Emergence of long-range correlations and bursty activity patterns in online communication.

Research has suggested that the activity occurring in a variety of social, economic, and technological systems exhibits long-range fluctuations in time. Pronounced levels of rapidly occurring events are typically observed over short periods of time, followed by long periods of inactivity. Relatively few studies, however, have shed light on the degree to which inhomogeneous temporal processes can be detected at, and emerge from, different levels of analysis. Here we investigate patterns of human activity within an online forum in which communication can be assessed at three intertwined levels: the micro level of the individual users; the meso level of discussion groups and continuous sessions; and the macro level of the whole system. To uncover the relation between different levels, we conduct a number of numerical simulations of a zero-crossing model in which users' behavior is constrained by progressively richer and more realistic rules of social interaction. Results indicate that, when users are solipsistic, their bursty behavior is not sufficient for generating heavy-tailed interevent time distributions at a higher level. However, when users are socially interdependent, the power spectra and interevent time distributions of the simulated and real forums are remarkably similar at all levels of analysis. Social interaction is responsible for the aggregation of multiple bursty activities at the micro level into an emergent bursty activity pattern at a higher level. We discuss the implications of the findings for an emergentist account of burstiness in complex systems.