Construction and Control of Genetic Regulatory Networks:A Multivariate Markov Chain Approach

In the post-genomic era, the construction and control of genetic regulatory networks using gene expression data is a hot research topic. Boolean networks (BNs) and its extension Probabilistic Boolean Networks (PBNs) have been served as an effective tool for this purpose. However, PBNs are difficult to be used in practice when the number of genes is large because of the huge computational cost. In this paper, we propose a simplified multivariate Markov model for approximating a PBN The new model can preserve the strength of PBNs, the ability to capture the inter-dependence of the genes in the network, qnd at the same time reduce the complexity of the network and therefore the computational cost. We then present an optimal control model with hard constraints for the purpose of control/intervention of a genetic regulatory network. Numerical experimental examples based on the yeast data are given to demonstrate the effectiveness of our proposed model and control policy.

Switching-based stabilization of aperiodic sampled-data Boolean control networks with all subsystems unstable

We aim to further study the global stability of Boolean control networks(BCNs)under aperiodic sampleddata control(ASDC).According to our previous work,it is known that a BCN under ASDC can be transformed into a switched Boolean network(SBN),and further global stability of the BCN under ASDC can be obtained by studying the global stability of the transformed SBN.Unfortunately,since the major idea of our previous work is to use stable subsystems to offset the state divergence caused by unstable subsystems,the SBN considered has at least one stable subsystem.The central thought in this paper is that switching behavior also has good stabilization;i.e.,the SBN can also be stable with appropriate switching laws designed,even if all subsystems are unstable.This is completely different from that in our previous work.Specifically,for this case,the dwell time(DT)should be limited within a pair of upper and lower bounds.By means of the discretized Lyapunov function and DT,a sufficient condition for global stability is obtained.Finally,the above results are demonstrated by a biological example.

Preface

A preface for the September 2007 issue of the 'Journal of Computational Mathematics' is presented.

MODELING GENETIC REGULATORY NETWORKS:A DELAY DISCRETE DYNAMICAL MODEL APPROACH

Modeling genetic regulatory networks is an important research topic in genomic research and computationM systems biology. This paper considers the problem of constructing a genetic regula- tory network （GRN） using the discrete dynamic system （DDS） model approach. Although considerable research has been devoted to building GRNs, many of the works did not consider the time-delay effect. Here, the authors propose a time-delay DDS model composed of linear difference equations to represent temporal interactions among significantly expressed genes. The authors also introduce interpolation scheme and re-sampling method for equalizing the non-uniformity of sampling time points. Statistical significance plays an active role in obtaining the optimal interaction matrix of GRNs. The constructed genetic network using linear multiple regression matches with the original data very well. Simulation results are given to demonstrate the effectiveness of the proposed method and model.

An average-value-at-risk criterion for Markov decision processes with unbounded costs

We study the Markov decision processes under the average-value-at-risk criterion.The state space and the action space are Borel spaces,the costs are admitted to be unbounded from above,and the discount factors are state-action dependent.Under suitable conditions,we establish the existence of optimal deterministic stationary policies.Furthermore,we apply our main results to a cash-balance model.