ShantanuT01/DACTYL-Pretraining huggingface dataset:
Theory of the first-order phase transition in contact statistical manifold has been proposed to describe interface systems. The theory has not limitations of known Van der Waals-like phase transitions theories. Based on this approach, geometrothermodynamics of gravitating systems with axially symmetric metric is investigated. It has been shown that such geometrothermodynamics occurs in space-ti,e with Newman-Unti-Tamburino metric.
We study the onset of spin superfluidity, namely coherent spin transport mediated by a topological spin texture, in frustrated exchange-dominated magnetic systems, engendered by an external magnetic field. We show that for typical device geometries used in nonlocal magnetotransport experiments, the magnetic field stabilizes a spin superflow against fluctuations, up to a critical current. For a given current, the critical field depends on the precessional frequency of the texture, which can be separately controlled. We contrast such dynamic stabilization of a spin superfluid to the conventional approaches based on topological stabilization.
Progenitors of long GRBs, and core-collapse supernovae in general, may have two separate mechanisms driving the outflows: quasi-isotropic neutrino-driven supernova explosions followed by a highly collimated relativistic outflow driven by the GRB central engine, a black hole or a magnetar. We consider the dynamics of the second GRB-driven explosion propagating through expanding envelope generated by the passage of the primary supernova shock. Beyond the central core, in the region of steep density gradient created by the SN shock breakout, the accelerating secondary quasi-spherical GRB shock become unstable to corrugation and under certain conditions may form a highly collimated jet, a "chimney", when a flow expands almost exclusively along a nearly cylindrically collimated channel. Thus, weakly non-spherical driving and/or non-spherical initial conditions of the wind cavity may produce highly non-spherical, jetted outflows. For a constant luminosity GRB central engine, this occurs for density gradient in the envelope \rho ~ r^{-\omega} steeper than \omega >4.
In our recent letter [1] we discussed that thermodynamics is violated in quantum Brownian motion beyond the weak coupling limit. In his comment, Tasaki [2] derives an inequality for the relative entropy and claims, without making any dynamical assumption, that the Clausius inequality is valid, thus contradicting our statements [1]. Here we point out that the claim is unfunded, since the author did not properly identify the concept of heat. Tasaki also applies the inequality to Thomson's formulation of the second law. This application is invalid as well, since the author did not correctly identify the concept of work. Therefore, Tasaki's inequality is perfectly compatible with our findings.
Particle multiplicities and ratios in the microcanonical ensemble of relativistic gases near production thresholds are studied. It is shown that the ratio of heavy to light particle multiplicity may be enhanced in comparison to its thermodynamic limit.
The early detection of drowsiness has become vital to ensure the correct and safe development of several industries' tasks. Due to the transient mental state of a human subject between alertness and drowsiness, automated drowsiness detection is a complex problem to tackle. The electroencephalography signals allow us to record variations in an individual's brain's electrical potential, where each of them gives specific information about a subject's mental state. However, due to this type of signal's nature, its acquisition, in general, is complex, so it is hard to have a large volume of data to apply techniques of Deep Learning for processing and classification optimally. Nevertheless, Capsule Neural Networks are a brand-new Deep Learning algorithm proposed for work with reduced amounts of data. It is a robust algorithm to handle the data's hierarchical relationships, which is an essential characteristic for work with biomedical signals. Therefore, this paper presents a Deep Learning-based method for drowsiness detection with CapsNet by using a concatenation of spectrogram images of the electroencephalography signals channels. The proposed CapsNet model is compared with a Convolutional Neural Network, which is outperformed by the proposed model, which obtains an average accuracy of 86,44% and 87,57% of sensitivity against an average accuracy of 75,86% and 79,47% sensitivity for the CNN, showing that CapsNet is more suitable for this kind of datasets and tasks.
