Relative clock verifies endogenous bursts of human dynamics

¹ Web Sciences Center, University of Electronic Science and Technology of China - Chengdu 610054, PRC
² Department of Physics, Centre for Nonlinear Studies, and Beijing-Hong Kong-Singapore Joint Centre for Nonlinear and Complex Systems (Hong Kong), Hong Kong Baptist University - Kowloon Tong, Hong Kong, PRC
³ Department of Physics, The Chinese University of Hong Kong - Shatin, Hong Kong, PRC

^a zhutou@ustc.edu

Received: 8 November 2011
Accepted: 21 November 2011

Abstract

Temporal bursts are widely observed in many human-activated systems, which may result from both endogenous mechanisms like the highest-priority-first protocol and exogenous factors like the seasonality of activities. To distinguish the effects from different mechanisms is thus of theoretical significance. This letter reports a new timing method by using a relative clock, namely the time length between two consecutive events of an agent is counted as the number of other agents' events appeared during this interval. We propose a model, in which agents act either in a constant rate or with a power-law inter-event time distribution, and the global activity either keeps unchanged or varies periodically vs. time. Our analysis shows that the bursts caused by the heterogeneity of global activity can be eliminated by setting the relative clock, yet the bursts from real individual behaviors still exist. We perform extensive experiments on four large-scale systems, the search engine by AOL, a social bookmarking system —Delicious, a short-message communication network, and a microblogging system —Twitter. Seasonality of global activity is observed, yet the bursts cannot be eliminated by using the relative clock.