ShantanuT01/DACTYL-Pretraining huggingface dataset:
Using pointwise semigroup techniques, we establish sharp rates of decay in space and time of a perturbed reaction diffusion front to its time-asymptotic limit. This recovers results of Sattinger, Henry and others of time-exponential convergence in weighted $L^p$ and Sobolev norms, while capturing the new feature of spatial diffusion at Gaussian rate. Novel features of the argument are a point-wise Green function decomposition reconciling spectral decomposition and short-time Nash-Aronson estimates and an instantaneous tracking scheme similar to that used in the study of stability of viscous shock waves.
AGN, such as blazars, are most often observed during flare states, primarily due to ease of detection. We report microvariability observations of one blazar, however, while in a historically low state. Comparisons of the amplitude of the variability between high and low states are made. These observations strongly suggest that the relativistic jet associated with the central source of this object is responsible for the observed microvariability (as opposed to a source within the accretion disk).
New congruences are found for Andrews' smallest parts partition function spt(n). The generating function for spt(n) is related to the holomorphic part alpha(24z) of a certain weak Maass form M(z) of weight 3/2. We show that a normalized form of the generating function for spt(n) is an eigenform modulo 72 for the Hecke operators T(p^2) for primes p > 3, and an eigenform modulo t for t = 5, 7 or 13 provided that (t, 6p) = 1. The result for the modulus 3 was observed earlier by the author and considered by Ono and Folsom. Similar congruences for higher powers of t (namely 5^6, 7^4 and 13^2) occur for the coefficients of the function alpha(z). Analogous results for the partition function were found by Atkin in 1966. Our results depend on the recent result of Ono that M[p](z/24) is a weakly holomorphic modular form of weight 3/2 for the full modular group where   M[p](z) = M(z)|T(p^2) - chi(p)(1 + p)M(z).
Upon quotienting by units, the elements of norm 1 in a number field $K$ form a countable subset of a torus of dimension $r_1 + r_2 - 1$ where $r_1$ and $r_2$ are the numbers of real and pairs of complex embeddings. When $K$ is Galois with cyclic Galois group we demonstrate that this countable set is equidistributed in a finite cover of this torus with respect to a natural partial ordering induced by Hilbert's Theorem 90.
We summarize some of the recent developments which link certain problems in combinatorial theory related to random growth to random matrix theory.
The question of Fermi liquid vs. non-Fermi liquid behavior induced by strong correlations is one of the prominent problems in metallic local moment systems. As standard models for such systems, the SU(N)xSU(M) Anderson impurity models exhibit both Fermi liquid and non-Fermi liquid behavior, depending on their symmetry. Taking the Anderson model as an example, these lectures first give an introduction to the auxiliary boson method to describe correlated systems governed by a strong, short-range electronic repulsion. It is then shown how to include the relevant low-lying excitations (coherent spin flip and charge fluctuation processes), while preserving the local gauge symmetry of the model. This amounts to a conserving T-matrix approximation (CTMA). We prove a cancellation theorem showing that the CTMA incorporates all leading and subleading infrared singularities at any given order in a self-consistent loop expansion of the free energy. As a result, the CTMA recovers the correct infrared behavior of the auxiliary particle propagators, indicating that it correctly describes both the Fermi and the non-Fermi regimes of the Anderson model.
Much of the structure of macroscopic evolution equations for relaxation to equilibrium can be derived from symmetries in the dynamical fluctuations around the most typical trajectory. For example, detailed balance as expressed in terms of the Lagrangian for the path-space action leads to gradient zero-cost flow. We find a new such fluctuation symmetry that implies GENERIC, an extension of gradient flow where a Hamiltonian part is added to the dissipative term in such a way as to retain the free energy as Lyapunov function.
On the basis of a dilatation invariant Lagrangian, governed equations are determined for probability density and gauge potential of the non-stationary self-similar stochastic system. It is shown that an automodel regime is observed at small time interval determined by the Tsallis' parameter $q>1$. An exponential falling down happens at large time where the dilatation parameter and the partial scale tend to constant values.
