Abstract: Apparatus and methods for estimating the internal structure of a physical domain (16), such as a volume of earth or of a human body, based on tomographic signals (18) having passed there through. Measurements of signals are inverted using an approximate extended Kalman filter to condition estimates of first and second spatial moments of stochastic random variables representing discrete estimates of one or more parameters describing the domain's internal structure. Measurement conditioning is alternated with upscaling in order to reduce the number of random variables used and also for the purpose of determining the geometry of the spatial regions of the domain represented by each of the random variables. Upscaling includes the use of cluster analysis for identification of random variables to merge, followed by random variable merging using random field union. Upscaling improves computational properties of the invention and can be used to identify discrete structural features in the domain. Various domain decomposition strategies can be employed to make the invention computationally feasible on even very large domains.
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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).