The major goal of this study was to create a continuous time Markov chain (CTMC) models of voltage gating of gap junction (GJ) channels formed of connexin protein. This goal was achieved by using the Piece Linear Aggregate (PLA) formalism to describe the function of GJs and transforming PLA into Markov process. Infinitesimal generator of CTMC was used to automate construction of Markov chain mo...

A fundamental question in biology is whether the network of interactions that regulate gene expression can be modeled by existing mathematical techniques. Studies of the ability to predict a gene’s state based on the states of other genes suggest that it may be possible to abstract sufficient information to build models of the system that retain steady-state behavioral characteristics of the re...

This work studies the parameter identification problem for the Markov chain choice model of Blanchet, Gallego, and Goyal used in assortment planning. In this model, the product selected by a customer is determined by a Markov chain over the products, where the products in the offered assortment are absorbing states. The underlying parameters of the model were previously shown to be identifiable...

Implementations of parallel genetic algorithms (GAs) with multiple populations are common, but they introduce several parameters whose effect on the quality of the search is not well understood. Parameters such as the number of populations, their size, the topology of communications, and the migration rate have to be set carefully to reach adequate solutions. This paper presents models that pre...

2 Continuous-Time Markov Chains 3 2.1 Time-homogeneous chains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Time-inhomogeneous chains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3 Embedded Discrete-Time Markov Chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.4 Conditional Expectations . . . . . . . . . . . . . . . . . . ...