We extend the No-Core Shell Model (NCSM) methodology to incorporate strangeness degrees of freedom and apply it to single-$\Lambda$ hypernuclei. After discussing the transformation of the hyperon-nucleon (YN) interaction into Harmonic-Oscillator (HO) basis and the Similarity Renormalization Group transformation applied to it to improve model-space convergence, we present two complementary formulations of the NCSM, one that uses relative Jacobi coordinates and symmetry-adapted basis states to fully exploit the symmetries of the hypernuclear Hamiltonian, and one working in a Slater determinant basis of HO states where antisymmetrization and computation of matrix elements is simple and to which an importance-truncation scheme can be applied. For the Jacobi-coordinate formulation, we give an iterative procedure for the construction of the antisymmetric basis for arbitrary particle number and present the formulae used to embed two- and three-baryon interactions into the many-body space. For the Slater-determinant formulation, we discuss the conversion of the YN interaction matrix elements from relative to single-particle coordinates, the importance-truncation scheme that tailors the model space to the description of the low-lying spectrum, and the role of the redundant center-of-mass degrees of freedom. We conclude with a validation of both formulations in the four-body system, giving converged ground-state energies for a chiral Hamiltonian, and present a short survey of the $A\le7$ hyper-helium isotopes.
So far, there are described in the literature two ways to superize the Liouville equation: for a scalar field (for $N\leq 4$) and for a vector-valued field (analogs of the Leznov--Saveliev equations) for N=1. Both superizations are performed with the help of Neveu--Schwarz superalgebra. We consider another version of these superLiouville equations based on the Ramond superalgebra, their explicit solutions are given by Ivanov--Krivonos' scheme. Open problems are offered.
Motivated by the first observation of coherent-elastic neutrino-nucleus scattering at the COHERENT experiment, we confront the neutrino dipole portal giving rise to the transition of the standard model neutrinos to sterile neutrinos with the recently released CENNS 10 data from the liquid argon as well as the CsI data of the COHERENT experiment. Performing statistical analysis of those data, we show how the transition magnetic moment can be constrained for the range of the sterile neutrino mass between 10 keV and 40 MeV.
We present a theory of spin and orbital states in Mott insulator $LaTiO_3$. The spin-orbital superexchange interaction between $d^1(t_{2g})$ ions in cubic crystal suffers from a pathological degeneracy of orbital states at classical level. Quantum effects remove this degeneracy and result in the formation of the coherent ground state, in which the orbital moment of $t_{2g}$ level is fully quenched. We find a finite gap for orbital excitations. Such a disordered state of local degrees of freedom on unfrustrated, simple cubic lattice is highly unusual. Orbital liquid state naturally explains observed anomalies of $LaTiO_3$.
A composite fermion edge state theory of current fluctuations, fractional quasiparticle charge and Johnson-Nyquist noise in the fractional quantum Hall regime is presented. It is shown that composite fermion current fluctuations and the charges of the associated quasiparticles are strongly renormalized by the interactions between composite fermions. The important interaction is that mediated by the fictitious electric field associated with composite fermion currents. The dressed current fluctuations and quasiparticle charges are calculated self-consistently in a mean field theory for smooth edges. Analytic results are obtained. The values of the fractional quasiparticle charges obtained agree with the predictions of previous theories in the incompressible regions of the 2DEG where those theories apply. In the compressible regions the magnitudes of the quasiparticle charges vary with position. Since Johnson-Nyquist noise arises from the compressible regions, it is due to quasiparticles whose charges differ from the simple fractions of $e$ that apply in the incompressible regions. Never the less, the Nyquist noise formula $S=4{k_B}T G$ is obeyed on fractional quantum Hall plateaus. Some implications for the interpretation of recent shot noise measurements in the fractional quantum Hall regime are briefly discussed.
