ShantanuT01/DACTYL-Pretraining huggingface dataset:
We consider a transport-diffusion equation with L\'{e}vy noises and H\"{o}lder continuous coefficients. By using the heat kernel estimates, we derive the Schauder estimates for the mild solutions. Moreover, when the transport term vanishes and $p=2$, we show that the H\"{o}lder index in space variable is optimal.
With orbital periods of the order of tens of minutes or less, the AM Canum Venaticorum stars are ultracompact, hydrogen deficient binaries with the shortest periods of any binary subclass, and are expected to be among the strongest gravitational wave sources in the sky. To date, the only known eclipsing source of this type is the P = 28 min binary SDSS J0926+3624. We present multiband, high time resolution light curves of this system, collected with WHT/ULTRACAM in 2006 and 2009. We supplement these data with additional observations made with LT/RISE, XMM_Newton and the Catalina Real-Time Transient Survey. From light curve models we determine the mass ratio to be q = M2 / M1 = 0.041 +/- 0.002 and the inclination to be 82.6 +/- 0.3 deg. We calculate the mass of the primary white dwarf to be 0.85 +/- 0.04 solar masses and the donor to be 0.035 +/- 0.003 solar masses, implying a partially degenerate state for this component. We observe superhump variations that are characteristic of an elliptical, precessing accretion disc. Our determination of the superhump period excess is in agreement with the established relationship between this parameter and the mass ratio, and is the most precise calibration of this relationship at low q. We also observe a quasi-periodic oscillation in the 2006 data, and we examine the outbursting behaviour of the system over a 4.5 year period.
Ge/Si(001) multilayer heterostructures containing arrays of low-temperature self-assembled Ge quantum dots and very thin Si$_x$Ge$_{1-x}$ layers of varying composition and complex geometry have been studied using Raman spectroscopy and scanning tunneling microscopy. The dependence of Raman spectra on the effective thickness of deposited Ge layers has been investigated in detail in the range from 4 to 18 \r{A}. The position and shape of both Ge and SiGe vibrational modes are of great interest since they are closely related to the strain and composition of the material that plays a role of active component in perspective optoelectronic devices based on such structures. In this work, we present an explanation for some peculiar features of Raman spectra, which makes it possible to control the quality of the grown heterostructures more effectively. A dramatic increase of intensity of both the Ge$-$Ge and Si$-$Ge bands for the structure containing Ge layers of 10 \r{A} and anomalous shift and broadening of the Si$-$Ge band for structures comprising Ge layers of 8 and 9 \r{A} thick were observed. In our model, the anomalous behavior of the Raman spectra with the change of thickness of deposited Ge is connected with the flatness of Ge layers as well as transitional SiGe domains formed via the stress-induced diffusion from {105} facets of quantum dots. The conclusions are supported by the STM studies and the numerical calculations.
We report the results of the evaluation of the ``concentration-density'' relation of galaxies in the local universe, taking advantage of the very large and homogeneous data set available from the Las Campanas Redshift Survey (Shectman et al. 1996). This data set consists of galaxies inhabiting the entire range of galactic environments, from the sparsest field to the densest clusters, thus allowing us to study environmental variations without combining multiple data sets with inhomogeneous characteristics. Concentration is quantified by the automatically-measured concentration index $C$, which is a good measure of a galaxy's bulge-to-disk ratio. The environment of the sample galaxies is characterized both by the three-space local galaxy density and by membership in groups and clusters. We find that the distribution of C in galaxy populations varies both with local density and with cluster/group membership: the fraction of centrally-concentrated galaxies increases with local galaxy density, and is higher in clusters than in the field. A comparison of the concentration-local density relation in clusters and the field shows that the two connect rather smoothly at the intermediate density regime, implying that the apparent cluster/field difference is only a manifestation of the variation with the local density. We conclude that the structure of galaxies is predominantly influenced by the local density and not by the broader environments characterized by cluster/field memberships.
