Joint ISI

Joint ISI Distribution

For each spike, a point is calculated where the X coordinate of the point is the current interspike interval and Y coordinate of the point is the preceding interspike interval. The density of these points is shown in the graph.

Parameters

Parameter	Description
Min Interval	Time axis minimum in seconds.
Max Interval	Time axis maximum in seconds
Bin	Bin size in seconds.
Log Axis Scale	An option to use Log10 axis scales.
Matrix Scale	Matrix color scale.
Smooth Matrix	An option to smooth matrix after calculation.
Smooth Radius	Radius of the smooth filter (in bins).
Smooth Colors	An option to smooth colors using bicubic splines.
Log Color Scale	An option to use Log10 color scale.
Select Data	If Select Data is From Time Range, only the data from the specified (by Select Data From and Select Data To parameters) time range will be used in analysis. See also Data Selection Options.
Select Data From	Start of the time range in seconds.
Select Data To	End of the time range in seconds.
Interval filter	Specifies the interval filter that will be used to preselect data before analysis. See also Data Selection Options.
Add to Results / Bin left	An option to add an additional vector (containing a left edge of each bin) to the matrix of numerical results.
Add to Results / Bin middle	An option to add an additional vector (containing a middle point of each bin) to the matrix of numerical results.
Add to Results / Bin right	An option to add an additional vector (containing a right edge of each bin) to the matrix of numerical results.
Send to Matlab	An option to send the matrix of numerical results to Matlab. See also Matlab Options.
Matrix Name	Specifies the name of the results matrix in Matlab workspace.
Matlab command	Specifies a Matlab command that is executed after the numerical results are sent to Matlab.
Send to Excel	An option to send numerical results or summary of numerical results to Excel. See also Excel Options.
Sheet Name	The name of the worksheet in Excel where to copy the numerical results.
TopLeft	Specifies the Excel cell where the results are copied. Should be in the form CR where C is Excel column name, R is the row number. For example, A1 is the top-left cell in the worksheet.

Summary of Numerical Results

The following information is available in the Summary of Numerical Results

Column	Description
Variable	Variable name.
YMin	Y axis minimum.
YMax	Y axis maximum.
Color Scale Min	Color scale minimum
Color Scale Max	Color scale maximum

Algorithm

If Use Log Bins and Axes option is not selected

Matrix of binCounts[x,y] is created. Each element of the matrix is initialized as zero.

For each spike that occurred at time t[i], the following values are calculated:

Interval_I = t[i] - t[i-1]
binX = (Interval_I - MinInterval)/Bin
Interval_I_Plus_1 = t[i+1] - t[i]
binY = (Interval_I_Plus_1 - MinInterval)/Bin

Then, the corresponding bin count is incremented:

binCounts[binX, binY] = binCounts[binX, binY] + 1

The graph shows binCounts matrix values using color scale.

If Use Log Bins and Axes option is selected

The i-th bin (i=1,2,…) is [IntMin * 10 ^ ((i -1)/D), IntMin * 10 ^ (i/D)), where D is the Number of Bins Per Decade.

binX = (log10(Interval_I) - log10(MinInterval))* NumBinsPerDecade
binY = (log10(Interval_I_Plus_1) - log10(MinInterval))* NumBinsPerDecade

Reference

For discussion on using logarithm of interspike intervals, see:

Alan D. Dorval, Probability distributions of the logarithm of inter-spike intervals yield accurate entropy estimates from small datasets. Journal of Neuroscience Methods 173 (2008) 129-139