Discrete time Markov chains (DTMCs) are commonly described by a state transition matrix that contains sufficient information to figure out the stationary state distribution of the Markov model. In this work, we propose recursive stochastic equations as an alternative description that clearly separates the functional behavior of the model from its random influences that determine the state trans...

A class of queueing networks which consist of single-server fork-join nodes with infinite buffers is examined to derive a representation of the network dynamics in terms of max-plus algebra. For the networks, we present a common dynamic state equation which relates the departure epochs of customers from the network nodes in an explicit vector form determined by a state transition matrix. We sho...

An approach for the analytical solution, free and forced, to systems of delay differential equations (DDEs) has been developed using the matrix Lambert function. To generalize the Lambert function solution for scalar DDEs to systems of DDEs, we introduce a new matrix, Q when the coefficient matrices in a system of DDEs do not commute. The solution is in the form of an infinite series of modes w...

Probabilistic Boolean networks (PBNs) have received much attention in modeling genetic regulatory networks. A PBN can be regarded as a Markov chain process and is characterised by a transition probability matrix. In this study, the authors propose efficient algorithms for constructing a PBN when its transition probability matrix is given. The complexities of the algorithms are also analysed. Th...

There are infinitely many transformations A of the eigenvectors resulting in a soft membership matrix χ satisfying the positivity and partition of unity constraints. Consequently, we have to determine the transformation A that satisfies some optimality condition. The starting point is the question whether it is possible to define some simplified dynamics on the coarse grained state space. Can w...

The study of folding and conformational changes of macromolecules by molecular dynamics simulations often requires the generation of large amounts of simulation data that are difficult to analyze. Markov (state) models (MSMs) address this challenge by providing a systematic way to decompose the state space of the molecular system into substates and to estimate a transition matrix containing the...

Using a model of spinless fermions in a lattice with nearest-neighbor and next-nearest-neighbor interactions, we show that the entropy of the reduced two-site density matrix the bond entropy can be used as an extremely accurate and easy to calculate numerical indicator for the critical parameters of the quantum phase transition when the basic ordering pattern has a two-site periodicity. The act...