论文标题
生命科学的重写理论：CTMC语义的统一理论
Rewriting Theory for the Life Sciences: A Unifying Theory of CTMC Semantics
论文作者
论文摘要
Kappa生物化学和Mød有机化学框架是迄今为止生命科学中重写理论方法的最强烈开发的应用之一。这些类型的重写理论的典型特征是必须在要重写的对象上实现某些结构性约束（从经验上发现蛋白质具有一定的位置签名，最多可以形成碳原子，最多可以形成四个键，...）。在本文中，我们为这些类型的重写理论的理论基础做出了贡献，这些概念和技术发展允许为随机重写系统实施连续时间马尔可夫链（CTMC）的通用理论。我们的核心数学概念是一种新颖的规则代数构建，用于在双重和sesqui-pushout语义上重写规则的相关设置，并通过适当的随机力学形式主义扩展增强，允许在模式计算统计的情况下得出动态进化方程。
The Kappa biochemistry and the MØD organo-chemistry frameworks are amongst the most intensely developed applications of rewriting theoretical methods in the life sciences to date. A typical feature of these types of rewriting theories is the necessity to implement certain structural constraints on the objects to be rewritten (a protein is empirically found to have a certain signature of sites, a carbon atom can form at most four bonds, ...). In this paper, we contribute to the theoretical foundations of these types of rewriting theory a number of conceptual and technical developments that permit to implement a universal theory of continuous-time Markov chains (CTMCs) for stochastic rewriting systems. Our core mathematical concepts are a novel rule algebra construction for the relevant setting of rewriting rules with conditions, both in Double- and in Sesqui-Pushout semantics, augmented by a suitable stochastic mechanics formalism extension that permits to derive dynamical evolution equations for pattern-counting statistics.
