ShantanuT01/DACTYL-Pretraining huggingface dataset:
Intuitively speaking, a bipartite graph is mirror if it can be drawn in the Cartesian plane in such a way that, the vertices of one stable are points in x=0, the vertices of the other stable set are points in x=1, the edges are straight line segments joining adjacent vertices and the resulting configuration is symmetric with respect to the line x=1/2. The concept of mirror bipartite graph appears naturally when studying certain types of products of graphs as for instance the Kronecker product. Motivated by this fact, we study mirror bipartite graphs from the point of view of their degree sequences and of their degree sets. We characterize the sequences of degrees of mirror bipartite graphs. We also show that from a given set P of positive integers, we can construct a bipartite graph of order 2max P, which is mirror. Furthermore, very little is known for the degree sequences of graphs with loops attached, when the number of loops attached is limited. We show in this paper that mirror bipartite graphs constitute a powerful tool to study the degree sequences of these graphs when the number of loops attached at each vertex is at most $1$.
A brief explanation of the meaning of the anthropic principle - as a prescription for the attribution of a priori probability weighting - is illustrated by various cosmological and local applications, in which the relevant conclusions are contrasted with those that could be obtained from (less plausible) alternative prescriptions such as the vaguer and less restrictive ubiquity principle, or the more sterile and restrictive autocentric principle.
We present a comprehensive set of observations of the interaction of p-mode oscillations with sunspots using surface-focused seismic holography. Maps of travel-time shifts, relative to quiet-Sun travel times, are shown for incoming and outgoing p modes as well as their mean and difference. We compare results using phase-speed filters with results obtained with filters that isolate single p-mode ridges, and further divide the data into multiple temporal frequency bandpasses. The f mode is removed from the data. The variations of the resulting travel-time shifts with magnetic-field strength and with the filter parameters are explored. We find that spatial averages of these shifts within sunspot umbrae, penumbrae, and surrounding plage often show strong frequency variations at fixed phase speed. In addition, we find that positive values of the mean and difference travel-time shifts appear exclusively in waves observed with phase-speed filters that are dominated by power in the low-frequency wing of the p1 ridge. We assess the ratio of incoming to outgoing p-mode power using the ridge filters and compare surface-focused holography measurements with the results of earlier published p-mode scattering measurements using Fourier-Hankel decomposition.
We analyze the time dependence of fluid variables in general relativistic, magnetohydrodynamic simulations of accretion flows onto a black hole with dimensionless spin parameter a/M=0.9. We consider both the case where the angular momentum of the accretion material is aligned with the black hole spin axis (an untilted flow) and where it is misaligned by 15 degrees (a tilted flow). In comparison to the untilted simulation, the tilted simulation exhibits a clear excess of inertial variability, that is, variability at frequencies below the local radial epicyclic frequency. We further study the radial structure of this inertial-like power by focusing on a radially extended band at 118 (M/10Msol)^-1 Hz found in each of the three analyzed fluid variables. The three dimensional density structure at this frequency suggests that the power is a composite oscillation whose dominant components are an over dense clump corotating with the background flow, a low order inertial wave, and a low order inertial-acoustic wave. Our results provide preliminary confirmation of earlier suggestions that disk tilt can be an important excitation mechanism for inertial waves.
Magnetic reconnection is a plasma phenomenon where a topological rearrangement of magnetic field lines with opposite polarity results in dissipation of magnetic energy into heat, kinetic energy and particle acceleration. Such a phenomenon is considered as an efficient mechanism for energy release in laboratory and astrophysical plasmas. An important question is how to make the process fast enough to account for observed explosive energy releases. The classical model for steady state magnetic reconnection predicts reconnection times scaling as $S^{1/2}$ (where $S$ is the Lundquist number) and yields times scales several order of magnitude larger than the observed ones. Earlier two-dimensional MHD simulations showed that for large Lundquist number the reconnection time becomes independent of $S$ ("fast reconnection" regime) due to the presence of the secondary tearing instability that takes place for $S \gtrsim 1 \times 10^4$. We report on our 3D MHD simulations of magnetic reconnection in a magnetically confined cylindrical plasma column under either a pressure balanced or a force-free equilibrium and compare the results with 2D simulations of a circular current sheet. We find that the 3D instabilities acting on these configurations result in a fragmentation of the initial current sheet in small filaments, leading to enhanced dissipation rate that becomes independent of the Lundquist number already at $S \simeq 1\times 10^3$.