Deep learning based virtual try-on system has achieved some encouraging progress recently, but there still remain several big challenges that need to be solved, such as trying on arbitrary clothes of all types, trying on the clothes from one category to another and generating image-realistic results with few artifacts. To handle this issue, we in this paper first collect a new dataset with all types of clothes, \ie tops, bottoms, and whole clothes, each one has multiple categories with rich information of clothing characteristics such as patterns, logos, and other details. Based on this dataset, we then propose the Arbitrary Virtual Try-On Network (AVTON) that is utilized for all-type clothes, which can synthesize realistic try-on images by preserving and trading off characteristics of the target clothes and the reference person. Our approach includes three modules: 1) Limbs Prediction Module, which is utilized for predicting the human body parts by preserving the characteristics of the reference person. This is especially good for handling cross-category try-on task (\eg long sleeves \(\leftrightarrow\) short sleeves or long pants \(\leftrightarrow\) skirts, \etc), where the exposed arms or legs with the skin colors and details can be reasonably predicted; 2) Improved Geometric Matching Module, which is designed to warp clothes according to the geometry of the target person. We improve the TPS based warping method with a compactly supported radial function (Wendland's \(\Psi\)-function); 3) Trade-Off Fusion Module, which is to trade off the characteristics of the warped clothes and the reference person. This module is to make the generated try-on images look more natural and realistic based on a fine-tune symmetry of the network structure. Extensive simulations are conducted and our approach can achieve better performance compared with the state-of-the-art virtual try-on methods.
Science opportunities and recommendations concerning optical/infrared polarimetry for the upcoming decade in the field of extragalactic astrophysics. Community-based White Paper to Astro2010 in response to the call for such papers.
We present results from simultaneous modeling of high angular resolution GBT/MUSTANG-2 90 GHz Sunyaev-Zel'dovich effect (SZE) measurements and XMM-XXL X-ray images of three rich galaxy clusters selected from the HSC-SSP Survey. The combination of high angular resolution SZE and X-ray imaging enables a spatially resolved multi-component analysis, which is crucial to understand complex distributions of cluster gas properties. The targeted clusters have similar optical richnesses and redshifts, but exhibit different dynamical states in their member galaxy distributions: a single-peaked cluster, a double-peaked cluster, and a cluster belonging to a supercluster. A large-scale residual pattern in both regular Compton-parameter $y$ and X-ray surface brightness distributions is found in the single-peaked cluster, indicating a sloshing mode. The double-peaked cluster shows an X-ray remnant cool core between two SZE peaks associated with galaxy concentrations. The temperatures of the two peaks reach $\sim20-30$ keV in contrast to the cool core component of $\sim2$ keV, indicating a violent merger. The main SZE signal for the supercluster is elongated along a direction perpendicular to the major axis of the X-ray core, suggesting a minor merger before core passage. The $S_X$ and $y$ distributions are thus perturbed at some level, regardless of the optical properties. We find that the integrated Compton $y$ parameter and the temperature for the major merger are boosted from those expected by the weak-lensing mass and those for the other two clusters show no significant deviations, which is consistent with predictions of numerical simulations.
We study the principal aspects of the interaction between acoustic phonons and two-dimensional electrons in quantizing magnetic fields corresponding to even denominator fractions. Using the composite fermion approach we derive the vertex of the electron-phonon coupling mediated by the Chern-Simons gauge field. We estimate acoustic phonon contribution to electronic mobility, phonon-drag thermopower, and hot electron energy loss rate, which all, depending on the temperature regime, are either proportional to lower powers of T than their zero field counterparts, or enhanced by the same numerical factor as the coefficient of surface acoustic wave attenuation.
We propose a new variational Monte Carlo (VMC) approach based on the Krylov subspace for large-scale shell-model calculations. A random walker in the VMC is formulated with the $M$-scheme representation, and samples a small number of configurations from a whole Hilbert space stochastically. This VMC framework is demonstrated in the shell-model calculations of $^{48}$Cr and $^{60}$Zn, and we discuss its relation to a small number of Lanczos iterations. By utilizing the wave function obtained by the conventional particle-hole-excitation truncation as an initial state, this VMC approach provides us with a sequence of systematically improved results.
