrhart polynomial for P have real part equal to -1/2. An elementary proof is given, and in each dimension the roots are described explicitly. We also present examples which demonstrate that this result cannot be extended to dimension six.
In this paper, we present results from long-term $V(RI)_{c}$ photometric observations of the pre-main-sequence stars V2764 Ori and LkH$\alpha$ 301, located in the field of the McNeil's Nebula within the Orion star-forming complex. Our observations were performed in the period from August 2004 to November 2021 with three telescopes and seven different types of CCD cameras. Photometric observations, especially concerning the long-term behavior of the stars, are missing in the literature. We present the first photometric monitoring for them, which cover 17 years. Our data indicate that the variability of both stars is typical for classical T Tauri stars.
The problem of counting derangements was initiated by Pierre Remonde de Motmort in 1708. A derangement is a permutation that has no fixed points and the derangement number Dn is the number of fixed point free permutations on an n element set. Furthermore, the derangement polynomials are natural extensions of the derangement numbers. In this paper, we study the derangement polynomials and numbers, their connections with cosine-derangement polynomials and sine-derangement polynomials and their applications to moments of some variants of gamma random variables.
The numerous results obtained with asteroseismology thanks to space missions such as CoRoT and Kepler are providing a new insight on stellar evolution. After five years of observations, CoRoT is going on providing high-quality data. We present here the analysis of the double star HD169392 complemented by ground-based spectroscopic observations. This work aims at characterizing the fundamental parameters of the two stars, their chemical composition, the acoustic-mode global parameters including their individual frequencies, and their dynamics. We have analysed HARPS observations of the two stars to retrieve their chemical compositions. Several methods have been used and compared to measure the global properties of acoustic modes and their individual frequencies from the photometric data of CoRoT. The new spectroscopic observations and archival astrometric values suggest that HD169392 is a wide binary system weakly bounded. We have obtained the spectroscopic parameters for both components, suggesting the origin from the same cloud. However, only the mode signature of HD169392 A has been measured within the CoRoT data. The signal-to-noise ratio of the modes in HD169392B is too low to allow any confident detection. We were able to extract mode parameters of modes for l=0, 1, 2, and 3. The study of the splittings and inclination angle gives two possible solutions with splittings and inclination angles of 0.4-1.0 muHz and 20-40 degrees for one case and 0.2-0.5 muHz and 55-86 degrees for the other case. The modeling of this star with the Asteroseismic Modeling Portal led to a mass of 1.15+/-0.01 Ms, a radius of 1.88+/-0.02 Rs, and an age of 4.33+/-0.12 Gyr, where the uncertainties are the internal ones.
We revisit the question of whether fluctuations in hydrodynamical, adiabatical matter could explain the observed structures in our Universe. We consider matter with variable equation of state $w=p_0/\ep_0$ and a concomitant (under the adiabatic assumption) density dependent speed of sound, $c_s$. We find a limited range of possibilities for a set up when modes start inside the Hubble radius, then leaving it and freezing out. For expanding Universes, power-law $w(\ep_0)$ models are ruled out (except when $c_s^2\propto w \ll 1$, requiring post-stretching the seeded fluctuations); but sharper profiles in $c_s$ do solve the horizon problem. Among these, a phase transition in $c_s$ is notable for leading to scale-invariant fluctuations if the initial conditions are thermal. For contracting Universes all power-law $w(\ep_0)$ solve the horizon problem, but only one leads to scale-invariance: $w\propto \ep_0^2$ and $c_s\propto \ep_0$. This model bypasses a number of problems with single scalar field cyclic models (for which $w$ is large but constant).
We consider the probability that a two-dimensional random walk starting from the origin never returns to the half-line $ (- \infty,0] \times {0}$ before time $n$. Let $X^{(1)}=(X_{1},X_{2})$ be the increment of the two-dimensional random walk. For an aperiodic random walk with moment conditions ($E[X_{2}]=0 $ and $ E[|X_{1}|^{\delta}]<\infty, E[|X_{2}|^{2+ \delta}]< \infty $ for some $ \delta \in (0,1)$), we obtain an asymptotic estimate (as $n \rightarrow \infty $) of this probability by assuming the behavior of the characteristic function of $X_{1}$ near zero.
