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Saturation levels revisited

In Section (p. ), I motivated my choice of 150 spikes/sec as the absolute saturation level response for all cell types. I will now show that choosing a different value basically amounts to a linear scaling of the response functions, so the actual value chosen does not matter all that much, as long as it is reasonable. The value should not be too much higher than the maximum represented in the data sets (less than 50), or the extrapolation will become too unreliable.

Following the procedure outlined in Section (p. ), I computed activation functions for the six cell types using a saturation response of 300 spikes/sec, or twice the value used before (the ``negative saturation'' level was likewise doubled). I then fitted the functions in the second set linearly to their counterparts in the first set, for instance for the +R-G functions:

where represents the +R-G function with a saturation level of 300 spikes/sec, the same but with a saturation level of 150 spikes/sec, and and are scalars. The Root Mean Square (RMS) error of fit over a data set of 231 points spaced in a regular grid (11 in the radiance domain and 21 in the wavelength domain) was minimized using the steepest gradient descent algorithm of Mathematica's FindMinimum function, as a function of and . Table summarizes the results, and Figures through graphically show the results and the errors of fit.

As is apparent from Table , the fit generally amounts to just scaling by a factor in each case (the offset is negligible), and the error of fit is relatively low, with a typical RMS error of 1-2%. The worst fit is for the function, probably because it operates closer to saturation levels than any other, but it is still quite reasonable. The scaling factors do vary for the different functions, but that is not important (subsequent normalization will cancel the effect of different factors anyway).