This dissertation is an application of new mathematical modeling to different physical and biophysical problems. We consider dynamical networks where properties of flows and their stochastic fluctuations are of interest. We aim to infer the probabilities of these properties in an unbiased, data-driven way. Our approach to drawing these inferences is the Principle of Maximum Caliber (Max Cal), a general variational principle for dynamical systems. Here we advance the methodology and give two applications in neuroscience. First, Max Cal is generally computationally infeasible for large, heterogeneous networks. We introduce here an approximate method, utilizing information from individual network nodes, to extend Max Cal to systems of any size and complexity. Second, brain activity is quite complex, sometimes chaotic, and sometimes involves multiple superimposed oscillatory patterns. Max Cal allows us to go beyond the more simplified but widely used Wilson-Cowan model and describe these features by accounting for refractory periods of neurons. Finally, we investigate the mechanisms by which complex patterns in the brain arise from the interconnections between different regions. Here we combine our modeling approach with fMRI experimental data. We find that younger, but not older, brains are poised at a critical point of global synchrony and that this transition is modulated by neuronal metabolic activity.
|Advisor:||Dill, Ken A.|
|Commitee:||Wang, Jin, Balazsi, Gabor, Mujica-Parodi, Lilianne R.|
|School:||State University of New York at Stony Brook|
|Department:||Applied Mathematics and Statistics|
|School Location:||United States -- New York|
|Source:||DAI-B 82/9(E), Dissertation Abstracts International|
|Subjects:||Statistical physics, Neurosciences|
|Keywords:||Biophysics, Computational Neuroscience, Dynamics, Maximum entropy, Statistical inference|
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