ShantanuT01/DACTYL-Pretraining huggingface dataset:
We give Deterministic Primality tests for large families of numbers. These tests were inspired in the recent and celebrated Agrawal-Kayal-Saxena (AKS) test. The AKS test has proved polynomial complexity O ((log n)^12) and they expect it to be O ((log n)^6) . Our tests have proved complexity O ((log n)^6). The complexity decreases to O ((log n)^4) as the power of 2 dividing n + 1 or n - 1 increases. On large enough primes, our tests, in their worst case, run at least 2^9 times faster than the AKS test.
Existing methods for single images raindrop removal either have poor robustness or suffer from parameter burdens. In this paper, we propose a new Adjacent Aggregation Network (A^2Net) with lightweight architectures to remove raindrops from single images. Instead of directly cascading convolutional layers, we design an adjacent aggregation architecture to better fuse features for rich representations generation, which can lead to high quality images reconstruction. To further simplify the learning process, we utilize a problem-specific knowledge to force the network focus on the luminance channel in the YUV color space instead of all RGB channels. By combining adjacent aggregating operation with color space transformation, the proposed A^2Net can achieve state-of-the-art performances on raindrop removal with significant parameters reduction.
We consider a static spherically symmetric thin shell wormhole collides with another thin shell consisting of ordinary matter. By employing the geometrical constraint, which leads to the conservation of energy and momentum, we show that the state after the collision can be solved from the initial data. In the low speed approximation, the solutions are rather simple. The shell may either bounce back or pass through the wormhole. In either case, the wormhole shrinks right after the collision. In the "bouncing" case, a surprising result is that the radial speeds before and after the collision satisfy an addition law, which is independent of the masses of the wormhole and the shell. Once the shell passes through the wormhole, we find that the shell always expands. However, the expansion rate is the same as its collapsing rate right before the collision. Finally, we find out the solution for the shell moving together with the wormhole.
A complex non-Newtonian fluid models the nematic liquid crystal flows confined in a bounded domain in $\mathbb{R}^3$ is considered. The system is a forced incompressible Navier-Stokes equation coupled with a parabolic type Q-tensor flows. Under suitable condition on the coefficients of the Landau-de Gennes energy functional, global strong solution for small initial data is proved.
The electroweak phase transition provides the most attractive framework to account for the baryon asymmetry of the universe. Comparing results of perturbative and nonperturbative studies is not straightforward, however, due to the different coupling constant definitions. The perturbative one stems from the $\bar{\mathrm{MS}}$ subtraction scheme, while the nonperturbative one uses the static quark potential. The momentum-space perturbative static potential is calculated in the SU(2)--Higgs model, and is Fourier transformed into coordinate space. Based on the connection between the coupling constants, two-loop perturbative and 4-dimensional lattice simulation results are contrasted. The thermodynamical parameters of the phase transition indicate that perturbative results are reliable only for low Higgs masses, far from the endpoint. The value of the endpoint can be refined to $72.1\pm1.4$ GeV. The Higgs mass range for which dimensional reduction yields reliable results is identified. As an extension of the standard model, the MSSM is also studied. Some useful trends are indicated by a simple one-loop perturbative approach: baryogenesis requirements are more easily met if the stop is lighter thanthe top; colour-breaking phase transition may be possible, etc. In order to perform 4D nonperturbative studies the supercomputer PMS was built at E\"otv\"os University. The results and the techniques of the simulations of the bosonic sector of the MSSM performed on PMS are presented. A phase diagram is given, the bubble wall is studied. The cosmologically relevant part of the parameter space is analysed. The results show that baryogenesis is possible within the MSSM if $m_h\leq 103\pm 4$ GeV.
