Research

Network Structure

Many engineering and social networks exhibit highly complex coupling rules that lead to the emergence of generic behavioral and structural features. For example, one of the main structural features of so-called “scale-free networks” is their heavy-tailed connectivity distribution, which can be found in computer networks such as the Internet, genetic regulatory networks, networks created by the formation of sexual partnerships, and many more. The main interest is to develop mathematical frameworks that capture the broad connectivity dynamics of growing networks and their emerging features.

Network Processes

Examples of cooperative systems include the distributed decision-making systems for a network of agents tasked with a search and rescue operation, a surveillance and attack mission, or a flexible manufacturing system. The spatially distributed nature of cooperative control problems implies that allocation algorithms must be distributed across multiple moving agents, and even though these agents may only sense local information about their immediate surroundings, they must still cooperate in order to accomplish a global common objective. The focus is on mathematical modeling of global spatial distributions (e.g., developing asynchronous discrete event system models), stability analysis of group behavior (e.g., using extensions of Lyapunov theory), and the impact of information flow constraints.

 

If you find something that interests you on these subjects, please send me an email; describe briefly what your interests are and what you have done in the area (include your GPA, class ranking, and papers published).