Abstract
The problem of computing the transient probability distribution of countably infinite multidimensional continuous-time Markov chains (CTMCs) arising in systems of stochastic chemical kinetics is addressed by a software tool. Starting from an initial probability distribution, time evolution of the probability distribution associated with the CTMC is described by a system of linear first-order ordinary differential equations, known as the chemical master equation (CME). The solver for the CME uses the time stepping implicit backward differentiation formulae (BDF). Solution vectors in BDF can be stored compactly during transient analysis in one of the Hierarchical Tucker Decomposition, Quantized Tensor Train, or Transposed Quantized Tensor Train formats.
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Acknowledgement
Part of this work is supported by the Alexander von Humboldt Foundation through the Research Group Linkage Programme. The research of M. Can Orhan is carried out during his PhD studies at Bilkent University and supported by The Scientific and Technological Research Council of Turkey under grant 2211-A. We thank the referees whose comments led to an improved manuscript.
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Dayar, T., Orhan, M.C. (2018). A Software Tool for the Compact Solution of the Chemical Master Equation. In: German, R., Hielscher, KS., Krieger, U. (eds) Measurement, Modelling and Evaluation of Computing Systems. MMB 2018. Lecture Notes in Computer Science(), vol 10740. Springer, Cham. https://doi.org/10.1007/978-3-319-74947-1_24
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DOI: https://doi.org/10.1007/978-3-319-74947-1_24
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