ShantanuT01/DACTYL-Pretraining huggingface dataset:
We calculate the self-energy of two-dimensional fermions that are coupled to transverse gauge fields, taking two-loop corrections into account. Given a bare gauge field propagator that diverges for small momentum transfers q as 1 / q^{eta}, 1 < eta < 2, the fermionic self-energy without vertex corrections vanishes for small frequencies omega as Sigma (omega) propto omega^{gamma with gamma = {frac{2}{1 + eta}} < 1. We show that inclusion of the leading radiative correction to the fermion - gauge field vertex leads to   Sigma (omega) propto omega^{gamma} [ 1 - a_{eta} ln (omega_0 / omega) ],   where a_{\eta} is a positive numerical constant and omega_0 is some finite energy scale. The negative logarithmic correction is consistent with the scenario that higher order vertex corrections push the exponent gamma to larger values.
Let $V=V(n,q)$ denote the vector space of dimension $n$ over the finite field with $q$ elements. A subspace partition ${\mathcal P}$ of $V$ is a collection of nontrivial subspaces of $V$ such that each nonzero vector of $V$ is in exactly one subspace of ${\mathcal P}$. For any integer $d$, the $d$-supertail of ${\mathcal P}$ is the set of subspaces in ${\mathcal P}$ of dimension less than $d$, and it is denoted by $ST$. Let $\sigma_q(n,t)$ denote the minimum number of subspaces in any subspace partition of $V$ in which the largest subspace has dimension $t$. It was shown by Heden et al. that $|ST|\geq \sigma_q(d,t)$, where $t$ is the largest dimension of a subspace in $ST$. In this paper, we show that if $|ST|=\sigma_q(d,t)$, then the union of all the subspaces in $ST$ constitutes a subspace under certain conditions.
In this paper we define (empirical) quadratic variations for a Gaussian isotropic random field $f$ on a unit sphere as sums over equidistant increments on one single geodesic line on the surface of the sphere. We prove a noncentral limit theorem for a fixed Fourier component of such a field as well as quantitative central limit theorems in the increasing frequency regime. Based on these results we propose estimators of the angular power spectrum and study their properties. Moreover, we show a quantitative central limit theorem for quadratic variations over the field $f$ and construct an estimator for the Hurst parameter of a $L^2(\mathbb S^2)$-valued fractional Brownian motion.
A sample of 229618 narrow emission-line galaxies is used to establish two new unambiguous type of evidence for supermassive black holes at the center of their nuclei: 1) the Seyfert 2 galaxies and LINERs follow the same characteristic power law relating the luminosity of ionized flux with that of the continuum; 2) both show the highest concentration of mass at their center, independent of the morphology of the galaxy, consistent with higher binding energies. The Full Width at Half Maximum is shown to be related with the mass concentration, suggesting that the kinetic energy of the gas in AGNs has a gravitational origin. Within the standard accretion model, the Transition-type Objects, Seyfert 2 galaxies and LINERs represent AGNs forming supermassive black holes on different mass-scales, or they could be related through an evolutionary process, the LINERs representing the end product of this evolution.
We study the absorption of scalar fields by extreme/exotic compact objects (ECOs) -- horizonless alternatives to black holes -- via a simple model in which dissipative mechanisms are encapsulated in a single parameter. Trapped modes, localized between the ECO core and the potential barrier at the photosphere, generate Breit-Wigner-type spectral lines in the absorption cross section. Absorption is enhanced whenever the wave frequency resonates with a trapped mode, leading to a spectral profile which differs qualitatively from that of a black hole. We introduce a model based on Nariai spacetime, in which properties of the spectral lines are calculated in closed form. We present numerically calculated absorption cross sections and transmission factors for example scenarios, and show how the Nariai model captures the essential features. We argue that, in principle, ECOs can be distinguished from black holes through their absorption spectra.
