论文标题
迈向动态系统的科学方法
Towards a Scientific Method for Dynamical Systems
论文作者
论文摘要
本文的前提是以下价值主张：模型描述一种现象系统时，它们是好的，并且当它们可以预测干预措施对系统的影响时，它们会更好。 我们介绍了一种形式主义，可以通过以大规模行动定律介导的培养皿网络指定基本组成过程来获得动力学模型。我们证明了此过程相对于普通的一阶差分方程在有理函数中的普遍性。此外，我们引入了一个简单的图形过程，用于计算正式中培养皿网的动力系统，我们用来恢复几个众所周知的动态系统。为了证明概念，我们使用我们的方法来获得HES1基因转录网络的微分方程模型，该模型可以预测网络的干预后行为。
The premise of this paper is the following value proposition: Models are good when they describe a system of phenomena, and they are better when they can predict the effect of interventions upon the system. We introduce a formalism by which dynamical system models can be obtained by specifying basic constituent processes in the form of petri nets, mediated by the Law of Mass Action. We prove the universality of this procedure with respect to ordinary first order differential equations in rational functions. In addition, we introduce a simple graphical procedure for calculating dynamical systems from petri nets in our formalism, which we use to recover several well-known dynamical systems. For proof-of-concept, we use our method to obtain a differential equation model for the HES1 gene transcription network that predicts post-intervention behaviours of the network.
