I'm quite excited to post here the abstract of a new paper, because
talking of correlations would bring to life so much discussion, and we
claimed in the paper that the method described there (a ``phase function'')
produces better results than a regular correlation function applied to
discrete events, such as arrival times or spike times. Of particular
mention
is the usefulness of this method when the number of arrival times is
very few,
say less than 10. For 10 arrival times, for example, an auto-correlation
function
will not be very useful, but a phase function might be able to show a clear
oscillatory profile without resorting to any smoothing. The paper uses
biological recordings for demonstration, but the method itself is quite
general.
Ready to use codes in Matlab/Octave and Mathematica are available as
supplementary material for the paper, and also in the link given below.
Better still, a JavaScript page is online (link below) to quickly try
out the
efficacy of this method. Your feedback is most welcome.
Thank you.... ramana dodla
PS: Please see the cover-art of the journal for bigger plots of phase
function applied to discrete events as few as 3, and as many as more
than 600.
TITLE: A Phase Function to Quantify Serial Dependence between Discrete
Samples
AUTHORS: Ramana Dodla and Charles J. Wilson
JOURNAL: Biophysical Journal 98:L05-L07, 2010
URL: http://dx.doi.org/10.1016/j.bpj.2009.11.003
ONLINE COMPUTATION:
http://marlin.life.utsa.edu/~ramana/phase_function_online/index.html
ABSTRACT:
Auto- and cross-correlation methods, when applied to discrete events, can
determine periodicity and correlation times within and between event train
sequences. However, if the number of available events for analysis is
too few,
the correlation techniques yield ambiguous and insufficient results. Here we
report a technique based on measurements of phases of event times that could
detect the periodicity even among very few discrete data points. The results
are demonstrated on in vitro neuronal spike time data, and are found to be
highly contrasting when compared with the correlation techniques. The
technique
could become invaluable, for example, for treating in vivo spike time
records
that often last very short duration, or for determining short timescales in
discrete biophysical experimental data.
COVER PICTURE:
A method based on relative phases between discrete time events is used to
capture the serial correlations in an experimental spike train. The figure
depicts phase correlations of a spike train with itself as a function of
time
lag by including an increasing number of time events. The top five
traces are
autophase function curves for a spike train with as few as 3, 4, 5, 6, and 7
time events, respectively. The bottom three traces use 14, 68, and 673 time
events, respectively. For a large number of events, the phase function
produces
a profile equivalent to a corresponding correlation function. But for a very
few number of events, it can show a measurable profile where a correlation
function may fail to reliably detect one.
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