Hu Yu, Trousdale James, Josić Krešimir, Shea-Brown Eric
Department of Applied Mathematics, University of Washington, Seattle, Washington 98195, USA.
Department of Mathematics, University of Houston, Houston, Texas 77204-5001, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Mar;89(3):032802. doi: 10.1103/PhysRevE.89.032802. Epub 2014 Mar 10.
How does connectivity impact network dynamics? We address this question by linking network characteristics on two scales. On the global scale, we consider the coherence of overall network dynamics. We show that such global coherence in activity can often be predicted from the local structure of the network. To characterize local network structure, we use "motif cumulants," a measure of the deviation of pathway counts from those expected in a minimal probabilistic network model. We extend previous results in three ways. First, we give acombinatorial formulation of motif cumulants that relates to the allied concept in probability theory. Second, we show that the link between global network dynamics and local network architecture is strongly affected by heterogeneity in network connectivity. However, we introduce a network-partitioning method that recovers a tight relationship between architecture and dynamics. Third, for a particular set of models, we generalize the underlying theory to treat dynamical coherence at arbitrary orders (i.e., triplet correlations and beyond). We show that at any order, only a highly restricted set of motifs impacts dynamical correlations.
连通性如何影响网络动态？我们通过在两个尺度上关联网络特征来解决这个问题。在全局尺度上，我们考虑整体网络动态的相干性。我们表明，活动中的这种全局相干性通常可以从网络的局部结构预测出来。为了表征局部网络结构，我们使用“基序累积量”，这是一种衡量路径计数与最小概率网络模型中预期路径计数偏差的指标。我们从三个方面扩展了先前的结果。第一，我们给出了基序累积量的组合公式，它与概率论中的相关概念有关。第二，我们表明全局网络动态与局部网络架构之间的联系受到网络连通性异质性的强烈影响。然而，我们引入了一种网络划分方法，该方法恢复了架构与动态之间的紧密关系。第三，对于一组特定的模型，我们推广了基础理论以处理任意阶的动态相干性（即三重相关性及更高阶）。我们表明，在任何阶上，只有一组高度受限的基序会影响动态相关性。