We investigate Calabi--Yau three folds which are small resolutions of fiber products of elliptic surfaces with section admitting reduced fibers. We start by the classification of all fibers that can appear on such varieties. Then, we find formulas to compute the Hodge numbers of obtained three folds in terms of the types of singular fibers of the elliptic surfaces. Next we study Kummer fibrations associated to these fiber products.
Black hole binaries exhibit a wide range of variability phenomena, from large-scale state changes to broadband noise and quasi-periodic oscillations, but the physical nature of much of this variability is poorly understood. We examine the variability properties of three GRMHD simulations of thin accretion disks around black holes of varying spin, producing light curves and power spectra as would be seen by observers. We find that the simulated power spectra show a broad feature at high frequency, which increases in amplitude with the inclination of the observer. We show that this high-frequency feature is a product of the Doppler effect and that its location is a function of the mass and spin of the black hole. This Doppler feature demonstrates that power spectral properties of the accretion disk can be tied to, and potentially used to determine, physical properties of the black hole.
Aims. We study the enigmatic B[e] star MWC 300 to investigate its disk and binary with milli-arcsecond-scale angular resolution. Methods. We observed MWC 300 with the VLTI/AMBER instrument in the H and K bands and compared these observations with temperature-gradient models to derive model parameters. Results. The measured low visibility values, wavelength dependence of the visibilities, and wavelength dependence of the closure phase directly suggest that MWC 300 consists of a resolved disk and a close binary. We present a model consisting of a binary and a temperature-gradient disk that is able to reproduce the visibilities, closure phases, and spectral energy distribution. This model allows us to constrain the projected binary separation (~4.4 mas or ~7.9 AU), the flux ratio of the binary components (~2.2), the disk temperature power-law index, and other parameters.
Unsupervised feature learning for point clouds has been vital for large-scale point cloud understanding. Recent deep learning based methods depend on learning global geometry from self-reconstruction. However, these methods are still suffering from ineffective learning of local geometry, which significantly limits the discriminability of learned features. To resolve this issue, we propose MAP-VAE to enable the learning of global and local geometry by jointly leveraging global and local self-supervision. To enable effective local self-supervision, we introduce multi-angle analysis for point clouds. In a multi-angle scenario, we first split a point cloud into a front half and a back half from each angle, and then, train MAP-VAE to learn to predict a back half sequence from the corresponding front half sequence. MAP-VAE performs this half-to-half prediction using RNN to simultaneously learn each local geometry and the spatial relationship among them. In addition, MAP-VAE also learns global geometry via self-reconstruction, where we employ a variational constraint to facilitate novel shape generation. The outperforming results in four shape analysis tasks show that MAP-VAE can learn more discriminative global or local features than the state-of-the-art methods.
Jet substructure tools have proven useful in a number of high-energy particle-physics studies. A particular case is the discrimination, or tagging, between a boosted jet originated from an electroweak boson (signal), and a standard QCD parton (background). A common way to achieve this is to cut on a measure of the radiation inside the jet, i.e. a jet shape. Over the last few years, analytic calculations of jet substructure have allowed for a deeper understanding of these tools and for the development of more efficient ones. However, analytic calculations are often limited to the region where the jet shape is small. In this paper we introduce a new approach in perturbative QCD to compute jet shapes for a generic boosted jets, waiving the above limitation. We focus on an example common in the substructure literature: the jet mass distribution after a cut on the $N$-subjettiness $\tau_{21}$ ratio, extending previous works to the region relevant for phenomenology. We compare our analytic predictions to Monte Carlo simulations for both plain and SoftDrop-groomed jets. We use our results to construct analytically a decorrelated tagger.
