Within systems biology there is an increasing interest in the stochastic behavior of biochemical reaction networks. An appropriate stochastic description is provided by the chemical master equation, which represents a continuous- time Markov chain (CTMC). Standard Uniformization (SU) is an efficient method for the transient analysis of CTMCs. For systems with very different time scales, such as biochemical reaction networks, SU is computationally expensive. In these cases, a variant of SU, called adaptive uniformization (AU), is known to reduce the large number of iterations needed by SU. The additional difficulty of AU is that it requires the solution of a birth process. In this paper we present an on-the-fly variant of AU, where we improve the original algorithm for AU at the cost of a small approximation error. By means of several examples, we show that our approach is particularly well-suited for biochemical reaction networks.
This research has been partially funded by the Swiss National Science Foundation under grant 205321-111840 and by the Cluster of Excellence on Multimodal Computing and Interaction at Saarland University.
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HIBI: High-Performance Computational Systems Biology
2009-10-14 – 2009-10-16
Didier F, Henzinger TA, Mateescu M, Wolf V. Fast adaptive uniformization of the chemical master equation. In: Vol 4. IEEE; 2009:118-127. doi:10.1109/HiBi.2009.23
Didier, F., Henzinger, T. A., Mateescu, M., & Wolf, V. (2009). Fast adaptive uniformization of the chemical master equation (Vol. 4, pp. 118–127). Presented at the HIBI: High-Performance Computational Systems Biology, Trento, Italy: IEEE. https://doi.org/10.1109/HiBi.2009.23
Didier, Frédéric, Thomas A Henzinger, Maria Mateescu, and Verena Wolf. “Fast Adaptive Uniformization of the Chemical Master Equation,” 4:118–27. IEEE, 2009. https://doi.org/10.1109/HiBi.2009.23.
F. Didier, T. A. Henzinger, M. Mateescu, and V. Wolf, “Fast adaptive uniformization of the chemical master equation,” presented at the HIBI: High-Performance Computational Systems Biology, Trento, Italy, 2009, vol. 4, no. 6, pp. 118–127.
Didier F, Henzinger TA, Mateescu M, Wolf V. 2009. Fast adaptive uniformization of the chemical master equation. HIBI: High-Performance Computational Systems Biology vol. 4. 118–127.
Didier, Frédéric, et al. Fast Adaptive Uniformization of the Chemical Master Equation. Vol. 4, no. 6, IEEE, 2009, pp. 118–27, doi:10.1109/HiBi.2009.23.
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