Hybrid numerical solution of the chemical master equation

Henzinger, Thomas A.; Mikeev, Linar; Mateescu, Maria; Wolf, Verena

doi:10.1145/1839764.1839772

Cited by 45 publications

(48 citation statements)

References 31 publications

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“…Now the question arises what the counterpart of the CME in case of the piecewise deterministic process (32)- (33) is. The answer can be found in [25,8]…”

Section: Piecewise Deterministic Process and Liouville-master Equationmentioning

confidence: 99%

Error Bound for Piecewise Deterministic Processes Modeling Stochastic Reaction Systems

Jahnke¹,

Kreim²

2012

Multiscale Model. Simul.

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Biological processes involving the random interaction of d species with integer particle numbers are often modeled by a Markov jump process on N d 0 . Realizations of this process can, in principle, be generated with the classical stochastic simulation algorithm proposed in [19], but for very reactive systems this method is usually inefficient. Hybrid models based on piecewise deterministic processes offer an attractive alternative which can decrease the simulation time considerably in applications where species with rather low particle numbers interact with very abundant species. We investigate the convergence of the hybrid model to the original one for a class of reaction systems with two distinct scales. Our main result is an error bound which states that, under suitable assumptions, the hybrid model approximates the marginal distribution of the discrete species and the conditional moments of the continuous species up to an error of O`M −1´w here M is the scaling parameter of the partial thermodynamic limit.

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“…Now the question arises what the counterpart of the CME in case of the piecewise deterministic process (32)- (33) is. The answer can be found in [25,8]…”

Section: Piecewise Deterministic Process and Liouville-master Equationmentioning

confidence: 99%

Error Bound for Piecewise Deterministic Processes Modeling Stochastic Reaction Systems

Jahnke¹,

Kreim²

2012

Multiscale Model. Simul.

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show abstract

“…We can obtain approximations of the state of a propagation ADT by applying a threshold abstraction for mass values [2], which considers only nodes that hold significant mass, and/or node aggregation [4], which aggregates many nodes into a single "abstract node" and propagates, in addition to probabilities, also conditional expectations of the node variables. Here we present only the threshold abstraction method.…”

Section: Methodsmentioning

confidence: 99%

Propagation models for computing biochemical reaction networks

Henzinger

Mateescu

2011

Proceedings of the 9th International Conference on Computational Methods in Systems Biology

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“…From Table II, we see that the obtained reward converges to a fixed value with increasing model parameter N. Therefore, if one is interested in the value obtained if the model parameters go towards infinity, methods concerned with the limiting behaviour [7,8,40, 1] might be more appropriate. As discussed in the introduction, our method targets at finding conservative bounds for the model under consideration.…”

Section: Case Studiesmentioning

confidence: 99%

Transient Reward Approximation for Continuous-Time Markov Chains

et al. 2015

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We are interested in the analysis of very large continuoustime Markov chains (CTMCs) with many distinct rates. Such models arise naturally in the context of reliability analysis, e. g., of computer network performability analysis, of power grids, of computer virus vulnerability, and in the study of crowd dynamics. We use abstraction techniques together with novel algorithms for the computation of bounds on the expected final and accumulated rewards in continuous-time Markov decision processes (CTMDPs). These ingredients are combined in a partly symbolic and partly explicit (symblicit) analysis approach. In particular, we circumvent the use of multi-terminal decision diagrams, because the latter do not work well if facing a large number of different rates. We demonstrate the practical applicability and efficiency of the approach on two case studies.

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Hybrid numerical solution of the chemical master equation

Cited by 45 publications

References 31 publications

Error Bound for Piecewise Deterministic Processes Modeling Stochastic Reaction Systems

Error Bound for Piecewise Deterministic Processes Modeling Stochastic Reaction Systems

Propagation models for computing biochemical reaction networks

Transient Reward Approximation for Continuous-Time Markov Chains

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