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.

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This article presents a technique for taking a sparse set of cache simulation data and fitting a multivariate model to fill in the missing points over a broad region of cache configurations. We extend previous work by its applicability to multiple miss rate components and its ability to model a wide range of cache parameters, including size, associativity and sharing. Miss rate models are useful for broad design exploration in which many cache configurations cannot be simulated directly due to limitations of trace collection setups or available resources. We show the effectiveness of the technique by applying it to two commercial workloads and presenting miss rate data for a broad design space with cache size, associativity, sharing and number of processors as variables. The fitted data match the simulation data very well. The various curves show how a miss rate model is useful for not only estimating the performance of specific configurations, but also for providing insight into miss rate trends. Furthermore, this modeling methodology is robust in the presence of corrupted simulation data and variations in simulation data from multiple sources.

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