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K-State Today

February 20, 2014

Mathematics Colloquium lecture today, Feb. 20

Submitted by Reta McDermott

Deena Schmidt, Case Western Reserve University, will present "Measuring Edge Importance for Random Processes on Graphs" as part of the mathematics department Colloquium lecture series at 2:30 p.m. Thursday, Feb. 20, in 122 Cardwell Hall.

The abstract for the lecture is: Mathematical models of cellular physiological mechanisms often represent transitions among functional states as stochastic processes on networks. Recently, Schmandt and Galan introduced the "stochastic shielding approximation" as a fast, accurate method for generating approximate sample paths from a finite state Markov process in which only a subset of states are observable. I conducted a rigorous analysis of this stochastic shielding heuristic, deriving a new quantitative measure of the contribution of individual edges in the graph to the accuracy of the approximation. In this talk, I will discuss my analysis and my extension of this method for a broad class of random graph models and for the Hodgkin-Huxley ion channel model. I will show how these results shed new light on the contributions of different ion channel transitions to the variability of neural systems. This approach can be applied to a variety of biological networks and has led to many challenging mathematical questions.