ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this paper we introduce and study a class of tableaux which we call permutation tableaux; these tableaux are naturally in bijection with permutations, and they are a distinguished subset of the Le-diagrams of Alex Postnikov. The structure of these tableaux is in some ways more transparent than the structure of permutations; therefore we believe that permutation tableaux will be useful in furthering the understanding of permutations. We give two bijections from permutation tableaux to permutations. The first bijection carries tableaux statistics to permutation statistics based on relative sizes of pairs of letters in a permutation and their places. We call these statistics weak excedance statistics, because of their close relation to weak excedances. The second bijection carries tableaux statistics (via the weak excedance statistics) to statistics based on generalized permutation patterns. We then give enumerative applications of these bijections. One nice consequence of these results is that the polynomial enumerating permutation tableaux according to their content generalizes both Carlitz' q-analog of the Eulerian numbers and the more recent q-analog of the Eulerian numbers of the second author. We conclude our paper with a list of open problems, some of which have now been solved by Burstein, Corteel, Eriksen, Reifegerste, and Viennot.
How to fully utilize polarization to enhance synthetic aperture radar (SAR) ship classification remains an unresolved issue. Thus, we propose a dual-polarization information guided network (DPIG-Net) to solve it.
High-entropy alloys are an intriguing new class of metallic materials that derive their properties from being multi-element systems that can crystallize as a single phase, despite containing high concentrations of five or more elements with different crystal structures. Here we examine an equiatomic medium-entropy alloy containing only three elements, CrCoNi, as a single-phase face-centered cubic (fcc) solid solution, which displays strength-toughness properties that exceed those of all high-entropy alloys and most multi-phase alloys. At room temperature the alloy shows tensile strengths of almost 1 GPa, failure strains of ~70%, and KJIc fracture-toughness values above 200 MPa.m1/2; at cryogenic temperatures strength, ductility and toughness of the CrCoNi alloy improve to strength levels above 1.3 GPa, failure strains up to 90% and KJIc values of 275 MPa.m1/2. Such properties appear to result from continuous steady strain hardening, which acts to suppress plastic instability, resulting from pronounced dislocation activity and deformation-induced nano-twinning.
On the measurement of thermoelectric power and Nernst coefficient, we used two kinds of shapes for a sample. One is "Bridge shape" and the other is, we call,"Fat-Bridge shape". The latter has 5 times wider main body than the former. We used pure n-InSb in this experiment, whose carrier condensation measured at 77K was $6.6 \times 10^{-14} cm^{-3}.$ The length of sample is 17mm and temperature difference induced between the edges in that direction were about $10^{\circ}$C or $100^{\circ}$C near a room temperature range of 0 to $100^{\circ}$C. Magnetic induction applied in the perpendicular direction to temperature gradient was in the range of 0 up to 4 Tesla. In the case of "Fat-Bridge shape", we detected about 10% smaller Nernst coefficient and 1 to 10% smaller thermoelectric power comparing to the "Bridge shape". We suppose this phenomena is due to the geometric contribution on the different shape of samples.
We present the QCD predictions for the azimuthal $\cos 2\varphi$ asymmetry in charm leptoproduction for the kinematics of the COMPASS experiment at CERN. The asymmetry is predicted to be large, about 15%. The radiative corrections to the QCD predictions for the $\cos 2\varphi$ distribution are estimated to be small, less than 10%. Our calculations show that the azimuthal asymmetry in charm production is well defined in pQCD: it is stable both perturbatively and parametrically, and practically insensitive to theoretical uncertainties in the input parameters. We analyze the nonperturbative contributions to the $\cos 2\varphi$ distribution due to the gluon transverse motion in the target and the $c$-quark fragmentation. Because of the $c$-quark low mass, the nonperturbative contributions are expected to be sizable, about (30--40)%. We conclude that extraction of the azimuthal asymmetries from available COMPASS data will provide valuable information about the transverse momentum dependent distribution of the gluon in the proton and the $c$-quark hadronization mechanism. Finally, we discuss the $\cos 2\varphi$ asymmetry as a probe of the gluonic analogue of the Boer-Mulders function, $h_{1}^{\perp g}$, describing the linear polarization of gluons inside unpolarized proton.
