ShantanuT01/DACTYL-Pretraining huggingface dataset:
Magnetic fields are ubiquitous in the interstellar medium but are notoriously difficult to study through observation. Making use of the advances in our understanding of MHD turbulence and turbulent reconnection, the Velocity Gradient Technique (VGT) was suggested and successfully applied to study magnetic fields utilizing spectroscopic data. Applying the tools developed for VGT to intensity statistics, we introduce the Intensity Gradients Technique (IGT) as a complementary tool that can be used synergistically with VGT. In this paper, we apply IGT to a diffuse HI region selected from the GALFA-HI survey and compare the intensity gradient maps with those obtained using velocity gradients as well as Planck polarization measurements. We demonstrate the possibility of using IGT and VGT for both studying the magnetic field and identifying shocks in the diffuse interstellar medium. We also explore the ability of IGT in locating self-gravitating regions and calculating Alfvenic Mach number, both alone and in combination with VGT and polarimetry. We compare IGT with the Histogram of Relative Orientation (HRO), which utilizes intensity gradients to characterize the relative orientation of column density structures and local magnetic fields.
Zariski chambers provide a natural decomposition of the big cone of an algebraic surface into rational locally polyhedral subcones that are interesting from the point of view of linear series. In the present paper we present an algorithm that allows to effectively determine Zariski chambers when the negative curves on the surface are known. We show how the algorithm can be used to compute the number of chambers on Del Pezzo surfaces.
We propose a consistent prescription for the derivation of the particle number and angular momentum projected QRPA (PQRPA) equation in the Generator Coordinate Method (GCM) framework for calculation of NME's of double-beta decay of axially deformed nuclei. We derive closed formulae for the calculation of excitation energies and wave functions of the intermediate nucleus.
The Large Area Telescope (LAT) on board the Gamma-ray Large-Area Space Telescope (GLAST) is a pair-conversion gamma-ray detector designed to explore the gamma-ray universe in the 20 MeV-300 GeV energy band. The Tracker subsystem of the LAT will perform tracking of electron and positrons to determine the origin of the gamma-ray. The design and performance of the GLAST LAT Tracker are described in this paper.
New calculations of the quasi-bound state positions in $K^{-}K^{-}pp$ kaonic nuclear cluster are performed using non-relativistic four-body Faddeev-type equations in AGS form. The corresponding separable approximation for the integral kernels in the three- and four-body kaonic clusters is obtained by using the Hilbert-Schmidt expansion procedure. Different phenomenological models of $\bar{K}N-\pi\Sigma$ potentials with one- and two-pole structure of $\Lambda$(1405) resonance and separable potential models for $\bar{K}$-$\bar{K}$ and nucleon-nucleon interactions, are used. The dependence of the resulting four-body binding energy on models of $\bar{K}N-\pi\Sigma$ interaction is investigated. We obtained the binding energy of the $K^{-}K^{-}pp$ quasi-bound state $\sim$ 80-94 MeV with the phenomenological $\bar{K}N$ potentials. The width is about $\sim$ 5-8 MeV for the two-pole models of the interaction, while the one-pole potentials give $\sim$ 24-31 MeV width.
We discuss a field-theoretical approach based on variational principle to derive the field and hydrodynamic equations of motion of baryonic matter governed by cosmological perturbations of dark matter and dark energy. The action depends on the gravitational and matter Lagrangian. The gravitational Lagrangian depends on the metric tensor and its first and second derivatives. The matter Lagrangian includes dark matter, dark energy and the ordinary baryonic matter. The total Lagrangian is expanded in an asymptotic Taylor series around the background manifold defined as a solution of Einstein's equations in the form of the Friedmann-Lemaitre-Robertson-Walker (FLRW) metric tensor. The small parameter of the decomposition is the magnitude of the metric tensor perturbation. Each term of the series expansion is gauge-invariant and all of them together form a basis for the successive post-Friedmannian approximations. The approximation scheme is covariant and the asymptotic nature of the Lagrangian decomposition does not require the post-Friedmannian perturbations to be small though computationally it works the most effectively when the perturbed metric is close enough to the background FLRW metric. The temporal evolution of the background metric is governed by dark matter and dark energy and we associate the large scale inhomogeneities in these two components as those generated by the primordial cosmological perturbations. The small scale inhomogeneities are generated by the condensations of baryonic matter considered as the bare perturbations. We explicitly work out the covariant field equations of the successive post-Friedmannian approximations of Einstein's equations and derive equations of motion of large and small scale inhomogeneities of dark matter and dark energy. We apply these equations to derive the post-Friedmannian equations of motion of the baryonic matter.
