ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this paper, we study the Waldschmidt constant of a generalized fat point subscheme $Z=m_1p_1+\cdots+m_rp_r$ of $\mathbb{P}^2$, where $p_1,\cdots,p_r$ are essentially distinct points on $\mathbb{P}^2$, satisfying the proximity inequalities. Furthermore, we prove its lower semi-continuity for $r\le 8$. Using this property, we also calculate the Waldschmidt constants of the fat point subschemes $Z=p_1+\cdots+p_5$ giving weak del Pezzo surfaces of degree 4.
A Markov operator $P$ on a probability space $(S,\Sigma,\mu)$, with $\mu$ invariant, is called {\it hyperbounded} if for some $1 \le p<q \le \infty$ it maps (continuously) $L^p$ into $L^q$.   We deduce from a recent result of Gl\"uck that a hyperbounded $P$ is quasi-compact, hence uniformly ergodic, in all $L^r(S,\mu)$, $1<r< \infty$. We prove, using a method similar to Foguel's, that a hyperbounded Markov operator has periodic behavior similar to that of Harris recurrent operators, and for the ergodic case obtain conditions for aperiodicity.   Given a probability $\nu$ on the unit circle, we prove that if the convolution operator $P_\nu f:=\nu*f$ is hyperbounded, then $\nu$ is atomless. We show that there is $\nu $ absolutely continuous such that $P_\nu$ is not hyperbounded, and there is $\nu$ with all powers singular such that $P_\nu$ is hyperbounded. As an application, we prove that if $P_\nu$ is hyperbounded, then for any sequence $(n_k)$ of distinct positive integers with   bounded gaps, $(n_kx)$ is uniformly distributed mod 1 for $\nu$ almost every $x$ (even when $\nu$ is singular).
We use astrometry, broad-band photometry and variability information from the Data Release 2 of ESA's Gaia mission (GDR2) to identify members of the Orphan Stream (OS) across the whole sky. The stream is traced above and below the celestial equator and in both Galactic hemispheres, thus increasing its visible length to ~ 210 degrees equivalent to ~150 kpc in physical extent. Taking advantage of the large number of RR Lyrae stars in the OS, we extract accurate distances and proper motions across the entire stretch of the tidal debris studied. As delineated by the GDR2 RR Lyrae, the stream exhibits two prominent twists in its shape on the sky which are accompanied by changes in the tangential motion. We complement the RR Lyrae maps with those created using GDR2 Red Giants and the DECam Legacy Survey Main Sequence Turn-Off stars. The behavior of the OS track on the sky is consistent across all three tracers employed. We detect a strong non-zero motion in the across-stream direction for a substantial portion of the stream. Such a misalignment between the debris track and the streaming velocity cannot be reproduced in a static gravitational potential and signals an interaction with a massive perturber.
Using the three versions of proximity potentials, namely proximity 1977, proximity 1988, and proximity 2000, we present a pocket formula for fusion barrier heights and positions. This was achieved by analyzing as many as 400 reactions with mass between 15 and 296. Our parametrized formula can reproduced the exact barrier heights and positions within an accuracy of $\pm1%$. A comparison with the experimental data is also in good agreement.
We study the torsion cohomology classes of Shimura varieties of type Kottwitz-Harris-Taylor and we show that " up to an arbitrary place " one can raise them to an automorphic representation. In application, to any mod $l$ system of Hecke eigenvalues appearing in the $\bar{\mathbb F}_l$-cohomology of a Shimura's variety of Kottwitz-Harris-Taylor type, we associate a $\bar{\mathbb F}_l$-Galois representation which Frobenius eigenvalues are given by Hecke's. Compared to the highly more general construction of Scholze, we gain both the simplicity of the proof and the control at places ramified and at those dividing $l$.
In this work, we discuss certain ballistic random walks in random environments on $\mathbb{Z}^d$, and prove the equivalence between the static and dynamic points of view in dimension $d\geq4$. Using this equivalence, we also prove a version of a local limit theorem which relates the local behavior of the quenched and annealed measures of the random walk by a prefactor.
