Detection and Tracking on Dynamic Random Networks - MP 140-07

We propose to develop a theory of detection and tracking on dynamic networks which harnesses rigorous mathematics to address the concerns of network analysts. The mathematical and operational communities are currently disconnected -- the network analyst employs unsophisticated technology, and the mathematician finds little of interest in the analyst's needs. We propose to bridge this culture gap by formalizing the analyst's needs in the rigorous language of detection and tracking theory, and then establishing a new field of study which will provide solutions for the analyst while being mathematically stimulating enough in its own right to attract researchers to solve these problems. The focus of the proposed Phase I work is the development of a theory of dynamic random graphs analogous to the well established static case, and the demonstration that the theory developed lays a foundation for the overarching goal of a detection and tracking theory on dynamic networks.