Random walks on simple graphs in connection with electrical resistor networks lead to the definition of Markov chains with transition probability matrix in terms of electrical conductances. We extend this definition to an effective transition matrix Pij to account for the probability of going from vertex i to any vertex j of the original connected graph G. Also, we present an algorithm based on...

This article demonstrates a new approach to analyzing UML designs using state and sequence diagrams. From multiple state diagrams, a super-state diagram which includes the cross-product of the selected states is built along with a transition matrix of possible transitions. The closure of the transition matrix is used to identify unreachable states and impossible transitions. Additionally, the c...

The problem of estimating a Markov transition matrix to statistically describe the dynamics underlying an observed process is frequently found in the physical and economical sciences. However, little attention has been paid to the fact that such an estimation is associated with statistical uncertainty, which depends on the number of observed transitions between metastable states. In turn, this ...

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...