236.

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Page 86
1.5.7—
Statistical Analysis of the Electrical Activity in Nerve Cells
1—
Pulse Number Distribution
Teich et al. divided their records of action potentials recorded from nerves in the ear into consecutive time windows. They counted the number of action potentials in each time window. They evaluated how often each number of action potentials occurred in these time windows. This is called the pulse number distribution.
For a non-fractal process, as the window size is increased, the pulse number distribution becomes smoother and more like a Gaussian distribution. This property is called the Central Limit Theorem. This was the case for the data from the vestibular cells involved in balance.
This was not the case for the data from the auditory cells involved in hearing. Those distributions became rougher as the length of the time window was increased. This roughness arises from correlations in the times between the action potentials.
The proof of the Central Limit Theorem requires that the variance exist and that it has a finite value. For a fractal, the variance is not defined, and thus the Central Limit Theorem does not apply. As more data are included fractal distributions do not become smoother or more Gaussian. Rather, the distributions become rougher because the correlations that link the deviations together in a self-similar way become more noticeable over longer times. Teich et al. wrote that ''the irregular nature of the long count pulse number distributions does not arise from statistical inaccuracies associated with insufficient data, but rather from event clustering inherent in the auditory neural spike train."
2—
Fano Factor
The Fano factor is equal to the variance divided by the mean of the number of action potentials in the time windows. For a non-fractal process where the time between the action potentials is random, the pulse number distribution is a Poisson distribution, and the Fano factor is 1. They found that the Fano factor increased with the length T of the time windows used to measure it. The Fano factor F had a power law scaling relationship that F was proportional to Td where d is the scaling exponent.

 
[Cover] [Abbreviated Contents] [Contents] [Index]


Fractals and Chaos Simplified for the Life Sciences
Fractals and Chaos Simplified for the Life Sciences
ISBN: 0195120248
EAN: 2147483647
Year: 2005
Pages: 261

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