The current state of knowledge about the interdependency between structure, dynamics, and behaviors of large infrastructure, communication, and social networks is only at the preliminary stage. In this project, we investigate real data projected out from empirical social networks, to develop methodologies and techniques for extracting relevant information and behavioral patterns from the underlying social network. With the availability and accessibility of vast amount of data in recent years, our project will not only gain fundamental knowledge, from a network science viewpoint, but also will create methodologies and techniques that could be applied to address strategic and urgent needs aligned with national priorities for network research.

For example, fighting irregular warfare (IW) is a complex and ambiguous inherently social phenomenon: "insurgency and counterinsurgency operations focusing on the control or influence of populations, not on the control of an adversary's forces or territory" (IW, Joint Operating Concept, 2007). To help operations in such an environment, we will develop and employ individual-based models to investigate social influencing and associated strategies in social networks. Our methods and models for community detection, community stability, and social influencing will be applicable to data sets of different types and spanning all scales, including those collected by the military.

Mainstream ideology does not freely spread into an "ideological vacuum" as standard models for social influencing assume, but instead, is severely inhibited by existing adversary or extremist opinion clusters, strengthened by the collective identity of the individuals forming these extremist clusters. Therefore we develop and employ models for social dynamics with multiple (potentially coexisting) opinions.

Investigating social dynamics and diffusion of opinions on empirical social graphs on graphs with multiple co-existing opinion clusters/communities, we will develop both heuristic and rigorous algorithmic methods to find influential nodes and to disintegrate or control adversary clusters in ideological warfare. We will systematically investigate the "influential hypothesis" in military-relevant scenarios.

Over the past few years, we and the other network science-researchers have been shifting the focus of network research from structure to dynamics (or function) in real-life networks. To accelerate this transition, in this research we study social dynamics on large-scale empirical social networks from a fundamental viewpoint. Our investigations will focus on the emergence and stability of communities in social graphs and the elimination of such communities by introducing agents committed to stabilizing society or by exerting external/media influence. 

Better understanding the processes that allow one species to invade the habitat of another will help answer fundamental questions in ecology. Just as importantly, understanding the processes of biological invasion to the point of prediction should enhance our capacity to respond effectively to invading species that impose economic problems on agriculture and threaten native biodiversity across North America.

Spatially structured biotic interactions generate demographic variation at the level of individuals; this variation can govern ecological invasion and competitive coexistence.  Temporal abiotic variation can directly modulate demographic rates, exerting further effects on competitors' dynamics. Theory for individual-based spatial processes has remained distinct from theory for population dynamics in temporally variable environments. In this project, we study the interplay between discrete, stochastic spatial interactions and temporally varying environmental forces, with a focus on competitive invasion. To advance understanding of the multi-scale ecological complexity predicted by the theory, and to identify novel predictions, we apply concepts of statistical physics.

When a superior competitor's invades an inferior resident species in a constant environment, and introduction occurs only rarely, spatial competition will be driven by local dispersal and mortality, so that we can apply the physical theory for nucleation of spatial systems. Low introduction rates and small environments may permit only single-cluster invasion by the superior competitor. Increasing the introduction rate or system size allows multi-cluster invasive growth. In both regimes, the invasion dynamics exhibits strong spatial correlation and stochasticity. Consequently, standard deterministic approaches fail to predict the behavior of the invasion process. However, for multi-cluster invasion, the time to competitive exclusion is approximated accurately by Avrami's law, an analytical framework of nucleation theory. The Avrami result links individual-level propagation and mortality rates to community-level features of spatial invasion, a major research objective in ecology. We are developing an integrative theory of stochastic spatial growth; judicious parameter choice should let the theory address data on invasive fronts ranging from the within-habitat to the biogeographic scale. To study invasion in two-dimensional environments, we analyze stochastic "roughening" of advancing fronts; several results apply to a broad class of spatial-growth models. Analysis has yielded novel predictions; habitat size (length of the front) should affect both invasion velocity and the expected location of the maximal invasive incursion beyond the front's mean position.

Most importantly, we are developing a new theory for spatial competition in a time-varying environment. If each species is alternately favored, single-cluster invasion may admit competitive coexistence via stochastic resonance, indicating a matching of the (stochastic) spatial-dynamic and (periodic) environmental time scales. The multi-cluster mode may exhibit different limit cycles and long-term coexistence through large-scale clustering of each species, depending on comparison of the population dynamics characteristic time scale and the period-length of environmental variation.

This research develops new approaches to understanding stochastic, nonlinear effects in ecological systems and will lead to insights concerning the way individual-based ecological interactions may amplify or attenuate environmental variability.