The real nonnegative inverse eigenvalue problem (RNIEP) is the problem of characterizing all possible real spectra of entrywise nonnegative matrices. This problem remains unsolved. Since the first result in this area announced by Suleimanova in 1949 and proved by Perfect in 1953, a number of realizability criteria or sufficient conditions for the existence of a nonnegative matrix with a given r...

In this paper, we determine the symmetrised density of a nonsingular doubly noncentral matrix variate beta type I and II distributions under different definitions.

In this note, we develop semi-analytical techniques to obtain the full correlational structure of a stochastic network of nonlinear neurons described by rate variables. Under the assumption that pairs of membrane potentials are jointly Gaussian – which they tend to be in large networks – we obtain deterministic equations for the temporal evolution of the mean firing rates and the noise covarian...

We consider the Hamiltonian cycle problem embedded in singularly perturbed (controlled) Markov chains. We also consider a functional on the space of stationary policies of the process that consists of the (1,1)-entry of the fundamental matrices of the Markov chains induced by these policies. We focus on the subset of these policies that induce doubly stochastic probability transition matrices w...

Low-Density Parity Check (LDPC) codes are linear block codes which perform closer to Shannon‟s limit. It is defined by the parity check matrix (PCM) which contains only a few ones in comparison to the number of zeros (sparsity). Stochastic based computation is a method to design lowprecision digital circuits. In stochastic computing, probabilities are encoded by random sequences of bits. In thi...

We describe a maximum entropy approach for computing volumes and counting integer points in polyhedra. To estimate the number of points from a particular set X ⊂ Rn in a polyhedron P ⊂ Rn we construct a probability distribution on the set X by solving a certain entropy maximization problem such that a) the probability mass function is constant on the set P ∩X and b) the expectation of the distr...

The paper is a brief survey of some recent new results and progress of the Laplacian spectra of graphs and complex networks (in particular, random graph and the small world network). The main contents contain the spectral radius of the graph Laplacian for given a degree sequence, the Laplacian coefficients, the algebraic connectivity and the graph doubly stochastic matrix, and the spectra of ra...

It is proved that a certain symmetric sequence (h0, h1, . . . , hd) of nonnegative integers arising in the enumeration of magic squares of given size n by row sums or, equivalently, in the generating function of the Ehrhart polynomial of the polytope of doubly stochastic n × n matrices, is equal to the h-vector of a simplicial polytope and hence that it satisfies the conditions of the g-theorem...

We have recently reported the phenomenon of doubly stochastic resonance [Phys. Rev. Lett. 85, 227 (2000)], a synthesis of noise-induced transition and stochastic resonance. The essential feature of this phenomenon is that multiplicative noise induces a bimodality and additive noise causes stochastic resonance behavior in the induced structure. In the present paper we outline possible applicatio...

Two graphs with adjacency matrices A and B are isomorphic if there exists a permutation matrix P for which the identity PAP = B holds. Multiplying through by P and relaxing the permutation matrix to a doubly stochastic matrix leads to the notion of fractional isomorphism. We show that the levels of the Sherali-Adams hierarchy of linear programming relaxations applied to fractional isomorphism i...