For any polynomial $p\left(x\right)$ over $\mathbb{F}_{l}$ we determine the asymptotic density of hyperelliptic curves over $\mathbb{F}_{q}$ of genus $g$ for which $p\left(x\right)$ divides the characteristic polynomial of Frobenius acting on the $l$-torsion of the Jacobian, and give an explicit formula for this density. We prove this result as a consequence of more general density theorems for quotients of Tate modules of such curves, viewed as modules over the Frobenius. The proof involves the study of measures on $R$-modules over arbitrary rings $R$ which are finite $\mathbb{Z}_{l}$-algebras. In particular we prove a result on the convergence of sequences of such measures, which can be applied to the moments computed in recent work of Lipnowski-Tsimerman to obtain the above results. We also extend the random model for finite $R$-modules proposed in that work to such rings $R$, and prove several of its properties. Notably the measure obtained is in general not inversely proportional to the size of the automorphism group.
We investigate the Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory and show that its formulations in twistor and momentum twistor space can be interchanged. In particular we show that the full symmetry can be thought of as the Yangian of the dual superconformal algebra, annihilating the amplitude with the MHV part factored out. The equivalence of this picture with the one where the ordinary superconformal symmetry is thought of as fundamental is an algebraic expression of T-duality. Motivated by this, we analyse some recently proposed formulas, which reproduce different contributions to amplitudes through a Grassmannian integral. We prove their Yangian invariance by directly applying the generators.
Absorbing boundary condition approach to nuclear breakup reactions is investigated. A key ingredient of the method is an absorbing potential outside the physical area, which simulates the outgoing boundary condition for scattered waves. After discretizing the radial variables, the problem results in a linear algebraic equation with a sparse coefficient matrix, to which efficient iterative methods can be applicable. No virtual state such as discretized continuum channel needs to be introduced in the method. Basic aspects of the method are discussed by considering a nuclear two-body scattering problem described with an optical potential. We then apply the method to the breakup reactions of deuterons described in a three-body direct reaction model. Results employing the absorbing boundary condition are found to accurately coincide with those of the existing method which utilizes discretized continuum channels.
We calculate the prediction for the anomalous weak-magnetic form factor of the tau lepton at $q^2=M_Z^2$ within the Standard Model. With all particles on-shell, this is a electroweak gauge invariant quantity. Its value is $a_\tau^w (M_Z^2)= - \;(2.10 + 0.61\, i) \times 10^{-6}$. We show that the transverse and normal components of the single-tau polarization of tau pairs produced at $e^+e^-$ unpolarized collisions are sensitive to the real and absorptive parts of the anomalous weak-magnetic dipole moment of the tau. The sensitivity one can achieve at LEP in the measurement of this dipole moment is discussed.
We constrain the H I photoionization rate $(\Gamma_{\rm HI})$ at $z \lesssim 0.45$ by comparing the flux probability distribution function and power spectrum of the Ly-$\alpha$ forest data along 82 QSO sightlines obtained using Cosmic Origins Spectrograph with models generated from smoothed particle hydrodynamic simulations. We have developed a module named "Code for Ionization and Temperature Evolution (CITE)" for calculating the intergalactic medium (IGM) temperature evolution from high to low redshifts by post-processing the GADGET-2 simulation outputs. Our method, that produces results consistent with other simulations, is computationally less expensive thus allowing us to explore a large parameter space. It also allows rigorous estimation of the error covariance matrix for various statistical quantities of interest. We find that the best-fit $\Gamma_{\rm HI}(z)$ increases with $z$ and follows $(4 \pm 0.1) \times 10^{-14}\:(1+z)^{4.99 \pm 0.12}$ s$^{-1}$. At any given $z$ the typical uncertainties $\Delta \Gamma_{\rm HI} / \Gamma_{\rm HI}$ are $\sim 25$ per cent which contains not only the statistical errors but also those arising from possible degeneracy with the thermal history of the IGM and cosmological parameters and uncertainties in fitting the QSO continuum. These values of $\Gamma_{\rm HI}$ favour the scenario where only QSOs contribute to the ionizing background at $z<2$. Our derived $3\sigma$ upper limit on average escape fraction is $0.008$, consistent with measurements of low-$z$ galaxies.
