Twitter Self-Organization to the Edge of a Phase Transition: Discrete-Time Model and Effective Early Warning Signals in Phase Space

Many real-world systems of various origins are capable of self-organization to the edge of a phase transition, characterized by avalanche-like behavior. Therefore, it is important, by observing the behavior of early warning measures for dynamical series generated by systems, to timely see the early warning signals (precursors) of such self-organization and, if necessary, take preventive measures. To date, convincing evidence of self-organization to the edge of a phase transition has been obtained, but no effective precursors for this self-organization have been found. This research explores precursors for the Twitter self-organization based on the analysis of the behavior of measures directly related to the critical slowdown of the network and measures of the phase space reconstructed by the Takens method for the series of the number of network users creating avalanches of retweets in the network, corresponding to the three debates of the 2016 United States Presidential Election. We hydrated the relevant Tweet IDs, which were obtained from the Harvard Dataverse using the Social Feed Manager, to form this series. Preliminarily, we explore the potential of measures for early detection of self-organization of sandpile cellular automata as systems with Twitter-equivalent self-organization mechanisms. The equivalence is justified in the proposed discrete-time model for Twitter self-organization to the edge of a phase transition. It is found that there are more moments of the Twitter self-organization than the moments of time when debates started, and Twitter stays at the edge of a phase transition longer than the debate lasts. The effective measures, as the measures with the lowest number of false early warning signals, among all studied measures and for all studied systems, are dispersion and correlation dimension. Obtained results are practically important in the design and implementation of early warning systems for the systems with similar mechanisms for sandpile cellular automata self-organization to the edge of a phase transition.