Making rare events happen: prediction and control of network extinction, switching, and other extreme processes

Many complex networks must operate in uncertain and dynamic environments. Over long time scales, combinations of random internal interactions and dynamical perturbations can organize to drive a network from one collective state to another. Such noise-induced large fluctuations may be associated with desirable outcomes, such as epidemic extinctions, or undesirable ones, such as switching in collective order, or loss of network synchrony. In this talk I will discuss a general formalism for predicting rare events in networks with internal and external noise, the role of topology in facilitating the most extreme network events, techniques for optimal network control that leverage uncertainty, and numerical solutions for the aforementioned when explicit formulas are unknown. Along the way, I will consider many examples: from epidemic dynamics to opinion formation and synchronization of coupled oscillators