De Lucia M, Bottaccio M, Montuori M, Pietronero L
INFM SMC-Dipartimento di Fisica, Università La Sapienza, Piazzale A. Moro 5, 00185 Rome, Italy.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Jan;71(1 Pt 2):016114. doi: 10.1103/PhysRevE.71.016114. Epub 2005 Jan 12.
Considerable effort in modern statistical physics is devoted to the study of networked systems. One of the most important example of them is the brain, which creates and continuously develops complex networks of correlated dynamics. An important quantity which captures fundamental aspects of brain network organization is the neural complexity C(X) introduced by Tononi et al. [Proc. Natl. Acad. Sci. USA 91, 5033 (1994)]. This work addresses the dependence of this measure on the topological features of a network in the case of a Gaussian stationary process. Both analytical and numerical results show that the degree of complexity has a clear and simple meaning from a topological point of view. Moreover, the analytical result offers a straightforward and faster algorithm to compute the complexity of a graph than the standard one.
现代统计物理学投入了大量精力来研究网络系统。其中最重要的一个例子就是大脑，它构建并持续发展出复杂的关联动力学网络。一个能够捕捉大脑网络组织基本特征的重要量是托诺尼等人 [《美国国家科学院院刊》91, 5033 (1994)] 引入的神经复杂性C(X)。这项工作探讨了在高斯平稳过程的情况下，该度量对网络拓扑特征的依赖性。分析结果和数值结果均表明，从拓扑学角度来看，复杂程度具有清晰而简单的意义。此外，与标准算法相比，分析结果提供了一种更直接、更快的计算图复杂性的算法。
