Sci Rep. 2012;2:397. doi: 10.1038/srep00397. Epub 2012 May 4.
Inhomogeneous temporal processes, like those appearing in human communications, neuron spike trains, and seismic signals, consist of high-activity bursty intervals alternating with long low-activity periods. In recent studies such bursty behavior has been characterized by a fat-tailed inter-event time distribution, while temporal correlations were measured by the autocorrelation function. However, these characteristic functions are not capable to fully characterize temporally correlated heterogenous behavior. Here we show that the distribution of the number of events in a bursty period serves as a good indicator of the dependencies, leading to the universal observation of power-law distribution for a broad class of phenomena. We find that the correlations in these quite different systems can be commonly interpreted by memory effects and described by a simple phenomenological model, which displays temporal behavior qualitatively similar to that in real systems.
非均匀的时间过程，如出现在人类交流、神经元尖峰脉冲串和地震信号中的过程，由具有高强度突发间隔的活动与长时间低强度活动周期交替组成。在最近的研究中，这种突发行为的特征是事件间时间分布的长尾分布，而时间相关性则通过自相关函数来测量。然而，这些特征函数不能完全描述具有时间相关性的非均匀行为。在这里，我们表明，突发周期内事件数量的分布是依赖性的一个很好的指标，导致广泛的一类现象的幂律分布的普遍观察。我们发现，这些截然不同的系统中的相关性可以通过记忆效应来共同解释，并通过一个简单的唯象模型来描述，该模型显示出与真实系统中相似的时间行为。
