BOCCI C

In this paper we study how perturbing a matrix changes its nonnegative rank. We prove that the nonnegative rank can only increase in a neighborhood of a matrix with no zero columns. Also, we describe some special families of perturbations. We show how our results relate to statistics in terms of the study of maximum likelihood estimation for...

In this work we study several types of diagonal-effect models for two-way contingency tables in the framework of Algebraic Statistics. We use both toric models and mixture models to encode the different behavior of the diagonal cells. We compute the invariants of these models and we explore their geometrical structure.

Given an undirected graph G, we define a new object H-G , called the mp-chart of G, in the max-plus algebra. We use it, together with the max-plus permanent, to describe the complexity of graphs. We show how to compute the mean and the variance of H-G in terms of the adjacency matrix of G and we give a central limit theorem for H-G . Finally,...