Structure-preserving discretization of the chemical master equation
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DOI: 10.1007/s10543-017-0651-3
Abstract: The chemical master equation is a differential equation to model stochastic reaction systems. Its solutions are nonnegative and $$\ell ^1$$ℓ1-contractive which is inherently related to their interpretation as probability densities. In this note, numerical discretizations… read more here.
Keywords: equation; master equation; chemical master; discretization ... See more keywords
Accurate analytic solution of chemical master equations for gene regulation networks in a single cell.
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DOI: 10.1103/physreve.97.012412
Abstract: Studying gene regulation networks in a single cell is an important, interesting, and hot research topic of molecular biology. Such process can be described by chemical master equations (CMEs). We propose a Hamilton-Jacobi equation method… read more here.
Keywords: single cell; gene regulation; chemical master; networks single ... See more keywords
Beyond the chemical master equation: Stochastic chemical kinetics coupled with auxiliary processes
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DOI: 10.1371/journal.pcbi.1009214
Abstract: The chemical master equation and its continuum approximations are indispensable tools in the modeling of chemical reaction networks. These are routinely used to capture complex nonlinear phenomena such as multimodality as well as transient events… read more here.
Keywords: equation; master equation; chemical master; beyond chemical ... See more keywords