Abstract
This dissertation focuses on extreme behavior in complex systems. Extreme events are an emergent property of many complex, nonlinear systems in which various interdependent components and their interaction lead to a competition between organized (interaction dominated) and irregular (fluctuation dominated) behavior. In this work we investigated several aspects of extreme events in pro-ISIS online social network system and the subsecond financial exchange market. We started by uncovering an ultrafast ecology driving the online support, featuring self-organized aggregates whose evolution exhibits novel adaptive mechanisms in response to external pressure. Then we investigated the anomalous contagion, we provided and analyzed a simple, yet highly non-trivial, model in which the processes of human mobility and infection dynamics co-exist with competing timescales, we showed that even in this static steady-state limit, a non-zero nodal mobility leads to a diverse set of outbreak profiles that is dramatically different from known forms, and yet matches well with recent real-world social outbreaks. In the quest to understand dynamical network mechanisms underlying aging of an online organism from birth to death, we present the continuous-time evolution of an online organism network from birth to death which crosses all organizational and temporal scales, from individual components through to the mesoscopic and entire system scale, we analyzed the body of pro-ISIS support that developed organically on VKontkate , and which made VKontakte a dominant social media site for ISIS recruitment, propaganda and financing. Our continuous-time study of its entire life cycle from initial growth (late 2014) until eventual death in late 2015, complements and extends existing landmark studies of dynamical networks. We also present a generalized gelation theory that describes human online aggregation in support of extremism. The theory that we develop shows that heterogeneous systems with aggregation rules based on objects' mutual affinity, can effectively delay the gel transition point and drastically alter its growth rate. We show that the theory provides an accurate description of the online extremist support for ISIS which started in late 2014. The last part of this dissertation, we focused on the important problem of how delayed information in such subsecond systems impacts their overall stability.