ShantanuT01/DACTYL-Pretraining huggingface dataset:
We present a theoretical model that describes electrical spin-detection at a ferromagnet/semiconductor interface. We show that the sensitivity of the spin detector has strong bias dependence which, in the general case, is dramatically different from that of the tunneling current spin polarization. We show that this bias dependence originates from two distinct physical mechanisms: 1) the bias dependence of tunneling current spin polarization, which is of microscopic origin and depends on the specific properties of the interface, and 2) the macroscopic electron spin transport properties in the semiconductor. Numerical results show that the magnitude of the voltage signal can be tuned over a wide range from the second effect which suggests a universal method for enhancing electrical spin-detection sensitivity in ferromagnet/semiconductor tunnel contacts. Using first-principles calculations we examine the particular case of a Fe/GaAs Schottky tunnel barrier and find very good agreement with experiment. We also predict the bias dependence of the voltage signal for a Fe/MgO/GaAs tunnel structure spin detector.
The aim of this paper is to derive a formula for the subwavelength resonance frequency of an encapsulated bubble with arbitrary shape in two dimensions. Using Gohberg-Sigal theory, we derive an asymptotic formula for this resonance frequency, as a perturbation away from the resonance of the uncoated bubble, in terms of the thickness of the coating. The formula is numerically verified in the case of circular bubbles, where the resonance can be efficiently computed using the multipole method.
The second-order Dirac equation (DE) and its velocity operator of graphene electrons in an electromagnetic field are obtained according to tight-binding k.p method. With extra terms included, they demonstrate the motion of graphene electrons more completely through a more complete Ehrenfest theorem and present finer properties of graphene electrons. Eigen-energy given by the second-order DE for field-free graphene indicates that extra terms may affect the trembling motion of graphene electrons. For graphene in a magnetic field, eigen-energy given by the second-order DE suggests that graphene electrons have a new kind of spin of a boson other than true electronic spin and pseudo-spin of Dirac particles, which will modify graphene properties such as the optical spectra.
The environment is known to affect the formation and evolution of galaxies considerably best visible through the well-known morphology-density relationship. In this paper we study the effect of environment on the evolution of early-type galaxies by analysing the stellar population properties of 3,360 galaxies morphologically selected by visual inspection from the SDSS in the redshift range 0.05<z<0.06. We find that the distribution of ages is bimodal with a strong peak at old ages and a secondary peak at young ages around ~ 2.5Gyr containing about 10 per cent of the objects. This is analogue to 'red sequence' and 'blue cloud' identified in galaxy populations usually containing both early and late type galaxies. The fraction of the young, rejuvenated galaxies increases with both decreasing galaxy mass and decreasing environmental density up to about 45 per cent. The rejuvenated galaxies have lower alpha/Fe ratios than the average and most of them show signs of ongoing star formation through their emission line spectra. All objects that host AGN in their centres without star formation are part of the red sequence population. We confirm and statistically strengthen earlier results that luminosity weighted ages, metallicities, and alpha/Fe element ratios of the red sequence population correlate well with velocity dispersion and galaxy mass. Most interestingly, however, these scaling relations are not sensitive to environmental densities and are only driven by galaxy mass. We infer that early-type galaxy formation has undergone a phase transition a few billion years ago around z~0.2. A self-regulated formation phase without environmental dependence has recently been superseded by a rejuvenation phase, in which the environment plays a decisive role possibly through galaxy interactions.
We study Maxwell's equations in time domain in an anisotropic medium. The goal of the paper is to solve an inverse boundary value problem for anisotropies characterized by scalar impedance $\alpha$. This means that the material is conformal, i.e., the electric permittivity $\epsilon$ and magnetic permeability $\mu$ are tensors satisfying $\mu =\alpha^2\epsilon$. This condition is equivalent to a single propagation speed of waves with different polarizations which uniquely defines an underlying Riemannian structure. The analysis is based on an invariant formulation of the system of electrodynamics as a Dirac type first order system on a Riemannian $3-$manifold with an additional structure of the wave impedance, $(M,g,\alpha)$, where $g$ is the travel-time metric. We study the properties of this system in the first part of the paper. In the second part we consider the inverse problem, that is, the determination of $(M,g,\alpha)$ from measurements done only on an open part of the boundary and on a finite time interval. As an application, in the isotropic case with $M\subset \R^3$, we prove that the boundary data given only on an open part of the boundary determine uniquely the domain $M$ and the coefficients $\epsilon$ and $\mu$.
