Differential equations and dynamical systems
Differential equations and dynamical systems
Model-Checking Algorithms for Continuous-Time Markov Chains
IEEE Transactions on Software Engineering
The Importance of Being (A Little Bit) Discrete
Electronic Notes in Theoretical Computer Science (ENTCS)
Analysing Biochemical Oscillation through Probabilistic Model Checking
Electronic Notes in Theoretical Computer Science (ENTCS)
Sliding Window Abstraction for Infinite Markov Chains
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Fast Adaptive Uniformization of the Chemical Master Equation
HIBI '09 Proceedings of the 2009 International Workshop on High Performance Computational Systems Biology
Query-based verification of qualitative trends and oscillations in biochemical systems
Theoretical Computer Science
Trend-Based analysis of a population model of the AKAP scaffold protein
Transactions on Computational Systems Biology XIV
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In systems biology, an interesting problem is to analyze and characterize the oscillatory and periodic behavior of a chemical reaction system. Traditionally, those systems have been treated deterministically and continuously via ordinary differential equations. In case of high molecule counts with respect to the volume this treatment is justified. But otherwise, stochastic fluctuations can have a high influence on the characteristics of a system as has been shown in recent publications. In this paper we develop an efficient numerical approach for analyzing the oscillatory and periodic character of user-defined observations on Markov population models (MPMs). MPMs are a special kind of continuous-time Markov chains that allow for a discrete representation of unbounded population counts for several population types and transformations between populations. Examples are chemical species and the reactions between them.