Reverse-engineering of polynomial dynamical systems
Reverse-engineering of polynomial dynamical systems
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DOI：
10.1016/j.aam.2006.08.004
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发表时间：
2007-10-01
影响因子：
1.1
通讯作者：
Stillman, Michael
中科院分区：
文献类型：
--
作者：
Jarrah, Abdul Salam;Laubenbacher, Reinhard;Stillman, Michael
有限域上的多元多项式动力系统已经在工程和数学生物学等领域得到了广泛的研究。一个重要的问题是根据动态特性的部分规范来构造这样的系统的模型，例如，从状态转换测量的集合。在这里，我们考虑静态模型，这是有向图，表示系统变量之间的因果关系，所谓的接线图。本文包含一个算法，计算所有可能的最小接线图为一组给定的状态转换测量。该文件还包含了几个模型选择的统计措施。该算法使用的主要工具是单项理想的准素分解。一个应用程序的基因调控网络的反向工程。该算法和统计措施在Macaulay 2中实现，并可从作者那里获得。(C)2006年爱思唯尔公司All rights reserved.
Multivariate polynomial dynamical systems over finite fields have been studied in several contexts, including engineering and mathematical biology. An important problem is to construct models of such systems frorn a partial specification of dynamic properties, e.g., from a collection of state transition measurements. Here, we consider static models, which are directed graphs that represent the causal relationships between system variables, so-called wiring diagrams. This paper contains an algorithm which computes all possible minimal wiring diagrams for a given set of state transition measurements. The paper also contains several statistical measures for model selection. The algorithm uses primary decomposition of monomial ideals as the principal tool. An application to the reverse-engineering of a gene regulatory network is included. The algorithm and the statistical measures are implemented in Macaulay 2, and are available from the authors. (C) 2006 Elsevier Inc. All rights reserved.