In this paper, we combine ideas from two different scientific traditions: 1) graph transformation systems (GTSs) stemming from the theory of formal languages and concurrency, and 2) mean field approximations (MFAs), a collection of approximation techniques ubiquitous in the study of complex dynamics. Using existing tools from algebraic graph rewriting, as well as new ones, we build a framework which generates rate equations for stochastic GTSs and from which one can derive MFAs of any order (no longer limited to the humanly computable). The procedure for deriving rate equations and their approximations can be automated. An implementation and example models are available online at https://rhz.github.io/fragger. We apply our techniques and tools to derive an expression for the mean velocity of a two-legged walker protein on DNA.
CITATION STYLE
Danos, V., Heindel, T., Honorato-Zimmer, R., & Stucki, S. (2020). Rate Equations for Graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 12314 LNBI, pp. 3–26). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-030-60327-4_1
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