February 20, 2014
Mathematics Colloquium lecture today, 1xbet online games login . 20
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, 1xbet online games login . 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.