We present a survey of the formaldehyde emission in nine class 0 protostars obtained with the IRAM 30m and the JCMT millimeter telescopes. Using a detailed radiative transfer code of the envelopes surrounding the protostars, we show that all but one of the observed objects show an inner warm evaporation region where the formaldehyde is much more abundant (up to three orders of magnitude) than in the outer cold part. The largest inner formaldehyde abundances are associated with the sources having the lowest submillimetric to bolometric luminosity ratio, i.e. with sources closer to the class I border. These abundances are compared with predictions from recent models of hot core chemistry.
We investigate the Tully-Fisher Relation (TFR) for a morphologically and kine- matically diverse sample of galaxies from the SAMI Galaxy Survey using 2 dimensional spatially resolved Halpha velocity maps and find a well defined relation across the stellar mass range of 8.0 < log(M*) < 11.5. We use an adaptation of kinemetry to parametrise the kinematic Halpha asymmetry of all galaxies in the sample, and find a correlation between scatter (i.e. residuals off the TFR) and asymmetry. This effect is pronounced at low stellar mass, corresponding to the inverse relationship between stellar mass and kinematic asymmetry found in previous work. For galaxies with log(M*) < 9.5, 25 +/- 3% are scattered below the root mean square (RMS) of the TFR, whereas for galaxies with log(M*) > 9.5 the fraction is 10 +/- 1% We use 'simulated slits' to directly compare our results with those from long slit spectroscopy and find that aligning slits with the photometric, rather than the kinematic, position angle, increases global scatter below the TFR. Further, kinematic asymmetry is correlated with misalignment between the photometric and kinematic position angles. This work demonstrates the value of 2D spatially resolved kinematics for accurate TFR studies; integral field spectroscopy reduces the underestimation of rotation velocity that can occur from slit positioning off the kinematic axis.
This paper studies the global structure of algebraic curves defined by generalized unitarity cut of four-dimensional three-loop diagrams with eleven propagators. The global structure is a topological invariant that is characterized by the geometric genus of the algebraic curve. We use the Riemann-Hurwitz formula to compute the geometric genus of algebraic curves with the help of techniques involving convex hull polytopes and numerical algebraic geometry. Some interesting properties of genus for arbitrary loop orders are also explored where computing the genus serves as an initial step for integral or integrand reduction of three-loop amplitudes via an algebraic geometric approach.
We give a proof of the existence of Asai, exterior square, and symmetric square local $L$-functions, $\gamma$-factors and root numbers in characteristic $p$, including the case of $p = 2$. Our study is made possible by developing the Langlands-Shahidi method over a global function field in the case of a Siegel Levi subgroup of a split classical group or a quasi-split unitary group. The resulting automorphic $L$-functions are shown to satisfy a rationality property and a functional equation. A uniqueness result of the author and G. Henniart allows us to show that the definitions provided in this article are in accordance with the local Langlands conjecture for ${\rm GL}_n$. Furthermore, in order to be self contained, we include a treatise of $L$-functions arising from maximal Levi subgroups of general linear groups.
A first-principles approach combining density functional and dynamical mean-field theories in conjunction with a quasi-atomic approximation for the strongly localized 4$f$ shell is applied to Nd$_{2}$Fe$_{14}$B-based hard magnets in order to evaluate crystal-field and exchange-field parameters at rare-earth sites and their corresponding single-ion contribution to the magnetic anisotropy. In pure Nd$_2$Fe$_{14}$B, our calculations reproduce the easy-cone to easy axis transition; theoretical magnetization curves agree quantitatively with experiment. Our study reveals that the rare-earth single-ion anisotropy in the "2-14-1" structure is strongly site-dependent, with the $g$ rare-earth site exhibiting a larger value. In particular, we predict that increased $f$ and $g$-site occupancy of $R=$ Ce and Dy, respectively, leads to an increase of the magnetic anisotropy of the corresponding (Nd,$R$)$_{2}$Fe$_{14}$B substituted compounds.
