相关论文: On effective equidistribution for higher step nilf…

In this work, we investigate a quasilinear subdiffusion model which involves a fractional derivative of order $\alpha \in (0,1)$ in time and a nonlinear diffusion coefficient. First, using smoothing properties of solution operators for…

The goal of this note is to state the optimal decay rate for solutions of the nonlinear fast diffusion equation and, in self-similar variables, the optimal convergence rates to Barenblatt self-similar profiles and their generalizations. It…

High frequency limit for most of wave phenomena is known as quasiclassical limit or ray optics limit. Propagation of waves in this limit is described in terms of wave fronts and rays. Wave front is a surface of constant phase whose points…

Continuous normalizing flows (CNFs) construct invertible mappings between an arbitrary complex distribution and an isotropic Gaussian distribution using Neural Ordinary Differential Equations (neural ODEs). It has not been tractable on…

Hierarchical structures, which include multiple levels, are prevalent in statistical and machine-learning models as well as physical systems. Extending the foundational result that the maximum entropy distribution under mean constraints is…

The focus of this paper is on the concurrent reconstruction of both the diffusion and potential coefficients present in an elliptic/parabolic equation, utilizing two internal measurements of the solutions. A decoupled algorithm is…

We develop a general transfer-matrix formalism for determining the growth rate of the Rayleigh-Taylor instability in a fluid system with spatially varying density and viscosity. We use this formalism to analytically and numerically treat…

Kinetic instabilities are one of the most challenging aspects in computational plasma physics. Accurately capturing their onset and evolution requires fine resolution of the high-dimensional distribution functions of each relevant species,…

We investigate possibilities to speed up iterative algorithms for non-blind image deconvolution. We focus on algorithms in which convolution with the point-spread function to be deconvolved is used in each iteration, and aim at accelerating…

In 1986, Dixon and McKee developed a discrete fractional Gr\"{o}nwall inequality [Z. Angew. Math. Mech., 66 (1986), pp. 535--544], which can be seen as a generalization of the classical discrete Gr\"{o}nwall inequality. However, this…

We consider the problem of approximating an analytic function on a compact interval from its values at $M+1$ distinct points. When the points are equispaced, a recent result (the so-called impossibility theorem) has shown that the best…

We establish an equidistribution theorem for the zeros of random holomorphic sections of high powers of a positive holomorphic line bundle. The equidistribution is associated with a family of singular moderate measures. We also give a…

In this article, we give explicit conditions for compact group extensions of hyperbolic flows (including geodesic flows on negatively curved manifolds) to exhibit quantifiable rates of mixing (or decay of correlations) with respect to the…

Recently, diffusion models (DMs) have made significant strides in high-quality image generation. However, the multi-step denoising process often results in considerable computational overhead, impeding deployment on resource-constrained…

Renormalization Group flows relate the values of couplings at different scales. Here, we go beyond the Renormalization Group flow of individual trajectories and derive an evolution equation for a distribution on the space of couplings. This…

We consider a lognormal diffusion process having a multisigmoidal logistic mean, useful to model the evolution of a population which reaches the maximum level of the growth after many stages. Referring to the problem of statistical…

This paper is devoted to improvements of functional inequalities based on scalings and written in terms of relative entropies. When scales are taken into account and second moments fixed accordingly, deficit functionals provide explicit…

We report on measurements of self-diffusion coefficients in discrete numerical simulations of steady, homogeneous, collisional shearing flows of nearly identical, frictional, inelastic spheres. We focus on a range of relatively high solid…

We consider a fully discrete and explicit scheme for the mean curvature flow of boundaries, based on an elementary diffusion step and a precise redistancing operation. We give an elementary convergence proof for the scheme under the…

The purpose of this note is to establish convergence of random walks on the moduli space of Abelian differentials on compact Riemann surfaces in two different modes: convergence of the $n$-step distributions from almost every starting point…