Context. OB stars are important building blocks of the Universe, but we have only a limited sample of them well understood enough from an asteroseismological point of view to provide feedback on the current evolutionary models. Our study adds one special case to this sample, with more observational constraints than for most of these stars.   Aims. Our goal is to analyse and interpret the pulsational behaviour of the B3 IV star HD 43317 using the CoRoT light curve along with the ground-based spectroscopy gathered by the Harps instrument. This way we continue our efforts to map the Beta Cep and SPB instability strips.   Methods. We used different techniques to reveal the abundances and fundamental stellar parameters from the newly-obtained high-resolution spectra. We used various time-series analysis tools to explore the nature of variations present in the light curve. We calculated the moments and used the pixel-by-pixel method to look for line profile variations in the high-resolution spectra.   Results. We find that HD 43317 is a single fast rotator (v_rot ~ 50% v_crit) and hybrid SPB/Beta Cep-type pulsator with Solar metal abundances. We interpret the variations in photometry and spectroscopy as a result of rotational modulation connected to surface inhomogeneities, combined with the presence of both g and p mode pulsations. We detect a series of ten consecutive frequencies with an almost constant period spacing of 6339 s as well as a second shorter sequence consisting of seven frequencies with a spacing of 6380 s. The dominant frequencies fall in the regime of gravito-inertial modes.
Charged domain walls are a type of domain walls in thin ferromagnetic films which appear due to global topological constraints. The non-dimensionalized micromagnetic energy for a uniaxial thin ferromagnetic film with in-plane magnetization $m \in \mathbb{S}^1$ is given by   \begin{align*}   E_\epsilon[m] \ = \   \epsilon\|\nabla m\|_{L^2}^2 + \frac {1}{\epsilon} \|m \cdot e_2\|_{L^2}^2   + \frac{\pi\lambda}{2|\ln\epsilon|} \|\nabla \cdot (m-M)\|_{\dot H^{-\frac{1}{2}}}^2,   \end{align*} where magnetization in $e_1$-direction is globally preferred and where $M$ is an arbitrary fixed background field to ensure global neutrality of magnetic charges. We consider a material in the form a thin strip and enforce a charged domain wall by suitable boundary conditions on $m$. In the limit $\epsilon \to 0$ and for fixed $\lambda> 0$, corresponding to the macroscopic limit, we show that the energy $\Gamma$-converges to a limit energy where jump discontinuities of the magnetization are penalized anisotropically. In particular, in the subcritical regime $\lambda \leq 1$ one-dimensional charged domain walls are favorable, in the supercritical regime $\lambda > 1$ the limit model allows for zigzaging two-dimensional domain walls.
We report a change in the trajectory of a well studied jet component of the quasar 3C279. The component changes in apparent projected speed and direction, and we find it to be moving with a Lorentz factor gamma >~ 15 at an initial angle of <~ 1 degree to the line of sight. The new trajectory of the component has approximately the same speed and direction as an earlier superluminal feature, originally seen in the early 1970s. The new direction for the component is also much better aligned with larger scale VLBA and VLA structure out to 0.1 arcseconds. We suggest that the trajectory change is a collimation event occurring at >~ 1 kiloparsec (deprojected) along the jet. While the change in trajectory on the sky appears to be 26 degrees the intrinsic change is <~ 1 degree. We estimate the Doppler factor prior to the change in direction to be D >~ 28 and after the change to be D >~ 23. Comparison to independent constraints on the Doppler factor suggest that the energy in the radiating particles cannot greatly exceed the energy in the magnetic field unless the volume filling factor is very much less than one.
