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...

A positive map between Euclidean Jordan algebras is a (symmetric cone) order preserving linear map. We show that the norm of such a map is attained at the unit element, thus obtaining an analog of the operator/matrix theoretic Russo-Dye theorem. A doubly stochastic map between Euclidean Jordan algebras is a positive, unital, and trace preserving map. We relate such maps to Jordan algebra automo...

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...

In this paper, we develop a regularization framework for image deblurring based on a new definition of the normalized graph Laplacian. We apply a fast scaling algorithm to the kernel similarity matrix to derive the symmetric, doubly stochastic filtering matrix from which the normalized Laplacian matrix is built. We use this new definition of the Laplacian to construct a cost function consisting...

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...