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MS DEFENSE
Edward AGARWALA
Department of Mathematics
Case Western Reserve University
"Food For Thought: When Information Optimization Falls to Optimize Utility"
Date: Thursday, May 28, 2009
Time:9:00-12:00 p.m.
Loation: Department of Mathematics, Seminar Room, Yost 300
Advisors: Dr. Peter Thomas
PHD DEFENSE
Rossana OCCHIPINTI
Department of Mathematics
Case Western Reserve University
"In Silico Testing of Hypotheses for Brain Energy Metabolism with New Computational Models within a Statistical Framework"
Date: Friday, May 29, 2009
Time: 1:30-4:30 p.m.
Loation: Department of Mathematics, Seminar Room, Yost 300
Advisors: Dr. Daniela Calvetti
ABSTRACT
The brain is a highly metabolic organ, characterized by the presence of different cell types, astrocytes, neurons and endothelial cells, interacting with each other and with specific tasks, whose regulatory mechanisms are still largely unknown. The difficulty in obtaining direct in vivo and in situ cell-type specific measurements of metabolite and intermediate concentrations has left many different hypotheses open
on the metabolic role of astrocytes and neurons, in particular on the primary source of energy for brain during stimulation. Computational models of cellular brain metabolism can help sorting out which presumed mechanisms are more likely under various conditions and eventually pro- viding a key to decode information from functional imaging modalities. In this thesis we present new six-compartment computational models of celluar brain metabolism which integrate astrocytes and glutatamatergic or GABAergic neurons, extracellular space and blood domains, with detailed biochemical reactions and signalling mechanisms. These models are governed by large systems of nonlinear
ordinary differential equations with many degrees of freedom. We study two different kinds of parameter estimation problems, one concerned with steady state and the other with dynamic situations, for which we propose a new Bayesian approach. The complexity of the models, the large discrepancy between the scarcity of available data and the huge number of unknown parameters make the steady state and dynamic
parameter estimation inverse problems severely underdetermined and ill-posed. While these features may be an obstacle for classical deterministic methods, they can be overcome in a Bayesian framework, where the unknowns are modelled as random variables and additional information in the form of prior belief about the solutions and the models can be incorporated in the estimation problem. Efficient Markov Chain Monte Carlo sampling techniques are designed and adapted to explore the posterior density, which is the solution of the problem in Bayesian inversion. We will show how this new methodology can be used to test different hypotheses on brain energetics and
interpret experimental data in the context of compartmentalized metabolism. The computational results are in remarkable agreement with experimental data and with proposed physiological and biochemical mechanisms on cellular brain metabolism.
MS DEFENSE
Huaizhi CHEN
Department of Mathematics
Case Western Reserve University
"Estimating stochastic volatility using particle filters"
Date: Thursday, June 25, 2009
Time:11:00-1:00 p.m.
Loation: Department of Mathematics, Seminar Room, Yost 300
Advisors: Dr. Daniela Calvetti
Case Western Reserve University
Department of Mathematics
10900 Euclid Avenue
Cleveland, Ohio 44106
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