Accretion discs are common in binary systems, and they are often found to be misaligned with respect to the binary orbit. The gravitational torque from a companion induces nodal precession in misaligned disc orbits. We calculate whether this precession is strong enough to overcome the internal disc torques communicating angular momentum. For typical parameters precession wins: the disc breaks into distinct planes that precess effectively independently. We run hydrodynamical simulations to check these results, and confirm that disc breaking is widespread and generally enhances accretion on to the central object. This applies in many cases of astrophysical accretion, e.g. supermassive black hole binaries and X--ray binaries.
We have shown that polarized neutron reflectometry can determine in a model-free way not only the mean magnetization of a ferromagnetic thin film at any point of a hysteresis cycle, but also the mean square dispersion of the magnetization vectors of its lateral domains. This technique is applied to elucidate the mechanism of the magnetization reversal of an exchange-biased Co/CoO bilayer. The reversal process above the blocking temperature is governed by uniaxial domain switching, while below the blocking temperature the reversal of magnetization for the trained sample takes place with substantial domain rotation.
We introduce left and right-layered trees as trees with a specific representation and define the excess of a tree. Applying these ideas, we show a range-relaxed graceful labeling which improves on the upper bound for maximum vertex label given by Van Bussel. For the case when the tree is a lobster of size $m$ and diameter $d$, the labeling produces vertex labels no greater than $\frac{3}{2}m-\frac{1}{2}d$. Furthermore, we show that any lobster $T$ with $m$ edges and diameter $d$ has an edge-relaxed graceful bipartite labeling with at least $\max\{\frac{3m-d+6}{4},\frac{5m+d+15}{8}\}$ of the edge weights distinct, which is an improvement on a bound given by Rosa and \v{S}ir\'{a}\v{n} on the $\alpha$-size of trees, for $d<\frac{m+22}{7}$ and $d>\frac{5m-65}{7}$. We also show that there exists an edge-relaxed graceful labeling (not necessarily bipartite) with at least $\max\left\{\frac{3}{4}m+\frac{d-\nu}{8}+\frac{3}{2},\nu\right\}$ of the edge weights distinct, where $\nu$ is twice the size of a partial matching of $T$. This is an improvement on the gracesize bound of Rosa and \v{S}ir\'{a}\v{n} for certain values of $\nu$ and $d$. We view these results as a step towards Bermond's conjecture.
We develop a manifestly microscopic method to deal with strongly interacting nuclear systems that have different interactions in spin-singlet and spin-triplet states. In a first step we analyze variational wave functions that have been suggested to describe such systems, and demonstrate that the so-called commutator contributions can have important effects whenever the interactions in the spin-singlet and the spin-triplet states are very different. We then identify these contributions as terms that correspond, in the language of perturbation theory, to non-parquet diagrams. We include these diagrams in a way that is suggested by the Jastrow-Feenberg approach and show that the corrections from non-parquet contributions are, at short distances, larger than all other many-body effects.
