Abstract: While many large infrastructure networks, such as power, water, and natural gas systems, have similar physical properties governing flows, these systems tend to have distinctly different sizes and topological structures. This paper seeks to understand how these different size-scales and topological features can emerge from relatively simple design principles. Specifically, we seek to describe the conditions under which it is optimal to build decentralized network infrastructures, such as a microgrid, rather than centralized ones, such as a large high-voltage power system. While our method is simple it is useful in explaining why sometimes, but not always, it is economical to build large, interconnected networks and in other cases it is preferable to use smaller, distributed systems. The results indicate that there is not a single set of infrastructure cost conditions under which optimally-designed networks will have highly centralized architectures. Instead, as costs increase we find that average network sizes increase gradually according to a power-law. When we consider the reliability costs, however, we do observe a transition point at which optimally designed networks become more centralized with larger geographic scope. As the losses associated with node and edge failures become more costly, this transition becomes more sudden.
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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).