We propose an approach to nonlinear evolution equations with large and decaying external potentials that addresses the question of controlling globally-in-time the nonlinear interactions of localized waves in this setting. This problem arises when studying localized perturbations around (possibly non-decaying) special solutions of evolution PDEs, and trying to control the projection onto the continuous spectrum of the nonlinear radiative interactions. One of our main tools is the Fourier transform adapted to the Schr\"odinger operator $H=-\Delta+V$, which we employ at a nonlinear level. As a first step we analyze the spatial integral of the product of three generalized eigenfunctions of $H$, and determine the precise structure of its singularities. This leads to study bilinear operators with certain singular kernels, for which we derive product estimates of Coifman-Meyer type. This analysis can then be combined with multilinear harmonic analysis tools and the study of oscillations to obtain (distorted Fourier space analogues of) weighted estimates for dispersive and wave equations. As a first application we consider the nonlinear Schr\"odinger equation in $3$d in the presence of large decaying potential with no bound states, and with a $u^2$ non-linearity. The main difficulty is that a quadratic nonlinearity in $3$d is critical with respect to the Strauss exponent; moreover, this nonlinearity has non-trivial fully coherent interactions even when $V=0$. We prove quantitative global-in-time bounds and scattering for small solutions.
There is a huge and confusing literature about inorganic crystal structure prediction. The word "prediction" is used sometimes as meaning "structure determination" since the process described needs the knowledge of the chemical composition and of the cell parameters. Some clarifications are presented here together with a new software (GRINSP) and some of its predictions.
We derive a high-resolution formula for the $L^2$-quantization errors of Riemann-Liouville processes and the sharp Kolmogorov entropy asymptotics for related Sobolev balls. We describe a quantization procedure which leads to asymptotically optimal functional quantizers. Regular variation of the eigenvalues of the covariance operator plays a crucial role.
We propose a simple algorithm generating labelled posets of given size according to the almost uniform distribution. By "almost uniform" we understand that the distribution of generated posets converges in total variation to the uniform distribution. Our method is based on a Markov chain generating directed acyclic graphs.
We present the first-ever images of the circumstellar environment of the carbon-rich AGB star II Lup in the infrared and sub-mm wavelengths, and the discovery of the envelope's non-spherical morphology with the use of high-angular resolution imaging techniques with the sparse aperture masking mode on NACO/VLT (that enables diffraction limited resolution from a single telescope) and with ALMA. We have successfully recovered images in $Ks$ (2.18$\mu$m), $L'$ (3.80$\mu$m) and $M'$ (4.78$\mu$m), that revealed the non-spherical morphology of the circumstellar envelope around II Lup. The stellar surface of the AGB star is unresolved (i.e. $\leq30$ mas in $Ks$) however the detected structure extends up to 110 mas from the star in all filters. Clumps have been found in the $Ks$ maps, while at lower emission levels a hook-like structure appears to extend counter-clockwise from the south. At larger spatial scales, the circumstellar envelope extends up to approximately 23 arcsec, while its shape suggests a spiral at four different molecules, namely CO, SiO, CS and HC$_3$N, with an average arm spacing of 1.7 arcsec which would imply an orbital period of 128 years for a distance of 590pc.
We carry out a systematic study of 4d $\mathcal{N} = 2$ preserving S-folds of F-theory 7-branes and the worldvolume theories on D3-branes probing them. They consist of two infinite series of theories, which we denote following the original papers by $\mathcal{S}^{(r)}_{G,\ell}$ for $\ell = 2,3,4$ and $\mathcal{T}^{(r)}_{G,\ell}$ for $\ell = 2,3,4,5,6$. Their distinction lies in the discrete torsion carried by the S-fold and in the difference in the asymptotic holonomy of the gauge bundle on the 7-brane. We study various properties of these theories, using diverse field theoretical and string theoretical methods.
Stable laws can be tempered by modifying the L\'evy measure to cool the probability of large jumps. Tempered stable laws retain their signature power law behavior at infinity, and infinite divisibility. This paper develops random walk models that converge to a tempered stable law under a triangular array scheme. Since tempered stable laws and processes are useful in statistical physics, these random walk models can provide a basic physical model for the underlying physical phenomena.