A non-equilibrium picture of thermodynamics is discussed at the apparent horizon of FRW universe in $f(R,T)$ gravity, where $R$ is the Ricci scalar and $T$ is the trace of the energy-momentum tensor. We take two forms of the energy-momentum tensor of dark components and demonstrate that equilibrium description of thermodynamics is not achievable in both cases. We check the validity of the first and second law of thermodynamics in this scenario. It is shown that the Friedmann equations can be expressed in the form of first law of thermodynamics $T_hdS'_h+T_hd_{\jmath}S'=-dE'+W'dV$, where $d_{\jmath}S'$ is the entropy production term. Finally, we conclude that the second law of thermodynamics holds both in phantom and non-phantom phases.
We present a general definition of damage spreading in a pair of models. Using this general framework, one can define damage spreading in an objective manner, that does not depend on the particular dynamic procedure that is being used. The formalism is applied to the Domany-Kinzel cellular automaton in one dimension; the active phase of this model is shown to consist of three sub-phases, characterized by different damage-spreading properties.
We consider the problem of finding a function defined on $(0,\infty)$ from a countable set of values of its Laplace transform. The problem is severely ill-posed. We shall use the expansion of the function in a series of Laguerre polynomials to convert the problem in an analytic interpolation problem. Then, using the coefficients of Lagrange polynomials we shall construct a stable approximation solution.
The formulation of the First and Second Principles of thermodynamics for a particle in contact with a heat bath and submitted to an external force is analyzed, by means of the Boltzmann-Lorentz kinetic equation. The possible definitions of the thermodynamic quantities are discussed in the light of the H theorem verified by the distribution of the particle. The work fluctuation relations formulated by Bochkov and Kuzovlev, and by Jarzynski, respectively, are derived from the kinetic equation. In addition, particle simulations using both the direct simulation Monte Carlo method and Molecular Dynamics, are used to investigate the practical accuracy of the results. Work distributions are also measured, and they turn out to be rather complex. On the other hand, they seem to depend very little, if any, on the interaction potential between the intruder and the bath.
We report on a recent multi-band optical photometric and polarimetric observational campaign of the blazar OJ 287 which was carried out during September 2016 -- December 2017. We employed nine telescopes in Bulgaria, China, Georgia, Japan, Serbia, Spain and the United States. We collected over 1800 photometric image frames in BVRI bands and over 100 polarimetric measurements over ~175 nights. In 11 nights with many quasi-simultaneous multi-band (V, R, I) observations, we did not detect any genuine intraday variability in flux or color. On longer timescales, multiple flaring events were seen. Large changes in color with respect to time and in a color--magnitude diagram were seen, and while only a weak systematic variability trend was noticed in color with respect to time, the color--magnitude diagram shows a bluer-when-brighter trend. Large changes in the degree of polarization, and substantial swings in the polarization angle were detected. The fractional Stokes parameters of the polarization showed a systematic trend with time in the beginning of these observations, followed by chaotic changes and then an apparently systematic variation at the end. These polarization changes coincide with the detection and duration of the source at very high energies as seen by VERITAS. The spectral index shows a systematic variation with time and V-band magnitude. We briefly discuss possible physical mechanisms that could explain the observed flux, color, polarization, and spectral variability.
The Ca II K filtergrams from Kodaikanal Solar Observatory have been used to study the solar activity. The images are dominated by the chromospheric network and plages. Programs have been developed to obtain the network and plage indices from the daily images as functions of solar latitude and time. Preliminary results from the analysis are reported here. The network and plage indices were found to follow the sunspot cycle. A secondary peak is found during the declining activity period in both the indices. A comparison of network indices from the northern and the southern hemispheres shows that the former is more active than latter. However such an asymmetry is not clearly seen in the case of plage index.
We propose a generalization of the color codes based on finite groups $G$. For non-abelian groups, the resulting model supports non-abelian anyonic quasiparticles and topological order. We examine the properties of these models such as their relationship to Kitaev quantum double models, quasiparticle spectrum, and boundary structure.
These lectures give an overview of the ongoing application of effective field theory (EFT) and renormalization group (RG) concepts and methods to density functional theory (DFT), with special emphasis on the nuclear many-body problem.
