Crowd behaviour challenges our fundamental understanding of social phenomena.Involving complex interactions between multiple temporal and spatial scales ofactivity, its governing mechanisms defy conventional analysis. Using 1.5million Twitter messages from the 15M movement in Spain as an example ofmultitudinous self-organization, we describe the coordination dynamics of thesystem measuring phase-locking statistics at different frequencies usingwavelet transforms, identifying 8 frequency bands of entrained oscillationsbetween 15 geographical nodes. Then we apply maximum entropy inference methodsto describe Ising models capturing transient synchrony in our data at eachfrequency band. The models show that 1) all frequency bands of the systemoperate near critical points of their parameter space and 2) while fastfrequencies present only a few metastable states displaying all-or-nonesynchronization, slow frequencies present a diversity of metastable states ofpartial synchronization. Furthermore, describing the state at each frequencyband using the energy of the corresponding Ising model, we compute transferentropy to characterize cross-scale interactions between frequency bands,showing 1) a cascade of upward information flows in which each frequency bandinfluences its contiguous slower bands and 2) downward information flows whereslow frequencies modulate distant fast frequencies.
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