We analyse the data for the proton structure function $F_2$ over the entire $Q^2$ domain, including especially low $Q^2$, in terms of perturbative and non-perturbative QCD contributions. The small distance configurations are given by perturbative QCD, while the large distance contributions are given by the vector dominance model and, for the higher mass $q \bar{q}$ states, by the additive quark approach. The interference between states of different $q\bar{q}$ mass (in the perturbative contribution) is found to play a crucial role in obtaining an excellent description of the data throughout the whole $Q^2$ region, including photoproduction.
We consider scattering of elastic waves on parallel wedge dislocations in the geometric theory of defects or, equivalently, scattering of point particles and light rays on cosmic strings. Dislocations are described as torsion singularities located on parallel lines, and trajectories of phonons are assumed to be the corresponding extremals. Extremals are found for arbitrary distribution of the dislocations in the monopole, dipole, and quadrupole approximation and the scattering angle is obtained. Examples of continuous distribution of wedge and edge dislocations are considered. We have found that for deficit angles close to -2\pi a star located behind a cosmic string may have any even number of images, 2,4,6,... The close relationship between dislocations and conformal maps is elucidated in detail.
The distance, star formation history and global properties of the Local Group dIrr galaxy SagDIG are derived based on an [I-(V-I)] colour--magnitude diagram of ~1550 stars. A distance of 1.06+/-0.10 Mpc is obtained from the I magnitude of the TRGB. This corresponds to 1.17 Mpc to the barycenter of the Local Group and 1.34 to M 31, being DDO 210, at 0.35 Mpc, the nearest galaxy to SagDIG. The metallicity is estimated from the colour of the RGB to be [Fe/H]=-2.45+/-0.25. SagDIG is hence a probable member of the Local Group and a candidate for the lowest-metallicity star forming galaxy known.   The radial density profile of the galaxy has been obtained together with other integrated properties (magnitude, colour and central surface density). The galaxy density profile is fitted by an exponential law of scale length 27.1", corresponding to 140 pc.   The star formation history of SagDIG has been analysed, based on synthetic colour-magnitude diagrams. The galaxy is currently in a high star formation activity epoch, forming stars at a rate about 10 times greater than the average for its entire life. This is a common feature of galaxies classified as dIrrs.
We demonstrate that the profile of the space-resolved spectral function at finite temperature provides a signature of Wigner localization for electrons in quantum wires and semiconducting carbon nanotubes. Our numerical evidence is based on the exact diagonalization of the microscopic Hamiltonian of few particles interacting in gate-defined quantum dots. The minimal temperature required to suppress residual exchange effects in the spectral function image of (nanotubes) quantum wires lies in the (sub-) Kelvin range.
Consider the continuous-time Markov Branching Process. In critical case we consider a situation when the generating function of intensity of transformation of particles has the infinite second moment, but its tail regularly varies in sense of Karamata. First we discuss limit properties of transition functions of the process. We prove local limit theorems and investigate ergodic properties of the process. Further we investigate limiting probability function conditioned to be never extinct. Hereupon we obtain a new stochastic population process as a continuous-time Markov chain called the Markov Q-Process. We study main properties of Markov Q-Process.
This paper completes the project started in [10]; to solve the edge-isoperimetric problem on the (generalized and extended) Sierpinski graph, S(n,m). We prove that initial segments of lexicographic order are solutions of the EIP for all n,m.
Noise injection-based regularization, such as Dropout, has been widely used in image domain to improve the performance of deep neural networks (DNNs). However, efficient regularization in the point cloud domain is rarely exploited, and most of the state-of-the-art works focus on data augmentation-based regularization. In this paper, we, for the first time, perform systematic investigation on noise injection-based regularization for point cloud-domain DNNs. To be specific, we propose a series of regularization techniques, namely DropFeat, DropPoint and DropCluster, to perform noise injection on the point feature maps at the feature level, point level and cluster level, respectively. We also empirically analyze the impacts of different factors, including dropping rate, cluster size and dropping position, to obtain useful insights and general deployment guidelines, which can facilitate the adoption of our approaches across different datasets and DNN architectures.   We evaluate our proposed approaches on various DNN models for different point cloud processing tasks. Experimental results show our approaches enable significant performance improvement. Notably, our DropCluster brings 1.5%, 1.3% and 0.8% higher overall accuracy for PointNet, PointNet++ and DGCNN, respectively, on ModelNet40 shape classification dataset. On ShapeNet part segmentation dataset, DropCluster brings 0.5%, 0.5% and 0.2% mean Intersection-over-union (IoU) increase for PointNet, PointNet++ and DGCNN, respectively. On S3DIS semantic segmentation dataset, DropCluster improves the mean IoU of PointNet, PointNet++ and DGCNN by 3.2%, 2.9% and 3.7%, respectively. Meanwhile, DropCluster also enables the overall accuracy increase for these three popular backbone DNNs by 2.4%, 2.2% and 1.8%, respectively.
