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The project examines the structure and function of dynamic networks by formulating and analyzing probabilistic models for temporally evolving networks and processes occurring on them. In addition, the project seeks practical and efficient statistical methods for network inference. The project is primarily motivated by national security concerns surrounding counter-terrorism and cybersecurity, but outcomes should be directly relevant in biological, social, and physical science applications as well as mathematical areas of probability theory, combinatorics, and graph theory.
Cybersecurity and counter-terrorism efforts motivate three main technical objectives: (I) to establish a mathematical theory that explains both structural phenomena and temporal dependence in real world networks, (II) to develop efficient computational techniques for inferring networks from data, and (III) to analyze how structural changes affect processes that occur on networks, such as spread of disease, epidemic thresholds, and dissemination of information. Achievement of these outcomes will rely on computational tools as well as mathematical techniques from combinatorics, algebra, percolation theory, probability, and statistics
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SBE: Small: Statistical Models and Methods for Dynamic Complex Networks