Autocorrelograms

Autocorrelogram shows the conditional probability of a spike at time t0+t on the condition that there is a spike at time t0.

Parameters

Parameter	Description
XMin	Time axis minimum in seconds.
XMax	Time axis maximum in seconds.
Bin	Bin size in seconds.
Normalization	Histogram units (Counts/Bin, Probability or Spikes/Second). See Algorithm below.
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.
Int. filter type	Specifies if the analysis will use a single or multiple interval filters.
Interval filter	Specifies the interval filter(s) that will be used to preselect data before analysis. See also Data Selection Options.
Create filter on-the-fly	Specifies if a temporary interval filter needs to be created (and used to preselect data).
Create filter around	Specifies an event that will be used to create a temporary filter.
Start offset	Offset (in seconds, relative to the event specified in Create filter around parameter) for the start of interval for the temporary filter.
End offset	Offset (in seconds, relative to the event specified in Create filter around parameter) for the end of interval for the temporary filter.
Fix overlaps	An option to automatically merge the overlapping intervals in the temporary filter.
Overlay Graphs	An option to draw several histograms in each graph. This option requires that Int. filter type specifies that multiple interval filters will be used (either Table (row) or Table (col)).
Smooth	Option to smooth the histogram after the calculation. See Post-Processing Options for details.
Smooth Filter Width	The width of the smooth filter. See Post-Processing Options for details.
Draw confidence limits	An option to draw the confidence limits.
Confidence (%)	Confidence level (percent). See Confidence Limits for details.
Conf. mean calculation	An option that specifies how the mean firing rate (that is used in the derivation of the confidence limits) is calculated. There are 2 options: Use data selection and Use all file. See Confidence Limits for details.
Conf. display	An option to draw confidence limits either as horizontal lines or as a colored background.
Conf. line style	Line style for drawing confidence limits (used when Conf. display is Lines).
Conf. background color	Background color for drawing confidence limits (used when Conf. display is Colored Background).
Draw mean freq.	An option to draw a horizontal line representing the expected histogram value for a Poisson spike train. See Confidence Limits for details.
Mean line style	Line style for drawing mean frequency.
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	Histogram minimum.
YMax	Histogram maximum.
Spikes	The number of spikes used in calculation.
Filter Length	The length of all the intervals of the interval filter (if a filter was used) or the length or the recording session (in seconds).
Mean Freq.	Mean firing rate (Spikes/Filter_Length).
Mean Hist.	The mean of the histogram bin values.
St. Dev. Hist.	The standard deviation of the histogram bin values.
Conf. Low	Lower confidence level.
Conf. High	Upper confidence level.
Mean	Expected mean value of the histogram.
Norm. Factor	Normalization factor. Bin counts are divided by this value. See Normalization in Algorithm below.
Time of Minimum	Position of the histogram minimum (in seconds). If there are multiple bins in the histogram where the bin value is equal to the histogram minimum, this value represents the position of the first such bin.
Time of Maximum	Position of the histogram maximum (in seconds). If there are multiple bins in the histogram where the bin value is equal to the histogram maximum, this value represents the position of the first such bin.

Algorithm

In general, the Autocorrelogram shows the conditional probability of a spike in the spike train at time t on the condition that there is a spike at time zero.

The time axis is divided into bins. The first bin is [XMin, XMin+Bin). The second bin is [XMin+Bin, XMin+Bin*2), etc. The left end is included in each bin, the right end is excluded from the bin.

Let ts[i] be the spike train (each ts is the timestamp).

For each timestamp ts[k]:

calculate the distances from this spike to all other spikes in the spike train:

d[i] = ts[i] - ts[k]

for each i except i equal to k:

if d[i] is inside the first bin, increment the bin counter for the first bin:

if d[i] >= XMin and d[i] < XMin + Bin
then bincount[1] = bincount[1] + 1

if d[i] is inside the second bin, increment the bin counter for the second bin:

if d[i] >= XMin+Bin and d[i] < XMin + Bin*2
then bincount[2] = bincount[2] + 1

and so on… .

If Normalization is Counts/Bin, no further calculations are performed.

If Normalization is Probability, bin counts are divided by the number of spikes in the spike train.

Note that the Probability normalization makes sense only for small values of Bin. For Probability normalization to be valid (so that the values of probability are between 0 and 1), there should be no more than one spike in each bin. For example, if the Bin value is large and for each`` ts[k]`` above there are many d[i] values such that d[i] >= XMin and d[i] < XMin + Bin, the bin count for the first bin can exceed the number of spikes in the spike train. Then, the probability value (bincount[1]/number_of_spikes) could be larger than 1.

If Normalization is Spikes/Sec, bin counts are divided by NumSpikes*Bin, where NumSpikes is the number of spikes in the spike train.