The impact of stochastic gas motions on the metal distribution in cluster core is evaluated. Peaked abundance profiles are a characteristic feature of clusters with cool cores and abundance peaks are likely associated with the brightest cluster galaxies (BCGs) which dwell in cluster cores. The width of the abundance peaks is however significantly broader than the BCG light distribution, suggesting that some gas motions are transporting metals originating from within the BCG. Assuming that this process can be treated as diffusive and using the brightest X-ray cluster A426 (Perseus) as an example, we estimate that a diffusion coefficient of the order of $2 10^{29} {\rm cm^2 s^{-1}}$ is needed to explain the width of the observed abundance profiles. Much lower (higher) diffusion coefficients would result in too peaked (too shallow) profiles. Such diffusion could be produced by stochastic gas motions and our analysis provides constraints on the product of their characteristic velocity and their spatial coherence scale. We speculate that the activity of the supermassive black hole of the BCG is driving the stochastic gas motions in cluster cores. When combined with the assumption that the dissipation of the same motions is a key gas heating mechanism, one can estimate both the velocity and the spatial scale of such a diffusive processes.
Based on extensive numerical simulations, accounting for electrostatic interactions and dissipative electron-phonon scattering, we propose experimentally realizable geometries capable of sustaining electronic pre-turbulence in graphene samples. In particular, pre-turbulence is predicted to occur at experimentally attainable values of the Reynolds number between 10 and 50, over a broad spectrum of frequencies between 10 and 100 GHz.
Splitting trees are those random trees where individuals give birth at constant rate during a lifetime with general distribution, to i.i.d. copies of themselves. The width process of a splitting tree is then a binary, homogeneous Crump--Mode--Jagers (CMJ) process, and is not Markovian unless the lifetime distribution is exponential. Here, we allow the birth rate to be infinite, that is, pairs of birth times and lifespans of newborns form a Poisson point process along the lifetime of their mother, with possibly infinite intensity measure. A splitting tree is a random (so-called) chronological tree. Each element of a chronological tree is a (so-called) existence point $(v,\tau)$ of some individual $v$ (vertex) in a discrete tree, where $\tau$ is a nonnegative real number called chronological level (time). We introduce a total order on existence points, called linear order, and a mapping $\varphi$ from the tree into the real line which preserves this order. The inverse of $\varphi$ is called the exploration process, and the projection of this inverse on chronological levels the contour process. For splitting trees truncated up to level $\tau$, we prove that thus defined contour process is a L\'evy process reflected below $\tau$ and killed upon hitting 0. This allows to derive properties of (i) splitting trees: conceptual proof of Le Gall--Le Jan's theorem in the finite variation case, exceptional points, coalescent point process, age distribution; (ii) CMJ processes: one-dimensional marginals, conditionings, limit theorems, asymptotic numbers of individuals with infinite vs finite descendances.
We report the detection of the linear radical HC4N in the C-rich envelope of IRC+10216. After HCCN, HC4N is the second member of the allenic chain family HC_(2n)N observed in space. The column density of HC4N is found to be 1.5 10**12 cm**(-2). The abundance ratio HC2N/HC4N is 9, a factor of two larger than the decrement observed for the cyanopolyynes HC$_(2n+1)N/HC_(2n+3)N. Linear HC_4N has a 3-Sigma electronic ground state and is one of the 3 low-energy isomeric forms of this molecule. We have searched for the bent and ringed HC4N isomers, but could only derive an upper limit to their column densities of about 3 10**(12) cm**(-2).
Froissart Bound implies that the total proton-proton cross-section (or equivalently structure function) cannot rise faster than the logarithmic growth $\log^2 s \sim \log^2 (1/x)$, where \textit{s} is the square of the center of mass energy and \textit{x} is the Bjorken variable. In the present report, compatibility of such behavior will be shown in case of Transverse Momentum Dependent Parton Distributions Functions (TMDPDF) or TMDs for the model of proton based on self-similarity.
