Related papers: Generalized Radon--Nikodym Spectral Approach. Appl…
A single trapped ion interacting with laser light in a radiofrequency trap is considered by diagonalization of full Hamiltonian of the system in a suitable basis. The energies, eigenvectors, probabilities of finding the atom in the ground…
In this paper, locally Lipschitz functions acting between infinite dimensional normed spaces are considered. When the range is a dual space and satisfies the Radon--Nikod\'ym property, Clarke's generalized Jacobian will be extended to this…
A modified Radon transform for noisy data is introduced and its inversion formula is established. The problem of recovering the multivariate probability density function $f$ from the moments of its modified Radon transform $\widehat{R}f$ is…
The achievement of spectral super-resolution sensing is critically important for a variety of applications, such as radar, remote sensing, and wireless communication. However, in compressed spectrum sensing, challenges such as spectrum…
Reconstruction of equations of motion from incomplete or noisy data and dimension reduction are two fundamental problems in the study of dynamical systems with many degrees of freedom. For the latter extensive efforts have been made but…
Properties of solutions of generic hyperbolic systems with multiple characteristics with diagonalizable principal part are investigated. Solutions are represented as a Picard series with terms in the form of iterated Fourier integral…
The paper investigates the problem of performing correlation analysis when the number of observations is very large. In such a case, it is often necessary to combine the random observations to achieve dimensionality reduction of the…
In the present paper the Renormalization Group (RG) method is adopted as a tool for a constructive analysis of the properties of the Frobenius-Perron Operator. The renormalization group reduction of a generic symplectic map in the case,…
We introduce a general formulation of the fluctuation-dissipation relations (FDR) holding also in far-from-equilibrium stochastic dynamics. A great advantage of this version of the FDR is that it does not require the explicit knowledge of…
The invariant distribution, which is characterized by the stationary Fokker-Planck equation, is an important object in the study of randomly perturbed dynamical systems. Traditional numerical methods for computing the invariant distribution…
We propose an approach to multivariate nonparametric regression that generalizes reduced rank regression for linear models. An additive model is estimated for each dimension of a $q$-dimensional response, with a shared $p$-dimensional…
This work studies reduced order modeling (ROM) approaches to speed up the solution of variational data assimilation problems with large scale nonlinear dynamical models. It is shown that a key requirement for a successful reduced order…
A general problem of current interest is the analysis of diffusion problems in singularly perturbed domains, within which small subdomains are removed from the domain interior and boundary conditions imposed on the resulting holes. One…
We consider propagation of instability fronts in conservative nonlinear wave systems by the Whitham method. Whitham modulation equations for periodic solutions of the generalized Klein-Gordon equation are solved in the limit of…
This paper has two main goals: (a) establish several statistical properties---consistency, asymptotic distributions, and convergence rates---of stationary solutions and values of a class of coupled nonconvex and nonsmoothempirical risk…
Neutron and x-ray scattering experiments traditionally rely upon histogrammed data sets, which are analysed using least-squares curve fitting of multiple probability distribution components to quantify separately the various scientific…
Being able to effectively locate saddle (and other fixed) points in dynamical systems holds tremendous implications in a number of applications in engineering and science, among which the study of rare events in molecular simulations stands…
We prove sharp estimates on the time-average behavior of the squared absolute value of the Fourier transform of some absolutely continuous measures that may have power-law singularities, in the sense that their Radon-Nikodym derivatives…
The Random Coupling Model (RCM) is a statistical approach for studying the scattering properties of linear wave chaotic systems in the semi-classical regime. Its success has been experimentally verified in various over-moded wave settings,…
Stretched-exponential relaxation is a widely observed phenomenon found in ordered ferromagnets as well as glassy systems. One modeling approach connects this behavior to a droplet dynamics described by an effective Langevin equation for the…