In this paper we present an analytic method for calculating the transition probability between two random Gaussian matrices with given eigenvalue spectra in the context of Dyson Brownian motion. We show that in the Coulomb gas language, in large N limit, memory of the initial state is preserved in the form of a universal linear potential acting on the eigenvalues. We compute the likelihood of a...

Classical dynamics in SU(2) Matrix theory is investigated. A classical chaosorder transition is found. For the angular momentum small enough (even for small coupling constant) the system exhibits a chaotic behavior, for angular momentum large enough the system is regular.

We study an evolutionary game model based on a transition matrix approach, in which the total change in the proportion of a population playing a given strategy is summed directly over contributions from all other strategies. This general approach combines aspects of the traditional replicator model, such as preserving unpopulated strategies, with mutation-type dynamics, which allow for nonzero ...

This paper describes a compression algorithm for probability transition matrices. The compressed matrix is itself a probability transition matrix. In general the compression is not error-free, but the error appears to be small even for high levels of compression.

The transition matrix, which characterizes a discrete time homogeneous Markov chain, is a stochastic matrix. A stochastic matrix is a special nonnegative matrix with each row summing up to 1. In this paper, we focus on the computation of the stationary distribution of a transition matrix from the viewpoint of the Perron vector of a nonnegative matrix, based on which an algorithm for the station...

We propose a Dynamic Boolean Network in which a state of a Boolean network and an output label associated with the state are interacting with each other, and a transition matrix keeps changing perpetually. We extrapolate a mutation of a transition matrix as T → Q−1TQ where T is a transition matrix and Q is a matrix representation of a permutation P (where the objects permuted are states of DBN)...

This paper investigates the reliability characteristics of a complex system having nine subsystems arranged in the form of 3x3 matrix in which each row contains three subsystems. The configuration of the row is of the type 2-out-of-3: F. Each subsystem has n units connected in series. The system fails if any one row containing three subsystems fails. The considered system analyzed incorporating...