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This ebook constitutes the refereed court cases of the foreign convention on Computational equipment in platforms 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 various recommendations from laptop technology, resembling language layout, concurrency idea, software program engineering, and formal tools, for biologists, physicists, and mathematicians attracted to the systems-level knowing of mobile procedures.
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Additional resources for Computational Methods in Systems Biology
McGraw-Hill, New York (1960) 15. : Stochastic approach to chemical kinetics. Journal of Applied Probability 4, 413–478 (1967) 16. : Stochastic Processes in Physics and Chemistry. Elsevier, Amsterdam (1992) 17. : A rigorous derivation of the chemical master equation. Physica A 188, 404–425 (1992) 18. : Modelling and simulation of intracellular dynamics: Choosing an appropriate framework. IEEE Transactions On NanoBioScience 3(3), 200–207 (2004) 19. : Markov Chains. Springer, Heidelberg (1999) 20.
Since the only requirement for the application of Importance Sampling is absolute continuity of the probability measures involved, there is a great freedom in how to change the measure. It is only necessary that all reaction paths that are possible (have positive probability) under the original measure remain possible. 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.
In fact, not surprisingly, Cao, Li and Petzold  showed that an optimized implementation of the direct method is indeed more eﬃcient than the Next Reaction Method. We also like to state that it seems not obvious that it is statistically harmless to reuse calculated random numbers since this may introduce bias to the resulting estimators. To get an intuitive understanding of our doubts, assume that at a certain time in the simulation a random number is generated that implies a very large tentative time of a particular reaction.