ShantanuT01/DACTYL-Pretraining huggingface dataset:
This document describes a Fortran 95 package for carrying out DGLAP evolution and other common manipulations of parton distribution functions (PDFs). The PDFs are represented on a grid in x-space so as to avoid limitations on the functional form of input distributions. Good speed and accuracy are obtained through the representation of splitting functions in terms of their convolution with a set of piecewise polynomial basis functions, and Runge-Kutta techniques are used for the evolution in Q. Unpolarised evolution is provided to NNLO, including heavy-quark thresholds in the MSbar scheme, and longitudinally polarised evolution to NLO. The code is structured so as to provide simple access to the objects representing splitting functions and PDFs, making it possible for a user to extend the facilities already provided. A streamlined interface is also available, facilitating use of the evolution part of the code from F77 and C/C++.
We consider the generalized two-dimensional Zakharov-Kuznetsov equation $u_t+\partial_x \Delta u+\partial_x(u^{k+1})=0$, where $k\geq3$ is an integer number. For $k\geq8$ we prove local well-posedness in the $L^2$-based Sobolev spaces $H^s(\mathbb{R}^2)$, where $s$ is greater than the critical scaling index $s_k=1-2/k$. For $k\geq 3$ we also establish a sharp criteria to obtain global $H^1(\R^2)$ solutions. A nonlinear scattering result in $H^1(\R^2)$ is also established assuming the initial data is small and belongs to a suitable Lebesgue space.
General spinning brane bound states are constructed, along with their near-horizon limits which are relevant as dual descriptions of non-commutative field theories. For the spinning D-brane world volume theories with a B-field a general analysis of the gauge coupling phase structure is given, exhibiting various novel features, already at the level of zero angular momenta. We show that the thermodynamics is equivalent to the commutative case at large N and we discuss the possibility and consequences of finite N. As an application of the general analysis, the range of validity of the thermodynamics for the NCSYM is discussed. In view of the recently conjectured existence of a 7-dimensional NCSYM, the thermodynamics of the spinning D6-brane theory, for which a stable region can be found, is presented in detail. Corresponding results for the spinning M5-M2 brane bound state, including the near-horizon limit and thermodynamics, are given as well.
This note simplifies the proof of a recent result on the oscillation of the prime product in Martens Theorem, and provides a quantitative expression for the error term. In addition, the corresponding oscillation results for the finite sums of the reciprocal of the primes up to a fixed number and other finite sums and products are also given.
In this paper, we investigate the dynamics behaviors of genuine multipartite Einstein-Podolsky-Rosen steering (GMS) and genuine multipartite nonlocality (GMN), and explore how to recover the lost GMS and GMN under a mixed decoherence system. Explicitly, the decoherence system can be modeled by that a tripartite Werner-type state suffers from the non-Markovian regimes and one subsystem of the tripartite is under a non-inertial frame. The conditions for steerable and nonlocal states can be obtained with respect to the tripartite Werner-type state established initially. GMS and GMN are very fragile and vulnerable under the influence of the collective decoherence. GMS and GMN will vanish with growing intensity of the Unruh effect and the non-Markovian reservoir. Besides, all achievable GMN's states are steerable, while not every steerable state (GMS's state) can achieve nonlocality. It means that the steering-nonlocality hierarchy is still tenable and GMN's states are a strict subset of the GMS's states in such a scenario. Subsequently, we put forward an available methodology to recover the damaged GMS and GMN. It turns out that the lost GMS and GMN can be effectively restored, and the ability of GMS and GMN to suppress the collective decoherence can be enhanced.
Let $A$ be a sequence of positive integers and $P(A)$ be the set of all integers which are the finite sum of distinct terms of $A$. For given positive integers $u\in\{4,7,8\}\cup\{u:u\ge11\}$ and $v\ge 3u+5$ we know that $u+v+1$ is the critical value of $b_3$ such that there exists a sequence $A$ of positive integers for which $P(A)=\mathbb{N}\backslash \{u<v<b_3<\cdots\}$. In this paper, we obtain the critical value of $b_k$.
