节点和边上事件间隔时间同时重尾分布的生成模型
Generative models of simultaneously heavy-tailed distributions of inter-event times on nodes and edges
摘要：
代表人类活动的离散事件之间的间隔，以及其他类型的事件，往往服从重尾分布，其对网络上的集体动力学，如传染过程的影响已被深入研究。文献支持这种重尾分布存在于与网络中的个体节点和个体边缘相关联的事件间时间。然而，节点和边的事件间时间的重尾分布的同时存在是一个不平凡的现象，其起源一直难以捉摸。在本研究中，我们提出了一个生成模型及其变体来解释这一现象。我们假设每个节点独立地根据连续时间两状态马尔可夫过程在高活动状态和低活动状态之间转换，并且对于主模型，当且仅当边缘的两个端节点都处于高活动状态时，边缘上的事件以高速率发生。换句话说，只有当两个节点都喜欢与其他节点交互时，两个节点才会频繁交互。该模型产生的事件间时间分布的个别节点和边缘，类似于在某些尺度上的重尾分布。它还在连续的事件间隔时间内产生正相关，这是对人类活动经验数据的另一种程式化观察。我们希望我们的建模框架提供了一个有用的基准调查非泊松事件序列驱动的时间网络上的动态。
英文摘要：
Intervals between discrete events representing human activities, as well as other types of events, often obey heavy-tailed distributions, and their impacts on collective dynamics on networks such as contagion processes have been intensively studied. The literature supports that such heavy-tailed distributions are present for inter-event times associated with both individual nodes and individual edges in networks. However, the simultaneous presence of heavy-tailed distributions of inter-event times for nodes and edges is a non-trivial phenomenon, and its origin has been elusive. In the present study, we propose a generative model and its variants to explain this phenomenon. We assume that each node independently transits between a high-activity and low-activity state according to a continuous-time two-state Markov process and that, for the main model, events on an edge occur at a high rate if and only if both end nodes of the edge are in the high-activity state. In other words, two nodes interact frequently only when both nodes prefer to interact with others. The model produces distributions of inter-event times for both individual nodes and edges that resemble heavy-tailed distributions across some scales. It also produces positive correlation in consecutive inter-event times, which is another stylized observation for empirical data of human activity. We expect that our modeling framework provides a useful benchmark for investigating dynamics on temporal networks driven by non-Poissonian event sequences.
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