Stochastic problems in signal transduction and gene control - Hans G. Othmer
Students would investigate the role of stochastic noise in signaling and gene control with a view toward understanding when it can be beneficial (as in bacterial evolution) and when it is harmful. A general objective would be to understand how network structure enhances or attenuates noise and determine whether there are general principles that emerge from this.
Some knowledge of differential equations, linear algebra, and basic probability theory.
The influence of network structure on neuronal network dynamics - Duane Q. Nykamp
Students will investigate the influence of network topology on the dynamics of neuronal networks. A central goal will be to explore how covariations among edges in a random network influence ability of the network to enter states such as synchronized firing of the neurons. Students will look for implications for how network structure may promote or diminish the likelihood of pathological behaviors such as seizures.
Include differential equations, linear algebra, and basic probability theory.