In this work, we present digital and graphical atlases of spectra of both the solar disk-center and of the limb near the Solar poles using data taken at the UTS-IAP & RIAAM (the University of Tabriz Siderostat, telescope and spectrograph jointly developed with the Institut d'Astrophysique de Paris and Research Institute for Astronomy and Astrophysics of Maragha). High resolution and high signal-to-noise ratio (SNR)CCD-slit spectra of the sun for 2 different parts of the disk, namely for $\mu$~=~1.0 (solar center) \& for $\mu$~=~ 0.3 solar limb) are provided and discussed. While there are several spectral atlases of the solar disk-center, this is the first spectral atlas ever produced for the solar limb at this spectral range. The resolution of the spectra is about \emph{R}~$\sim$~70 000 ($\Delta\lambda$~$\sim$~0.09 {\AA} with the signal-to-noise ratio (SNR) of 400$-$600. The full atlas covers the 3980 to 7100 {\AA} spectral regions and contains 44 pages with three partial spectra of the solar spectrum put on each page to make it compact. The difference spectrum of the normalized solar disk-center and the solar limb is also included in the graphic presentation of the atlas to show the difference of line profiles, including far wings. The identification of the most significant solar lines is included in the graphic presentation of the atlas. Telluric lines are producing a definite signature on the difference spectra which is easy to notice. At the end of this paper we present only two sample pages of the whole atlas while the graphic presentation of the whole atlas along with its ASCII file can be accessed via the ftp server of the CDS in Strasbourg via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via this link \footnote{\url{http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/other/ApSS}}.
We study a coupled system of two parabolic equations in one space dimension. This system is singular because of the presence of one term with the inverse of the gradient of the solution. Our system describes an approximate model of the dynamics of dislocation densities in a bounded channel submitted to an exterior applied stress. The system of equations is written on a bounded interval with Dirichlet conditions and requires a special attention to the boundary. The proof of existence and uniqueness is done under the use of two main tools: a certain comparison principle on the gradient of the solution, and a parabolic Kozono-Taniuchi inequality
A space-periodic ground state is shown to exist for lattices of point ions in $\R^3$ coupled to the Schr\"odinger and scalar fields. The coupling requires the renormalization of the selfaction because of the singularity of the Coulomb potential. The ground state is constructed by minimization of the renormalized energy per cell. This energy is bounded from below when the charge of each ion is positive. The elementary cell is necessarily neutral.
An example of a cold massive core, JCMT 18354-0649S, a possible high mass analogue to a low mass star forming core is studied. Line and continuum observations from JCMT, Mopra Telescope and Spitzer are presented and modelled in detail using a 3D molecular line radiative transfer code. In almost every way JCMT 18354-0649S is a scaled-up version of a typical low mass core with similar temperatures, chemical abundances and densities. The difference is that both the infall velocity and the turbulent width of the line profiles are an order of magnitude larger. While the higher infall velocity is expected due to the large mass of JCMT 18354-0649S, we suggest that the dissipation of this highly supersonic turbulence may lead to the creation of dense clumps of gas that surround the high mass core.
We point out the possibility of the {\em partial} conservation of the seniority quantum number when most eigenstates are mixed in seniority but some remain pure. This situation occurs in nuclei for the $g_{9/2}$ and $h_{9/2}$ shells where it is at the origin of the existence of seniority isomers in the ruthenium and palladium isotopes. It also occurs for $f$ bosons.