We develop a model of the white dwarf (WD) - red dwarf (RD) binaries AR Sco and AE Aqr as systems in a transient propeller stage of highly asynchronous intermediate polars. The WDs are relatively weakly magnetized with magnetic field of $\sim 10^6$ G. We explain the salient observed features of the systems due to the magnetospheric interaction of two stars. Currently, the WD's spin-down is determined by the mass loading of the WD's magnetosphere from the RD's at a mild rate of $\dot{M}_{WD} \sim 10^{-11} M_\odot $/yr. Typical loading distance is determined by the ionization of the RD's wind by the WD's UV flux. The WD was previously spun up by a period of high accretion rate from the RD via Roch lobe overflow with $\dot{M} \sim 10^{-9} M_\odot $/yr, acting for as short a period as tens of thousands of years. The non-thermal X-ray and optical synchrotron emitting particles originate in reconnection events in the magnetosphere of the WD due to the interaction with the flow from the RD. In the case of AR Sco, the reconnection events produce signals at the WD's rotation and beat periods - this modulation is due to the changing relative orientation of the companions' magnetic moments and resulting variable reconnection conditions. Radio emission is produced in the magnetosphere of the RD, we hypothesize, in a way that it is physically similar to the Io-induced Jovian decametric radiation.
This article concerns the formation and structure of dark matter halos, including (1) their radial density profiles, (2) their abundance, and (3) their merger rates. The last topic may be relevant to the nature of the small, bright, high-redshift galaxies discovered by the Lyman break technique. (1) Study of a statistical sample of galaxy-mass dark halos in high-resolution Adaptive Refinement Tree simulations shows that they have a central density profile p(r) \propto 1/r^g with g \approx 0.2, in agreement with data on dark-matter-dominated disk galaxies. We present recent, higher resolution results on this. (2) Another important new result is that the Press-Schechter approximation predicts about twice as many galaxy-mass halos at z=0 as are present in large dissipationless N-body simulations; more generally, PS overpredicts the abundance of M ~< 0.1M_* halos at all redshifts. (3) Finally, we discuss the assembly of these halos, in particular the merger rate of (sub-)halos at high redshift and the distribution of the starbursts that these mergers are likely to trigger. If most of the Lyman-break galaxies are such starbursts, this perhaps resolves the apparent paradox that these galaxies appear to cluster like massive halos (~10^{12} M_\odot), while their relatively low linewidths and their spectral energy distributions suggest that they have relatively low mass (few X 10^{10} M_\odot) and young ages (few X 10^8 yr). It also predicts much more star formation at high redshift in CDM-type hierarchical models for structure formation than if only quiescent star formation is included.
Domain wall dynamics in a magnetoelectric antiferromagnet is analyzed, and its implications for magnetoelectric memory applications are discussed. Cr$_2$O$_3$ is used in the estimates of the materials parameters. It is found that the domain wall mobility has a maximum as a function of the electric field due to the gyrotropic coupling induced by it. In Cr$_2$O$_3$ the maximal mobility of 0.1 m/(s$\times$Oe) is reached at $E\approx0.06$ V/nm. Fields of this order may be too weak to overcome the intrinsic depinning field, which is estimated for B-doped Cr$_2$O$_3$. These major drawbacks for device implementation can be overcome by applying a small in-plane shear strain, which blocks the domain wall precession. Domain wall mobility of about 0.7 m/(s$\times$Oe) can then be achieved at $E=0.2$ V/nm. A split-gate scheme is proposed for the domain-wall controlled bit element; its extension to multiple-gate linear arrays can offer advantages in memory density, programmability, and logic functionality.
It is an easy observation that a natural greedy approach yields a $\left(d-O(1)\right)$-factor approximation algorithm for the maximum induced matching problem in $d$-regular graphs. The only considerable and non-trivial improvement of this approximation ratio was obtained by Gotthilf and Lewenstein using a combination of the greedy approach and local search, where understanding the performance of the local search was the challenging part of the analysis. We study the performance of their local search when applied to general graphs, $C_4$-free graphs, $\{C_3,C_4\}$-free graphs, $C_5$-free graphs, and claw-free graphs. As immediate consequences, we obtain approximation algorithms for the maximum induced matching problem restricted to the $d$-regular graphs in these classes.
