Stochastic modeling of cascade dynamics: A unified approach for simple and complex contagions across homogeneous and heterogeneous threshold distributions on networks.

The COVID-19 pandemic has underscored the importance of understanding, forecasting, and avoiding infectious processes, as well as the necessity for understanding the diffusion and acceptance of preventative measures. Simple contagions, like virus transmission, can spread with a single encounter, while complex contagions, such as preventive social measures (e.g.

Modular tipping points: How local network structure impacts critical transitions in networked spin systems.

Critical transitions describe a phenomenon where a system abruptly shifts from one stable state to an alternative, often detrimental, stable state. Understanding and possibly preventing the occurrence of a critical transition is thus highly relevant to many ecological, sociological, and physical systems. In this context, it has been shown that the underlying network structure of a system heavily impacts the transition behavior of that system.

Correction: Critical transitions in degree mixed networks: A discovery of forbidden tipping regions in networked spin systems.

[This corrects the article DOI: 10.1371/journal.pone.

Predicting critical transitions in assortative spin-shifting networks.

Methods to forecast critical transitions, i.e. abrupt changes in systems' equilibrium states have relevance in scientific fields such as ecology, seismology, finance and medicine among others.

Critical transitions in degree mixed networks: A discovery of forbidden tipping regions in networked spin systems.

Critical transitions can be conceptualized as abrupt shifts in the state of a system typically induced by changes in the system's critical parameter. They have been observed in a variety of systems across many scientific disciplines including physics, ecology, and social science. Because critical transitions are important to such a diverse set of systems it is crucial to understand what parts of a system drive and shape the transition.