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The Dirac delta is used to model a tall narrow spike function (an impulse), and other similar abstractions such as a point charge, point mass or electron point.
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During analysis, neuronal response was represented as a spike density function that was generated by convolving spike times with a 5-ms Gaussian function (Richmond et al. 1987).
Common methods for estimating firing rates include the rate histogram, the reciprocal interspike interval, and the spike density function.
These include the calculation of the peristimulus time histogram or spike density function [4, 5, 20] and the development of algorithms to calculate an 'average' or 'central' spike train [29].
Yet, for a pair of neurons with different rates ( σ V 1 ≠ σ V 2 ) the spike correlation function ν cond is asymmetric, indicating that the lower rate neuron spikes on average after the higher rate neuron.
In the rate model, the LNc spiking rate averaged over the duration of each stimulus presentation replaces the spike density function in the response matrix (see below).
Calculating the spike density function (SDF, defined as f(t) = ∑exp−(t−ti 2/σ2, where ti is the time of the ith spike and σ = 400 ms).
Averages of the spike density function, collapsing all spatial phases, were calculated for each orientation and for each of the 6 stimulus conditions separately.
In this mock example the moving average of the membrane potential seems to provide very similar information as the spike density function.
The neuronal discharge rate (spikes/s) was obtained by calculating the average firing rate during a 200 ms window centered 100 ms around the highest activity of the spike density function histograms.
The resulting spike density function peaks strongly around potential burst locations, where the spike density is especially high.
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