A number of L2$_1$ phase alloys (composition X$_2$YZ) are half-metallic. Although this structure is typically described in terms of an fcc Bravais lattice with a 4 atom basis, it can be viewed more simply as a variant of bcc or B2 in which planes of X$_2$ alternate with planes of YZ along the 001 direction. Using ab-initio electronic structure calculations, we have investigated planar insertions along 001 into the L2$_1$ structure. For most scenarios, insertion of single or double atomic layers of Cr into Co$_2$MnGe or Co$_2$MnSi did not destroy the half-metallic property. One insertion of a Cr layer into Co$_2$MnGe was observed to increase the gap. In fact, we observed that for a large number of insertions using various transition metals or combinations of transition metals and non-transition metals, the band gap in the minority channel at the Fermi energy remains. An ad hoc rule that seems to partially capture the tendency to form half-metals can be formulated as: "001 planar insertions that can plausibly yield 8 down spin electrons on the X$_2$ layer and 4 down spin electrons on the YZ layer yield half-metals".
Let $R$ be a commutative ring with $1\in R$ and $R^{\ast}$ be the multiplicative group of its units. In 1969, Nagell introduced the exceptional unit $u$ if both $u$ and $1-u$ belong to $R^{\ast}$. Let $\mathbb{Z}_n$ be the ring of residue classes modulo $n$. In this paper, given an integer $k\ge 2$, we obtain an exact formula for the number of ways to represent each element of $ \mathbb{Z}_n$ as the sum of $k$ exceptional units. This generalizes a recent result of J. W. Sander for the case $k=2$.
Let H=A+UBU* where A and B are two N-by-N Hermitian matrices and U is a Haar-distributed random unitary matrix, and let \mu_H, \mu_A, and \mu_B be empirical measures of eigenvalues of matrices H, A, and B, respectively. Then, it is known (see, for example, Pastur-Vasilchuk, CMP, 2000, v.214, pp.249-286) that for large N, measure \mu_H is close to the free convolution of measures \mu_A and \mu_B, where the free convolution is a non-linear operation on probability measures.   The large deviations of the cumulative distribution function of \mu_H from its expectation have been studied by Chatterjee in in JFA, 2007, v. 245, pp.379-389. In this paper we improve Chatterjee's concentration inequality and show that it holds with the rate which is quadratic in N.   In addition, we prove a local law for eigenvalues of H, by showing that the normalized number of eigenvalues in an interval converges to the density of the free convolution of \mu_A and \mu_B provided that the interval has width (log N)^{-1/2}.
These are the notes for a series of lectures given at the Clay Mathematical Institute Summer School in Buzios, July 11 - August 7, 2010. We review some of the recent aspects of scaling limits of random trees and planar maps, in particular via their relations with bijective enumeration and Gromov-Hausdorff convergence.
Let f be a non-CM newform of weight k > 1.   Let L be a subfield of the coefficient field of f.   We completely settle the question of the density of the set of primes p such that the p-th coefficient of f generates the field L. This density is determined by the inner twists of f. As a particular case, we obtain that in the absence of non-trivial inner twists, the density is 1 for L equal to the whole coefficient field. We also present some new data on reducibility of Hecke polynomials, which suggest questions for further investigation.
Materials that demonstrate large magnetoresistance have attracted significant interest for many decades. Recently, extremely large tunnel magnetoresistance (TMR) has been reported by several groups across ultrathin CrI$_3$ by exploiting the weak antiferromagnetic coupling between adjacent layers. Here, we report a comparative study of TMR in all three chromium trihalides (CrX$_3$, X= Cl, Br, or I) in the two-dimensional limit. As the materials exhibit different transition temperatures and interlayer magnetic ordering in the ground state, tunneling measurements allow for an easy determination of the field-temperature phase diagram for the three systems. By changing sample thickness and biasing conditions, we then demonstrate how to maximize and further tailor the TMR response at different temperatures for each material. In particular, near the magnetic transition temperature, TMR is non-saturating up to the highest fields measured for all three compounds owing to the large, field-induced exchange coupling.
