描述系统的复杂性：多变量“集合复杂性”与系统生物学的信息基础
Describing the complexity of systems: multi-variable "set complexity" and the information basis of systems biology
摘要：
上下文依赖性是描述复杂性的核心。关键的“集复杂性”的成对定义，我们使用信息论的方法来制定系统复杂性的一般措施。我们研究多变量依赖的属性开始与交互信息的概念。然后，我们提出了一个新的措施，无偏检测多变量的依赖关系，“差分交互信息。两个变量的这个数量减少到以前提出的成对“集合复杂性”，作为生物系统中信息的上下文相关度量。我们在这里将其推广到任意数量的变量。“微分相互作用信息”的临界极限性质是推广的关键。这种测量扩展了以前关于生物信息的想法，并为复杂性的研究提供了更复杂的基础。“微分交互作用信息”的性质也为数据分析提供了新的途径。给定系统测量的数据集，差分交互信息可以提供集体依赖性的度量，其可以用描述复杂系统交互模式的超图来表示。我们调查这种分析使用模拟数据集。广义集的复杂性度量，多变量依赖分析，超图的结合是我们的中心结果。虽然我们的重点是复杂的生物系统，但我们的结果适用于任何复杂的系统。
英文摘要：
Context dependence is central to the description of complexity. Keying on the pairwise definition of "set complexity" we use an information theory approach to formulate general measures of systems complexity. We examine the properties of multi-variable dependency starting with the concept of interaction information. We then present a new measure for unbiased detection of multi-variable dependency, "differential interaction information." This quantity for two variables reduces to the pairwise "set complexity" previously proposed as a context-dependent measure of information in biological systems. We generalize it here to an arbitrary number of variables. Critical limiting properties of the "differential interaction information" are key to the generalization. This measure extends previous ideas about biological information and provides a more sophisticated basis for study of complexity. The properties of "differential interaction information" also suggest new approaches to data analysis. Given a data set of system measurements differential interaction information can provide a measure of collective dependence, which can be represented in hypergraphs describing complex system interaction patterns. We investigate this kind of analysis using simulated data sets. The conjoining of a generalized set complexity measure, multi-variable dependency analysis, and hypergraphs is our central result. While our focus is on complex biological systems, our results are applicable to any complex system.
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