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 interspike 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 ISIdistribution 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 “deadtime” (
t
0
) to the distribution of
τ
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 Spring '09
 Winslow
 Normal Distribution, Probability distribution, Probability theory, probability density function, homogeneous Poisson process

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