Journal
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
Volume 105, Issue 41, Pages 15649-15653Publisher
NATL ACAD SCIENCES
DOI: 10.1073/pnas.0803685105
Keywords
complex systems; human dynamics
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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 You Tube. 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 to social systems [Ruelle, D (2004) Phys Today 57:48-53] and [Roehner BM, et al., (2004) Int J Mod Phys C 15:809-834], and provides a unique framework for the investigation of timing in complex systems.
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