Download Computational Methods in Systems Biology: International by Raya Khanin, Desmond J. Higham (auth.), Muffy Calder, PDF

By Raya Khanin, Desmond J. Higham (auth.), Muffy Calder, Stephen Gilmore (eds.)

This booklet constitutes the refereed court cases of the overseas convention on Computational tools in structures Biology, CMSB 2007, held in Edinburgh, Scotland, September 20-21, 2007.

The sixteen revised complete papers offered have been rigorously reviewed and chosen. The papers current a number of thoughts from computing device technological know-how, comparable to language layout, concurrency concept, software program engineering, and formal equipment, for biologists, physicists, and mathematicians attracted to the systems-level figuring out of mobile processes.

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Additional resources for Computational Methods in Systems Biology: International Conference CMSB 2007, Edinburgh, Scotland, September 20-21, 2007. Proceedings

Example text

E. 80 differently perturbed parameter settings. Table 1 contains the runtimes of matching simulations with the direct method and the simultaneous method. With the direct method 8 and 80, respectively, separate simulation experiments, each consisting of 104 simulation runs up to the given time horizons, were done according to Algorithm 1. , perturbed parameter settings were simulated with 104 simulation runs according to Algorithm 2. Not surprisingly, the runtime Simultaneous Stochastic Simulation of Multiple Perturbations 29 Table 1.

Hence, when a simulation is performed under P ∗ the sample mean of Y L is an unbiased estimator for EP [Y ]. As usual, the variance of the sample mean can be unbiasedly estimated by its sample variance. From that, confidence intervals can be obtained as another important indicator of statistical robustness. Choosing P ∗ in place of P is referred to as the change of measure, and when the aim is to apply Importance Sampling for variance reduction purposes, it is the essential part and the art of Importance Sampling to perform this change of measure such that estimators with significantly reduced variance are achieved.

That means each probability measure on the path space that meets the aforementioned condition can be considered, even non-Markovian models are allowed as long as they assign positive probabilities to all possible reaction paths. Nevertheless, we should avoid a large increase in trajectory generation efforts compared to the original measure. Thus, obviously the most natural (and valid) change of measure is to remain in the Markovian world and the easiest way is to simply change the original propensity functions to ”Importance Sampling propensity functions” α∗m such that for all m ∈ {1, .

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