Any Dark Energy (DE) or Modified Gravity (MG) model that deviates from a cosmological constant requires a consistent treatment of its perturbations, which can be described in terms of an effective entropy perturbation and an anisotropic stress. We have considered a recently proposed generic parameterisation of DE/MG perturbations and compared it to data from the Planck satellite and six galaxy catalogues, including temperature-galaxy (Tg), CMB lensing-galaxy and galaxy-galaxy (gg) correlations. Combining these observables of structure formation with tests of the background expansion allows us to investigate the properties of DE/MG both at the background and the perturbative level. Our constraints on DE/MG are mostly in agreement with the cosmological constant paradigm, while we also find that the constraint on the equation of state w (assumed to be constant) depends on the model assumed for the perturbation evolution. We obtain $w=-0.92^{+0.20}_{-0.16}$ (95% CL; CMB+gg+Tg) in the entropy perturbation scenario; in the anisotropic stress case the result is $w=-0.86^{+0.17}_{-0.16}$. Including the lensing correlations shifts the results towards higher values of w. If we include a prior on the expansion history from recent Baryon Acoustic Oscillations (BAO) measurements, we find that the constraints tighten closely around $w=-1$, making it impossible to measure any DE/MG perturbation evolution parameters. If, however, upcoming observations from surveys like DES, Euclid or LSST show indications for a deviation from a cosmological constant, our formalism will be a useful tool towards model selection in the dark sector.
We study the crossover between thermodynamic Casimir forces arising from long-range fluctuations due to Goldstone modes and those arising from critical fluctuations. Both types of forces exist in the low-temperature phase of O$(n)$ symmetric systems for $n>1$ in a $d$-dimensional ${L_\parallel^{d-1} \times L}$ slab geometry with a finite aspect ratio $\rho = L/L_\parallel$. Our finite-size renormalization-group treatment for periodic boundary conditions describes the entire crossover from the Goldstone regime with a nonvanishing constant tail of the finite-size scaling function far below $T_c$ up to the region far above $T_c$ including the critical regime with a minimum of the scaling function slightly below $T_c$. Our analytic result for $\rho \ll 1$ agrees well with Monte Carlo data for the three-dimensional XY model. A quantitative prediction is given for the crossover of systems in the Heisenberg universality class.
The identification and characterisation of low-mass binaries is of importance for a range of astrophysical investigations. Low-mass binaries in young ($\sim10 - 100 $ Myr) moving groups (YMGs) are of particular significance as they provide unique opportunities to calibrate stellar models and evaluate the ages and coevality of the groups themselves. Low-mass M-dwarfs have pre-main sequence life times on the order of $\sim100$ Myr and therefore are continually evolving along a mass-luminosity track throughout the YMG phase, providing ideal laboratories for precise isochronal dating, if a model-independent dynamical mass can be measured. AstraLux lucky imaging multiplicity surveys have recently identified hundreds of new YMG low-mass binaries, where a subsample of M-dwarf multiples have estimated orbital periods less than 50 years. We have conducted a radial velocity survey of a sample of 29 such targets to complement the astrometric data. This will allow enhanced orbital determinations and precise dynamical masses to be derived in a shorter timeframe than possible with astrometric monitoring alone, and allow for a more reliable isochronal analysis. Here we present radial velocity measurements for our sample over several epochs. We report the detection of the three-component spectroscopic multiple 2MASS J05301858-5358483, for which the C component is a new discovery, and forms a tight pair with the B component. Originally identified as a YMG member, we find that this system is a likely old field interloper, whose high chromospheric activity level is caused by tidal spin-up of the tight BC pair. Two other triple systems with a tight pair exist in the sample, but for the rest of the targets we find that additional tidally synchronized companions are highly unlikely, providing further evidence that their high chromospheric activity levels are generally signatures of youth.
We determine the interface tension for the 100, 110 and 111 interface of the simple cubic Ising model with nearest-neighbour interaction using novel simulation methods. To overcome the droplet/strip transition and the droplet nucleation barrier we use a newly developed combination of the multimagnetic algorithm with the parallel tempering method. We investigate a large range of inverse temperatures to study the anisotropy of the interface tension in detail.
