Rhythms of the collective brain: Metastable synchronization and   cross-scale interactions in connected multitudes
  Crowd behaviour challenges our fundamental understanding of social phenomena. Involving complex interactions between multiple temporal and spatial scales of activity, its governing mechanisms defy conventional analysis. Using 1.5 million Twitter messages from the 15M movement in Spain as an example of multitudinous self-organization, we describe the coordination dynamics of the system measuring phase-locking statistics at different frequencies using wavelet transforms, identifying 8 frequency bands of entrained oscillations between 15 geographical nodes. Then we apply maximum entropy inference methods to describe Ising models capturing transient synchrony in our data at each frequency band. The models show that 1) all frequency bands of the system operate near critical points of their parameter space and 2) while fast frequencies present only a few metastable states displaying all-or-none synchronization, slow frequencies present a diversity of metastable states of partial synchronization. Furthermore, describing the state at each frequency band using the energy of the corresponding Ising model, we compute transfer entropy to characterize cross-scale interactions between frequency bands, showing 1) a cascade of upward information flows in which each frequency band influences its contiguous slower bands and 2) downward information flows where slow frequencies modulate distant fast frequencies. 
Miguel Aguilera
physics.soc-ph cs.SI nlin.AO q-bio.NC