Correction to the Chiral Magnetic Effect from axial-vector interaction

The recent lattice calculation at finite axial chemical potential suggests that the induced current density of the chiral magnetic effect (CME) is somehow suppressed comparing with the standard analytical formula. We show in a NJL-type model of QCD that such a suppression is a natural result when considering the influence of the attractive axial-vector interaction. We point out that the lattice result doesn't need to be quantitatively consistent with the analytical formula due to the chirality density-density correlation. We also investigate the nonperturbative effect of instanton molecules on the CME. Since an unconventional repulsive axial-vector interaction is induced, the CME will be enhanced significantly by the instanton-anti-instanton pairings. Such a prediction needs to be tested by more improved lattice simulations. We further demonstrate that the axial-vector interaction plays an important role on the $T-\mu_A$ phase diagram.Comment: 9 pages,5 figures, references added, some comments modified. Final version for PR

Large deviations for quasilinear parabolic stochastic partial differential equations

In this paper, we establish the Freidlin-Wentzell's large deviations for quasilinear parabolic stochastic partial differential equations with multiplicative noise, which are neither monotone nor locally monotone. The proof is based on the weak convergence approach

Markov Selection and WW-strong Feller for 3D Stochastic Primitive Equations

This paper studies some analytical properties of weak solutions of 3D stochastic primitive equations with periodic boundary conditions. The martingale problem associated to this model is shown to have a family of solutions satisfying the Markov property, which is achieved by means of an abstract selection principle. The Markov property is crucial to extend the regularity of the transition semigroup from small times to arbitrary times. Thus, under a regular additive noise, every Markov solution is shown to have a property of continuous dependence on initial conditions, which follows from employing the weak-strong uniqueness principle and the Bismut-Elworthy-Li formula

Stochastic Optimization with Importance Sampling

Uniform sampling of training data has been commonly used in traditional stochastic optimization algorithms such as Proximal Stochastic Gradient Descent (prox-SGD) and Proximal Stochastic Dual Coordinate Ascent (prox-SDCA). Although uniform sampling can guarantee that the sampled stochastic quantity is an unbiased estimate of the corresponding true quantity, the resulting estimator may have a rather high variance, which negatively affects the convergence of the underlying optimization procedure. In this paper we study stochastic optimization with importance sampling, which improves the convergence rate by reducing the stochastic variance. Specifically, we study prox-SGD (actually, stochastic mirror descent) with importance sampling and prox-SDCA with importance sampling. For prox-SGD, instead of adopting uniform sampling throughout the training process, the proposed algorithm employs importance sampling to minimize the variance of the stochastic gradient. For prox-SDCA, the proposed importance sampling scheme aims to achieve higher expected dual value at each dual coordinate ascent step. We provide extensive theoretical analysis to show that the convergence rates with the proposed importance sampling methods can be significantly improved under suitable conditions both for prox-SGD and for prox-SDCA. Experiments are provided to verify the theoretical analysis.Comment: 29 page