In this paper, we study the spatial averages of the solution to the parabolic Anderson model driven by a space-time Gaussian homogeneous noise that is colored in time and space. We establish quantitative central limit theorems (CLT) of this spatial statistics under some mild assumptions, by using the Malliavin-Stein approach. The highlight of this paper is the obtention of rate of convergence in the colored-in-time setting, where one can not use It\^o's calculus due to the lack of martingale structure. In particular, modulo highly technical computations, we apply a modified version of second-order Gaussian Poincar\'e inequality to overcome this lack of martingale structure and our work improves the results by Nualart-Zheng (2020 \emph{Electron. J. Probab.}) and Nualart-Song-Zheng (2021 \emph{ALEA, Lat. Am. J. Probab. Math. Stat.}).
We show that the influence of spin-orbit (SO) coupling on the weak localization effect for electrons in graphene depends on the lack or presence of z/-z symmetry in the system. While for z/-z asymmetric SO coupling, disordered graphene should display a weak anti-localization behavior at lowest temperature, z/-z symmetric coupling leads to an effective saturation of decoherence time which can be partially lifted by an in-plane magnetic field, thus, tending to restore the weak localization effect.
We present a simple and microscopic physical model that breaks the ergodicity. Our model consists of coupled classical harmonic oscillators, and the motion of the tagged particle obeys the generalized Langevin equation satisfying the second fluctuation dissipation theorem. It is found that although the nonergodicity strength, which is expected to detect the ergodicity breaking, for this model vanishes, the velocity auto correlation function of the tagged particle asymptotically oscillates. We analyze the model by using the molecular dynamics and the exact diagonalization as well as the rigorous mapping to the generalized Langevin equation. Our analysis reveals that the asymptotic oscillation is caused by a localized mode with an isolated frequency from the continuous phonon spectrum.
We study the relaxations, surface energies, and work functions of low index metallic surfaces using pseudopotential plane-wave density-functional calculations within the generalized gradient approximation. We study here the (100), (110), and (111) surfaces of Al, Pd, Pt, and Au and the (0001) surface of Ti, chosen for their use as contact or lead materials in nanoscale devices. We consider clean, mostly non-reconstructed surfaces in the slab-supercell approximation. Particular attention is paid to the convergence of these quantities with respect to slab thickness; furthermore, different methodologies for the calculation of work functions and surfaces energies are compared. We find that the use of bulk references for calculations of surface energies and work functions can be detrimental to convergence unless numerical grids are closely matched, especially when surface relaxations are being considered. Our results and comparison show that calculated values often do not quantitatively match experimental values. This may be understandable for the surface relaxations and surface energies, where experimental values can have large error, but even for the work functions, neither local nor semi-local functionals emerge as an accurate choice for every case.
We propose an adaptive approach for non local means (NLM) image filtering termed as non local adaptive clipped means (NLACM), which reduces the effect of outliers and improves the denoising quality as compared to traditional NLM. Common method to neglect outliers from a data population is computation of mean in a range defined by mean and standard deviation. In NLACM we perform the median within the defined range based on statistical estimation of the neighbourhood region of a pixel to be denoised. As parameters of the range are independent of any additional input and is based on local intensity values, hence the approach is adaptive. Experimental results for NLACM show better estimation of true intensity from noisy neighbourhood observation as compared to NLM at high noise levels. We have verified the technique for speckle noise reduction and we have tested it on ultrasound (US) image of lumbar spine. These ultrasound images act as guidance for injection therapy for treatment of lumbar radiculopathy. We believe that the proposed approach for image denoising is first of its kind and its efficiency can be well justified as it shows better performance in image restoration.
Self-avoidance is a common mechanism to improve the efficiency of a random walker for covering a spatial domain. However, how this efficiency decreases when self-avoidance is impaired or limited by other processes has remained largely unexplored. Here we use simulations to study the case when the self-avoiding signal left by a walker both (i) saturates after successive revisits to a site, and (ii) evaporates, or dissappears, after some characteristic time. We surprisingly reveal that the mean cover time becomes minimum for intermediate values of the evaporation time, leading to the existence of a nontrivial optimum management of the self-avoiding signal. We argue that this is a consequence of complex blocking effects caused by the interplay with the signal saturation and, remarkably, we show that the optimum becomes more and more significant as the domain size increases.
