# Today Alaa Moussawi defended a Physics Ph.D. thesis entitled "Complex Systems: a Stability Analysis," supervised by NEST Professors Gyorgy Korniss and Boleslaw K. Szymanski

Today, Alaa Moussawi defended a Physics Ph.D. thesis entitled "Complex Systems: a Stability Analysis," supervised by Professors Gyorgy Korniss and Boleslaw K. Szymanski. The thesis focuses on complex systems that arise in many environments, and can be useful in modeling many aspects of physical and social systems. The maintenance and operation of these systems is poorly understood for many applications. We study the transmission and distribution grid as networks, and we investigate their temporal evolution, and the spread of cascades in such systems. We also analyze the occurrence of anomalies and future outcomes of such anomalies in the distribution grid. In addition, we introduce a stochastic method for optimal heterogeneous distribution of resources (node capacities) subject to a fixed total cost.

On a less theoretical and more application-oriented note, we study anomaly occurrences in the distribution grid. We utilize data harvested from phasor measurement units (PMUs) in the distribution grid. The department of energy (DOE) placed these remote sensors in various locations throughout the distribution grid in the past decade in an effort to improve the grid monitoring, resilience, and maintenance efficiency. First, we identify the occurrence of anomalies in the data set. This is performed through a statistical measure indicating the likelihood of an incoming signal. Next the data is classified into one of nine expert-identified classes. Learning algorithms are then trained on this data set that has been labeled by the expert. The performance of the model is investigated.

Finally, we study the persistence of states in various systems under the respective system dynamics. Lattices in one and two dimensions as well as complete and Erdos-Renyi graphs are investigated. A contact process and diffusion process are applied to these networks, and the evolution of persistence (being the probability that a site remains in the same state until time t) is investigated. We find the expected and theoretically backed results known in the literature for one and two dimensional lattices. We find a non-trivial behavior in Erdos-Renyi graphs, and find the expected trivial behavior in complete graphs. We discovered that when certain conditions are met, the persistence found for diffusive models and for contact processes yields the same critical decay exponent, suggesting that there are underlying dynamics governing the persistence of the system that are not entirely controlled by the model dynamics.