A brief review of various numerical techniques used in loop quantum cosmology and results is presented. These include the way extensive numerical simulations shed insights on the resolution of classical singularities, resulting in the key prediction of the bounce at the Planck scale in different models, and the numerical methods used to analyze the properties of the quantum difference operator and the von Neumann stability issues. Using the quantization of a massless scalar field in an isotropic spacetime as a template, an attempt is made to highlight the complementarity of different methods to gain understanding of the new physics emerging from the quantum theory. Open directions which need to be explored with more refined numerical methods are discussed.
We have searched for dust in an optical sample of 910 Early-Type Galaxies (ETG) in the Virgo cluster (447 of which are optically complete at m_pg <= 18.0), extending also to the dwarf ETG, using Herschel images at 100, 160, 250, 350 and 500 microns. Dust was found in 52 ETG (46 are in the optically complete sample), including M87 and another 3 ETG with strong synchrotron emisssion. Dust is detected in 17% of ellipticals, 41% of lenticulars, and in about 4% of dwarf ETG. The dust-to-stars mass ratio increases with decreasing optical luminosity, and for some dwarf ETG reaches values similar to those of the dusty late-type galaxies. Slowly rotating ETG are more likely to contain dust than fast rotating ones. Only 8 ETG have both dust and HI, while 39 have only dust and 8 have only HI, surprisingly showing that only rarely dust and HI survive together. ETG with dust appear to be concentrated in the densest regions of the cluster, while those with HI tend to be at the periphery. ETG with an X-ray active SMBH are more likely to have dust and vice versa the dusty ETG are more likely to have an active SMBH.
Sr2IrO4 is a magnetic insulator driven by spin-orbit interaction (SOI) whereas the isoelectronic and isostructural Sr2RhO4 is a paramagnetic metal. The contrasting ground states have been shown to result from the critical role of the strong SOI in the iridate. Our investigation of structural, transport, magnetic and thermal properties reveals that substituting 4d Rh4+ (4d5) ions for 5d Ir4+(5d5) ions in Sr2IrO4 directly reduces the SOI and rebalances the competing energies so profoundly that it generates a rich phase diagram for Sr2Ir1-xRhxO4 featuring two major effects: (1) Light Rh doping (0\leqx\leq0.16) prompts a simultaneous and precipitous drop in both the electrical resistivity and the magnetic ordering temperature TC, which is suppressed to zero at x = 0.16 from 240 K at x=0. (2) However, with heavier Rh doping (0.24< x<0.85 (\pm0.05)) disorder scattering leads to localized states and a return to an insulating state with spin frustration and exotic magnetic behavior that only disappears near x=1. The intricacy of Sr2Ir1-xRhxO4 is further highlighted by comparison with Sr2Ir1-xRuxO4 where Ru4+(4d4) drives a direct crossover from the insulating to metallic states.
In a recent Letter [Phys. Rev. Lett. {\bf 100}, 120501 (2008)], Avron {\em et al.} discuss a time reordering scheme to achieve efficient "across-generation" of entangled photon pairs in a semiconductor quantum dot with a suppressed biexciton binding energy. They demonstrate that the scheme can be implemented using time delay between the generated photons. In this Comment, we derive an exact expression for the concurrence of the time delayed photons, and show that the predicted values by Avron {\em et al.} are not achievable, which stems from an approximation used in their approximate theoretical analysis.
The observation of a SM-like Higgs boson in multiple channels at the LHC allows the extraction of Higgs couplings to gauge bosons and fermions. The precision achievable at the LHC, for an integrated luminosity of 200 fb^{-1}, is reviewed and updated.