We report here on a method to fabricate and characterize highly perfect, periodically rippled graphene monolayers and islands, epitaxially grown on single crystal metallic substrates under controlled UHV conditions. The periodicity of the ripples is dictated by the difference in lattice parameters of graphene and substrate, and, thus, it is adjustable. We characterize its perfection at the atomic scale by means of STM and determine its electronic structure in the real space by local tunnelling spectroscopy. There are periodic variations in the geometric and electronic structure of the graphene monolayer. We observe inhomogeneities in the charge distribution, i.e a larger occupied Density Of States at the higher parts of the ripples. Periodically rippled graphene might represent the physical realization of an ordered array of coupled graphene quantum dots. The data show, however, that for rippled graphene on Ru(0001) both the low and the high parts of the ripples are metallic. The fabrication of periodically rippled graphene layers with controllable characteristic length and different bonding interactions with the substrate will allow a systematic experimental test of this fundamental problem.
Relativistic transport phenomena are important from both theoretical and practical point of view. Accordingly, hydrodynamics of relativistic gas has been extensively studied theoretically. Here, we introduce a three-dimensional canonical model of hard-sphere relativistic gas which allows us to impose appropriate temperature gradient along a given direction maintaining the system in a non-equilibrium steady state. We use such a numerical laboratory to study the appropriateness of the so-called first order (Chapman-Enskog) relativistic hydrodynamics by calculating various transport coefficients. Our numerical results are consistent with predictions of such a theory for a wide range of temperatures. Our results are somewhat surprising since such linear theories are not consistent with the fundamental assumption of the special theory of relativity ($v\leq c$). We therefore seek to explain such results by studying the appropriateness of diffusive transport in the relativistic gas, comparing our results with that of a classical gas. We find that the relativistic correction (constraint) in the hydrodynamic limit amounts to small negligible corrections, thus indicating the validity of the linear approximation in near equilibrium transport phenomena.
We present a revised TRGB calibration, accurate to 2.7% of distance. A modified TRGB magnitude corrected for the color dependence of the TRGB, the QT magnitude, is introduced for better measurement of the TRGB. We determine the color-magnitude relation of the TRGB from photometry of deep images of HST/ACS fields around eight nearby galaxies. The zero-point of the TRGB at the fiducial metallicity ([Fe/H]=-1.6 ((V-I)_{0,TRGB}=1.5)) is obtained from photometry of two distance anchors, NGC 4258 (M106) and the LMC, to which precise geometric distances are known: M_{QT,TRGB}=-4.023+-0.073 mag from NGC 4258 and M_{QT,TRGB}=-4.004+-0.096 mag from the LMC. A weighted mean of the two zero-points is M_{QT,TRGB}=-4.016+-0.058 mag. Quoted uncertainty is ~2 times smaller than those of the previous calibrations. We compare the empirical TRGB calibration derived in this study with theoretical stellar models, finding that there are significant discrepancies, especially for red color ((F606W-F814W)_0 > 2.5). We provide the revised TRGB calibration in several magnitude systems for future studies.
In this work we study the phenomenon of increasing stability in the inverse boundary value problem for the Schr\"odinger equation. This problem was previously considered by Isakov in which he discussed the phenomenon in different ranges of the wave number (or energy). The main contribution of this work is to provide a unified and easier approach to the same problem based on the complex geometrical optics solutions.
Wilson's original formulation of the renormalization group is perturbative in nature. We here present an alternative derivation of the infinitesimal momentum shell RG, akin to the Wegner and Houghton scheme, that is a priori exact. We show that the momentum-dependence of vertices is key to obtain a diagrammatic framework that has the same one-loop structure as the vertex expansion of the Wetterich equation. Momentum dependence leads to a delayed functional differential equation in the cutoff parameter. Approximations are then made at two points: truncation of the vertex expansion and approximating the functional form of the momentum dependence by a momentum-scale expansion. We exemplify the method on the scalar $\varphi^{4}$-theory, computing analytically the Wilson-Fisher fixed point, its anomalous dimension $\eta(d)$ and the critical exponent $\nu(d)$ non-perturbatively in $d\in[3,4]$ dimensions. The results are in reasonable agreement with the known values, despite the simplicity of the method.
