Multichannel Systems NeuroExplorer - Manual (Page 64)

Trough Z-score Trough Z-score. See Peak and Trough Statistics below.
Trough/Mean Histogram trough value divided by the background mean value.
Trough Position Trough position (in seconds).
Trough Half Height The Y value of the half height of the trough, i.e.
histogram_background_mean + (trough-mean)/2.
Trough Width at Half
Height Trough width at the trough half height level (in seconds).
Algorithm
In general, the Perievent Histogram shows the conditional probability of a spike in the spike train at
time t0+t on the condition that there is a reference event (or reference spike) at time t0.
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 ref[i] be the array of timestamps of the reference event,
ts[i] be the spike train (each ts is the timestamp)
For each timestamp ref[k]:
1) calculate the distances from this event (or spike) to all the spikes in the spike train:
d[i] = ts[i] - ref[k]
2) for each i:
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 reference events.
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 ref[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 reference events. Then, the probability value
(bincount[1]/number_of_reference_events) could be larger than 1.
If Normalization is Spikes/Sec, bin counts are divided by NumRefEvents*Bin, where
NumRefEvents is the number of reference events.
If Normalization is Z-score, bin_value = (bin_count - Confidence_mean)/sqrt(Confidence_mean),
where Confidence_mean is the expected mean bin count calculated according to Conf. mean
calculation parameter. Please note that bin counts are assumed to have Poisson distribution
(therefore, standard deviation is equal to square root of expected mean) and Z-score can be
considered to have Normal distribution only for large values (more than 10) of the Confidence_mean.
Peak and Trough Statistics
Page 62