Image rasterization is a mature technique in computer graphics, while image vectorization, the reverse path of rasterization, remains a major challenge. Recent advanced deep learning-based models achieve vectorization and semantic interpolation of vector graphs and demonstrate a better topology of generating new figures. However, deep models cannot be easily generalized to out-of-domain testing data. The generated SVGs also contain complex and redundant shapes that are not quite convenient for further editing. Specifically, the crucial layer-wise topology and fundamental semantics in images are still not well understood and thus not fully explored. In this work, we propose Layer-wise Image Vectorization, namely LIVE, to convert raster images to SVGs and simultaneously maintain its image topology. LIVE can generate compact SVG forms with layer-wise structures that are semantically consistent with human perspective. We progressively add new bezier paths and optimize these paths with the layer-wise framework, newly designed loss functions, and component-wise path initialization technique. Our experiments demonstrate that LIVE presents more plausible vectorized forms than prior works and can be generalized to new images. With the help of this newly learned topology, LIVE initiates human editable SVGs for both designers and other downstream applications. Codes are made available at https://github.com/Picsart-AI-Research/LIVE-Layerwise-Image-Vectorization.
The stationary isotropic Poisson line process was used to derive upper bounds on mean excess network geodesic length in Aldous and Kendall [Adv. in Appl. Probab. 40 (2008) 1-21]. The current paper presents a study of the geometry and fluctuations of near-geodesics in the network generated by the line process. The notion of a "Poissonian city" is introduced, in which connections between pairs of nodes are made using simple "no-overshoot" paths based on the Poisson line process. Asymptotics for geometric features and random variation in length are computed for such near-geodesic paths; it is shown that they traverse the network with an order of efficiency comparable to that of true network geodesics. Mean characteristics and limiting behavior at the center are computed for a natural network flow. Comparisons are drawn with similar network flows in a city based on a comparable rectilinear grid. A concluding section discusses several open problems.
A subgraph of an edge-coloured complete graph is called rainbow if all its edges have different colours. The study of rainbow decompositions has a long history, going back to the work of Euler on Latin squares. In this paper we discuss three problems about decomposing complete graphs into rainbow trees: the Brualdi-Hollingsworth Conjecture, Constantine's Conjecture, and the Kaneko-Kano-Suzuki Conjecture. We show that in every proper edge-colouring of $K_n$ there are $10^{-6}n$ edge-disjoint spanning isomorphic rainbow trees. This simultaneously improves the best known bounds on all these conjectures. Using our method we also show that every properly $(n-1)$-edge-coloured $K_n$ has $n/9$ edge-disjoint rainbow trees, giving further improvement on the Brualdi-Hollingsworth Conjecture.
We prove the irrationality of some factorial series. To do so we combine methods from elementary and analytic number theory with methods from the theory of uniform distribution.