Afterglows of gamma-ray bursts are observed to produce light curves with the flux following power law evolution in time. However, recent observations reveal bright flares at times on the order of minutes to days. One proposed explanation for these flares is the interaction of a relativistic blast wave with a circumburst density transition. In this paper, we model this type of interaction computationally in one and two dimensions, using a relativistic hydrodynamics code with adaptive mesh refinement called ram, and analytically in one dimension. We simulate a blast wave traveling in a stellar wind environment that encounters a sudden change in density, followed by a homogeneous medium, and compute the observed radiation using a synchrotron model. We show that flares are not observable for an encounter with a sudden density increase, such as a wind termination shock, nor for an encounter with a sudden density decrease. Furthermore, by extending our analysis to two dimensions, we are able to resolve the spreading, collimation, and edge effects of the blast wave as it encounters the change in circumburst medium. In all cases considered in this paper, we find that a flare will not be observed for any of the density changes studied.
We use the first Gaia data release, combined with RAVE and APOGEE spectroscopic surveys, to investigate the origin of halo stars within <~3 kpc from the Sun. We identify halo stars kinematically, as moving with a relative speed of at least 220 km/s with respect to the local standard of rest. These stars are in general more metal-poor than the disk, but surprisingly, half of our halo sample is comprised of stars with [Fe/H]>-1. The orbital directions of these metal-rich halo stars are preferentially aligned with the disk rotation, in sharp contrast with the isotropic orbital distribution of the more metal-poor halo stars. We find similar properties in the Latte cosmological zoom-in simulation of a Milky Way-like galaxy from the FIRE project. In Latte, metal-rich halo stars formed primarily inside of the solar circle, while lower-metallicity halo stars preferentially formed at larger distances (extending beyond the virial radius). This suggests that metal-rich halo stars in the Solar neighborhood in fact formed in-situ within the Galactic disk rather than having been accreted from satellite systems. These stars, currently on halo-like orbits, therefore have likely undergone substantial radial migration/heating.
We focus our attention on Monte Carlo simulations of crystallization, which is one of the most important processes occurring in nature and technology of materials. Special attention is paid to the crystallization shrinkage and its consequences onto the growth of the new crystalline phase. We show that crystallization shrinkage stops after reaching the percolation threshold and that this is not the final stage of the crystallization process. Based on experimental evidences on sintering of diopside-albite systems and computer simulations we argue that crystallization continues inside the grains where the remaining liquid melt is a subject of accumulation of stress and because the stress relaxation by change in the volume is forbidden due to the already formed rigid core, the so called crystallization induced porosity appears. We show that even a relatively simple short range potential as the Lennard-Jones one, reveals such a complicated phenomenon as the crystallization induced porosity, which has a great importance onto the mechanical properties of the newly crystallized material.
The Smoluchowski equation with a time dependent delta function sink is solved exactly for many special cases. In all other cases the problem can be reduced to an integral equation. It is shown that by knowing the probability distribution at the position of sink, one can derive analytical expression for probability distribution everywhere. Thus the problem is reduced from a PDE in two variables to an integral equation of one. As far as the authors knowledge, we are the first one to provide an exact analytical solution of Smoluchowski equation for a parabolic potential with time dependent sink.
Let G be a complex semi-simple Lie group and let P,Q be a pair of parabolic subgroups of G such that Q contains P. Consider the flag varieties G/P, G/Q and Q/P. We show that certain structure constants in H^*(G/P) with respect to the Schubert basis can be written as a product of structure constants coming from H^*(G/Q) and H^*(Q/P) in a very natural way. The primary application is to compute Levi-movable structure constants defined by Belkale and Kumar. We also give a generalization of this product formula in the branching Schubert calculus setting.
Topological insulators (TIs) are promising for achieving dissipationless transport devices due to the robust gapless states inside the insulating bulk gap. However, currently realized 2D TIs, quantum spin Hall (QSH) insulators, suffer from ultra-high vacuum and extremely low temperature. Thus, seeking for desirable QSH insulators with high feasibility of experimental preparation and large nontrivial gap is of great importance for wide applications in spintronics. Based on the first-principles calculations, we predict a novel family of two-dimensional (2D) QSH insulators in transition-metal halide MX (M = Zr, Hf; X = Cl, Br, and I) monolayers with large nontrivial gaps of 0.12$-$0.4 eV, comparable with bismuth (111) bilayer (0.2 eV), stanene (0.3 eV) and larger than ZrTe$_5$ (0.1 eV) monolayers and graphene-based sandwiched heterstructures (30$-$70 meV). Their corresponding 3D bulk materials are weak topological insulators from stacking QSH layers, and some of bulk compounds have already been synthesized in experiment. The mechanism for 2D QSH effect in this system originates from a novel d$-$d band inversion, which is different from conventional band inversion between s$-$s orbitals, or p$-$p orbitals. The realization of pure layered MX monolayers may be prepared by exfoliation from their 3D bulk phases, thus holding great promise for nanoscale device applications and stimulating further efforts on transition metal-based QSH materials.
