234.

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

Page 84

		1.5.6— Example Where the Variance Does Not Exist: Electrical Activity in Nerve Cells

		Transient changes in the electrical voltage across the cell membrane, called action potentials, travel along the surface of nerve cells. Information is passed down the nerve axon in the timing between the action potentials.

		Teich et al. analyzed the timing of the action potentials from nerves in the ear connected to the auditory cells that encode information about sound and from nerves connected to the vestibular cells that encode information about acceleration that is used for balance. They divided their records into consecutive time windows and counted the number of action potentials in each window. They determined how the number of action potentials in each time window depended on the length of the time windows. The time resolution was set by the length of the time windows. Thus they determined how the properties of the timing of the action potentials depended on the time resolution used to measure them.

		For example, they studied the number of action potentials per second in each time window, which is called the firing rate. They evaluated the firing rate for time windows of different lengths. For a non-fractal, the fluctuations in the firing rate would be less in longer windows, because the statistical inaccuracies would average out. Instead, for the auditory nerve cells involved in hearing, they found that the variation in the firing rate decreased more slowly than for a non-fractal as the window length increased.

		This result is surprising if you only know about the statistical properties of non-fractal distributions. For those distributions the fluctuations decrease at a certain rate as more data are included.

		However, for fractal distributions, the fluctuations decrease more slowly as more data are included. Thus their result implies that the firing rate is fractal. This means that the action potentials are correlated with each other. These small correlations become more significant when the action potentials are analyzed over longer times in the longer time windows.

 

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