The non-equilibrium statistical mechanics and kinetic theory for a model of a confined quasi-two-dimensional gas of inelastic hard spheres is presented. The dynamics of the particles includes an effective mechanism to transfer the energy injected in the vertical direction to the horizontal degrees of freedom. The Enskog approximation is formulated and used as the basis to investigate the temperature and the distribution function of the steady state eventually reached by the system. An exact scaling of the distribution function of the system having implications on the form of its moments is pointed out. The theoretical predictions are compared with numerical results obtained by a particle simulation method, and a good agreement is found.
To study the dust obscured phase of the galaxy evolution during the peak of the Star Formation Rate (SFR) and the Black Hole Accretion Rate (BHAR) density functions ($z = 1 - 4$), rest frame mid-to-far infrared (IR) spectroscopy is needed. At these frequencies, dust extinction is at its minimum and a variety of atomic and molecular transitions, tracing most astrophysical domains, occur. The future IR space telescope mission, SPICA, fully redesigned with its $2.5\, \rm{m}$ mirror cooled down to $T < 8\, \rm{K}$, will be able to perform such observations. With SPICA, we will: 1) obtain a direct spectroscopic measurement of the SFR and of the BHAR histories, 2) measure the evolution of metals and dust to establish the matter cycle in galaxies, 3) uncover the feedback and feeding mechanisms in large samples of distant galaxies, either AGN- or starburst-dominated, reaching lookback times of nearly 12 Gyr. SPICA large-area deep surveys will provide low-resolution, mid-IR spectra and continuum fluxes for unbiased samples of tens of thousands of galaxies, and even the potential to uncover the youngest, most luminous galaxies in the first few hundred million years. In this talk a brief review of the scientific preparatory work that has been done in extragalactic astronomy by the SPICA Collaboration will be given.
We explicitly derive a connection between quantum circuits utilising IBM's quantum gate set and multivariate quadratic polynomials over integers modulo 8. We demonstrate that the action of a quantum circuit over input qubits can be written as generalized Walsh-Hadamard transform. Here, we derive the polynomials corresponding to implementations of the Swap gate and Toffoli gate using IBM-Q gate set.
In this work, the short-time dynamics of simple liquid is explored both analytically and numerically with the focus on the interplay between the density fluctuations in a volume surrounding a chosen particle and its random walk motion. The particles interact via the Lennard-Jones potential with parameters corresponding to liquid argon. For large times, analytical calculations based on the fluctuation theory provides an explicit expression reproducing isothermal change of the self-diffusion coefficient in liquid argon corresponding to the experimental data. These results lead to the conclusion that such behavior is based on the reduced mobility of particles reflected in their density fluctuations that can be equivalently achieved in the cases of either low temperatures and pressures (supercooling) or moderate temperatures and high pressures (overdamping).
$Context.$ The traditional approach to characterize the structure of molecular clouds is to map their line emission.   $Aims.$ We aim to test and apply a stratified random sampling technique that can characterize the line emission from molecular clouds more efficiently than mapping.   $Methods.$ We sampled the molecular emission from the Perseus cloud using the H2 column density as a proxy. We divided the cloud into ten logarithmically spaced column density bins, and we randomly selected ten positions from each bin. The resulting 100 cloud positions were observed with the IRAM 30m telescope, covering the 3mm-wavelength band and parts of the 2 and 1mm bands.   $Results.$ We focus our analysis on 11 molecular species detected toward most column density bins. In all cases, the line intensity is tightly correlated with the H2 column density. For the CO isotopologs, the trend is relatively flat, while for high-dipole moment species such as HCN, CS, and HCO+ the trend is approximately linear. We reproduce this behavior with a cloud model in which the gas density increases with column density, and where most species have abundance profiles characterized by an outer photodissociation edge and an inner freeze-out drop. The intensity behavior of the high-dipole moment species arises from a combination of excitation effects and molecular freeze out, with some modulation from optical depth. This quasi-linear dependence with the H2 column density makes the gas at low column densities dominate the cloud-integrated emission. It also makes the emission from most high-dipole moment species proportional to the cloud mass inside the photodissociation edge.   $Conclusions.$ Stratified random sampling is an efficient technique for characterizing the emission from whole molecular clouds. It shows that despite the complex appearance of Perseus, its molecular emission follows a relatively simple pattern.