We measured the first azimuthal distributions of triple--differential cross sections of neutrons emitted in heavy-ion collisions, and compared their maximum azimuthal anisotropy ratios with Boltzmann--Uehling--Uhlenbeck (BUU) calculations with a momentum-dependent interaction. The BUU calculations agree with the triple- and double-differential cross sections for positive rapidity neutrons emitted at polar angles from 7 to 27 degrees; however, the maximum azimuthal anisotropy ratio for these free neutrons is insensitive to the size of the nuclear incompressibility modulus K characterizing the nuclear matter equation of state.
The merger of two neutron stars is a very complex process. In order to disentangle the various steps through which it takes place it is mandatory to examine all the signals we can detect: gravitational waves and electromagnetic waves, in a huge spectrum ranging from X and $\gamma$-rays down to infrared and radio. Each of these signals provides a message and the totality of this information will allow us not only to understand the process of the merger but also the behavior of matter at those extreme conditions.
Detection of out-of-distribution (OoD) samples in the context of image classification has recently become an area of interest and active study, along with the topic of uncertainty estimation, to which it is closely related. In this paper we explore the task of OoD segmentation, which has been studied less than its classification counterpart and presents additional challenges. Segmentation is a dense prediction task for which the model's outcome for each pixel depends on its surroundings. The receptive field and the reliance on context play a role for distinguishing different classes and, correspondingly, for spotting OoD entities. We introduce MOoSe, an efficient strategy to leverage the various levels of context represented within semantic segmentation models and show that even a simple aggregation of multi-scale representations has consistently positive effects on OoD detection and uncertainty estimation.
This book is not meant to be another compendium of select inequalities, nor does it claim to contain the latest or the slickest ways of proving them. This project is rather an attempt at describing how most functional inequalities are not merely the byproduct of ingenious guess work by a few wizards among us, but are often manifestations of certain natural mathematical structures and physical phenomena. Our main goal here is to show how this point of view leads to "systematic" approaches for not just proving the most basic functional inequalities, but also for understanding and improving them, and for devising new ones - sometimes at will, and often on demand.
We investigate the time evolution of the density of kinks in the spin-1/2 quantum Ising spin chain after a sudden quench in the transverse field strength, and find that it relaxes to a value which depends on the initial and the final values of the transverse field, with an oscillating power-law decay. We provide analytical estimates of the long-time behavior and of the asymptotic value reached after complete relaxation, and discuss the role of quantum criticality in the quench dynamics. We show that, for a dynamics at the critical point, the residual density of kinks after the quench can be described by equilibrium statistical mechanics at a finite temperature dictated by the energy of the state after the quench. On the other hand, outside of criticality it does not exhibit thermalization.
Several observations from Fermi-LAT, up to few hundred GeV, and from H.E.S.S., up to $\sim$ 10 TeV, reported an intense $\gamma$-ray emission from the inner part of the Galactic plane. After the subtraction of point-like contributions, the remaining $\gamma$-ray spectrum can provide important hints about the cosmic-ray (CR) population in that region. In particular, the diffuse spectrum measured by both Fermi-LAT and H.E.S.S. in the Galactic Ridge is significantly harder with respect to the rest of the Galaxy. These results were recently interpreted in terms of a comprehensive CR transport model which, adopting a spatial dependent diffusion coefficient and convective velocity, reproduces Fermi-LAT results on the whole sky as well as local CR spectra. We showed as that model predicts a significantly harder neutrino diffuse emission compared to conventional scenarios: The predicted signal is able to account for a significant fraction of the astrophysical flux measured by IceCube. In this contribution, we use the same setup to calculate the expected neutrino flux from several windows in the inner Galactic plane and compare the results with IceCube observations and the sensitivities of Mediterranean neutrino telescopes. In particular, for the ANTARES experiment, we compare the model expectations with the upper limits obtained from a recent unblinded data-analysis focused on the galactic ridge region. Moreover, we also show the expectations from the galactic ridge for the future KM3NeT observatory, whose position is optimal to observe this portion of the sky.
