Generalized master equations for non-Poisson dynamics on networks
Generalized master equations for non-Poisson dynamics on networks
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DOI：
10.1103/physreve.86.046102
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发表时间：
2012-10-08
影响因子：
2.4
通讯作者：
Lambiotte, Renaud
中科院分区：
文献类型：
--
作者：
Hoffmann, Till;Porter, Mason A.;Lambiotte, Renaud
研究时间网络的传统方法是聚合边缘的动态以创建静态加权网络。这隐含地假设边缘受泊松过程控制，这在经验时间网络中通常不是这种情况。因此，我们研究了非泊松事件间统计对边动态的影响，并将广义主方程的概念应用于网络上连续时间随机游走的研究。我们证明，当基础过程是泊松分布时，该方程可简化为标准速率方程，并且其平稳解由有效转移矩阵确定，其前导特征向量易于计算。我们进行数值模拟，并在假设所有边具有相同等待时间分布的情况下得出平稳解的分析结果。我们讨论了我们的工作对时间网络动态过程以及考虑其非平凡随机性质的网络诊断的构建的影响。
The traditional way of studying temporal networks is to aggregate the dynamics of the edges to create a static weighted network. This implicitly assumes that the edges are governed by Poisson processes, which is not typically the case in empirical temporal networks. Accordingly, we examine the effects of non-Poisson inter-event statistics on the dynamics of edges, and we apply the concept of a generalized master equation to the study of continuous-time random walks on networks. We show that this equation reduces to the standard rate equations when the underlying process is Poissonian and that its stationary solution is determined by an effective transition matrix whose leading eigenvector is easy to calculate. We conduct numerical simulations and also derive analytical results for the stationary solution under the assumption that all edges have the same waiting-time distribution. We discuss the implications of our work for dynamical processes on temporal networks and for the construction of network diagnostics that take into account their nontrivial stochastic nature.