Reentrant phase transitions in threshold driven contagion on multiplex networks

Social contagion induced by uncertain information

Information and individual activities often spread globally through the network of social ties. While social contagion phenomena have been extensively studied within the framework of threshold models, it is common to make an assumption that may be violated in reality: each individual can observe the neighbors' states without error. Here, we analyze the dynamics of global cascades under uncertainty in an otherwise standard threshold model. Each individual uses statistical inference to estimate the probability distribution of the number of active neighbors when deciding whether to be active, which gives a probabilistic threshold rule. Unlike the deterministic threshold model, the spreading process is generally nonmonotonic, as the inferred distribution of neighbors' states may be updated as a new signal arrives. We find that social contagion may occur as a self-fulfilling event in that misperception may trigger a cascade in regions where cascades would never occur under certainty.

Diffusion dynamics of competing information on networks

Information diffusion on social networks has been described as a collective outcome of threshold behaviors in the framework of threshold models. However, since the existing models do not take into account individuals' optimization problems, it remains an open question what dynamics emerge in the diffusion process when individuals face multiple (and possibly incompatible) information sources. Here, we develop a microfounded general threshold model that enables us to analyze the collective dynamics of individual behavior in the propagation of multiple information sources. The analysis reveals that the virality of competing information sources is fundamentally indeterminate. When individuals maximize coordination with neighbors, the diffusion process is described as a saddle path, thereby leading to unpredictable symmetry breaking. When individuals' choices are irreversible, there is a continuum of stable equilibria where a certain degree of social polarization takes place by chance.

Dynamics of cascades on burstiness-controlled temporal networks

Burstiness, the tendency of interaction events to be heterogeneously distributed in time, is critical to information diffusion in physical and social systems. However, an analytical framework capturing the effect of burstiness on generic dynamics is lacking. Here we develop a master equation formalism to study cascades on temporal networks with burstiness modelled by renewal processes. Supported by numerical and data-driven simulations, we describe the interplay between heterogeneous temporal interactions and models of threshold-driven and epidemic spreading. We find that increasing interevent time variance can both accelerate and decelerate spreading for threshold models, but can only decelerate epidemic spreading. When accounting for the skewness of different interevent time distributions, spreading times collapse onto a universal curve. Our framework uncovers a deep yet subtle connection between generic diffusion mechanisms and underlying temporal network structures that impacts a broad class of networked phenomena, from spin interactions to epidemic contagion and language dynamics.