We present a method for generating exact diagonal $G_2$-cosmological solutions in dilaton gravity coupled to a radiation perfect fluid and with a cosmological potential of a special type. The method is based on the symmetry group of the system of $G_2$-field equations. Several new classes of explicit exact inhomogeneous perfect fluid scalar-tensor cosmologies are presented.
Lacking realistic ground truth data, image denoising techniques are traditionally evaluated on images corrupted by synthesized i.i.d. Gaussian noise. We aim to obviate this unrealistic setting by developing a methodology for benchmarking denoising techniques on real photographs. We capture pairs of images with different ISO values and appropriately adjusted exposure times, where the nearly noise-free low-ISO image serves as reference. To derive the ground truth, careful post-processing is needed. We correct spatial misalignment, cope with inaccuracies in the exposure parameters through a linear intensity transform based on a novel heteroscedastic Tobit regression model, and remove residual low-frequency bias that stems, e.g., from minor illumination changes. We then capture a novel benchmark dataset, the Darmstadt Noise Dataset (DND), with consumer cameras of differing sensor sizes. One interesting finding is that various recent techniques that perform well on synthetic noise are clearly outperformed by BM3D on photographs with real noise. Our benchmark delineates realistic evaluation scenarios that deviate strongly from those commonly used in the scientific literature.
It is known that large deviations of sums of subexponential random variables are most likely realised by deviations of a single random variable. In this article we give a detailed picture of how subexponential random variables are distributed when a large deviation of their sum is observed.
The space of n (ordered) points on the projective line, modulo automorphisms of the line, is one of the most important and classical examples of an invariant theory quotient, and is one of the first examples given in any course. Generators for the ring of invariants have been known since the end of the nineteenth century, but the question of the relations has remained surprisingly open, and it was not even known that the relations have bounded degree. We show that the ideal of relations is generated in degree at most four, and give an explicit description of the generators. The result holds for arbitrary weighting of the points. If all the weights are even (e.g. in the case of equal weight for odd n), we show that the ideal of relations is generated by quadrics. The proof is by degenerating the moduli space to a toric variety, and following an enlarged set of generators through this degeneration.
We present a quantum fingerprinting protocol relying on two-photon interference which does not require a shared phase reference between the parties preparing optical signals carrying data fingerprints. We show that the scaling of the protocol, in terms of transmittable classical information, is analogous to the recently proposed and demonstrated scheme based on coherent pulses and first-order interference, offering comparable advantage over classical fingerprinting protocols without access to shared prior randomness. We analyze the protocol taking into account non-Poissonian photon statistics of optical signals and a variety of imperfections, such as transmission losses, dark counts, and residual distinguishability. The impact of these effects on the protocol performance is quantified with the help of Chernoff information.
We will study solvability of nonlinear second-order elliptic system of partial differential equations with nonlinear boundary conditions. We study the generalized Steklov Robin eigensystem (with possibly matrices weights) in which the spectral parameter is both in the system and on the boundary. We prove the existence of solutions for nonlinear system when both nonlinearities in the differential system and on the boundary interact, in some sense, with the generalized spectrum of Steklov Robin. The method of proof makes use of Leray-Schauder degree.
We study new primality tests based on linear recurrent sequences of degree two exploiting a matricial approach. The classical Lucas test arises as a particular case and we see how it can be easily improved. Moreover, this approach shows clearly how the Lucas pseudoprimes are connected to the Pell equation and the Brahamagupta product. We also introduce a new specific primality test, which we will call generalized Pell test. We perform some numerical computations on the new primality tests and, for the generalized Pell test, we do not any pseudoprime up to $10^{10}$.
The role of superfluidity in the incompressibility and in the symmetry energy is studied in nuclear matter and finite nuclei. Several pairing interactions are used: surface, mixed and isovector dependent. Pairing has a small effect on the nuclear matter incompressibility at saturation density, but the effects are significant at lower densities. The pairing effect on the centroid energy of the isoscalar Giant Monopole Resonance (GMR) is also evaluated for Pb and Sn isotopes by using a microscopic constrained-HFB approach, and found to change at most by 10% the nucleus incompressibility $K_A$. It is shown by using the Local Density Approximation (LDA) that most of the pairing effect on the GMR centroid come from the low-density nuclear surface.
