随机连通动力系统中函数连通性的小世界拓扑
Small-world topology of functional connectivity in randomly connected dynamical systems
摘要：
现实世界复杂系统的表征越来越多地涉及到使用图论研究其拓扑结构。在全球网络的性质，小世界性质，包括存在相对较短的路径和高度聚类的网络，是最多的讨论和研究之一。当处理耦合动力系统时，系统单元之间的联系通常通过测量观测到的时间序列的成对统计依赖性（功能连接性）来量化。我们认为，功能连接的方法导致向上偏估计的小世界特征（相对于常用的随机图模型），由于部分传递性的接受功能连接的措施，如相关系数。特别是，这可能会导致观察的小世界特性的连接图估计从通用随机连接的动态系统。的普遍性和鲁棒性的现象是记录其表现形式在一个多元线性自回归过程中的广泛的参数研究，与讨论的潜在相关性的非线性过程和措施。
英文摘要：
Characterization of real-world complex systems increasingly involves the study of their topological structure using graph theory. Among global network properties, small-world property, consisting in existence of relatively short paths together with high clustering of the network, is one of the most discussed and studied. When dealing with coupled dynamical systems, links among units of the system are commonly quantified by a measure of pairwise statistical dependence of observed time series (functional connectivity). We argue that the functional connectivity approach leads to upwardly biased estimates of small-world characteristics (with respect to commonly used random graph models) due to partial transitivity of the accepted functional connectivity measures such as the correlation coefficient. In particular, this may lead to observation of small-world characteristics in connectivity graphs estimated from generic randomly connected dynamical systems. The ubiquity and robustness of the phenomenon is documented by an extensive parameter study of its manifestation in a multivariate linear autoregressive process, with discussion of the potential relevance for nonlinear processes and measures.
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