In this note we show that for a given controllable pair (A,B) and any λ > 0, a gain matrix K can be chosen so that the transition matrix e of the system ẋ = (A + BK)x decays at the exponential rate e and the overshoot of the transition matrix can be bounded by Mλ for some constants M and L that are independent of λ. As a consequence, for any h > 0, a gain matrix K can be chosen so that the magn...

We study the mixing rate of non-backtracking random walks on graphs by looking at non-backtracking walks as walks on the directed edges of a graph. A result known as Ihara’s Theorem relates the adjacency matrix of a graph to a matrix related to non-backtracking walks on the directed edges. We prove a weighted version of Ihara’s Theorem which relates the transition probability matrix of a non-ba...

FePt nanoparticles with thermally stable room-temperature ferromagnetism are investigated. The monodisperse nanoparticles are prepared by chemical synthesis and a salt-matrix annealing technique. Structural and magnetic characterizations confirm the phase transition from the disordered face-centered cubic structure. In this paper, 3 nm FePt nanoparticles are first synthesized by superhydride re...

In this paper we study the connection between matrix measures and random walks with a block tridiagonal transition matrix. We derive sufficient conditions such that the blocks of the n-step block tridiagonal transition matrix of the Markov chain can be represented as integrals with respect to a matrix valued spectral measure. Several stochastic properties of the processes are characterized by m...

In this short paper, new properties of transition matrix were introduced. Eigen values for small order transition matrices are calculated in flexible method. For benefit of these properties applications of these properties were studied in the solution of Markov's chain via steady state vector, and information theory via channel entropy. The implemented test examples were promised for usages. Ke...

for an m-state homogeneous irreducible Markov chain with transition probability matrix Qm×m is known, but the chain requires updating by altering some of its transition probabilities or by adding or deleting some states. Suppose that the updated transition probability matrix Pn×n is also irreducible. The updating problem is to compute the updated stationary distribution π = (π1, π2, . . . , πn)...

Given an aperiodic random walk on a finite graph, an expression will be derived for the hitting times in terms of the eigenvalues of the transition matrix. The process of diagonalizing the transition matrix and its associated fundamental matrix will be discussed. These results will then be applied to a random walk on a rook graph. Lastly, a cover time bound depending on the hitting times will b...

This paper describes a graph-spectral method for path estimation. Our aim is to find a maximum probability path through a lattice of pixel sites. We characterise the path recovery problem using a site transition matrix. A graph-spectral analysis of the transition matrix reveals how the maximum probability path can be located using an eigenvector of the associated normalised affinity matrix. We ...

Reconstructing the logical network from the transition matrix is benefit for learning the logical meaning of the algebraic result from the algebraic representation of a BN. And so far there has no method to convert the matrix expression back to the logic expression for a BN with an arbitrary topology structure. Based on the canonical form and Karnaugh map, we propose a method for reconstructing...