Chromomagnetic and chromoelectric dipole interactions of the top quark are studied in a model independent framework. Limits are set on the scale of new physics that might lead to such contributions using available Tevatron data. Prospects at the LHC are reviewed.
In this paper, we prove a process-level, also known as level-3 large deviation principle for a very general class of simple point processes, i.e. nonlinear Hawkes process, with a rate function given by the process-level entropy, which has an explicit formula.
Neutrino 2012 proceedings of recent results from the IceCube experiment.
The paper is devoted to the properties of the Lagrange spectrum left endpoints and so-called attainable numbers.
Given a graph $G$ on the vertex set $V$, the non-matching complex of $G$, $\mathsf{NM}_k(G)$, is the family of subgraphs $G' \subset G$ whose matching number $\nu(G')$ is strictly less than $k$. As an attempt to generalize the result by Linusson, Shareshian and Welker on the homotopy types of $\mathsf{NM}_k(K_n)$ and $\mathsf{NM}_k(K_{r,s})$ to arbitrary graphs $G$, we show that (i) $\mathsf{NM}_k(G)$ is $(3k-3)$-Leray, and (ii) if $G$ is bipartite, then $\mathsf{NM}_k(G)$ is $(2k-2)$-Leray. This result is obtained by analyzing the homology of the links of non-empty faces of the complex $\mathsf{NM}_k(G)$, which vanishes in all dimensions $d\geq 3k-4$, and all dimensions $d \geq 2k-3$ when $G$ is bipartite. As a corollary, we have the following rainbow matching theorem which generalizes the result by Aharoni, Berger, Chudnovsky, Howard and Seymour: Let $E_1, \dots, E_{3k-2}$ be non-empty edge subsets of a graph and suppose that $\nu(E_i\cup E_j)\geq k$ for every $i\ne j$. Then $E=\bigcup E_i$ has a rainbow matching of size $k$. Furthermore, the number of edge sets $E_i$ can be reduced to $2k-1$ when $E$ is the edge set of a bipartite graph.
Spontaneous violation of Lorentz symmetry by the vacuum condensation of an antisymmetric $2$-tensor is considered. The coset construction for nonlinear realization of spacetime symmetries is employed to build the most general low-energy effective action for the Goldstone modes interacting with photons. We analyze the model within the context of the Standard-Model Extension and noncommutative QED. Experimental bounds for some parameters of the model are discussed, and we readdress the subtle issues of stability and causality in Lorentz non-invariant scenarios. Besides the two photon polarizations, just one Goldstone mode must be dynamical to set a sensible low-energy effective model, and the enhancement of the stability by accounting interaction terms points to a protection against observational Lorentz violation.
We introduce a probabilistic approach to the problem of counting dwarf satellites around host galaxies in databases with limited redshift information. This technique is used to investigate the occurrence of satellites with luminosities similar to the Magellanic Clouds around hosts with properties similar to the Milky Way in the object catalog of the Sloan Digital Sky Survey. Our analysis uses data from SDSS Data Release 7, selecting candidate Milky-Way-like hosts from the spectroscopic catalog and candidate analogs of the Magellanic Clouds from the photometric catalog. Our principal result is the probability for a Milky-Way-like galaxy to host N_{sat} close satellites with luminosities similar to the Magellanic Clouds. We find that 81 percent of galaxies like the Milky Way are have no such satellites within a radius of 150 kpc, 11 percent have one, and only 3.5 percent of hosts have two. The probabilities are robust to changes in host and satellite selection criteria, background-estimation technique, and survey depth. These results demonstrate that the Milky Way has significantly more satellites than a typical galaxy of its luminosity; this fact is useful for understanding the larger cosmological context of our home galaxy.
A recent cosmological model is recapitulated which deduces the correct mass, radius and age of the universe as also the Hubble constant and other well known apparently coincidental relations. It also predicts an ever expanding accelerating universe as is confirmed by latest supernovae observations. Finally the Big Bang model is recovered as a suitable limiting case.