The present letter explores the electrocaloric effect (ECE) in the lead free oxide Ba0.8Ca0.2Ti0.95Ge0.05O3 ceramics (BCTG). The electrocaloric responsivity (dT/dE) was determined by two different methods using the Maxwell relationship (dT/dE)~(dP/dT)_E. In a first well-known indirect method, P-E hysteresis loops were measured in a wide temperature range from which the pyroelectric coefficient p_E=(dP/dT)_E and thus (dT/dE) were determined by derivation of P(T,E) data. In the second novel method the pyroelectric coefficient p_E and consequently the electrocaloric responsivity was determined by direct measurements of the pyroelectric currents under different applied electric fields. Within the experimental error good agreement was obtained between two methods with an electrocaloric responsivity equal to 0.18 +/- 0.05 10-6 K.m.V-1 was obtained at about 410 K
We study the effects of large-scale density fluctuations on strong gravitational lensing. Previous studies have focused mostly on weak lensing, since large-scale structure alone cannot produce multiple images. When a galaxy or cluster acts as a primary lens, however, we find that large-scale structure can produce asymmetric shear of the same order as the lens itself. Indeed, this may explain the origin of the large shear found in lens models in conflict with the small ellipticity of the observed galaxy light distributions. We show that large-scale structure changes the lens equation to the form of a generalized quadrupole lens, which affects lens reconstruction. Large-scale structure also changes the angular diameter distance at a given redshift. The precise value depends on the lens and source redshifts and on the large-scale structure power spectrum, but the induced $1\sigma$ uncertainty in determinations of the Hubble constant from measurements of time delays is of order $5-10 \%$. If observations of lensing can constrain the magnitude of the shear which is due to large-scale structure, it would provide a direct probe of the overall amplitude of mass fluctuations.
We investigate wave amplification through the Electron Cyclotron Maser mechanism.   We derive a semi-analytic approximation formula giving the frequencies at which the absorption coefficient is negative. The coefficients still need to be computed to obtain the largest, and therefore the dominant, coefficient.
We present a new expression for the Weyl scalar Psi_4 that can be used in numerical relativity to extract the gravitational wave content of a spacetime. The formula relies upon the identification of transverse tetrads, namely the ones in which Psi_1=Psi_3=0. It is well known that tetrads with this property always exist in a general Petrov type I spacetime. A sub-class of these tetrads naturally converges to the Kinnersley tetrad in the limit of Petrov type D spacetime. However, the transverse condition fixes only four of the six parameters coming from the Lorentz group of transformations applied to tetrads. Here we fix the tetrad completely, in particular by giving the expression for the spin-boost transformation that was still unclear. The value of Psi_4 in this optimal tetrad is given as a function of the two curvature invariants I and J.
The gravitational wave source GW190412 is a binary black hole (BBH) merger with three unique properties: i) its mass ratio is about 0.28, the lowest found so far, ii) it has a relatively high positive effective spin parameter \chi_eff=0.25, and iii) it is observed to be precessing due to in-plane projected spin of the binary with an in-plane precession parameter \chi_p=0.3. The two main formation channels of BBH formation fail to account for GW190412: field formation scenarios cannot explain the observed precession unless by invoking large natal kicks, and dynamical assembly in dense stellar systems is inefficient in producing such low mass-ratio BBH mergers. Here, we investigate whether "double mergers" in wide hierarchical quadruple systems in the "3+1" configuration could explain the unique properties of GW190412. In this scenario, a compact object quadruple system experiences two mergers: first, two compact objects in the innermost orbit merge due to secular chaotic evolution. At a later time, the merged compact object coalesces with another compact object due to secular Lidov-Kozai oscillations. We find that our scenario is consistent with GW190412. In particular, we find a preferential projected spin around \chi_p=0.2. However, the likelihood of a double merger is small and the formation efficiency of these systems is uncertain. If GW190412 originated from a double merger in a 3+1 quadruple, we find a strong constraint that the first merger likely occurred between roughly equal-mass BHs in the innermost orbit, since the recoil velocity from unequal-mass BHs would otherwise have disrupted the system.
These are (mostly) expository notes for lectures on affine Stanley symmetric functions given at the Fields Institute in 2010. We focus on the algebraic and combinatorial parts of the theory. The notes contain a number of exercises and open problems.
In this paper, we compute the fundamental group of the complement of linear torus curves of maximal contact and we show that it is isomorphic that of generic linear torus curves.
We consider the problem of embedding a symmetric configuration with block size 3 in an orientable surface in such a way that the blocks of the configuration form triangular faces and there is only one extra large face. We develop a sufficient condition for such an embedding to exist given any orientation of the configuration, and show that this condition is satisfied for all configurations on up to 19 points. We also show that there exists a configuration on 21 points which is not embeddable in any orientation. As a by-product, we give a revised table of numbers of configurations, correcting the published figure for 19 points. We give a number of open questions about embeddability of configurations on larger numbers of points.
