Robust dynamic classes revealed by measuring the response function of a social system.

Area of Science:

• Complex Systems Science
• Social Network Analysis
• Statistical Physics

Background:

• Understanding collective human dynamics is crucial for modeling social systems.
• Previous models often simplify activity patterns, overlooking complex relaxation behaviors.
• The fluctuation-dissipation theorem provides a framework for analyzing equilibrium systems, but its extension to social dynamics is challenging.

Purpose of the Study:

• To investigate the relaxation response of a social system after bursts of activity.
• To identify and classify patterns in collective human dynamics using large-scale data.
• To develop a model explaining the observed relaxation phenomena in social systems.

Main Methods:

• Analysis of time series data of daily views for approximately 5 million YouTube videos.
• Statistical analysis to identify activity patterns, including Poisson processes and power-law relaxations.
• Development and validation of an epidemic model on a social network.

Main Results:

• Most YouTube video activity follows a Poisson process.
• A significant number of activity bursts exhibit power-law relaxation in view timing.
• Identified three distinct classes of relaxation exponents, allowing for classification of collective dynamics.
• An epidemic model incorporating power-law waiting times and cascading actions successfully explains the observed relaxations.

Conclusions:

• Collective human dynamics in social systems exhibit distinct relaxation patterns after activity bursts.
• Power-law relaxation exponents provide a means to classify these dynamics.
• An extended fluctuation-dissipation theorem framework, incorporating epidemic-like processes, offers a novel approach to studying timing in complex social systems.