A promising way of testing the impact of a magnetic field on internal mixing (core overshooting, internal rotation) in main-sequence B-type stars is to perform asteroseismic studies of a sample of magnetic pulsators. The CoRoT satellite revealed that the B3IV star HD 43317 is a hybrid SPB/beta Cep-type pulsator that has a wealth of pulsational constraints on which one can perform a seismic modelling, in particular, probing the extent of its convective core and mixing processes. Moreover, indirect indicators of a magnetic field in the star were observed: rotational modulation due to chemical or temperature spots and X-ray emission. Our goal was to directly investigate the field in HD 43317 and, if it is magnetic, to characterise it. We collected data with the Narval spectropolarimeter installed at TBL (T\'elescope Bernard Lyot, Pic du Midi, France) and applied the least-squares deconvolution technique to measure the circular polarisation of the light emitted from HD 43317. We modelled the longitudinal field measurements directly with a dipole. Zeeman signatures in the Stokes V profiles of HD 43317 are clearly detected and rotationally modulated, which proves that this star exhibits an oblique magnetic field. The modulation with the rotation period deduced from the CoRoT light curve is also confirmed, and we found a field strength at the poles of about 1 kG. Our result must be taken into account in future seismic modelling work of this star.
Let $X$ be a Hyperk\"ahler manifold, and let $H$ be an ample divisor on $X$. We give a lower bound in terms of the Beauville-Bogomolov form $q(H)$ for the twisted cotangent bundle $\Omega_X \otimes H$ to be pseudoeffective. If $X$ is deformation equivalent to the Hilbert scheme of a K3 surface the lower bound can be written down explicitly and we study its optimality.
Face presentation attacks have become an increasingly critical concern when face recognition is widely applied. Many face anti-spoofing methods have been proposed, but most of them ignore the generalization ability to unseen attacks. To overcome the limitation, this work casts face anti-spoofing as a domain generalization (DG) problem, and attempts to address this problem by developing a new meta-learning framework called Regularized Fine-grained Meta-learning. To let our face anti-spoofing model generalize well to unseen attacks, the proposed framework trains our model to perform well in the simulated domain shift scenarios, which is achieved by finding generalized learning directions in the meta-learning process. Specifically, the proposed framework incorporates the domain knowledge of face anti-spoofing as the regularization so that meta-learning is conducted in the feature space regularized by the supervision of domain knowledge. This enables our model more likely to find generalized learning directions with the regularized meta-learning for face anti-spoofing task. Besides, to further enhance the generalization ability of our model, the proposed framework adopts a fine-grained learning strategy that simultaneously conducts meta-learning in a variety of domain shift scenarios in each iteration. Extensive experiments on four public datasets validate the effectiveness of the proposed method.
We construct explicit models of particle dark matter where the attractive force in the dark matter sector creates a narrow near-threshold resonance that qualitatively changes the energy dependence of the annihilation cross section. In these models, the resonant enhancement of the dark matter annihilation can easily source the excess of energetic leptons observed by experiments on PAMELA and FERMI satellites. The distinct feature of these models is that by construction the enhancement of the annihilation cross section shuts off when the dark matter velocity falls below the typical Milky Way values, thus automatically satisfying constraints on dark matter annihilation imposed by the CMB anisotropies and gamma ray constraints from satellite galaxies.
In this survey we report on some recent results related to various singular phenomena arising in the study of some classes of nonlinear elliptic equations. We establish qualitative results on the existence, nonexistence or the uniqueness of solutions and we focus on the following types of problems: (i) blow-up boundary solutions of logistic equations; (ii) Lane-Emden-Fowler equations with singular nonlinearities and subquadratic convection term. We study the combined effects of various terms involved in these problems: sublinear or superlinear nonlinearities, singular nonlinear terms, convection nonlinearities, as well as sign-changing potentials. We also take into account bifurcation nonlinear problems and we establish the precise rate decay of the solution in some concrete situations. Our approach combines standard techniques based on the maximum principle with non-standard arguments, such as the Karamata regular variation theory.
