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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).