Features of heterogeneously charged systems at their liquid-liquid critical point.

Recently synthesized colloids and biological systems such as proteins, viruses and monoclonal antibodies are heterogeneously charged, i.e., different regions of their surfaces carry different amounts of positive or negative charge. Because of charge inhomogeneity, electrostatic interactions between these units through the surrounding medium are intrinsically anisotropic, meaning that they are characterized not only by the attraction between oppositely charged regions but also by the repulsion between like-charged areas. Recent experiments have shown that the liquid-liquid phase separation of these systems can be driven by anisotropic electrostatic interactions, but it is not clear how the emerging aggregates are affected by charge imbalance and charge patchiness. The ability to experimentally control these two quantities calls for a theoretical understanding of their interplay, which we address here at the critical point. We consider a coarse-grained model of anisotropically charged hard spheres whose interaction potential is grounded in a robust mean field theory and perform extensive numerical Monte Carlo simulations to understand the aggregation behavior of these units at the critical point. Stemming from the simplicity of the model, we address the interplay between charge imbalance and charge patchiness with the use of three parameters only and fully rationalize how these features impact the critical point of the model by means of thermodynamic-independent pair properties.

Critical avalanches of susceptible-infected-susceptible dynamics in finite networks.

We investigate the avalanche temporal statistics of the susceptible-infected-susceptible (SIS) model when the dynamics is critical and takes place on finite random networks. By considering numerical simulations on annealed topologies we show that the survival probability always exhibits three distinct dynamical regimes. Size-dependent crossover timescales separating them scale differently for homogeneous and for heterogeneous networks. The phenomenology can be qualitatively understood based on known features of the SIS dynamics on networks. A fully quantitative approach based on Langevin theory is shown to perfectly reproduce the results for homogeneous networks, while failing in the heterogeneous case. The analysis is extended to quenched random networks, which behave in agreement with the annealed case for strongly homogeneous and strongly heterogeneous networks.

Universality, criticality and complexity of information propagation in social media.

Statistical laws of information avalanches in social media appear, at least according to existing empirical studies, not robust across systems. As a consequence, radically different processes may represent plausible driving mechanisms for information propagation. Here, we analyze almost one billion time-stamped events collected from several online platforms - including Telegram, Twitter and Weibo - over observation windows longer than ten years, and show that the propagation of information in social media is a universal and critical process. Universality arises from the observation of identical macroscopic patterns across platforms, irrespective of the details of the specific system at hand. Critical behavior is deduced from the power-law distributions, and corresponding hyperscaling relations, characterizing size and duration of avalanches of information. Statistical testing on our data indicates that a mixture of simple and complex contagion characterizes the propagation of information in social media. Data suggest that the complexity of the process is correlated with the semantic content of the information that is propagated.

Percolation theory of self-exciting temporal processes.

We investigate how the properties of inhomogeneous patterns of activity, appearing in many natural and social phenomena, depend on the temporal resolution used to define individual bursts of activity. To this end, we consider time series of microscopic events produced by a self-exciting Hawkes process, and leverage a percolation framework to study the formation of macroscopic bursts of activity as a function of the resolution parameter. We find that the very same process may result in different distributions of avalanche size and duration, which are understood in terms of the competition between the 1D percolation and the branching process universality class. Pure regimes for the individual classes are observed at specific values of the resolution parameter corresponding to the critical points of the percolation diagram. A regime of crossover characterized by a mixture of the two universal behaviors is observed in a wide region of the diagram. The hybrid scaling appears to be a likely outcome for an analysis of the time series based on a reasonably chosen, but not precisely adjusted, value of the resolution parameter.