Most of known RR Lyraes are type ab RR Lyraes (RRLab), and they are the excellent tool to map the Milky Way and its substructures. We find that 1148 RRLab stars determined by Drake et al.(2013) have been observed by spectroscopic surveys of SDSS and LAMOST. We derived radial velocity dispersion, circular velocity and mass profile from 860 halo tracers in our paper I. Here, we present the stellar densities and radial velocity distributions of thick disk and halo of the Milky Way. The 288 RRLab stars located in the thick disk have the mean metallicity of [Fe/H]$=-1.02$. Three thick disk tracers have the radial velocity lower than 215 km $\rm s^{-1}$. With 860 halo tracers which have a mean metallicity of [Fe/H]$=-1.33$, we find a double power-law of $n(r) \propto r^{-2.8}$ and $n(r) \propto r^{-4.8}$ with a break distance of 21 kpc to express the halo stellar density profile. The radial velocity dispersion at 50 kpc is around 78 km $\rm s^{-1}$.
For a prime $\ell$ and an abelian variety $A$ over a global field $K$, the $\ell$-parity conjecture predicts that, in accordance with the ideas of Birch and Swinnerton-Dyer, the $\mathbb{Z}_{\ell}$-corank of the $\ell^{\infty}$-Selmer group and the analytic rank agree modulo $2$. Assuming that $\mathrm{char} K > 0$, we prove that the $\ell$-parity conjecture holds for the base change of $A$ to the constant quadratic extension if $\ell$ is odd, coprime to $\mathrm{char} K$, and does not divide the degree of every polarization of $A$. The techniques involved in the proof include the \'{e}tale cohomological interpretation of Selmer groups, the Grothendieck-Ogg-Shafarevich formula, and the study of the behavior of local root numbers in unramified extensions.
We find an analog of the electric-magnetic duality, which is a $Z_2$ transformation between magnetic and electric sectors of the static and rotationally symmetric solutions in a class of (2+1)-dimensional Einstein-Maxwell-Dilaton gravity theories. The theories in our consideration include, in particular, one parameter class of theories continuously connecting the Banados-Teitelboim-Zanelli (BTZ) gravity and the low energy string effective theory. When there is no $U(1)$ charge, we have $O(2)$ or $O(1,1)$ symmetry, depending on a parameter that specifies each theory. Via the $Z_2$ transformation, we obtain exact magnetically charged solutions from the known electrically charged solutions. We explain the relationship between the $Z_2$ transformation and $O(2,Z)$ symmetry, and comment on the $T$-duality of the string theory.
We show that the S-Euclidean minimum of an ideal class is a rational number, generalizing a result of Cerri. We also give some corollaries which explain the relationship of our results with Lenstra's notion of a norm-Euclidean ideal class and the conjecture of Barnes and Swinnerton-Dyer on quadratic forms. The proof is self-contained but uses ideas from ergodic theory and topological dynamics, particularly those of Berend.
The world-line path-integral representation of fermion propagators is discussed. Particular attention is paid to the representation of $\gamma_5$, which is connected to the realization of manifest world-line supersymmetry.
A linear stability analysis of the hydrodynamic equations with respect to the homogeneous cooling state is performed to study the conditions for stability of a suspension of solid particles immersed in a viscous gas. The dissipation in such systems arises from two different sources: inelasticity in particle collisions and viscous friction dissipation due to the influence of gas phase on solid particles. The starting point is a suspension model based on the (inelastic) Enskog kinetic equation where the effect of the interstitial gas phase on the dynamics of grains is modeled via a viscous drag force. The study is carried out in two different steps. First, the transport coefficients of the system are obtained by solving the Enskog equation by means of the Chapman-Enskog method up to first order in spatial gradients. Once the transport properties are known, then the corresponding linearized hydrodynamic equations are solved to get the dispersion relations. In contrast to previous studies [V. Garz\'o \emph{et al.}, Phys. Rev. E \textbf{93}, 012905 (2016)], the hydrodynamic modes are \emph{analytically} obtained as functions of the parameter space of the system. As expected, linear stability shows $d-1$ transversal (shear) modes (where $d$ is the dimensionality of the system) and a longitudinal "heat" mode to be unstable with respect to long enough wavelength excitations. The results also show that the main effect of gas phase is to decrease the value of the critical length $L_c$ (beyond which the system becomes unstable) with respect to its value for a dry granular fluid. Comparison with direct numerical simulations for $L_c$ shows a good agreement for conditions of practical interest.
