Cox, Steven J.2009-06-032009-06-032007Kellems, Anthony Richard. "Efficient and accurate simulation of integrate-and-fire neuronal networks in the hippocampus." (2007) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/20512">https://hdl.handle.net/1911/20512</a>.https://hdl.handle.net/1911/20512This thesis evaluates a method of computing highly accurate solutions for network simulations of integrate-and-fire (IAF) neurons. Simulations are typically evolved using time-stepping, but since the IAF model is composed of linear first-order ODEs with hard thresholds, explicit solutions in terms of integrals of exponentials exist and can be approximated using quadrature. The technique presented here utilizes Clenshaw-Curtis quadrature to approximate these integrals to high accuracy. It uses the secant method to more precisely identify spike times, thus yielding more accurate solutions than do time-stepping methods. Additionally, modeling synaptic input with delta functions permits the quadrature method to be practical for simulating largescale networks. I determine general conditions under which the quadrature method is faster and more accurate than time-stepping methods. In order to make these methods accessible to other researchers, I introduce and develop software designed for simulating networks of IAF hippocampal cells.62 p.application/pdfengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.MathematicsThesisTHESIS MATH.SCI. 2007 KELLEMS