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1.  Steady-State Analysis of Genetic Regulatory Networks Modelled by Probabilistic Boolean Networks 
Probabilistic Boolean networks (PBNs) have recently been introduced as a promising class of models of genetic regulatory networks. The dynamic behaviour of PBNs can be analysed in the context of Markov chains. A key goal is the determination of the steady-state (long-run) behaviour of a PBN by analysing the corresponding Markov chain. This allows one to compute the long-term influence of a gene on another gene or determine the long-term joint probabilistic behaviour of a few selected genes. Because matrix-based methods quickly become prohibitive for large sizes of networks, we propose the use of Monte Carlo methods. However, the rate of convergence to the stationary distribution becomes a central issue. We discuss several approaches for determining the number of iterations necessary to achieve convergence of the Markov chain corresponding to a PBN. Using a recently introduced method based on the theory of two-state Markov chains, we illustrate the approach on a sub-network designed from human glioma gene expression data and determine the joint steadystate probabilities for several groups of genes.
PMCID: PMC2447305  PMID: 18629023
2.  Model selection in genomics. 
Environmental Health Perspectives  2003;111(6):A328-A329.
PMCID: PMC1241516  PMID: 12760836
3.  Data extraction from composite oligonucleotide microarrays 
Nucleic Acids Research  2003;31(7):e36.
Microarray or DNA chip technology is revolutionizing biology by empowering researchers in the collection of broad-scope gene information. It is well known that microarray-based measurements exhibit a substantial amount of variability due to a number of possible sources, ranging from hybridization conditions to image capture and analysis. In order to make reliable inferences and carry out quantitative analysis with microarray data, it is generally advisable to have more than one measurement of each gene. The availability of both between-array and within-array replicate measurements is essential for this purpose. Although statistical considerations call for increasing the number of replicates of both types, the latter is particularly challenging in practice due to a number of limiting factors, especially for in-house spotting facilities. We propose a novel approach to design so-called composite microarrays, which allow more replicates to be obtained without increasing the number of printed spots.
PMCID: PMC152821  PMID: 12655024

Results 1-3 (3)