We show how a graph algorithm for finding matching labeled paths in pairs of labeled directed graphs can be used to perform model invalidation for a class of dynamical systems including regulatory network models of relevance to systems biology. In particular, given a partial order of events describing local minima and local maxima of observed quantities from experimental time series data, we produce a labeled directed graph we call the pattern graph for which every path from root to leaf corresponds to a plausible sequence of events. We then consider the regulatory network model, which can itself be rendered into a labeled directed graph we call the search graph via techniques previously developed in computational dynamics. Labels on the pattern graph correspond to experimentally observed events, while labels on the search graph correspond to mathematical facts about the model. We give a theoretical guarantee that failing to find a match invalidates the model. As an application we consider gene regulatory models for the yeast S. cerevisiae.

中文翻译：

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通过时间序列进行模型拒绝和参数缩减。

我们展示了如何使用在标记有向图对中查找匹配标记路径的图算法来对一类动态系统（包括与系统生物学相关的调节网络模型）执行模型失效。特别是，给定描述实验时间序列数据中观察到的数量的局部最小值和局部最大值的事件的部分顺序，我们生成一个标记的有向图，我们称之为模式图，其中从根到叶的每条路径都对应于一个合理的事件序列。然后我们考虑监管网络模型，它本身可以通过先前在计算动力学中开发的技术呈现为标记的有向图，我们称之为搜索图。模式图上的标签对应于实验观察到的事件，而搜索图上的标签对应于有关模型的数学事实。我们给出了一个理论上的保证，即如果找不到匹配，模型就会失效。作为一种应用，我们考虑酿酒酵母的基因调控模型。