Let S be a K3 surface. In part I of this paper, we constructed a representation of the group Aut D(S), of auto-equivalences of the derived category of S. We interpreted this infinite dimensional representation, as the natural action of Aut D(S) on the cohomology of all moduli spaces of stable sheaves (with primitive Mukai vectors) on S. The main result, of part I, is the precise relation of this action with the monodromy of the Hilbert schemes S^[n] of points on the surface. The proof of the above result was reduced, in part I, to the case of two monodromy operators of S^[n], associated with choices of line bundles on the surface S, of degree 2n-4 and 2n respectively. When n=1, the first sequence of monodromy operators specializes to the reflection by a -2 curve. The n=1 case of the second sequence is related to the Galois involution, of a double cover of the projective plane, branched along a sextic. We complete the proof by treating these two sequences of examples.
Content-based image retrieval (CBIR) is one of the most active research areas in multimedia information retrieval. Given a query image, the task is to search relevant images in a repository. Low level features like color, texture, and shape feature vectors of an image are always considered to be an important attribute in CBIR system. Thus the performance of the CBIR system can be enhanced by combining these feature vectors. In this paper, we propose a novel CBIR framework by applying to index using multiclass SVM and finding the appropriate weights of the individual features automatically using the relevance ratio and mean difference. We have taken four feature descriptors to represent color, texture and shape features. During retrieval, feature vectors of query image are combined, weighted and compared with feature vectors of images in the database to rank order the results. Experiments were performed on four benchmark datasets and performance is compared with existing techniques to validate the superiority of our proposed framework.
We present a search for CO(1->0) emission in three Local Group dwarf irregular galaxies: IC5152, the Phoenix dwarf, and UGCA438, using the ATNF Mopra radio telescope. Our scans largely cover the optical extent of the galaxies and the stripped HI cloud West of the Phoenix dwarf. Apart from a tentative but non-significant emission peak at one position in the Phoenix dwarf, no significant emission was detected in the CO spectra of these galaxies. For a velocity width of 6 km/s, we derive 4sigma upper limits of 0.03 K km/s, 0.04 K km/s and 0.06 K km/s for IC5152, the Phoenix dwarf and UGCA438, respectively. This is an improvement of over a factor of 10 compared with previous observations of IC5152; the other two galaxies had not yet been observed at millimeter wavelengths. Assuming a Galactic CO-to-H_2 conversion factor, we derive upper limits on the molecular gas mass of 6.2 x 10^4 M_sun, 3.7 x 10^3 M_sun and 1.4 x 10^5 M_sun for IC5152, the Phoenix dwarf and UGCA438, respectively. We investigate two possible causes for the lack of CO emission in these galaxies. On the one hand, there may be a genuine lack of molecular gas in these systems, in spite of the presence of large amounts of neutral gas. However, in the case of IC5152 which is actively forming stars, molecular gas is at least expected to be present in the star forming regions. On the other hand, there may be a large increase in the CO-to-H_2 conversion factor in very low-metallicity dwarfs (-2 <= [Fe/H] <= -1), making CO a poor tracer of the molecular gas content in dwarf galaxies.
In this paper a class of Ornstein--Uhlenbeck processes driven by compound Poisson processes is considered. The jumps arrive with exponential waiting times and are allowed to be two-sided. The jumps are assumed to form an iid sequence with distribution a mixture (not necessarily convex) of exponential distributions, independent of everything else. The fact that downward jumps are allowed makes passage of a given lower level possible both by continuity and by a jump. The time of this passage and the possible undershoot (in the jump case) is considered. By finding partial eigenfunctions for the infinitesimal generator of the process, an expression for the joint Laplace transform of the passage time and the undershoot can be found.   From the Laplace transform the ruin probability of ever crossing the level can be derived. When the drift is negative this probability is less than one and its asymptotic behaviour when the initial state of the process tends to infinity is determined explicitly.   The situation where the level to cross decreases to minus infinity is more involved: The level to cross plays a much more fundamental role in the expression for the joint Laplace transform than the initial state of the process. The limit of the ruin probability in the positive drift case and the limit of the distribution of the undershoot in the negative drift case is derived.
