regularity of spike series
Glen M. Sizemore
gmsizemore2 at yahoo.com
Tue Jan 27 14:49:50 EST 2004
MJ: I agree that the first step ought to be visual inspection of the ISI
distribution. However, it is not correct, as someone else suggested,
that a peaked ISI distribution wouldn't produce periodicity. In fact,
drawing spikes randomly from a gaussian distribution is a good way to
synthesize a periodic spiketrain that has a peaky autocorrelogram
(depending on the width of the gaussian, of course).
GS: Hmmm........really? I thought autocorrelelograms revealed sequential
dependencies. I appreciate the correction.
"Matt Jones" <jonesmat at physiology.wisc.edu> wrote in message
news:b86268d4.0401271126.7bd0407c at posting.google.com...
> mats_trash at hotmail.com (mat) wrote in message
news:<43525ce3.0401220431.67b6948f at posting.google.com>...
> > Can anyone direct me to literature on useful metrics of regularity in
> > spike series. I've plotted autocorrelograms to see if any whopping
> > peaks appear but to no avail. On cursory reading I came accros papers
> > on 'Approximate Entropy' but I don't think my datasets contain enough
> > spikes to make this a valid measure.
> >
> > Many thanks
>
>
> Hi,
>
> I guess it depends on what you mean by regularity. The autocorrelegram
> should reveal periodicity, but if there's a lot of "background"
> spiking (i.e., scattered spikes that don't follow the periodicity of
> the other spikes) that'll produce a large fuzzy baseline in the
> autocorrelogram, upon which peaks might be difficult to detect.
>
> I agree that the first step ought to be visual inspection of the ISI
> distribution. However, it is not correct, as someone else suggested,
> that a peaked ISI distribution wouldn't produce periodicity. In fact,
> drawing spikes randomly from a gaussian distribution is a good way to
> synthesize a periodic spiketrain that has a peaky autocorrelogram
> (depending on the width of the gaussian, of course).
>
> A good graphical way of observing regularity (not just periodicity,
> but higher order regularity too) is to construct what's known as a
> "first return plot" (sometimes also called a Poincare plot). This is
> easy, you make a 2D scatter plot of each ISI versus the ISI that
> immediately followed it (i.e., plot ISI(n) vs ISI(n+1), where n goes
> from 1 through the total number of spikes).
>
> If there is significant "regularity", this will show up as clusters of
> points in the return plot. For example, if the spiketrain highly
> periodic, there would be a single dense cluster somewhere on the line
> of identity (ISI(n) = ISI(n+1)). If there were a multiperiodic orbit,
> say, where the system oscillates short interval -> long interval ->
> short interval -> long interval, then there would be two clusters of
> points symmetrically opposite each other across the line of identity.
>
> Unfortunately many systems (including the one you're studying) display
> orbits that are even more complex than the examples above, where
> visual inspection isn't quite good enough to detect the underlying
> structure. The "clusters" become to diffuse and overlapping to
> identify without additional mathematical tools.
>
> There have been several papers about detecting higher order structure
> in neuronal time series that you might find useful. You may want to
> check out these papers, which use return plots to study dynamics in
> slices under "epileptic" conditions:
>
> Schiff SJ, Jerger K, Duong DH, Chang T, Spano ML, Ditto WL.
> Controlling chaos in the brain.
> Nature. 1994 Aug 25; 370(6491): 615-20.
>
> Aitken PG, Sauer T, Schiff SJ.
> Looking for chaos in brain slices.
> J Neurosci Methods. 1995 Jun; 59(1): 41-8.
>
> Slutzky MW, Cvitanovic P, Mogul DJ.
> Manipulating epileptiform bursting in the rat hippocampus using chaos
> control and adaptive techniques.
> IEEE Trans Biomed Eng. 2003 May; 50(5): 559-70.
>
> Slutzky MW, Cvitanovic P, Mogul DJ.
> Deterministic chaos and noise in three in vitro hippocampal models of
> epilepsy.
> Ann Biomed Eng. 2001; 29(7): 607-18.
>
>
>
> Cheers,
>
> Matt
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