Solutions for cylindrically symmetric spacetimes in f(R) gravity are studied. As a first approach, R=constant is assumed. A solution was found such that it is equivalent to a result given by Azadi et al. for R=0 and a metric was found for R=constant different from zero. Comparison with the case of general relativity with cosmological constant is made and the metric constants are given in terms of \Lambda. Overlap with arXiv:0810.4673 [gr-qc] by A. Azadi, D. Momeni and M. Nouri-Zonoz
The dynamics of supercritical fluids, a state of matter beyond the gas-liquid critical point, changes from diffusive to oscillatory motions at high pressure. This transition is believed to occur across a locus of thermodynamic states called the Frenkel line. The Frenkel line has been extensively investigated from the viewpoint of the dynamics, but its structural meaning is not still well understood. This letter interprets the mesoscopic picture of the Frenkel line entirely based on a topological and geometrical framework. This discovery makes it possible to understand the mechanism of rigid/non-rigid transition based not on the dynamics of individual atoms, but on their instantaneous configurations. The topological classification method reveals that the percolation of solid-like structures occurs above the rigid-nonrigid crossover densities.
We study the contribution to flavor changing neutral current processes from box diagrams with light higgsinos and squarks. Starting with just the Cabbibo Kobayashi Maskawa (CKM) phase, we find contributions to the $K^0$ and $B^0$ meson mass matrices that are out of phase with the Standard Model contributions in the case of substantial mixing between the up-type squarks. This difference in phase could be large enough to be detected at the proposed $B$ factories, with interesting implications for the unitarity triangle of CKM matrix elements.
Using fermionic techniques, we compute exactly the large deviation function (ldf) of the time-integrated injected power in several one-dimensional dissipative systems of classical spins. The dynamics are T=0 Glauber dynamics supplemented by an injection mechanism, which is taken as a Poissonian flipping of one particular spin. We discuss the physical content of the results, specifically the influence of the rate of the Poisson process on the properties of the ldf.
In this paper we prove a large deviation principle for the empirical drift of a one-dimensional Brownian motion with self-repellence called the Edwards model. Our results extend earlier work in which a law of large numbers, respectively, a central limit theorem were derived. In the Edwards model a path of length $T$ receives a penalty $e^{-\beta H_T}$, where $ H_T$ is the self-intersection local time of the path and $\beta\in(0,\infty)$ is a parameter called the strength of self-repellence. We identify the rate function in the large deviation principle for the endpoint of the path as $\beta^{\frac 23} I(\beta^{-\frac 13}\cdot)$, with $I(\cdot)$ given in terms of the principal eigenvalues of a one-parameter family of Sturm-Liouville operators. We show that there exist numbers $0<b^{**}<b^*<\infty$ such that: (1) $I$ is linearly decreasing on $[0,b^{**}]$; (2) $I$ is real-analytic and strictly convex on $(b^{**},\infty)$; (3) $I$ is continuously differentiable at $b^{**}$; (4) $I$ has a unique zero at $b^*$. (The latter fact identifies $b^*$ as the asymptotic drift of the endpoint.) The critical drift $b^{**}$ is associated with a crossover in the optimal strategy of the path: for $b\geq b^{**}$ the path assumes local drift $b$ during the full time $T$, while for $0\leq b<b^{**}$ it assumes local drift $b^{**}$ during time $\frac{b^{**}+b}{2b^{**}}T$ and local drift $-b^{**}$ during the remaining time $\frac{b^{**}-b}{2b^{**}}T$. Thus, in the second regime the path makes an overshoot of size $\frac{b^{**}-b}{2}T$ in order to reduce its intersection local time.
