Abstract: In complex adaptive systems, the topological properties of the interaction network are strong governing influences on the rate of flow of information throughout the system. For example, in epidemiological models, the structure of the underlying contact network has a pronounced impact on the rate of spread of infectious disease throughout a population. Similarly, in evolutionary systems, the topology of potential mating interactions (i.e., population structure) affects the rate of flow of genetic information and therefore affects selective pressure. One commonly employed method for quantifying selective pressure in evolutionary algorithms is through the analysis of the dynamics with which a single favorable mutation spreads throughout the population (a.k.a. takeover time analysis). While models of takeover dynamics have been previously derived for several specific regular population structures, these models lack generality. In contrast, so-called pair approximations have been touted as a general technique for rapidly approximating the flow of information in spatially structured populations with a constant (or nearly constant) degree of nodal connectivities, such as in epidemiological and ecological studies. In this work, we reformulate takeover time analysis in terms of the well-known Susceptible-Infectious-Susceptible model of disease spread and adapt the pair approximation for takeover dynamics. Our results show that the pair approx- imation, as originally formulated, is insufficient for approximating pre-equibilibrium dynamics, since it does not properly account for the interaction between the size and shape of the local neighborhood and the population size. After parameterizing the pair approximation to account for these influences, we demonstrate that the resulting pair approximation can serve as a general and rapid approximator for takeover dynamics on a variety of spatially-explicit regular interaction topologies with varying population sizes and varying uptake and reversion probabilities. Strengths, limitations, and potential applications of the pair approximation to evolutionary computation are discussed.
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Bongard's work focuses on understanding the general nature of cognition, regardless of whether it is found in humans, animals or robots. This unique approach focuses on the role that morphology and evolution plays in cognition. Addressing these questions has taken him into the fields of biology, psychology, engineering and computer science.
Danforth is an applied mathematician interested in modeling a variety of physical, biological, and social phenomenon. He has applied principles of chaos theory to improve weather forecasts as a member of the Mathematics and Climate Research Network, and developed a real-time remote sensor of global happiness using messages from Twitter: the Hedonometer. Danforth co-runs the Computational Story Lab with Peter Dodds, and helps run UVM's reading group on complexity.
Laurent studies the interaction of structure and dynamics. His research involves network theory, statistical physics and nonlinear dynamics along with their applications in epidemiology, ecology, biology, and sociology. Recent projects include comparing complex networks of different nature, the coevolution of human behavior and infectious diseases, understanding the role of forest shape in determining stability of tropical forests, as well as the impact of echo chambers in political discussions.
Hines' work broadly focuses on finding ways to make electric energy more reliable, more affordable, with less environmental impact. Particular topics of interest include understanding the mechanisms by which small problems in the power grid become large blackouts, identifying and mitigating the stresses caused by large amounts of electric vehicle charging, and quantifying the impact of high penetrations of wind/solar on electricity systems.
Bagrow's interests include: Complex Networks (community detection, social modeling and human dynamics, statistical phenomena, graph similarity and isomorphism), Statistical Physics (non-equilibrium methods, phase transitions, percolation, interacting particle systems, spin glasses), and Optimization(glassy techniques such as simulated/quantum annealing, (non-gradient) minimization of noisy objective functions).