In this paper we consider estimating the number of solutions to multiplicative equations in finite fields when the variables run through certain sets with high additive structure. In particular, we consider estimating the multiplicative energy of generalized arithmetic progressions in prime fields and of boxes in arbitrary finite fields and obtain sharp bounds in more general scenarios than previously known. Our arguments extend some ideas of Konyagin and Bourgain and Chang into new settings.
We consider a population of $N$ labeled random walkers moving on a substrate, and an excitation jumping among the walkers upon contact. The label $\mathcal{X}(t)$ of the walker carrying the excitation at time $t$ can be viewed as a stochastic process, where the transition probabilities are a stochastic process themselves. Upon mapping onto two simpler processes, the quantities characterizing $\mathcal{X}(t)$ can be calculated in the limit of long times and low walkers density. The results are compared with numerical simulations. Several different topologies for the substrate underlying diffusion are considered.
We present high-resolution ($\sim 1"$), 1.5 GHz continuum observations of the brightest cluster galaxies (BCGs) of 13 CLASH (Cluster Lensing And Supernova survey with Hubble) clusters at $0.18<z<0.69$ with the Karl G. Jansky Very Large Array (JVLA). Radio emission is clearly detected and characterized for 11 BCGs, while for two of them we obtain only upper limits to their radio flux ($<0.1$ mJy at 5$\sigma$ confidence level). We also consider five additional clusters whose BCG is detected in FIRST or NVSS. We find radio powers in the range from $2\times 10^{23}$ to $\sim 10^{26}$ $W~Hz^{-1}$ and radio spectral indices $\alpha_{1.5}^{30}$ (defined as the slope between 1.5 and 30 GHz) distributed from $\sim -1$ to $-0.25$ around the central value $\langle \alpha \rangle= - 0.68$. The radio emission from the BCGs is resolved in three cases (Abell 383, MACS J1931, and RX J2129), and unresolved or marginally resolved in the remaining eight cases observed with JVLA. In all the cases the BCGs are consistent with being powered by active galactic nuclei (AGN). The radio power shows a positive correlation with the BCG star formation rate, and a negative correlation with the central entropy of the surrounding intracluster medium (ICM) except in two cases (MACS J1206 and CL J1226). Finally, over the restricted range in radio power sampled by the CLASH BCGs, we observe a significant scatter between the radio power and the average mechanical power stored in the ICM cavities.
We prove the `weight elimination' part of the weight part of Serre's conjecture for mod 2 Galois representations for rank two unitary groups, by modifying the results in arXiv:1203.2552 and arXiv:1309.0527.
Since the DAMA/LIBRA collaboration released updated results from their search for the annual modulation signal expected from Dark Matter (DM) scattering in their NaI detectors, we have fitted the updated DAMA result for the modulation amplitudes for a Weakly Interacting Massive Particle (WIMP) signal, parameterizing the interaction with nuclei in terms of the most general effective Lagrangian for a WIMP particle spin 1/2, systematically assuming dominance of one of the 14 possible interaction terms and a standard Maxwellian for the WIMP velocity distribution. We find that most of the couplings of the non-relativistic effective Hamiltonian can provide a better fit compared to the standard Spin Independent interaction case, and with a reduced fine-tuning of the three parameters (WIMP mass, WIMP-nucleon effective cross-section and ratio between the WIMP-neutron and the WIMP-proton couplings). In addition, effective models for which the cross section depends explicitly on the WIMP incoming velocity can provide a better fit of the DAMA data at large values of $m_{\chi}$ compared to the standard velocity-independent cross-section due to a different phase of the modulation amplitudes. All the best fit solutions are in tension with exclusion plots of both XENON1T and PICO60.