The critical behavior of a complex N-component order parameter Ginzburg-Landau model with isotropic and cubic interactions describing antiferromagnetic and structural phase transitions in certain crystals with complicated ordering is studied in the framework of the four-loop renormalization group (RG) approach in $(4-\ve)$ dimensions. By using dimensional regularization and the minimal subtraction scheme, the perturbative expansions for RG functions are deduced and resummed by the Borel-Leroy transformation combined with a conformal mapping. Investigation of the global structure of RG flows for the physically significant cases N=2 and N=3 shows that the model has an anisotropic stable fixed point governing the continuous phase transitions with new critical exponents. This is supported by the estimate of the critical dimensionality $N_c=1.445(20)$ obtained from six loops via the exact relation $N_c={1/2} n_c$ established for the complex and real hypercubic models.
We present a bundle-adjustment-based algorithm for recovering accurate 3D human pose and meshes from monocular videos. Unlike previous algorithms which operate on single frames, we show that reconstructing a person over an entire sequence gives extra constraints that can resolve ambiguities. This is because videos often give multiple views of a person, yet the overall body shape does not change and 3D positions vary slowly. Our method improves not only on standard mocap-based datasets like Human 3.6M -- where we show quantitative improvements -- but also on challenging in-the-wild datasets such as Kinetics. Building upon our algorithm, we present a new dataset of more than 3 million frames of YouTube videos from Kinetics with automatically generated 3D poses and meshes. We show that retraining a single-frame 3D pose estimator on this data improves accuracy on both real-world and mocap data by evaluating on the 3DPW and HumanEVA datasets.
It has previously been shown [W. Rudnicki, Phys. Lett. A 224, 45 (1996)] that a generic gravitational collapse cannot result in a naked singularity accompanied by closed timelike curves. An important role in this result plays the so-called inextendibility condition, which is required to hold for certain incomplete null geodesics. In this paper, a theorem is proved that establishes some relations between the inextendibility condition and the rate of growth of the Ricci curvature along incomplete null geodesics. This theorem shows that the inextendibility condition may hold for a much more general class of singularities than only those of the strong curvature type. It is also argued that some earlier cosmic censorship results obtained for strong curvature singularities can be extended to singularities corresponding to the inextendibility condition.
We investigate the Mott transition in the anisotropic kagom\'e lattice Hubbard model using the cellular dynamical mean field theory combined with continuous-time quantum Monte Carlo simulations. By calculating the double occupancy and the density of states, we determine the interaction strength of the first-order Mott transition and show that it becomes small as the anisotropy increases. We also calculate the spin correlation functions and the single-particle spectrum, and reveal that the quasiparticle and magnetic properties change dramatically around the Mott transition; the spin correlations are strongly enhanced and the quasiparticle bands are deformed. We conclude that such dramatic changes are due to the enhancement of anisotropy associated with the relaxation of frustration around the Mott transition.
We investigate the geodesic motion in the background of Kerr-Sen Black Hole arising in the heterotic string theory. The nature of effective potential is discussed in radial as well as latitudinal direction. A special class of spherical photon orbits is obtained along with the expression for the turning point for radial photons. Dependence of photon motion within this class of solution is discussed explicitly in view of the different Black Hole parameters. We have discussed the allowed regions for geodesic motion of massless test particles around Kerr- Sen Black Hole in more generalised way by including non-equatorial motion of the photons into the account. The conditions for different types of possible orbits are discussed with specific parameter values along with the corresponding orbit structure. No terminating orbits are possible for photons due to non-zero Black Hole charge. Observables on the angular plane (viz. bending of light and perihelion precession for massive test particles) are analysed as special cases. We have also calculated the rotation and mass parameters for Kerr-Sen Black Hole in terms of the red/blue shifts of the photons in circular and equatorial orbits emitted by the massive test particles which represent stars or other probable sources of photons.
The two-dimensional dense O(n) loop model for $n=1$ is equivalent to the bond percolation and for $n=0$ to the dense polymers or spanning trees. We consider the boundary correlations on the half space and calculate the probability $P_b$ that a cluster of bonds has a single common point with the boundary. In the limit $n\rightarrow 0$, we find an analytical expression for $P_b$ using the generalized Kirchhoff theorem.