We analyse two classes of Einstein-Podolsky-Rosen (EPR)-steering inequalities, the violation of which can be used to demonstrate EPR-steering with an entangled two-qubit Werner state: linear inequalities and quadratic inequalities. We discuss how post-selection of results (by appeal to the fair sampling assumption) can compromise the rigour of these inequalities in experimental tests of EPR-steering. By considering the worst-case scenarios in which detector inefficiency or other loss could be exploited within a local hidden-state model, we derive inequalities that enable rigorous but loss-tolerant demonstrations of EPR-steering. The linear inequalities, and special cases of the quadratic inequalities, have been used in recent experiments. Our results indicate that regardless of the number of settings used, quadratic inequalities are never better, and often worse, than linear inequalities.
Fast arbitrary neural style transfer has attracted widespread attention from academic, industrial and art communities due to its flexibility in enabling various applications. Existing solutions either attentively fuse deep style feature into deep content feature without considering feature distributions, or adaptively normalize deep content feature according to the style such that their global statistics are matched. Although effective, leaving shallow feature unexplored and without locally considering feature statistics, they are prone to unnatural output with unpleasing local distortions. To alleviate this problem, in this paper, we propose a novel attention and normalization module, named Adaptive Attention Normalization (AdaAttN), to adaptively perform attentive normalization on per-point basis. Specifically, spatial attention score is learnt from both shallow and deep features of content and style images. Then per-point weighted statistics are calculated by regarding a style feature point as a distribution of attention-weighted output of all style feature points. Finally, the content feature is normalized so that they demonstrate the same local feature statistics as the calculated per-point weighted style feature statistics. Besides, a novel local feature loss is derived based on AdaAttN to enhance local visual quality. We also extend AdaAttN to be ready for video style transfer with slight modifications. Experiments demonstrate that our method achieves state-of-the-art arbitrary image/video style transfer. Codes and models are available.
Tensions between cosmological measurements by different surveys or probes have always been important --- and are presently much discussed --- as they may lead to evidence of new physics. Several tests have been devised to probe the consistency of datasets given a cosmological model, but they often have undesired features such as dependence on the prior volume, or burdensome requirements such as that of near-Gaussian posterior distributions. We propose a new quantity, defined in a similar way as the Bayesian evidence ratio, in which these undesired properties are absent. We test the quantity on simple models with Gaussian and non-Gaussian likelihoods. We then apply it to data from the Planck satellite: we investigate the consistency of $\Lambda$CDM model parameters obtained from TT and EE angular power spectrum measurements, as well as the mutual consistency of cosmological parameters obtained from large scale (multipoles, $\ell<1000$) and small scale ($\ell \geq 1000$) portions of each measurement and find no significant discrepancy in the six-dimensional $\Lambda$CDM parameter space.
We study a fermion field coupled to a scalar via a Yukawa term. The scalar field is the $\phi^4$ model with an impurity that preserves half of the BPS property. We analyze the spectrum of the defects of the model and collisions between them both close to the BPS regime and not. As the fermion binds to these defects, it may be transferred from one to the other, which we quantify via overlaps, known as Bogoliubov coefficients. BPS collisions are less likely to transfer the fermion between defects and can be adiabatic for non-relativistic velocities, especially for small coupling constants. Moreover, closer to the BPS limit only a small fraction of the fermion number is radiated away. In contrast, non-BPS collisions lead to more radiation in the fermion field and excitation of the fermion to higher bound states, and the result is more sensitive to the parameters.
