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A wavelet-like model for distributions of objects in natural and man-made terrestrial environments is developed. The model is constructed in a self-similar fashion, with the sizes, amplitudes, and numbers of objects occurring at a constant…
The aim of this work is to ascertain the characterization of the existence of coexistence states for a class of cooperative systems supported by the study of an associated non--local equation through classical variational methods. Thanks to…
Two methods are explained to exactly solve Maxwell's equations where permittivity, permeability and conductivity may vary in space. In the constitutive relations, retardation is regarded. If the material properties depend but on one…
This review presents an upgraded wave theory adapted to the high fluctuation level of driven realistic i.e. non-idealized plasmas. Above all, this means giving up the well-known concept of a linear wave theory in favor of a thoroughly…
Coherent structures are solutions to reaction-diffusion systems that are time-periodic in an appropriate moving frame and spatially asymptotic at $x=\pm\infty$ to spatially periodic travelling waves. This paper is concerned with sources…
The evolution of the amplitude of two nonlinearly interacting waves is considered, via a set of coupled nonlinear Schroedinger-type equations. The dynamical profile is determined by the wave dispersion laws (i.e. the group velocities and…
In this paper we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In the general case we have the solution as a multiresolution expansion in the base of…
We provide a detailed study of the dynamics obtained by linearizing the Korteweg-de Vries equation about one of its periodic traveling waves, a cnoidal wave. In a suitable sense, linearly analogous to space-modulated stability, we prove…
We derive a mode-coupling theory for the slow dynamics of fluids confined in disordered porous media represented by spherical particles randomly placed in space. Its equations display the usual nonlinear structure met in this theoretical…
We describe a mathematical formalism and numerical algorithms for identifying and tracking slowly mixing objects in nonautonomous dynamical systems. In the autonomous setting, such objects are variously known as almost-invariant sets,…
We consider a class of nonconvex energy functionals that lies in the framework of the peridynamics model of continuum mechanics. The energy densities are functions of a nonlocal strain that describes deformation based on pairwise…
In many environmental applications involving spatially-referenced data, limitations on the number and locations of observations motivate the need for practical and efficient models for spatial interpolation, or kriging. A key component of…
We consider varying coefficient Cox models with high-dimensional covariates. We apply the group Lasso method to these models and propose a variable selection procedure. Our procedure copes with variable selection and structure…
In this article, we construct discrete tight frames for $L^2(\mathbb{S}^{d-1})$, $d\geq3$, which consist of localized polynomial wavelets with adjustable degrees of directionality. In contrast to the well studied isotropic case, these…
We develop data-driven methods for incorporating physical information for priors to learn parsimonious representations of nonlinear systems arising from parameterized PDEs and mechanics. Our approach is based on Variational Autoencoders…
Over the last decade, nonparametric methods have gained increasing attention for modeling complex data structures due to their flexibility and minimal structural assumptions. In this paper, we study a general multivariate nonparametric…
In this paper, we investigate the well-posedness of a nonlinear dispersive model with variable coefficients that describes the evolution of surface waves propagating through a one-dimensional shallow water channel of finite length with…
Identifying a coupled dynamical system out of many plausible candidates, each of which could serve as the underlying generator of some observed measurements, is a profoundly ill posed problem that commonly arises when modelling real world…
We are interested in exploring interacting particle systems that can be seen as microscopic models for a particular structure of coupled transport flux arising when different populations are jointly evolving. The scenarios we have in mind…
We show how fundamental ideas from signal processing, multiscale theory and wavelets may be applied to non-linear dynamics. The problems from dynamics include iterated function systems (IFS), dynamical systems based on substitution such as…