论文标题
图的速率方程
Rate Equations for Graphs
论文作者
论文摘要
在本文中，我们结合了来自两种不同科学传统的思想：1）源于形式语言和并发理论的图形转换系统（GTSS），以及2）平均场近似（MFA），这是一系列近似技术在复杂动力学研究中无处不在。使用代数图重写的现有工具以及新工具，我们构建了一个框架，该框架生成了随机GTSS的速率方程式，并且可以从中得出任何顺序的MFA（不再限于可计算的人类计算）。得出速率方程及其近似值的过程可以自动化。可以在https://rhz.github.io/fragger上在线获得实现和示例模型。我们应用我们的技术和工具来得出DNA上两腿步行者蛋白的平均速度的表达式。
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.
