Graduate Student Seminar

Speaker 1: Xinxuan Li

Title

The Computational Model of the Thalamocortical System

Abstract

The Thalamocortical System occupies the majority of the mammalian brain and accounts for most of the increase in brain size during evolution. Spindles are prominent oscillations that occur in the Thalamus Reticular Nucleus (TRN). To generate spindle in TRN, Destexhe et al (1994) proposes a computation model of isolated TRN based on Hodgkin-Huxley model with certain network topology. At this point, the GABAergic synapses is considered as inhibitory. By applying newer recording technology which minimizes the perturbation of concentration of chloride, Beierlein et al (2012) shows that the GABAergic synapse is excitatory in TRN, which contradict to the dogma that GABAergic synapse is inhibitory in TRN. To reproduce spindle with depolarizing GABAergic envelop in computational model, the electrical synapses, morphology of the TRN and other factors need to take into account.  This talk introduces the basic computational model of TRN and discusses the importance of the network morphology.

Speaker 2: Ting Wang

Title

Efficiency of Girsanov transformation approach for parameter sensitivities of density dependent processes

Abstract

Intracellular chemical reactions are best modeled by a Markov process in continuous time with the non-negative integer lattice as state space. The jump rates typically depend on certain system parameters. Computing the parametric sensitivity of system's behavior is essential in determining robustness of systems as well as in estimating parameters from observed data.

Monte Carlo methods for numerical computation of parametric sensitivities fall into three categories: finite difference (FD) methods, pathwise derivative (PD) method and the Girsanov transform (GT) method. Among these methods, GT method has the advantage that it provides us a unbiased estimator.

However, it has been numerically observed that it is less efficient (has higher variance) than other methods like PD method. A modified GT method\227centered Girsanov method (CGT) which is more efficient, has been proposed to replace the GT method.

We provide both analysis and numerical results showing that for a class of Markov processes known as density dependent processes, the efficiency of the GT method scales as $\mathcal{O}(N^{1/2})$ while that of CGT method scales as $\mathcal{O}(1)$, where $N$ isthe system size parameter. In many practical systems $N$ is modestly large and as such one can use CGT method to replace the GT method.