The Null Surface Formulation of General Relativity is developed for 2+1 dimensional gravity. The geometrical meaning of the metricity condition is analyzed and two approaches to the derivation of the field equations are presented. One method makes explicit use of the conformal factor while the other only uses conformal information. The resulting set of equations contain the same geometrical meaning as the 4-D formulation without the technical complexities of the higher dimensional analog. A canonical family of null surfaces in this formulation, the light cone cuts of null infinity, are constructed on asymptotically flat space times and some of their kinematical aspects discussed. A particular example, which nevertheless contains most of the generic features is explicitly constructed and analyzed, revealing the behavior predicted in the full theory.
LIGO's discovery of a gravitational wave from two merging black holes (BHs) of similar masses rekindled suggestions that primordial BHs (PBHs) make up the dark matter (DM). If so, PBHs would add a Poissonian isocurvature density fluctuation component to the inflation-produced adiabatic density fluctuations. For LIGO's BH parameters, this extra component would dominate the small-scale power responsible for collapse of early DM halos at z>10, where first luminous sources formed. We quantify the resultant increase in high-z abundances of collapsed halos that are suitable for producing the first generation of stars and luminous sources. The significantly increased abundance of the early halos would naturally explain the observed source-subtracted near-IR cosmic infrared background (CIB) fluctuations, which cannot be accounted for by known galaxy populations. For LIGO's BH parameters this increase is such that the observed CIB fluctuation levels at 2 to 5 micron can be produced if only a tiny fraction of baryons in the collapsed DM halos forms luminous sources. Gas accretion onto these PBHs in collapsed halos, where first stars should also form, would straightforwardly account for the observed high coherence between the CIB and unresolved cosmic X-ray background in soft X-rays. We discuss modifications possibly required in the processes of first star formation if LIGO-type BHs indeed make up the bulk or all of DM. The arguments are valid only if the PBHs make up all, or at least most, of DM, but at the same time the mechanism appears inevitable if DM is made of PBHs.
We present the fractional distribution of spectroscopic subtypes, range and distribution of surface temperatures, and kinematical properties of the white dwarfs within 25pc of the sun. There is no convincing evidence of halo white dwarfs in the total 25 pc sample of 224 white dwarfs. There is also little to suggest the presence of genuine thick disk subcomponent members within 25 parsecs. It appears that the entire 25 pc sample likely belong to the thin disk. We also find no significant kinematic differences with respect to spectroscopic subtypes. The total DA to non-DA ratio of the 25 pc sample is 1.8, a manifestation of deepening envelope convection which transforms DA stars with sufficiently thin H surface layers into non-DAs. We compare this ratio with the results of other studies. We find that at least 11% of the white dwarfs within 25 parsecs of the sun (the DAZ and DZ stars) have photospheric metals that likely originate from accretion of circumstellar material (debris disks) around them. If this interpretation is correct, then it suggests the possibility that a similar percentage have planets, asteroid-like bodies or debris disks orbiting them. Our volume-limited sample reveals a pileup of DC white dwarfs at the well-known cutoff in DQ white dwarfs at Tef about 6000K. Mindful of small number statistics, we speculate on its possible evolutionary significance. We find that the incidence of magnetic white dwarfs in the 25 pc sample is at least 8%, in our volume-limited sample, dominated by cool white dwarfs. We derive approximate formation rates of DB and DQ degenerates and present a preliminary test of the evolutionary scenario that all cooling DB stars become DQ white dwarfs via helium convective dredge-up with the diffusion tail of carbon extending upward from their cores.
