复杂系统中候选相关变量子集的搜索
The search for candidate relevant subsets of variables in complex systems
摘要：
在本文中，我们描述了一种方法来识别“相关子集”的变量，有用的了解组织的动力系统。属于相关子集的变量应该与同一相关子集的其他变量具有强集成，并且与其他系统变量具有弱得多的相互作用。在此基础上，扩展了神经网络的研究成果，引入了一种信息论测度，即动态聚类指数，用以识别良好的候选相关子集。该方法不需要系统变量之间的关系的任何先前的知识，但依赖于它们的值在时间上的观察。我们在几个应用领域，包括：（一）随机布尔网络，其中整个网络是由不同的子网络与不同的拓扑关系（独立或相互作用的子网络）;（二）领导者-追随者的动态，受噪声和波动;（三）催化反应网络中的流动反应器;（四）在真核生物中的MAPK信号通路。该方法的有效性已经过测试的情况下，数据是由一个已知的动态模型和动态聚类指数方法的应用，以揭示其组织的重要方面;然而，重要的是要强调，它也可以适用于时间序列来自外地数据没有任何参考模型。鉴于它是基于值集合的相对频率，该方法也可以应用于数据在时间上没有排序的情况。最后给出了改进动态聚类指数分析复杂系统组织的范围和有效性的几个指标。
英文摘要：
In this paper we describe a method to identify "relevant subsets" of variables, useful to understand the organization of a dynamical system. The variables belonging to a relevant subset should have a strong integration with the other variables of the same relevant subset, and a much weaker interaction with the other system variables. On this basis, extending previous works on neural networks, an information-theoretic measure is introduced, i.e. the Dynamical Cluster Index, in order to identify good candidate relevant subsets. The method does not require any previous knowledge of the relationships among the system variables, but relies on observations of their values in time. We show its usefulness in several application domains, including: (i) random boolean networks, where the whole network is made of different subnetworks with different topological relationships (independent or interacting subnetworks); (ii) leader-follower dynamics, subject to noise and fluctuations; (iii) catalytic reaction networks in a flow reactor; (iv) the MAPK signaling pathway in eukaryotes. The validity of the method has been tested in cases where the data are generated by a known dynamical model and the Dynamical Cluster Index method is applied in order to uncover significant aspects of its organization; however it is important to stress that it can also be applied to time series coming from field data without any reference to a model. Given that it is based on relative frequencies of sets of values, the method could be applied also to cases where the data are not ordered in time. Several indications to improve the scope and effectiveness of the Dynamical Cluster Index to analyze the organization of complex systems are finally given.
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