We classify the non-toric, $\mathbb Q$-factorial, Gorenstein, log terminal Fano threefolds of Picard number one that admit an effective action of a two-dimensional algebraic torus.
In the aim of determining accurate iron abundances in stars, this work is meant to empirically calibrate H-collision cross-sections with iron, where no quantum mechanical calculations have been published yet. Thus, a new iron model atom has been developed, which includes hydrogen collisions for excitation, ionization and charge transfer processes. We show that collisions with hydrogen leading to charge transfer are important for an accurate non-LTE modeling. We apply our calculations on several benchmark stars including the Sun, the metal-rich star {\alpha} Cen A and the metal-poor star HD140283.
We have collected continuum data of a sample of D-type symbiotic stars. By modelling their spectral energy distribution in a colliding-wind theoretical scenario we have found the common characteristics to all the systems: 1) at least two dust shells are clearly present, one at \sim 1000 K and the other at \sim 400 K; they dominate the emission in the IR; 2) the radio data are explained by thermal self-absorbed emission from the reverse shock between the stars; while 3) the data in the long wavelength tail come from the expanding shock outwards the system; 4) in some symbiotic stars, the contribution from the WD in the UV is directly seen. Finally, 5) for some objects soft X-ray emitted by bremsstrahlung downstream of the reverse-shock between the stars are predicted. The results thus confirm the validity of the colliding wind model and the important role of the shocks. The comparison of the fluxes calculated at the nebula with those observed at Earth reveals the distribution throughout the system of the different components, in particular the nebulae and the dust shells. The correlation of shell radii with the orbital period shows that larger radii are found at larger periods. Moreover, the temperatures of the dust shells regarding the sample are found at 1000 K and <=400 K, while, in the case of late giants, they spread more uniformly throughout the same range.
The bending of a carbon nanotube is studied by considering the structural evolution of a carbon nanotorus from elastic deformation to the onset of the kinks and eventually to the collapse of the walls of the nanotorus. The changes in the electronic properties due to {\it non-local} deformation are contrasted with those due to {\it local} deformation to bring out the subtle issue underlying the reason why there is only a relatively small reduction in the electrical conductance in the former case even at large bending angles while there is a dramatic reduction in the conductance in the latter case at relatively small bending angles.
We present a phenomenological modification of the standard perturbation theory prediction for the bispectrum in redshift space that allows us to extend the model to mildly non-linear scales over a wide range of redshifts, $z\leq1.5$. We find that we can describe the bispectrum of dark matter particles with $\sim5%$ accuracy for $k_i\lesssim0.10\,h/{\rm Mpc}$ at $z=0$, for $k_i\lesssim0.15\,h/{\rm Mpc}$ at $z=0.5$, for $k_i\lesssim0.17\,h/{\rm Mpc}$ at $z=1.0$ and for $k_i\lesssim0.20\,h/{\rm Mpc}$ at $z=1.5$. We also test that the fitting formula is able to describe with similar accuracy the bispectrum of cosmologies with different $\Omega_m$, in the range $0.2\lesssim \Omega_m \lesssim 0.4$, and consequently with different values of the logarithmic grow rate $f$ at $z=0$, $0.4\lesssim f(z=0) \lesssim 0.6$. We apply this new formula to recover the bias parameters, $f$ and $\sigma_8$, by combining the redshift space power spectrum monopole and quadrupole with the bispectrum monopole for both dark matter particles and haloes. We find that the combination of these three statistics can break the degeneracy between $b_1$, $f$ and $\sigma_8$. For dark matter particles the new model can be used to recover $f$ and $\sigma_8$ with $\sim1%$ accuracy. For dark matter haloes we find that $f$ and $\sigma_8$ present larger systematic shifts, $\sim10%$. The systematic offsets arise because of limitations in the modelling of the interplay between bias and redshift space distortions, and represent a limitation as the statistical errors of forthcoming surveys reach this level. Conveniently, we find that these residual systematics are mitigated for combinations of parameters. The improvement on the modelling of the bispectrum presented in this paper will be useful for extracting information from current and future galaxy surveys. [abridged]
We have obtained 1-2 A resolution optical Echellette spectra of the nuclear star cluster in the nearby starburst galaxy NGC 4449. The light is clearly dominated by a very young (6-10 Myr) population of stars. For our age dating, we have used recent population synthesis models to interpret the observed equivalent width of stellar absorption features such as the HI Balmer series and the CaII triplet around 8500 A. We also compare the observed spectrum of the nuclear cluster to synthesized spectra of simple stellar populations of varying ages. All these approaches yield a consistent cluster age. Metallicity estimates based on the relative intensities of various ionization lines yield no evidence for significant enrichment in the center of this low mass galaxy: the metallicity of the nuclear cluster is about one fourth of the solar value, in agreement with independent estimates for the disk material of NGC 4449.
