Markov chains are fundamental tools used throughout the sciences and engineering; the design and analysis of Markov Chains has been a focus of theoretical computer science for the last 20 years. A Markov Chain takes a random walk in a large state space Ω, converging to a target stationary distribution π over Ω. The number of steps needed for the random walk to have distribution close to π is th...

This study aims to develop a new one-vendor multiple-buyers integrated inventory model. We believe that our proposed model can forecast the demand of all buyers in coming future by using data have already existed and minimize total cost-for both vendors. In recent days, Markov chain approach has played one critical methods forecasting Supply Chain Management (SCM) field. The this is analysis sp...

Computing the stationary distribution of a large finite or countably infinite state space Markov Chain has become central to many problems such as statistical inference and network analysis. Standard methods involve large matrix multiplications as in power iteration, or simulations of long random walks, as in Markov Chain Monte Carlo (MCMC). For both methods, the convergence rate is is difficul...

In previous work we developed a method to model software testing data, including both failure events and correct behavior, as a finitestate, discrete-parameter, recurrent Markov chain. We then showed how direct computation on the Markov chain could yield various reliability related test measures. Use of the Markov chain allows us to avoid common assumptions about failure rate distributions and ...

0. Introductory Remarks. This collection which I refer to as “Barebones Background for Markov Chains" is really a set of notes for lectures I gave during the spring quarters of 2001 and 2003 on Markov chains, leading up to Markov Chain Monte Carlo. The prerequisite needed for this is a knowledge of some basic probability theory and some basic analysis. This is really not a basic course in Marko...

1. Abstract 2. Introduction 3. Computational Approaches for Identifying Gene Modules 3.1. Advanced Statistical Approaches 3.2. Matrix Decomposition Approaches 4. Computational Approaches for Inferring Gene Connectivity 4.1. ODE-based Models 4.2. Bayesian Networks 4.3. Coexpression Networks 4.4. Probabilistic Boolean Networks 4.5. Inference from Multiple Sources of Data 5. Network Analysis in Si...

Hierarchical Markovian models are a useful paradigm for the speciication and quantitative analysis of models arising from complex systems. Although techniques for a very eecient analysis of large scale hierarchical Markovian models have been developed recently, the size of the Markov chain underlying a complex hierarchical model often prohibits an analysis on contemporary computer equipment. Ho...