This thesis solves estimation and control problems in computational
neuroscience, mathematically dealing with the first-passage times of diffusion
stochastic processes. We first derive estimation algorithms for model parameters
from first-passage time observations, and then we derive algorithms for the
control of first-passage times. Finally, we solve an optimal design
problem which combines elements of the first two: we ask how to elicit
first-passage times such as to facilitate model estimation based on said
first-passage observations.
The main mathematical tools used are the Fokker-Planck partial differential
equation for evolution of probability densities, the Hamilton-Jacobi-Bellman
equation of optimal control and the adjoint optimization principle from optimal
control theory.
The focus is on developing computational schemes for the
solution of the problems. The schemes are implemented and are tested for a wide
range of parameters.
| Identifer | oai:union.ndltd.org:uottawa.ca/oai:ruor.uottawa.ca:10393/34866 |
| Date | January 2016 |
| Creators | Iolov, Alexandre V. |
| Contributors | Longtin, Andre |
| Publisher | Université d'Ottawa / University of Ottawa |
| Source Sets | Université d’Ottawa |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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