Computing Poisson probabilities
Communications of the ACM
Numerical transient analysis of Markov models
Computers and Operations Research
Programming with abstract data types
Proceedings of the ACM SIGPLAN symposium on Very high level languages
Hybrid method for the chemical master equation
Journal of Computational Physics
IEEE Transactions on Computers
Inexact Uniformization Method for Computing Transient Distributions of Markov Chains
SIAM Journal on Scientific Computing
25 Years of Model Checking
Adaptive Discrete Galerkin Methods Applied to the Chemical Master Equation
SIAM Journal on Scientific Computing
Approximation of Event Probabilities in Noisy Cellular Processes
CMSB '09 Proceedings of the 7th International Conference on Computational Methods in Systems Biology
Formalisms for Specifying Markovian Population Models
RP '09 Proceedings of the 3rd International Workshop on Reachability Problems
A modified uniformization method for the solution of the chemical master equation
Computers & Mathematics with Applications
Fast Adaptive Uniformization of the Chemical Master Equation
HIBI '09 Proceedings of the 2009 International Workshop on High Performance Computational Systems Biology
Simulation methods in systems biology
SFM'08 Proceedings of the Formal methods for the design of computer, communication, and software systems 8th international conference on Formal methods for computational systems biology
Proceedings of the 8th International Conference on Computational Methods in Systems Biology
8th Conference on Computational Methods in Systems Biology
Hybrid numerical solution of the chemical master equation
Proceedings of the 8th International Conference on Computational Methods in Systems Biology
SABRE: A Tool for Stochastic Analysis of Biochemical Reaction Networks
QEST '10 Proceedings of the 2010 Seventh International Conference on the Quantitative Evaluation of Systems
Propagation models for computing biochemical reaction networks
Proceedings of the 9th International Conference on Computational Methods in Systems Biology
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We introduce propagation models (PMs), a formalism able to express several kinds of equations that describe the behavior of biochemical reaction networks. Furthermore, we introduce the propagation abstract data type (PADT), which separates concerns regarding different numerical algorithms for the transient analysis of biochemical reaction networks from concerns regarding their implementation, thus allowing for portable and efficient solutions. The state of a propagation abstract data type is given by a vector that assigns mass values to a set of nodes, and its $({\bf next})$ operator propagates mass values through this set of nodes. We propose an approximate implementation of the $({\bf next})$ operator, based on threshold abstraction, which propagates only "significant" mass values and thus achieves a compromise between efficiency and accuracy. Finally, we give three use cases for propagation models: the chemical master equation (CME), the reaction rate equation (RRE), and a hybrid method that combines these two equations. These three applications use propagation models in order to propagate probabilities and/or expected values and variances of the model's variables.