In this paper we give an elementary proof of the Fundamental Theorem of Algebra for polynomials over the rational tropical semi-ring. We prove that, tropically, the rational numbers are algebraically closed. We provide a simple algorithm for factoring tropical polynomials of a single variable. A central idea is the concept of least-coefficient polynomials as representatives for classes of functionally equivalent polynomials. This idea has importance far beyond the proof of the Fundamental Theorem of Tropical Algebra.
Using a joint approach of density functional theory and model calculations, we demonstrate that a prototypical charge ordered half-doped manganite, La$_{1/2}$Ca$_{1/2}$MnO$_3$ is multiferroic. The combination of a peculiar charge-orbital ordering and a tendency to form spin dimers breaks inversion symmetry, leads to a ferroelectric ground-state with a polarization up to several $\mu C/cm^2$. The presence of improper ferroelectricity does not depend on hotly debated structural details of this material: in the Zener-polaron structure we find a similar dramatic ferroelectric response with a large polarization of purely magnetic origin.
We show that the Lambert series $f(x)=\sum d(n) x^n$ is irrational at $x=1/b$ for negative integers $b < -1$ using an elementary proof that finishes an incomplete proof of Erdos.
Direction-dependent anisotropic exchange is a common feature of magnetic systems with strong spin-orbit coupling. Here we study the effect of such exchange upon macroscopic magnetic anisotropy for a face-centered-cubic model. By several theoretical techniques, we show that, both in the paramagnetic and ordered phases, the magnetic anisotropy is induced by fluctuations. Moreover, the magnetic anisotropy differs in the paramagnetic and ordered phases: in the paramagnetic phase the susceptibility is maximum along the $\langle111\rangle$ directions, while the magnetic moments orient along $\langle110\rangle$ or $\langle100\rangle$ in the ordered phase. We suggest that such "anisotropy switching" can be a common feature of strongly spin-orbit coupled magnets.
Simulations of tidal streams show that close encounters with dark matter subhalos induce density gaps and distortions in on-sky path along the streams. Accordingly, observing disrupted streams in the Galactic halo would substantiate the hypothesis that dark matter substructure exists there, while in contrast, observing collimated streams with smoothly varying density profiles would place strong upper limits on the number density and mass spectrum of subhalos. Here, we examine several measures of stream "disruption" and their power to distinguish between halo potentials with and without substructure and with different global shapes. We create and evolve a population of 1280 streams on a range of orbits in the Via Lactea II simulation of a Milky Way-like halo, replete with a full mass range of {\Lambda}CDM subhalos, and compare it to two control stream populations evolved in smooth spherical and smooth triaxial potentials, respectively. We find that the number of gaps observed in a stellar stream is a poor indicator of the halo potential, but that (i) the thinness of the stream on-sky, (ii) the symmetry of the leading and trailing tails, and (iii) the deviation of the tails from a low-order polynomial path on-sky ("path regularity") distinguish between the three potentials more effectively. We find that globular cluster streams on low-eccentricity orbits far from the galactic center (apocentric radius ~ 30-80 kpc) are most powerful in distinguishing between the three potentials. If they exist, such streams will shortly be discoverable and mapped in high dimensions with near-future photometric and spectroscopic surveys.
We analyze the origin of interference disappearance in which-path double aperture experiments. We show that we can unambiguously define an observable momentum transfer between the quantum particle and the path detector and we prove in particular that the so called ``momentum transfer free'' experiments can be in fact logically interpreted in term of momentum transfer.
We prove a closed formula for the derivative, of any order, of a implicit function, in terms of some binomial building blocks, and explain the combinatorics behind the coefficients appearing in the formula.