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Brain physics, cerebrospinal fluid dynamics, hydrocephalus, mathematical modeling in neurosciences, stochastic differential equations, stochastic optimal control
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Full-Text Articles in Medicine and Health Sciences
Processing Random Signals In Neuroscience, Electrical Engineering And Operations Research, Kalyan Raman
Processing Random Signals In Neuroscience, Electrical Engineering And Operations Research, Kalyan Raman
Wayne State University Dissertations
The topic of this dissertation is the study of noise in electrical engineering, neuroscience, biomedical engineering, and operations research through mathematical models that describe, explain, predict and control dynamic phenomena. Noise is modeled through Brownian Motion and the research problems are mathematically addressed by different versions of a generalized Langevin equation. Our mathematical models utilize stochastic differential equations (SDEs) and stochastic optimal control, both of which were born in the soil of electrical engineering. Central to this dissertation is a brain-physics based model of cerebrospinal fluid (CSF) dynamics, whose structure is fundamentally determined by an electrical circuit analogy. Our general …