A linear dynamical model for the development of the turbulent energy cascade was introduced in Apolina ' rio et al. (J. Stat. Phys., 186, 15 (2022)). This partial differential equation, randomly stirred by a forcing term which is smooth in space and delta- ...
We study the rapid stabilization of the heat equation on the 1-dimensional torus using the backstepping method with a Fredholm transformation. This classical framework allows us to present the backstepping method with Fredholm transformations for the Lapla ...
An existence result is presented for the dynamical low rank (DLR) approximation for random semi-linear evolutionary equations. The DLR solution approximates the true solution at each time instant by a linear combination of products of deterministic and sto ...
In this paper, we provide a Banach-space formulation of supervised learning with generalized total-variation (gTV) regularization. We identify the class of kernel functions that are admissible in this framework. Then, we propose a variation of supervised l ...
Adaptive networks have the capability to pursue solutions of global stochastic optimization problems by relying only local interactions within neighborhoods. The diffusion of information through repeated interactions allows for globally optimal behavior, w ...
Fractional operators are widely used in mathematical models describing abnormal and nonlocal phenomena. Although there are extensive numerical methods for solving the corresponding model problems, theoretical analysis such as the regularity result, or the ...
Given a sequence L & x2d9;epsilon of Levy noises, we derive necessary and sufficient conditions in terms of their variances sigma 2(epsilon) such that the solution to the stochastic heat equation with noise sigma(epsilon)-1L & x2d9;epsilon converges in law ...
Mathematical models involving multiple scales are essential for the description of physical systems. In particular, these models are important for the simulation of time-dependent phenomena, such as the heat flow, where the Laplacian contains mixed and ind ...
This paper is devoted to the distributed complexity of finding an approximation of the maximum cut in graphs. A classical algorithm consists in letting each vertex choose its side of the cut uniformly at random. This does not require any communication and ...
Models for cardiac mechanics require an activation mechanism properly representing the stress-strain relations in the contracting myocardium. In this paper, we propose a new activation model that accounts for the transmural heterogeneities observed in myoc ...
Surface scattering is the key limiting factor to thermal transport in dielectric crystals as the length scales are reduced or when temperature is lowered. To explain this phenomenon, it is commonly assumed that the mean free paths of heat carriers are boun ...