We report on evidence of the inhomogeneity (multiplicity) of the stellar population in the Galactic globular cluster (GC) NGC 3201, which is irregularly reddened across its face. We carried out a more detailed and careful analysis of our recently published new multi-color photometry in a wide field of the cluster with particular emphasis on the U band. Using the photometric data corrected for differential reddening, we found for the first time two key signs of the inhomogeneity in the cluster's stellar population and of its radial variation in the GC. These are (1) an obvious trend in the color-position diagram, based on the (U-B) color-index, of red giant branch (RGB) stars, which shows that the farther from the cluster's center, the bluer on average the (U-B) color of the stars is; and (2) the dependence of the radial distribution of sub-giant branch (SGB) stars in the cluster on their U magnitude, where brighter stars are less centrally concentrated than their fainter counterparts at a confidence level varying between 99.2% and 99.9% depending on the color-index used to select the stars. The same effects were recently found by us in the GC NGC 1261. However, contrary to NGC 1261, we are not able to unambiguously suggest which of the sub-populations of SGB/RGB stars can be the progenitor of blue and red horizontal branch stars of the cluster. Apart from M4, NGC 3201 is another GC very probably with an inhomogeneous stellar population, which has essentially lower mass than the most massive Galactic GCs where multiple stellar populations were unambiguously detected for the first time
Starting from the light-cone plasma (LCP) distribution of gluons produced in proton-proton collisions, we derive the invariant charged-particle yield dN/dyd^2pT in heavy-ion collisions. Multiple scattering of partons in the other nucleus leads to pT broadening, which depends on the centrality of the collision. The resulting change of the LCP parameters determines the distributions of charged particles. The charged-particle multiplicity dN/deta at eta=0 normalized to the number of participating nucleons has a universal centrality dependence, common to RHIC and LHC. This universal increase is of geometrical origin. Such a universality can be broken by the energy dependent coherence effect, shadowing and mutual boosting of the saturation scales. However, we found these effects to essentially compensate each other, leaving the centrality dependence of multiplicity approximately universal.
The TGRS (Transient Gamma-Ray Spectrometer) experiment is a high-resolution germanium detector launched on the WIND satellite on Nov. 1, 1994. Although primarily intended to study gamma-ray bursts and solar flares, TGRS also has the capability of studying slower transients (e.g. x-ray novae) and certain steady sources. We present here results on the narrow 511 keV annihilation line from the general direction of the Galactic Center accumulated over the period Jan. 1995 through Oct. 1995. These results were obtained from the TGRS occultation mode, in which a lead absorber occults the Galactic Center region for 1/4 of each spacecraft rotation, thus chopping the 511 keV signal. The occulted region is a band in the sky of width 16 degrees that passes through the Galactic Center. We detect the narrow annihilation line from the galactic center with flux = $(1.64\pm0.09)\times10^{-3} {photons} {cm}^{-2} {s}^{-1}$. The data are consistent with a single point source at the galactic center, but a distributed source of extent up to ~30 degrees cannot be ruled out. No evidence for temporal variability on time scales longer than 1 month was found.
The idea that the TeV air showers, thought to be produced by >10 TeV gamma rays from Mrk 501, can be mimicked by coherent bunches of sub-TeV photons is reexamined, focusing on fundamental considerations. In particular, it is shown that the minimum spot size of the beam of pulsed TeV photons arriving at Earth is on the order of a few kilometers, unless a lens with certain characteristics is placed between the TeV laser and Earth. The viability of the laser production mechanism proposed by Harwit et al. (2000) is also reassessed.
In this paper we consider the asymptotic behaviour of all moments of the interparticle distance and of all mixed moments of an isotropic Brownian stochastic flow which serves as a smooth approximation of the Arratia flow.
The number of homomorphisms from a finite graph $F$ to the complete graph $K_n$ is the evaluation of the chromatic polynomial of $F$ at $n$. Suitably scaled, this is the Tutte polynomial evaluation $T(F;1-n,0)$ and an invariant of the cycle matroid of $F$. De la Harpe and Jaeger \cite{dlHJ95} asked more generally when is it the case that a graph parameter obtained from counting homomorphisms from $F$ to a fixed graph $G$ depends only on the cycle matroid of $F$. They showed that this is true when $G$ has a generously transitive automorphism group (examples include Cayley graphs on an abelian group, and Kneser graphs).   Using tools from multilinear algebra, we prove the converse statement, thus characterizing finite graphs $G$ for which counting homomorphisms to $G$ yields a matroid invariant. We also extend this result to finite weighted graphs $G$ (where to count homomorphisms from $F$ to $G$ includes such problems as counting nowhere-zero flows of $F$ and evaluating the partition function of an interaction model on $F$).