As an unstable light pure leptonic system, positronium is a very specific probe atom to test bound state QED. In contrast to ordinary QED for free leptons, the bound state QED theory is not so well understood and bound state approaches deserve highly accurate tests. We present a brief overview of precision studies of positronium paying special attention to uncertainties of theory as well as comparison of theory and experiment. We also consider in detail advantages and disadvantages of positronium tests compared to other QED experiments.
Co10Ge3O16 crystallizes in an intergrowth structure featuring alternating layers of spinel and rock salt. Variable-temperature powder synchrotron X-ray and neutron diffraction, magnetometry, and heat capacity experiments reveal a magnetostructural transition at T_N = 203 K. This rhombohedral-to-monoclinic transition involves a slight elongation of the CoO6 octahedra along the apical axis. Below T_N, the application of a large magnetic field causes a reorientation of the Co^2+ Ising spins. This metamagnetic transition is first-order as evidenced by a latent heat observed in temperature-dependent measurements. This transition is initially seen at T = 180 K as a broad upturn in the M-H near H_C = 3.9 T. The upturn sharpens into a kink at T = 120 K and a "butterfly" shape emerges, with the transition causing hysteresis at high fields while linear and reversible behavior persists at low fields. H_C decreases as temperature is lowered and the loops at positive and negative fields merge beneath T = 20 K. The antiferromagnetism is described by k_M = (00 1/2) and below T = 20 K a small uncompensated component with k_M = (000) spontaneously emerges. Despite the Curie-Weiss analysis and ionic radius indicating the Co2+ is in its high-spin state, the low-temperature M-H trends toward saturation at M_S = 1.0 uB/Co. We conclude that the field-induced state is a ferrimagnet, rather than a S = 1/2 ferromagnet. The unusual H-T phase diagram is discussed with reference to other metamagnets and Co(II) systems.
The main aim is to give a rigorous statement and proof of the slogan "the d-fold tensor product of distributions is an Euler system for GL_d". Of the few known examples of Euler systems, we look at those of cyclotomic units and of Beilinson-Kato elements. The cyclotomic units satisfy distribution property, and this is the key to the proof of the norm relation property for GL_1. For the Beilinson-Kato elements, the Siegel units satisfy distribution property, and the 2-fold tensor product, giving rise to elements in the K_2 of modular curves, satisfies the norm relation for GL_2. We make this common property clear, generalizing everything to GL_d.   As an application (our main arithmetic result), we construct elements in the motivic cohomology of Drinfeld modular schemes with integral coefficient and show that the norm relation common to Euler systems (i.e., the norm of one element is described using the local L-factor times another element) hold.   We use the language of Y-sites which was introduced in [Kon-Ya3] in order to simplify the computation common to the theory of automorphic forms. Instead of double cosets, we work more systematically with torsion modules and Q-morphisms between them. The idea is that torsion modules are level structures, and Q-morphisms induce morphisms between some moduli spaces. Chapters 1 and 3 serve as a sequel: further generalities on Y-sites, more examples of Y-sites, and proofs of some statements in loc.cit are given. An application is also given: we provide a group theoretic formulation of a conjecture of Tamagawa on affine curves over an algebraic closure of a finite field.
We present observations of ro-vibrational OH and CO emission from the Herbig Be star HD 100546. The emission from both molecules arises from the inner region of the disk extending from approximately 13 AU from the central star. The velocity profiles of the OH lines are narrower than the velocity profile of the [O I] 6300 Angstrom line indicating that the OH in the disk is not cospatial with the O I. This suggests that the inner optically thin region of the disk is largely devoid of molecular gas. Unlike the ro-vibrational CO emission lines, the OH lines are highly asymmetric. We show that the average CO and average OH line profiles can be fit with a model of a disk comprised of an eccentric inner wall and a circular outer disk. In this model, the vast majority of the OH flux (75%) originates from the inner wall, while the vast majority of the CO flux (65%) originates on the surface of the disk at radii greater than 13 AU. Eccentric inner disks are predicted by hydrodynamic simulations of circumstellar disks containing an embedded giant planet. We discuss the implications of such a disk geometry in light of models of planet disk tidal interactions and propose alternate explanations for the origin of the asymmetry.
