Graduate Student Seminar

Speaker 1: Qing Ji

Title

Approximation of the Fisher Information Matrix for the Finite Mixture Model

Abstract

Derivation of the Fisher Information Matrix(FIM) in the finite mixture model is tedious at least and usually not in closed form.  A diagonal matrix was proposed for a mixture of Binomial distributions in (Blischke, 1962) as an approximation.  The performance of a similar type of approximation for a mixture of two Poisson distributions is evaluated and compared to the true FIM.  The simulation shows that difference between the true and approximated FIM is smaller as sample size and distance between means of two distributions increase.  We are also trying to relax the group sampling constraint inherited from Blischke's paper, replacing it with a Markov Chain scheme.

Speaker 2: Janita Patwardhan

Title

The Interaction of Calcium and Metabolic Oscillations in Pancreatic β-Cells

Abstract

Patients with diabetes have high blood glucose levels, often due to improper insulin secretion from pancreatic β-cells. To further understand the process of insulin secretion, we used the Dual Oscillator Model to examine the synchronization of electrical and metabolic oscillations of electrically coupled β- cells. It has been found that for certain parameters, the metabolic oscillations depend on the calcium oscillations.  In order to study the effects of that dependence on synchronization, we tested three behaviors: calcium oscillation dependent metabolic oscillations, calcium oscillation independent metabolic oscillations, and a mix of both. We used a Pearson correlation to quantify the synchrony of the cell traces. As expected, synchrony increased with stronger calcium or voltage coupling for most behaviors. However, with the calcium dependent metabolic oscillations, increasing the calcium coupling with a high voltage coupling between cells lead to desynchronization. This unintuitive behavior has been seen previously in a two-cell model, but needs to be further investigated.