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sbe ii hw 4

# sbe ii hw 4 - 580.422 System Bioengineering II...

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580.422 System Bioengineering II: Neurosciences (Spring 2008) Sensory Systems Homework #2 (Prof. Xiaoqin Wang) [Note: Please include Matlab codes with your homework] A “spike train” (i.e., a sequence of action potentials) is a discrete stochastic process that can be quantitatively described by its inter-spike interval (ISI, denoted as τ ) distribution. τ is a random variable whose probability density function and probability distribution function are denoted as p( τ ) and F(t) , respectively. The simplest model of spike trains is the homogeneous Poisson process . The ISI-distribution of a homogeneous Poisson process is an exponential function as follows. p 1 ( τ ) = 0 τ < 0 p 1 ( τ ) = λ e - λ τ τ 0, λ 0 (Eq.1) where λ is a constant equivalent to mean firing rate. Because neurons have “refractory periods”, the homogeneous Poisson process does not adequately model realistic spikes trains. Assume you can simulate the “absolute refractory period” by adding a “dead-time” ( t 0 ) to the distribution of τ

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sbe ii hw 4 - 580.422 System Bioengineering II...

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