Passive scalar equation is considered in a turbulent homogeneous incompressible Gaussian velocity field. The turbulent nature of the field results in non-smooth coefficients in the equation. A strong, in the stochastic sense, solution of the equation is constructed using the Wiener Chaos, and the properties of the solution are studied. The results apply to both viscous and conservative motions....

Bayesian matrix completion has been studied based on a low-rank matrix factorization formulation with promising results. However, little work has been done on Bayesian matrix completion based on the more direct spectral regularization formulation. We fill this gap by presenting a novel Bayesian matrix completion method based on spectral regularization. In order to circumvent the difficulties of...

The relaxation of electronically excited atomic manganese isolated in solid rare gas matrices is observed from recorded emission spectra, to be strongly site specific. z 6P state excitation of Mn atoms isolated in the red absorption site in Ar and Kr produces narrow a 4D and a 6D state emissions while blue-site excitation produces z 6P state fluorescence and broadened a 4D and a 6D emissions. M...

With the recent experimental advance in our precise knowledge of the neutrino oscillation parameters, the correct form of the 3 × 3 neutrino mass matrix is now approximately known. I discuss how this may be obtained from symmetry principles, using as examples the finite groups A 4 and Z 3 , in two complete theories of leptons (and quarks). ——— Preprint version of talk at the 9th Adriatic Meetin...

The goal of this paper is to find methods for solving various quadratic optimization problems, mostly arising from computer vision (image segmentation and contour grouping). We consider mainly two problems: Problem 1. Let A be an n× n Hermitian matrix and let b ∈ C be any vector, maximize z∗Az + z∗b+ b∗z subject to z∗z = 1, z ∈ C. Problem 2. If A is a real n× n symmetric matrix and b ∈ R is any...

It is well known that the eigenvalues of any unitary matrix lie on the unit circle. The purpose of this paper is to prove that the eigenvalues of any matrix polynomial, with unitary coefficients, lie inside the annulus A 1 2 ,2 (0) := { z ∈ C | 1 2 < |z| < 2 } . The foundations of this result rely on an operator version of Rouché’s theorem and the intermediate value theorem.

The distance matrix of a tree is extensively investigated in the literature. The classical result concerns the determinant of the matrix D (see Graham and Pollak [7]), which asserts that if T is any tree on n vertices then det(D) = (−1)(n− 1)2. Thus, det(D) is a function dependent only on n, the number of vertices of the tree. The formula for the inverse of the matrix D was obtained in a subseq...

We describe primal, dual and primal-dual steepest-descent potential reduction methods for linear and convex minimization on the simplex in Rn and present their precise iteration complexity analyses depending on the problem dimension and the Lipschitz parameter of the constraint matrix or the convex objective function. In these methods, no matrix needs to be ever inversed so that they are pure f...

In this paper, we study the following extremal problem and its relevance to the sum of the so-called superoptimal singular values of a matrix function: Given an m × n matrix function Φ, when is there a matrix function Ψ * in the set A n,m k such that Z T trace(Φ(ζ)Ψ * (ζ))dm(ζ) = sup Ψ∈A n,m k ˛ ˛ ˛ ˛ Z T trace(Φ(ζ)Ψ(ζ))dm(ζ) ˛ ˛ ˛ ˛ ? The set A n,m k is defined by A n,m k def = n Ψ ∈ H 1 0 (Mn...

The trace formula for SL{2,Z) can be developed for vector-valued functions which satisfy an automorphic condition involving a group representation n . This paper makes this version explicit for the class of representations which can be realized as representations of the finite group PSL(2,Z/q) for some prime q . The body of the paper is devoted to computing, for the singular representations n ,...