Graduate Student Seminar

Speaker 1: Xinxuan Li

Title

Computational Models of Thalamocortical System

Abstract

The thalamocortical system is critical for diverse functions, including memory, attention and consciousness. Key to this system is the thalamic reticular nucleus (TRN) that regulates thalamocortical circuits. Our goal is to derive a computational model consistent with all current experimental data.  We will consider intrinsic mechanisms of a single TRN neuron to produce spindle rhythmicity, and extrinsic mechanisms of muti-cell model to generate spindle oscillations.  In this talk, I will focus on the intrinsic mechanisms of the TRN neurons.  To compare with experimental results, we collected and derived three modified Hodgkin-Huxley based computational models.  In the end, we connect some of the single cell models together to form a network, in order to generate sleep spindles.

Speaker 2: Mona Hajghassem

Title

Multigrid preconditioners for boundary control of elliptic-constrained optimal control problems

Abstract

The goal of this project is to devise efficient multigrid algorithms for the boundary control of elliptic equations. Using a reduced formulation, our focus is on designing optimal order multigrid preconditioners for the Hessian of the reduced cost functional. Ideally, the preconditioners should approximate the reduced Hessian with optimal order with respect to the discretization of the elliptic equation. We show that for Dirichlet boundary control of elliptic equations the preconditioner is of suboptimal quality, though still efficient.  Instead, for Neumann boundary control, numerical results suggest the preconditioner to be of optimal order. This project is part of a larger research program on developing efficient solution methods for optimal control problems with PDE constraints.