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.

中文翻译：

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图形的速率方程

在本文中，我们结合了来自两种不同科学传统的想法：1) 源自形式语言和并发理论的图转换系统 (GTS)，以及 2) 平均场近似 (MFA)，这是研究中无处不在的近似技术的集合复杂的动力学。使用来自代数图重写的现有工具以及新工具，我们构建了一个框架，该框架可为随机 GTS 生成速率方程，并且可以从中推导出任何阶数的 MFA（不再限于人类可计算的）。推导速率方程及其近似的过程可以自动化。实现和示例模型可在 https://rhz.github.io/fragger 在线获得。我们应用我们的技术和工具来推导出 DNA 上两条腿步行者蛋白的平均速度的表达式。