We draw a parallel between hashtag time series and neuron spike trains. In each case, the process presents complex dynamic patterns including temporal correlations, burstiness, and all other types of nonstationarity. We propose the adoption of the so-called local variation in order to uncover salient dynamical properties, while properly detrending for the time-dependent features of a signal. The methodology is tested on both real and randomized hashtag spike trains, and identifies that popular hashtags present regular and so less bursty behavior, suggesting its potential use for predicting online popularity in social media.

Citation: Temporal We study complex time series (spike trains) of online user communication while spreading messages about the discovery of the Higgs boson in Twitter. We focus on online social interactions among users such as retweet, mention, and reply, and construct different types of active (performing an action) and passive (receiving an action) spike trains for each user. The spike trains are analyzed by means of local variation, to quantify the temporal behavior of active and passive users, as a function of their activity and popularity. We show that the active spike trains are bursty, independently of their activation frequency. For passive spike trains, in contrast, the local variation of popular users presents uncorrelated (Poisson random) dynamics. We further characterize the correlations of the local variation in different interactions. We obtain high values of correlation, and thus consistent temporal behavior, between retweets and mentions, but only for popular users, indicating that creating online attention suggests an alignment in the dynamics of the two interactions.

A hydrophilic floating sphere that is denser than water drifts to an amplitude maximum (antinode) of a surface standing wave. A few identical floaters therefore organize into antinode clusters. However, beyond a transitional value of the floater concentration φ, we observe that the same spheres spontaneously accumulate at the nodal lines, completely inverting the self-organized particle pattern on the wave. From a potential energy estimate we show (i) that at low φ antinode clusters are energetically favorable over nodal ones and (ii) how this situation reverses at high φ, in agreement with the experiment.

When a dense monolayer of macroscopic spheres floats on chaotic capillary Faraday waves, a coexistence of large scale convective motion and caging dynamics typical for jammed systems is observed. We subtract the convective mean flow using a homogenization or coarse graining method and reveal subdiffusion for the caging time scales followed by a diffusive regime at later times. We apply the methods of dynamic heterogeneity and show that the typical time and length scales of the fluctuations due to rearrangements of observed particle groups significantly increase when the system approaches its densest experimentally accessible concentration. To connect the system to the dynamic criticality literaturewe fit power laws to our results. The resultant critical exponents are consistent with those found in dense suspensions of colloids indicating universal stochastic dynamics.PACS numbers: 47.57. Gc, 64.60.Ht, 64.70.qj, 83.80.Fg, 68.03.Cd Small-scale events can dominate statistical systems to such an extent that one observes phenomena on a global scale. From the classical to the quantum limit, microscopic fluctuations may even change the phase of matter when appropriate control parameters are tuned to critical values [1,2]. Even if their origin and nature is not always understood, these spatiotemporal microscopic fluctuations can drive common observable behavior near to such a phase transition. For classical particulate systems, a vast range of materials exhibits a sudden change to a rigid state called a glass or jamming transition. Thermal systems, e.g., supercooled liquids at a critical temperature, or emulsions and colloidal suspensions at a critical packing fraction [3][4][5][6], exhibit a glass transition. Furthermore, athermal systems such as foams and granulates experience a jamming transition, also at a critical packing fraction [7][8][9][10][11]. In all these systems, transient spatial fluctuations lead to a large scale cooperative motion of their constituents near the transition [3,[12][13][14][15][16][17][18][19].In this Letter, we investigate the dynamics of the collective events near the jamming transition in an alternative experiment: Macroscopic spheres floating on the surface of capillary Faraday waves. Our control parameter is the floating sphere concentration φ on the surface which is varied from a moderate value to the maximum value attainable experimentally. Erratic forces due to the surface waves [20] and the attractive capillary interaction among the spheres [21, 22] make our system markedly different from the previously studied ones [14,15,17,23,24]: A distinct feature is a large scale convection of the spheres on the wave which (for all φ) forms naturally and strongly affects the visible dynamics. We aim to understand to what extent concepts from the glass and jamming literature -such as dynamical heterogeneity (DH) and dynamical criticality (DC)-still hold in this convective system. To do so we subtract the convective mean flow using a coarse graining (CG) method and analyze the features of ou...