UC Santa Barbara

The scientific world has witnessed a significant paradigm shift in recent years: that the networks should not be studied in isolation from the processes taking place over them and the large amounts of data derived and generated by them. Science has now embraced a systems approach that captures the effect of the interconnections between individual units and the behavior of a network system. This dissertation provides modeling and analysis of dynamical phenomena over interconnected network systems.

In chapter 1, we review a class of deterministic nonlinear models for the propagation of infectious diseases over contact networks with strongly-connected topologies. We consider network models for susceptible-infected (SI), susceptible-infected-susceptible (SIS), and

susceptible-infected-recovered (SIR) settings. In each setting, we provide a comprehensive nonlinear analysis of equilibria, stability properties, convergence, monotonicity, positivity, and threshold conditions.

The recent convergence of research in social sciences, dynamic modeling, and network science has encouraged reexamining the collective team behavior from a quantitative perspective. Research shows that teams cannot be understood fully by studying their members in isolation. To study the coordination and control features of a group task, the multiple subgroups' performances must be fitted together. On such decomposed tasks, group performance is more than a simple union of subgroup performances. This work aims to understand how patterns of interactions among teams impact performance.

In chapter 2, we investigate the implications of dierent forms of multi-group connecviiitivity. Four multi-group connectivity modalities are considered: co-memberships, edge bundles, bridges, and liaison hierarchies. We propose generative models to generate these four modalities. Our models are variants of planted partition or stochastic block models conditioned under certain topological constraints. We report findings of a comparative analysis in which we evaluate these structures, controlling for their edge densities and sizes, on mean rates of information propagation, convergence times to consensus, and steady state deviations from the consensus value in the presence of noise as network size increases.

In chapter 3, we present a strategic network formation model predicting the emergence of multigroup structures. Individuals decide to form or remove links based on the benets and costs those connections carry; we focus on bilateral consent for link formation. We are interested in structures that arise to resolve coordination issues and, specifically, structures in which groups are linked through bridging, redundant, and co-membership interconnections. We characterize the conditions under which certain structures are stable and study their efficiency as well as the convergence of formation dynamics.