Abstract: Most current efforts in near-infrared optical tomography are effectively limited to two-dimensional reconstructions due to the computationally intensive nature of full three-dimensional (3-D) data inversion. Previously, we described a new computationally efficient and statistically powerful inversion method APPRIZE (automatic progressive parameter-reducing inverse zonation and estimation). The APPRIZE method computes minimum-variance estimates of parameter values (here, spatially variant absorption due to a fluorescent contrast agent) and covariance, while simultaneously estimating the number of parameters needed as well as the size, shape, and location of the spatial regions that correspond to those parameters. Estimates of measurement and model error are explicitly incorporated into the procedure and implicitly regularize the inversion in a physically based manner. The optimal estimation of parameters is bounds-constrained, precluding infeasible values. In this paper, the APPRIZE method for optical imaging is extended for application to arbitrarily large 3-D domains through the use of domain decomposition. The effect of sub-domain size on the performance of the method is examined by assessing the sensitivity for identifying 112 randomly located single-voxel heterogeneities in 58 3-D domains. Also investigated are the effects of unmodeled heterogeneity in background optical properties. The method is tested on simulated frequency-domain photon migration measurements at 100 MHz in order to recover absorption maps owing to fluorescent contrast agent. This study provides a new approach for computationally tractable 3-D optical tomography.
[edit database entry]
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).