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Conference Papers Year : 2020

Rate Equations for Graphs

Abstract

In this paper, we combine ideas from two different scientifictraditions: 1) graph transformation systems (GTSs) stemming from thetheory of formal languages and concurrency, and 2) mean field approx-imations (MFAs), a collection of approximation techniques ubiquitousin the study of complex dynamics. Using existing tools from algebraicgraph rewriting, as well as new ones, we build a framework which gener-ates rate equations for stochastic GTSs and from which one can deriveMFAs of any order (no longer limited to the humanly computable). Theprocedure for deriving rate equations and their approximations can beautomated. An implementation and example models are available onlineat https://rhz.github.io/fragger. We apply our techniques and tools toderive an expression for the mean velocity of a two-legged walker proteinon DNA.
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Dates and versions

hal-03096240 , version 1 (04-01-2021)

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Vincent Danos, Tobias Heindel, Ricardo Honorato-Zimmer, Sandro Stucki. Rate Equations for Graphs. CMSB 2020 - 18th International Conference Computational Methods in Systems Biology, Sep 2020, Konstanz / Virtual, Germany. pp.3-26, ⟨10.1007/978-3-030-60327-4_1⟩. ⟨hal-03096240⟩
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