Dragomir Tsonev (UFAM, Manaus) Title: ON THE SPECTRA OF GEOMETRIC OPERATORS EVOLVING WITH GEOMETRIC FLOWS Abstract: In this work we generalise various recent results on the evolution and monotonicity of the eigenvalues of certain geometric operators under specified geometric flows. Given a compact Riemannian manifold (M, g(t)) and a smooth function η ∈ C(M) we consider the family of operators∆−...

Representing distributions over permutations can be a daunting task due to the fact that the number of permutations of n objects scales factorially in n. One recent way that has been used to reduce storage complexity has been to exploit probabilistic independence, but as we argue, full independence assumptions impose strong sparsity constraints on distributions and are unsuitable for modeling r...

Consider a matrix X, whose N rows have information on the attainments of N inviduals. Each column, therefore, hosts the distribution of each attainment across the population. The number of columns/variables is D. A typical attainment element of the matrix is: xnd (2 R), that is, the attainment of individual n in dimension/variable d. In the identi…cation stage, the variable-speci…c poverty line...

We develop the quantum inverse scattering method for the one-dimensional Hubbard model on the infinite interval at zero density. R-matrix and monodromy matrix are obtained as limits from their known counterparts on the finite interval. The R-matrix greatly simplifies in the considered limit. The new R-matrix contains a submatrix which turns into the rational R-matrix of the XXX-chain by an appr...

Abstract. Assume that f is Dunkl polyharmonic in R (i.e. (∆h) f = 0 for some integer p, where ∆h is the Dunkl Laplacian associated to a root system R and to a multiplicity function κ, defined on R and invariant with respect to the finite Coxeter group). Necessary and successful condition that f is a polynomial of degree ≤ s for s ≥ 2p− 2 is proved. As a direct corollary, a Dunkl harmonic functi...

Any symmetric affinity function w : V × V → R+ defined on a discrete set V induces Euclidean space structure on V . In particular, an undirected graph specified by an affinity (or adjacency ) matrix can be considered as a metric topological space. We have calculated the visual representations of the probabilistic locus for a chain, a polyhedron, and a finite 2-dimensional lattice.

In this paper we define a new type of rings ”almost powerhermitian rings” (a generalization of almost hermitian rings) and establish several sufficient conditions over a ring R such that, every regular matrix admits a diagonal power-reduction.

This paper considers the problem of recovering a group sparse signal matrix Y = [y1, · · · ,yL] from sparsely corrupted measurements M = [A(1)y1, · · · ,A(L)yL] + S, where A(i)’s are known sensing matrices and S is an unknown sparse error matrix. A robust group lasso (RGL) model is proposed to recover Y and S through simultaneously minimizing the l2,1-norm of Y and the l1-norm of S under the me...

A graphG = (V , E) is said to admit a system ofμ collective additive tree r-spanners if there is a system T (G) of at most μ spanning trees of G such that for any two vertices u, v of G a spanning tree T ∈ T (G) exists such that the distance in T between u and v is at most r plus their distance in G. In this paper, we examine the problem of finding ‘‘small’’ systems of collective additive tree ...

Commuting transfer matrices of U q (X (1) r) vertex models obey the functional relations which can be viewed as an X r type Toda field equation on discrete space time. Based on analytic Bethe ansatz we present, for X r = D r , a new expression of its solution in terms of determinants and Pfaffians.