In this paper the three-dimensional divisorial contractions $f\colon Y\to (X\ni P)$ are classified provided that $\Exc f=E$ is an irreducible divisor, $f(E)=P$, the variety $Y$ has canonical singularities and $(X\ni P)$ is a toric terminal singularity.
We give sharp regularity conditions, ensuring the backward uniquess property to a class of parabolic operators.
We consider QCD radiative corrections to the production of four charged leptons in hadron collisions. We present the computation of the next-to-leading order QCD corrections to the loop-induced gluon fusion contribution. Our predictions include, for the first time, also the quark-gluon partonic channels. The computed corrections, which are formally of ${\cal O}(\alpha_{\rm s}^3)$, turn out to increase the loop-induced Born-level result by an amount ranging from 75% to 71% as $\sqrt{s}$ ranges from 8 to 13 TeV. We combine our result with state-of-the-art NNLO corrections to the quark annihilation channel, and present updated predictions for fiducial cross sections and distributions for this process.
Recent works have advanced the performance of self-supervised representation learning by a large margin. The core among these methods is intra-image invariance learning. Two different transformations of one image instance are considered as a positive sample pair, where various tasks are designed to learn invariant representations by comparing the pair. Analogically, for video data, representations of frames from the same video are trained to be closer than frames from other videos, i.e. intra-video invariance. However, cross-video relation has barely been explored for visual representation learning. Unlike intra-video invariance, ground-truth labels of cross-video relation is usually unavailable without human labors. In this paper, we propose a novel contrastive learning method which explores the cross-video relation by using cycle-consistency for general image representation learning. This allows to collect positive sample pairs across different video instances, which we hypothesize will lead to higher-level semantics. We validate our method by transferring our image representation to multiple downstream tasks including visual object tracking, image classification, and action recognition. We show significant improvement over state-of-the-art contrastive learning methods. Project page is available at https://happywu.github.io/cycle_contrast_video.
The method of spectral decimation is applied to an infinite collection of self--similar fractals. The sets considered belong to the class of nested fractals, and are thus very symmetric. An explicit construction is given to obtain formulas for the eigenvalues of the Laplace operator acting on these fractals.
Deep networks have been successfully applied to visual tracking by learning a generic representation offline from numerous training images. However the offline training is time-consuming and the learned generic representation may be less discriminative for tracking specific objects. In this paper we present that, even without offline training with a large amount of auxiliary data, simple two-layer convolutional networks can be powerful enough to develop a robust representation for visual tracking. In the first frame, we employ the k-means algorithm to extract a set of normalized patches from the target region as fixed filters, which integrate a series of adaptive contextual filters surrounding the target to define a set of feature maps in the subsequent frames. These maps measure similarities between each filter and the useful local intensity patterns across the target, thereby encoding its local structural information. Furthermore, all the maps form together a global representation, which is built on mid-level features, thereby remaining close to image-level information, and hence the inner geometric layout of the target is also well preserved. A simple soft shrinkage method with an adaptive threshold is employed to de-noise the global representation, resulting in a robust sparse representation. The representation is updated via a simple and effective online strategy, allowing it to robustly adapt to target appearance variations. Our convolution networks have surprisingly lightweight structure, yet perform favorably against several state-of-the-art methods on the CVPR2013 tracking benchmark dataset with 50 challenging videos.
We discuss the impact of recent Belle data on our description of the pion transition form factor based on the assumption that a perturbative formalism and a nonperturbative one can be matched in a physically acceptable manner at a certain hadronic scale $Q_{0}$. We discuss the implications of the different parameters of the model in comparing with world data and conclude that within experimental errors our description remains valid. Thus we can assert that the low $Q^2$ nonperturbative description together with an additional $1/Q^2$ term at the matching scale have a strong influence on the $Q^2$ behavior up to very high values of $Q^2$ .