One investigates the Hitchin systems over "large limit" curves.
Buch and Rim\'{a}nyi proved a formula for specializations of double Grothendieck polynomials based on the Yang-Baxter equation related to the degenerate Hecke algebra. A geometric proof was found by Yong and Woo by constructing a Gr\"{o}bner basis for the Kazhdan-Lusztig ideals. In this note, we give an elementary proof for this formula by using only divided difference operators.
Quantum discrimination and estimation are pivotal for many quantum technologies, and their performance depends on the optimal choice of probe state and measurement. Here we show that their performance can be further improved by suitably tailoring the pulses that make up the interferometer. Developing an optimal control framework and applying it to the discrimination and estimation of a magnetic field in the presence of noise, we find an increase in the overall achievable state distinguishability. Moreover, the maximum distinguishability can be stabilized for times that are more than an order of magnitude longer than the decoherence time.
We present for the first time infrared observations of the nearby highly obscured galaxy Dwingeloo 1 (Dw1), including deep H-band imaging covering a total of 4.9x4.9 arcmin, together with J and Ks imaging of the central 2.5x2.5 arcmin. We used the small dispersion of the intrinsic infrared colors of spiral galaxies to determine an infrared H-band extinction of A_H = 0.47+/-0.11 mag towards Dw1. In using infrared colors, the uncertainties in the reddening and distance are reduced by a factor of three. The H-band magnitude corrected for extinction and the infrared Tully-Fisher relation are then used to estimate a distance modulus of (m-M)_0 = 28.62+/-0.27, and thus a distance of d = 5.3 {+0.7/-0.6} Mpc, which puts Dw1 at the far end of the IC342/Maffei 1 & 2 group. Our result is largely independent of the nature of the reddening law because we estimated both the reddening and the distance at the same wavelength range.
Energetic outflows from main sequence stars accreting mass at very high rates might account for the powering of some eruptive objects, such as merging main sequence stars, major eruptions of luminous blue variables, e.g., the Great Eruption of Eta Carinae, and other intermediate luminosity optical transients (ILOTs; Red Novae; Red Transients). These powerful outflows could potentially also supply the extra energy required in the common envelope process and in the grazing envelope evolution of binary systems. We propose that a massive outflow/jets mediated by magnetic fields might remove energy and angular momentum from the accretion disk to allow such high accretion rate flows. By examining the possible activity of the magnetic fields of accretion disks we conclude that indeed main sequence stars might accrete mass at very high rates, up to ~0.01 Mo/yr for solar type stars, and up to ~1 Mo/yr for very massive stars. We speculate that magnetic fields amplified in such extreme conditions might lead to the formation of massive bipolar outflows that can remove most of the disk's energy and angular momentum. It is this energy and angular momentum removal that allows the very high mass accretion rate on to main sequence stars.
Let $L_1$, $L_2$ $L_3$ be integer linear functions with no fixed prime divisor. We show there are infinitely many $n$ for which the product $L_1(n)L_2(n)L_3(n)$ has at most 7 prime factors, improving a result of Porter. We do this by means of a weighted sieve based upon the Diamond-Halberstam-Richert multidimensional sieve.
We prove the existence of tilting bundles on global quotient stacks that are produced by compatible finite group actions on flat families.
The basic purpose of the paper is to draw the attention of researchers to new possibilities of differentiation of similar signals having different nature. One of examples of such kind of signals is presented by seismograms containing recordings of earthquakes (EQ's) and technogenic explosions (TE's). We propose here a discrete stochastic model for possible solution of a problem of strong EQ's forecasting and differentiation of TE's from the weak EQ's. Theoretical analysis is performed by two independent methods: with the use of statistical theory of discrete non-Markov stochastic processes (Phys. Rev. E62,6178 (2000)) and the local Hurst exponent. Time recordings of seismic signals of the first four dynamic orthogonal collective variables, six various plane of phase portrait of four dimensional phase space of orthogonal variables and the local Hurst exponent have been calculated for the dynamic analysis of the earth states. The approaches, permitting to obtain an algorithm of strong EQ's forecasting and to differentiate TE's from weak EQ's, have been developed.