Dynamical, non-asymptotically flat black holes are best characterized by their apparent horizons. Cosmological black hole solutions of General Relativity exhibit two types of apparent horizon behaviours which, thus far, appeared to be completely disconnected. By taking the limit to General Relativity of a class of Brans-Dicke spacetimes, it is shown how one of these two behaviours is really a limit of the other.
We derive a sharp bound as the quantum speed limit (QSL) for the minimal evolution time of quantum open systems in the non-Markovian strong-coupling regime with initial mixed states by considering the effects of both renormalized Hamiltonian and dissipator. For a non-Markovian quantum open system, the possible evolution time between two arbitrary states is not unique, among the set of which we find that the minimal one and its QSL can decrease more steeply by adjusting the coupling strength of the dissipator, which thus provides potential improvements of efficiency in many quantum physics and quantum information areas.
The freeze out of the expanding systems, created in relativistic heavy ion collisions, is discussed. We combine kinetic freeze out equations with Bjorken type system expansion into a unified model. The important feature of the proposed scenario is that physical freeze out is completely finished in a finite time, which can be varied from 0 (freeze out hypersurface) to infinity. The dependence of the post freeze out distribution function on the freeze out time will be studied. As an example, model is completely solved and analyzed for the gas of pions. We shall see that the basic freeze out features, pointed out in the earlier works, are not smeared out by the expansion of the system. The entropy evolution in such a scenario is also studied.
In this paper we consider the stability of a class of deterministic and stochastic SEIRS epidemic models with delay. Indeed, we assume that the transmission rate could be stochastic and the presence of a latency period of $r$ consecutive days, where $r$ is a fixed positive integer, in the "exposed" individuals class E. Studying the eigenvalues of the linearized system, we obtain conditions for the stability of the free disease equilibrium, in both the cases of the deterministic model with and without delay. In this latter case, we also get conditions for the stability of the coexistence equilibrium. In the stochastic case we are able to derive a concentration result for the random fluctuations and then, using the Lyapunov method, that under suitable assumptions the free disease equilibrium is still stable.
The cross section for coincidence, quasielastic proton knock-out by electrons from a polarized K39 nucleus is computed in DWIA using an optical potential in describing the wave function of the ejected nucleon. The dependence of the FSI on the initial polarization angles of the nucleus is analyzed and explained in a new, semi-classical picture of the reaction in which the nuclear transparency decreases as a function of the amount of nuclear matter that the proton has to cross, thus providing a method for obtaining detailed information on its mean free path in finite nuclei. We propose a procedure to find the best initial kinematical conditions for minimizing the FSI which will be useful as a guide for future experiments with polarized nuclei.
Various algebraic properties of Heilbronn's exponential sum can be deduced through the use of supercharacter theory, a novel extension of classical character theory due to Diaconis-Isaacs and Andre. This perspective yields a variety of formulas and provides a method for computing the number of solutions to Fermat-type congruences.
Deep learning has paved the way for strong recognition systems which are often both trained on and applied to natural images. In this paper, we examine the give-and-take relationship between such visual recognition systems and the rich information available in the fine arts. First, we find that visual recognition systems designed for natural images can work surprisingly well on paintings. In particular, we find that interactive segmentation tools can be used to cleanly annotate polygonal segments within paintings, a task which is time consuming to undertake by hand. We also find that FasterRCNN, a model which has been designed for object recognition in natural scenes, can be quickly repurposed for detection of materials in paintings. Second, we show that learning from paintings can be beneficial for neural networks that are intended to be used on natural images. We find that training on paintings instead of natural images can improve the quality of learned features and we further find that a large number of paintings can be a valuable source of test data for evaluating domain adaptation algorithms. Our experiments are based on a novel large-scale annotated database of material depictions in paintings which we detail in a separate manuscript.