We investigate which elliptic PDEs that have the property that every viscosity supersolution is $W^{1,q}_{loc}(\Omega)$, $\Omega\subseteq\mathbb{R}^n$. The asymptotic cone of the operator's sublevel set seems to be essential. It turns out that much can be said if we know how this cone compares to the sublevel set of a certain minimal operator associated with the exponent $q$.
This paper presents a novel hierarchical spatiotemporal orientation representation for spacetime image analysis. It is designed to combine the benefits of the multilayer architecture of ConvNets and a more controlled approach to spacetime analysis. A distinguishing aspect of the approach is that unlike most contemporary convolutional networks no learning is involved; rather, all design decisions are specified analytically with theoretical motivations. This approach makes it possible to understand what information is being extracted at each stage and layer of processing as well as to minimize heuristic choices in design. Another key aspect of the network is its recurrent nature, whereby the output of each layer of processing feeds back to the input. To keep the network size manageable across layers, a novel cross-channel feature pooling is proposed. The multilayer architecture that results systematically reveals hierarchical image structure in terms of multiscale, multiorientation properties of visual spacetime. To illustrate its utility, the network has been applied to the task of dynamic texture recognition. Empirical evaluation on multiple standard datasets shows that it sets a new state-of-the-art.
We study possible correlations between ultrahigh energy cosmic rays (UHECRs), observed by Auger, AGASA and Yakutsk, and nearby active galactic nuclei (AGNs) and $Fermi$ sources. We consider the deflection effects by a Galactic magnetic field (GMF) model constrained by the most updated measurements. We found that the average deflection angles of UHECRs by the Galactic magnetic fields are less than $4^\circ$. A correlation between the Auger cosmic-ray events and nearby AGNs with a significance level of $\sim 4\sigma$ was found for the Auger UHECR data sets with or without deflection correction. No correlation was found between the AGASA/Yakutsk events with nearby AGNs. Marginal correlations between the Auger events and the $Fermi$ sources, and between AGASA events and $Fermi$ AGNs were found when the deflections calculated by the GMF model were considered. However, no correlation was found between the Yakutsk data and $Fermi$ sources. Some $Fermi$ sources are close to the arrival directions of UHECR events detected by Auger, AGASA, and Yakutsk, most of which are probably chance coincidence rather than objects producing UHECRs in the nearby Universe. Four $Fermi$ sources, NGC 4945, ESO 323-G77, NGC 6951, and Cen A, within 100~Mpc have UHECR events within $3.1^{\circ}$ from their positions, which could potentially be cosmic ray accelerators. However, the association can only be confirmed if more UHECRs are preferably detected in these directions.
In this work, we present a generalization to varieties and sheaves of the fundamental ideal of the Witt ring of a field by defining a sheaf of fundamental ideals $\tilde{I}$ and a sheaf of Witt rings $\tilde{W}$ in the obvious way. The Milnor conjecture then relates the associated graded of $\tilde{W}$ to Milnor K-theory and so allows the classical invariants of a bilinear space over a field to be extended to our setting using \'etale cohomology. As an application of these results, we calculate the Witt ring of a smooth curve with good reduction over a non-dyadic local field.