A generic framework to coarse-grain stochastic reaction networks by Abstract In...
summary
A reproducible method converts reaction networks into coarse-grained discrete models using Abstract Interpretation, an interval lattice and a discrete-time Markov chain semantics; overlapping intervals prevent spurious border oscillations and the framework computes probability bounds for transition pairs so one can tell which abstract transition is likeliest. A one-dimensional birth–death case yields closed-form chances 0.47 vs 0.53 to exit an interval, and a two-dimensional resource-competition example shows convergence to the steady-state interval, so the automatic coarse-graining proves more faithful than non-overlapping logical abstractions.
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chapters (7)
- 0:00Introduction
- 1:09Presentation outline
- 3:37Birth and death model
- 13:53Concrete and abstract semantics
- 19:55Multi-dimensional system
- 23:05Conclusion
- 23:48Q&A
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