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    Efficient and accurate simulation of integrate-and-fire neuronal networks in the hippocampus

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    Author
    Kellems, Anthony Richard
    Date
    2007
    Advisor
    Cox, Steven J.
    Degree
    Master of Arts
    Abstract
    This 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.
    Keyword
    Mathematics
    Citation
    Kellems, Anthony Richard. "Efficient and accurate simulation of integrate-and-fire neuronal networks in the hippocampus." (2007) Master’s Thesis, Rice University. https://hdl.handle.net/1911/20512.
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    • Rice University Electronic Theses and Dissertations [13403]

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    Managed by the Digital Scholarship Services at Fondren Library, Rice University
    Physical Address: 6100 Main Street, Houston, Texas 77005
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    Site Map