Standard treatments of general relativity accept the gravitational slowing of clocks as a primary phenomenon, requiring no further analysis as to cause. Rejecting this attitude, I argue that one or more of the fundamental "constants" governing the quantum mechanics of atoms must depend upon position in a gravitational field. A simple relationship governing the possible dependencies of e, h, c and m is deduced, and arguments in favor of the choice of the electron rest mass, m, are presented. The reduction of rest mass is thus taken to be the sole cause of clock slowing. Importantly, this dependency implies another effect, heretofore unsuspected, namely, the gravitational elongation of measuring rods. An alternate ("telemetric") system of measurement is introduced, leading to a metric that is conformally related to the usual proper metric. In terms of the new system, many otherwise puzzling phenomena may be simply understood. In particular,the geometry of the Schwarzschild space as described by the telemetric system differs profoundly from that described by proper measurments, leading to a very different understanding of the structure of black holes. The theory is extended to cosmology,leading to a remarkable alternate view of the structure and history of the universe.
In recent years, the black hole candidate X-ray binary system H1743-322 has undergone outbursts and it has been observed with X-ray and radio telescopes. We present 1.3 GHz MeerKAT radio data from the ThunderKAT Large Survey Project on radio transients for the 2018 outburst of H1743-322. We obtain seven detections from a weekly monitoring programme and use publicly available Swift X-ray Telescope and MAXI data to investigate the radio/X-ray correlation of H1743-322 for this outburst. We compare the 2018 outburst with those reported in the literature for this system and find that the X-ray outburst reported is similar to previously reported `hard-only' outbursts. As in previous outbursts, H1743-322 follows the `radio-quiet' correlation in the radio/X-ray plane for black hole X-ray binaries, and the radio spectral index throughout the outburst is consistent with the `radio-quiet' population.
In this paper we present the spectrum of entropy/area for Kehagias-Sfetsos (KS) black hole in Ho$\check{\textbf{r}}$ava-Lifshitz (HL)gravity via quasi-normal modes (QNM) approach. We show that in the massive case the mass parameter $\mu$ disappears in the entropy spectrum and only the quasinormal modes modified by a term which is proportional to the mass square term. Our calculations show that the charge like parameter $\frac{1}{2\omega}=Q^{2}$ appears in the surface gravity and our calculations can be applied to any spherically symmetric spacetime which has only one physically acceptable horizon. Our main difference between our calculations and what was done in \cite{1} is that the portion of charge and mass is included explicitly in the surface gravity and consequently in the QNM expression. Since the imaginary part of the QNM is related to the adiabatic invariance of the system and also to the entropy, surprisingly the mass parameter do not appear in the entropy spectrum. Our conclusion supported by some acclaims about that the scalar field parameters (charges) can not change the fundamental parameters in the 4-dimensional black holes.
Ultrahigh energy density batteries based on alpha-Li_xBN2 (1<x<3) positive electrode materials are predicted using density functional theory calculations. The utilization of the reversible LiBN2 + 2 Li+ + 2 e- -> Li3BN2 electrochemical cell reaction leads to a voltage of 3.62 V (vs Li/Li$^{+}$), theoretical energy densities of 3251 Wh/kg and 5927 Wh/L, with capacities of 899 mAh/g and 1638 mAh/cm3, while the cell volume of alpha-Li3BN2 changes only 2.8% per two-electron transfer. These values are far superior to the best existing or theoretically designed intercalation or conversion-based positive electrode materials. For comparison, the theoretical energy density of a Li-O2/peroxide battery is 3450 Wh/kg (including the weight of O2), that of a Li-S battery is 2600 Wh/kg, that of Li3Cr(BO3)(PO4) (one of the best designerintercalation materials) is 1700 Wh/kg, while already commercialized LiCoO2 allows for 568 Wh/kg. alpha-Li3BN2 is also known as a good Li-ion conductor with experimentally observed 3 mS/cm ionic conductivity and 78 kJ/mol (~ 0.8 eV) activation energy of conduction. The attractive features of alpha-LixBN2 (1<x<3) are based on a crystal lattice of 1D conjugated polymers with -Li-N-B-N- repeating units. When some of the Li is deintercalated from alpha-Li3BN2 the crystal becomes a metallic electron conductor, based on the underlying 1D conjugated pi-electron system. Thus alpha-LixBN2 (1<x<3) represents a new type of 1D conjugated polymers with great potential for energy storage and other applications.