(Abridged) We consider the interaction of a relativistically-moving shell, composed of thermal photons, a reversing magnetic field and a small admixture of charged particles, with a dense Wolf-Rayet wind. A thin outer layer of Wolf-Rayet material is entrained by the jet head; it cools and becomes Rayleigh-Taylor unstable, thereby providing an additional source of inertia and variability. Pair creation in the wind material, and the associated pre-acceleration, defines a characteristic radiative compactness at the point where the reverse shock has completed its passage back through the shell. We argue that the prompt gamma-ray emission is triggered by this external braking, at an optical depth ~1 to electron scattering. Torsional waves, excited by the forced reconnection of the reversing magnetic field, carry a fluctuating current, and are damped at high frequencies by the electrostatic acceleration of electrons and positrons. We show that inverse Compton radiation by the accelerated charges is stronger than their synchrotron emission, and is beamed along the magnetic field. Thermal radiation that is advected out from the base of the jet cools the particles. The observed relation between peak energy and isotropic luminosity is reproduced if the blackbody seeds are generated in a relativistic jet core that is subject to Kelvin-Helmholtz instabilities with the Wolf-Rayet envelope. This relation is predicted to soften to E_peak ~ L_iso^{1/4} below an isotropic luminosity L_iso ~ 3x10^{50} ergs/s. The duration of spikes in the inverse-Compton emission is narrower at higher frequencies, in agreement with the observed relation. The transition from prompt gamma-ray emission to afterglow can be explained by the termination of the thermal X-ray seed and the onset of synchrotron-self-Compton emission.
Long-slit echellograms of the high excitation planetary nebula NGC1501, reduced according to the methodology developed by Sabbadin et al. (2000a, b), allowed us to obtain the ``true'' distribution of the ionized gas in the eight nebular slices covered by the spectroscopic slit. A 3-D rendering procedure is described and applied, which assembles the tomographic maps and rebuilds the spatial structure. The images of NGC 1501, as seen in 12 directions separated by 15 deg, form a series of stereoscopic pairs giving surprising 3-D views in as many directions. The main nebula consists of an almost oblate ellipsoid of moderate ellipticity (a=44 arcsec, a/b=1.02, a/c=1.11), brighter in the equatorial belt, deformed by several bumps, and embedded in a quite homogeneous, inwards extended cocoon. Some reliability tests are applied to the rebuilt nebula; the radial matter profile, the small scale density fluctuations and the 2-D (morphology) - 3-D (structure) correlation are presented and analysed. The wide applications of the 3-D reconstruction to the morphology, physical conditions, ionization parameters and evolutionary status of expanding nebulae in general (planetary nebulae, nova and supernova remnants, shells around Population I Wolf-Rayet stars, nebulae ejected by symbiotic stars, bubbles surrounding early spectral type main sequence stars etc.) are introduced.
We study the effect of isospin degree of freedom on the balance energy (E$_{bal}$) as well as its mass dependence throughout the mass range 48-270 for two sets of isobaric systems with N/Z = 1 and 1.4 at different colliding geometries ranging from central to peripheral ones. Our findings reveal the dominance of Coulomb repulsion in isospin effects on E$_{bal}$ as well as its mass dependence throughout the range of the colliding geometry. Our results also indicate that the effect of symmetry energy and nucleon-nucleon cross section on E$_{bal}$ is uniform throughout the mass range and throughout the colliding geometry. We also present the counter balancing of nucleon-nucleon collisions and mean field by reducing the Coulomb and the counter balancing of Coulomb and mean filed by removing the nucleon-nucleon collisions.