The large domain discrepancy between faces captured in polarimetric (or conventional) thermal and visible domain makes cross-domain face verification a highly challenging problem for human examiners as well as computer vision algorithms. Previous approaches utilize either a two-step procedure (visible feature estimation and visible image reconstruction) or an input-level fusion technique, where different Stokes images are concatenated and used as a multi-channel input to synthesize the visible image given the corresponding polarimetric signatures. Although these methods have yielded improvements, we argue that input-level fusion alone may not be sufficient to realize the full potential of the available Stokes images. We propose a Generative Adversarial Networks (GAN) based multi-stream feature-level fusion technique to synthesize high-quality visible images from prolarimetric thermal images. The proposed network consists of a generator sub-network, constructed using an encoder-decoder network based on dense residual blocks, and a multi-scale discriminator sub-network. The generator network is trained by optimizing an adversarial loss in addition to a perceptual loss and an identity preserving loss to enable photo realistic generation of visible images while preserving discriminative characteristics. An extended dataset consisting of polarimetric thermal facial signatures of 111 subjects is also introduced. Multiple experiments evaluated on different experimental protocols demonstrate that the proposed method achieves state-of-the-art performance. Code will be made available at https://github.com/hezhangsprinter.
We study contact effects on electron transport across a molecular wire sandwiched between two semi-infinite (carbon) nanotube leads as a model for nanoelectrodes. Employing the Landauer scattering matrix approach we find that the conductance is very sensitive to parameters such as the coupling strength and geometry of the contact. The conductance exhibits markedly different behavior in the two limiting scenarios of single contact and multiple contacts between the molecular wire and the nanotube interfacial atoms. In contrast to a single contact the multiple-contact configuration acts as a filter selecting single transport channels. It exhibits a scaling law for the conductance as a function of coupling strength and tube diameter. We also observe an unusual narrow-to-broad-to-narrow behavior of conductance resonances upon decreasing the coupling.
We test the recent claim by Hu et al. (2008) that FeII emission in Type 1 AGN shows a systematic redshift relative to the local source rest frame and broad-line Hbeta. We compile high s/n median composites using SDSS spectra from both the Hu et al. sample and our own sample of the 469 brightest DR5 spectra. Our composites are generated in bins of FWHM Hbeta and FeII strength as defined in our 4D Eigenvector 1 (4DE1) formalism. We find no evidence for a systematic FeII redshift and consistency with previous assumptions that FeII shift and width (FWHM) follow Hbeta shift and FWHM in virtually all sources. This result is consistent with the hypothesis that FeII emission (quasi-ubiquitous in type 1 sources) arises from a broad-line region with geometry and kinematics the same as that producing the Balmer lines.
In this paper we count the number of some particular sextuple persymmetric rank i matrices over F_2.
The new Kondo material YbIr$_3$Si$_7$, similar to other Kondo insulators, has been reported to exhibit charge-neutral fermionic excitations through measurements of specific heat and thermal conductivity at low temperatures. We performed $^{29}$Si-NMR on YbIr$_3$Si$_7$ to investigate the magnetic response of charge-neutral fermions from a microscopic perspective. In low magnetic fields parallel to the $c$ axis, a single NMR peak in the paramagnetic state splits into three peaks below $T_{\rm N}$. In contrast, only a slight shift of the single NMR peak was observed in high magnetic fields. This spectral change as a function of the $c$-axis magnetic field is interpreted as spin-flop transition, at which the magnetic moments oriented along the $c$ axis (AF-I phase) are rotated to the $ab$ plane with ferromagnetic component along the $c$-axis (AF-II phase). In the vicinity of the spin-flop magnetic field $H_{\rm M}$, nuclear spin-lattice relaxation rate $1/T_1$ was found to be proportional to temperature at low temperatures, indicating the existence of charge-neutral fermions. Furthermore, a peak of $1/T_1$ vs. the $c$-axis magnetic field suggests that the charge-neutral fermions in YbIr$_3$Si$_7$ are closely related to its magnetic properties. Our findings shed light on the origin of charge-neutral fermions in insulators.
We construct a family of random matrix models for the q-deformed Gaussian random variables G_\mu=a_\mu+a^\star_\mu where the annihilation operators a_\mu and creation operators a^\star_\nu fulfil the q-deformed commutation relation a_\mu a^\star_\nu-q a^\star_\nu a_\mu=\Gamma_{\mu\nu}, \Gamma_{\mu\nu} is the covariance and 0<q<1 is a given number. Important feature of considered random matrices is that the joint distribution of their entries is Gaussian.