We study the relaxation response of a social system after endogenous and exogenous bursts of activity using the time-series of daily views for nearly 5 million videos on YouTube. We find that most activity can be described accurately as a Poisson process. However, we also find hundreds of thousands of examples in which a burst of activity is followed by an ubiquitous power-law relaxation governing the timing of views. We find that these relaxation exponents cluster into three distinct classes, and allow for the classification of collective human dynamics. This is consistent with an epidemic model on a social network containing two ingredients: A power law distribution of waiting times between cause and action and an epidemic cascade of actions becoming the cause of future actions. This model is a conceptual extension of the fluctuation-dissipation theorem [1, 2] to social systems, and provides a unique framework for the investigation of timing in complex systems.
In REF , Crane et al. investigate how a social system responds to bursts of exogenous and endogenous activity by using the time series of daily views of YouTube videos, and they find four different shapes for bursts.
Robust dynamic classes revealed by measuring the response function of a social system
Proceedings of the National Academy of Sciences of the United States of America
Proceedings of the National Academy of Sciences of the United States of America
Computer Science Physics Medicine