We present the analysis of the integrated spectral energy distribution (SED) from the ultraviolet (UV) to the far-infrared and H$\alpha$ of a sample of 29 local systems and individual galaxies with infrared (IR) luminosities between 10^11 Lsun and 10^11.8 Lsun. We have combined new narrow-band H$\alpha$+[NII] and broad-band g, r optical imaging taken with the Nordic Optical Telescope (NOT), with archival GALEX, 2MASS, Spitzer, and Herschel data. The SEDs (photometry and integrated H$\alpha$ flux) have been fitted with a modified version of the MAGPHYS code using stellar population synthesis models for the UV-near-IR range and thermal emission models for the IR emission taking into account the energy balance between the absorbed and re-emitted radiation. From the SED fits we derive the star-formation histories (SFH) of these galaxies. For nearly half of them the star-formation rate appears to be approximately constant during the last few Gyrs. In the other half, the current star-formation rate seems to be enhanced by a factor of 3-20 with respect to that occured ~1 Gyr ago. Objects with constant SFH tend to be more massive than starbursts and they are compatible with the expected properties of a main-sequence (M-S) galaxy. Likewise, the derived SFHs show that all our objects were M-S galaxies ~1 Gyr ago with stellar masses between 10^10.1 and 10^11.5 Msun. We also derived from our fits the average extinction (A_v=0.6-3 mag) and the polycyclic aromatic hydrocarbons (PAH) luminosity to L(IR) ratio (0.03-0.16). We combined the A_v with the total IR and H$\alpha$ luminosities into a diagram which can be used to identify objects with rapidly changing (increasing or decreasing) SFR during the last 100 Myr.
Several image pattern recognition tasks rely on superpixel generation as a fundamental step. Image analysis based on superpixels facilitates domain-specific applications, also speeding up the overall processing time of the task. Recent superpixel methods have been designed to fit boundary adherence, usually regulating the size and shape of each superpixel in order to mitigate the occurrence of undersegmentation failures. Superpixel regularity and compactness sometimes imposes an excessive number of segments in the image, which ultimately decreases the efficiency of the final segmentation, specially in video segmentation. We propose here a novel method to generate superpixels, called iterative over-segmentation via edge clustering (ISEC), which addresses the over-segmentation problem from a different perspective in contrast to recent state-of-the-art approaches. ISEC iteratively clusters edges extracted from the image objects, providing adaptive superpixels in size, shape and quantity, while preserving suitable adherence to the real object boundaries. All this is achieved at a very low computational cost. Experiments show that ISEC stands out from existing methods, meeting a favorable balance between segmentation stability and accurate representation of motion discontinuities, which are features specially suitable to video segmentation.
Luminous Infrared (IR) Galaxies (LIRGs) are an important cosmological class of galaxies as they are the main contributors to the co-moving star formation rate density of the universe at z=1. In this paper we present a GTO Spitzer IRS program aimed to obtain spectral mapping of a sample of 14 local (d<76Mpc) LIRGs. The data cubes map, at least, the central 20arcsec x 20arcsec to 30arcsec x 30arcsec regions of the galaxies, and use all four IRS modules covering the full 5-38micron spectral range. The final goal of this project is to characterize fully the mid-IR properties of local LIRGs as a first step to understanding their more distant counterparts. In this paper we present the first results of this GTO program. The IRS spectral mapping data allow us to build spectral maps of the bright mid-IR emission lines (e.g., [NeII], [NeIII], [SIII], H_2), continuum, the 6.2 and 11.3micron PAH features, and the 9.7micron silicate feature, as well as to extract 1D spectra for regions of interest in each galaxy. The IRS data are used to obtain spatially resolved measurements of the extinction using the 9.7micron silicate feature, and to trace star forming regions using the neon lines and the PAH features. We also investigate a number of AGN indicators, including the presence of high excitation emission lines and a strong dust continuum emission at around 6micron. We finally use the integrated Spitzer/IRS spectra as templates of local LIRGs. We discuss several possible uses for these templates, including the calibration of the star formation rate of IR-bright galaxies at high redshift. We also predict the intensities of the brightest mid-IR emission lines for LIRGs as a function of redshift, and compare them with the expected sensitivities of future space IR missions.