Let each site of the square lattice $\mathbb{Z}^2$ be independently assigned one of three states: a \textit{trap} with probability $p$, a \textit{target} with probability $q$, and \textit{open} with probability $1-p-q$, where $0<p+q<1$. Consider the following game: a token starts at the origin, and two players take turns to move, where a move consists of moving the token from its current site $x$ to either $x+(0,1)$ or $x+(1,0)$. A player who moves the token to a trap loses the game immediately, while a player who moves the token to a target wins the game immediately. Is there positive probability that the game is \emph{drawn} with best play -- i.e.\ that neither player can force a win? This is equivalent to the question of ergodicity of a certain family of elementary one-dimensional probabilistic cellular automata (PCA). These automata have been studied in the contexts of enumeration of directed lattice animals, the golden-mean subshift, and the hard-core model, and their ergodicity has been noted as an open problem by several authors. We prove that these PCA are ergodic, and correspondingly that the game on $\mathbb{Z}^2$ has no draws.   On the other hand, we prove that certain analogous games \emph{do} exhibit draws for suitable parameter values on various directed graphs in higher dimensions, including an oriented version of the even sublattice of $\mathbb{Z}^d$ in all $d\geq3$. This is proved via a dimension reduction to a hard-core lattice gas in dimension $d-1$. We show that draws occur whenever the corresponding hard-core model has multiple Gibbs distributions. We conjecture that draws occur also on the standard oriented lattice $\mathbb{Z}^d$ for $d\geq 3$, but here our method encounters a fundamental obstacle.
We perform a momentum-space calculation of the reaction $pp \rightarrow pp\pi ^0$ near threshold. Direct production and pion rescattering are taken into account. For the latter a T-matrix obtained from a microscopic model of the $\pi N$ interaction is employed. The effects of some approximations commonly used in studies of $ pp \rightarrow pp\pi ^0$ \ are discussed. We find that those approximations overestimate the cross section and also modify its energy dependence. We obtain a significant contribution from rescattering, but not nearly enough to describe the data.
In solar coronal loops, thermal non-equilibrium (TNE) is a phenomenon that can occur when the heating is both highly-stratified and quasi-constant. Unambiguous observational identification of TNE would thus permit to strongly constrain heating scenarios. Up to now, while TNE is the standard interpretation of coronal rain, the long-term periodic evolution predicted by simulations has never been observed yet. However, the detection of long-period intensity pulsations (periods of several hours) has been recently reported with SoHO/EIT, and this phenomenon appears to be very common in loops. Moreover, the three intensity-pulsation events that we recently studied with SDO/AIA show strong evidence for TNE in warm loops. In the present paper, a realistic loop geometry from LFFF extrapolations is used as input to 1D hydrodynamic simulations. Our simulations show that for the present loop geometry, the heating has to be asymmetrical to produce TNE. We analyse in detail one particular simulation that reproduces the average thermal behavior of one of the pulsating loop bundle observed with AIA. We compare the properties of this simulation with the properties deduced from the observations. The magnetic topology of the LFFF extrapolations points to the presence of sites of preferred reconnection at one footpoint, supporting the presence of asymmetric heating. In addition, we can reproduce the temporal large-scale intensity properties of the pulsating loops. This simulation further strengthens the interpretation of the observed pulsations as signatures of TNE. This thus gives important information on the heating localization and time scale for these loops.
The observed height distribution of clusters obtained in strained epitaxy has been often interpreted in terms of electronic effects. We show that some aspects can be explained classically by the interplay of strain and edge energies. We find that soft materials can transform directly from monolayer into thicker islands by two-dimensional (2D) multilayer nucleation and growth. There is a critical thickness decreasing with the force constant. Thinner islands are thermodynamically forbidden, due to the insufficient stress relaxation upon clustering particularly under tensile stress. At sufficiently large misfits the barrier for 2D multilayer nucleation is significantly smaller than the barrier for subsequent single-layer nucleation. The effects are found to be quantitatively reasonable and offer a plausible explanation for the absence of thin islands and 2D growth of flattop islands usually attributed to quantum size effects.