Mathematics Subject Classification (2000): 53C25, 53C40, 53C42.

A class of discrete-time M=G=1 queues, including both round robin and last come rst served service, in which customers are subject to permutations is considered. These time slotted queues, analogous to the symmetric queues of Kelly, are analyzed by examination of the time reversed process. Product form stationary distributions are found for a type of doubly stochastic server of Schassberger [5]...

We claim that both of these walks have the same mixing time. This fact is in fact true for any Markov chain on groups. In this case note that we are considering a Markov chain on the symmetric group Sn. In general consider any group G and suppose we have a set of generators {g1, . . . , gk}. In each time step we choose a generator from this set according to a probability distribution μ and we a...

We introduce another view of sequence evolution. Contrary to other approaches, we model the substitution process in two steps. First we assume (arbitrary) scaled branch lengths on a given phylogenetic tree. Second we allocate a Poisson distributed number of substitutions on the branches. The probability to place a mutation on a branch is proportional to its relative branch length. More importan...

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...