标题： 随机连接动力系统中功能连通性的小世界拓扑结构 显示英文标题

标题： Small-world topology of functional connectivity in randomly connected dynamical systems

摘要： 对现实世界复杂系统的表征越来越多地涉及使用图论研究其拓扑结构。 在全局网络特性中，小世界特性，即存在相对较短的路径以及网络的高聚类性，是最常被讨论和研究的特性之一。 在处理耦合动力系统时，系统的单元之间的连接通常通过观测时间序列的成对统计依赖性度量来量化（功能连接性）。 我们认为，由于所接受的功能连接性度量（如相关系数）的部分传递性，功能连接性方法会导致小世界特性的估计值偏高（相对于常用的随机图模型）。 特别是，这可能导致在从通用随机连接的动力系统中估计的连接图中观察到小世界特性。 通过在多变量线性自回归过程中对其表现的广泛参数研究，证明了该现象的普遍性和鲁棒性，并讨论了其对非线性过程和度量的潜在相关性。 显示英文摘要

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.