The radio light curves of SN 1993J are found to be well fit by a synchrotron spectrum, suppressed by external free-free absorption and synchrotron self-absorption. A standard r^-2 circumstellar medium is assumed, and found to be adequate. The magnetic field and number density of relativistic electrons behind the shock are determined. The strength of the magnetic field argues strongly for turbulent amplification behind the shock. The ratio of the magnetic and thermal energy density behind the shock is ~0.14. Synchrotron and Coulomb cooling dominate the losses of the electrons. The injected electron spectrum has a power law index -2.1, consistent with diffusive shock acceleration, and the number density scales with the thermal electron energy density. The total energy density of the relativistic electrons is, if extrapolated to gamma ~ 1, ~ 5x10^-4 of the thermal energy density. The free-free absorption required is consistent with previous calculations of the circumstellar temperature of SN 1993J, T_e ~ (2-10)x10^5 K. The relative importance of free-free absorption, Razin suppression, and the synchrotron self-absorption effect for other supernovae are briefly discussed. Guidelines for the modeling and interpretation of VLBI observations are given.
As part of our program to build a complete radio and X-ray database of all the 3CR extragalactic radio sources, we present an analysis of 93 sources for which Chandra archival data are available. Most of these sources have been already published. Here we provide a uniform re-analysis and present nuclear X-ray fluxes and X-ray emission associated with radio jet knots and hotspots using both publicly available radio images and new radio images that have been constructed from data available in the VLA archive. For about 1/3 of the sources in the selected sample a comparison between the Chandra and the radio observations was not reported in the literature: we find X-ray detections of 2 new radio jet knots and 17 hotspots. We also report the X-ray detection of extended emission from the intergalactic medium of 15 galaxy clusters, two of which were most likely unknown previously.
We present neural radiance fields for rendering and temporal (4D) reconstruction of humans in motion (H-NeRF), as captured by a sparse set of cameras or even from a monocular video. Our approach combines ideas from neural scene representation, novel-view synthesis, and implicit statistical geometric human representations, coupled using novel loss functions. Instead of learning a radiance field with a uniform occupancy prior, we constrain it by a structured implicit human body model, represented using signed distance functions. This allows us to robustly fuse information from sparse views and generalize well beyond the poses or views observed in training. Moreover, we apply geometric constraints to co-learn the structure of the observed subject -- including both body and clothing -- and to regularize the radiance field to geometrically plausible solutions. Extensive experiments on multiple datasets demonstrate the robustness and the accuracy of our approach, its generalization capabilities significantly outside a small training set of poses and views, and statistical extrapolation beyond the observed shape.
Everett's relative states interpretation of quantum mechanics has met with problems related to probability, the preferred basis, and multiplicity. The third theme, I argue, is the most important one. It has led to developments of the original approach into many-worlds, many-minds, and decoherence-based approaches. The latter especially have been advocated in recent years, in an effort to understand multiplicity without resorting to what is often perceived as extravagant constructions. Drawing from and adding to arguments of others, I show that proponents of decoherence-based approaches have not yet succeeded in making their ontology clear.
Let G be a graph with maximum degree \Delta whose vertex set is partitioned into parts V(G) = V_1 \cup ... \cup V_r. A transversal is a subset of V(G) containing exactly one vertex from each part V_i. If it is also an independent set, then we call it an independent transversal. The local degree of G is the maximum number of neighbors of a vertex v in a part V_i, taken over all choices of V_i and v \not \in V_i. We prove that for every fixed \epsilon > 0, if all part sizes |V_i| >= (1+\epsilon)\Delta and the local degree of G is o(\Delta), then G has an independent transversal for sufficiently large \Delta. This extends several previous results and settles (in a stronger form) a conjecture of Aharoni and Holzman. We then generalize this result to transversals that induce no cliques of size s. (Note that independent transversals correspond to s=2.) In that context, we prove that parts of size |V_i| >= (1+\epsilon)[\Delta/(s-1)] and local degree o(\Delta) guarantee the existence of such a transversal, and we provide a construction that shows this is asymptotically tight.