This paper is a contribution to the study of hereditary classes of finite graphs. We classify these classes according to the number of prime structures they contain. We consider such classes that are \emph{minimal prime}: classes that contain infinitely many primes but every proper hereditary subclass contains only finitely many primes. We give a complete characterization of such classes. In fact, each one of these classes is a well quasi ordered age and there are uncountably many of them. Eleven of these ages remain well quasi ordered when labels in a well quasi ordering are added. Among the remaining ones, countably many remain well quasi ordered when one label is added. Except for six examples, members of these ages we characterize are permutation graphs. In fact, every age which is not among the eleven ones is the age of a graph associated to a uniformly recurrent $0$-$1$ word on the integers. A characterization of minimal prime classes of posets and bichains is also provided.
The main result of the article reads: the distribution of a continuous starting from zero local martingale whose quadratic characteristic is almost surely absolutely continuous with respect to some non-random increasing continuous function is determined by the distribution of the quadratic characteristic. Functional limit theorem based on this characterization are proved.
Bell inequalities were meant to test quantum mechanics vs local hidden variable models, but can also be used to verify entanglement. For entanglement verification purposes one assumes the validity of quantum mechanics as well as quantum descriptions of one's measurements. With the help of these assumptions it is possible to derive a strengthened Bell inequality whose violation implies entanglement. We generalize known examples of such inequalities by relating the expectation value of the Bell operator to a particular quantitative measure of entanglement, namely the negativity. Moreover, we obtain statistics illustrating the fact that violating a given (strengthened or not) Bell inequality is a much more rare feat for a quantum state of two qubits than it is to be entangled.
For a class of polynomials $f \in \mathbb{Z}[X]$, which in particular includes all quadratic polynomials, and also trinomials of some special form, we show that, under some natural conditions (necessary for quadratic polynomials), the set of primes $p$ such that all iterations of $f$ are irreducible modulo $p$ is of relative density zero. Furthermore, we give an explicit bound on the rate of the decay of the density of such primes in an interval $[1, Q]$ as $Q \to \infty$. For this class of polynomials this gives a more precise version of a recent result of A. Ferraguti (2018), which applies to arbitrary polynomials but requires a certain assumption about their Galois group. Furthermore, under the Generalised Riemann Hypothesis we obtain a stronger bound on this density.
For calculation of the single-channel nucleon-nucleon scattering a phase-functions method has been proposed. Using a phase-functions method the following phase shifts of np- scattering numerically for 1S0-, 1P1-, 3P0-, 3P1-, 1D2-, 3D2-, 1F3-, 3F3-, 1G4-, 3G4- states are calculated. The calculations has been performed using realistic nucleon-nucleon Reid68 and Reid93 potentials. Obtained phase shifts for energy up to 350 MeV are in good agreement with the results obtained in the framework of other methods. Using the obtained phase shifts we have calculated the full cross-section np- scattering.
We present a grid-based non-parametric approach to obtain a triaxial three-dimensional luminosity density from its surface brightness distribution. Triaxial deprojection is highly degenerate and our approach illustrates the resulting difficulties. Fortunately, for massive elliptical galaxies, many deprojections for a particular line of sight can be discarded, because their projection along other lines of sight does not resemble elliptical galaxies. The near-elliptical isophotes of these objects imply near ellipsoidal intrinsic shapes. In fact, deprojection is unique for densities distributed on ellipsoidal shells. The constrained non-parametric deprojection method we present here relaxes this constraint and assumes that the contours of the luminosity density are boxy/discy ellipsoids with radially varying axis ratios. With this approach we are able to reconstruct the intrinsic triaxial densities of our test models, including one drawn from an $N$-body simulation. The method also allows to compare the relative likelihood of deprojections at different viewing angles. We show that the viewing orientations of individual galaxies with nearly ellipsoidal isophotal shapes can be constrained from photometric data alone.
I review recent results regarding the nucleon charge and magnetization densities as well as the shape of the nucleon. First, some phenomenolgical considerations that show that the shape of the proton is not round are discussed. Then model independent results regarding the neutron and proton charge density, and the proton magnetization density are presented. Finally, I show how the spin-dependent densities that reveal the shape of the proton can be measured via their relation with transverse momentum distributions. The present work is made possible by the recent tremendous experimental progress made at Bates, Mainz and Jefferson Laboratory.