Abstract: We modified a self-organizing map (SOM), a clustering artificial neural network, using variogram analyses to incorporate the spatial and temporal auto-correlation that exists in many surface and subsurface environmental datasets. The SOM reduces the dimensionality and clusters the data. The SOM is particularly effective with multiple data types (e.g. continuous, discrete and categorical variables). The standard SOM algorithm iteratively updates connection weights between the input parameters and the two-dimensional output mapping over a specified region of the estimation field. The method accounts for the anisotropy found in geologic and hydrologic datasets. The algorithm is tested on a unique dataset collected from a slab of Berea sandstone (1 m by 0.4 m). Air permeability, electrical resistivity and compressional wave velocity were measured on a 3 mm rectangular grid. Sparse testing data were drawn randomly from this exhaustive dataset for validating the new computational methods. We apply the method using biogeochemical data collected along a transect between the Vermont and New York shorelines of Lake Champlain, to demonstrate the ability to discriminate between different functional zones in the lake. This clustering method could be applied to a variety of terrestrial, aquatic, or subsurface biogeochemical or geophysical problems. Considering spatial auto-correlation in delineating regions or zones in environmental systems creates more accurate estimations.
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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).