# VI transfer function; insects; madness

[From Bill Powers (960221.0930 MST)]

Bruce Abbott (960221.0855 EST) --

Using a steady response rate would be rather uninformative, I
believe. For example, imagine using a steady rate of 1 resp/s,
with dt = 0.1 s. A response will be generated every tenth
iteration. Meanwhile the VI interval timer is decrementing toward
zero; when it reaches zero a reinforcer is set up. It may be that
this coincides with one of those MOD 10 responses, in which case
the reinforcer gets delivered immediately. Or it could happen on
the next iteration, or the next, etc, out to nine iterations.
Since the VI setup is random with respect to the response
generator, the probability that setup will occur on any given
iteration is constant, yielding a rectangular distribution of
delays between setup and collection with a mean of 10/2 iterations
or 0.5 s.

What you do is set up a steady response rate, let the simulation run,
and compute the average reinforcement rate when you have enough data to
get a meaningful result. Then you increment the response rate and do it
again, and so on until you have scanned the entire range of behavior
rates of interest. This will give you a curve showing the mean output
reinforcement rate as a function of input response rate. When I did
this, I got a curve that was closely matchable by a 1 - exp(-kt) curve.
You could also fit your "linear" curve to it (your curve isn't really
linear, is it?).

My interest in assessing how the feedback function changes as a
function of response distribution came about initially ...

If you have a true characterization of the feedback function, it will be
independent of response distribution. Of course with different
distributions of inputs, you will get different distributions of output,
but that does not mean that the feedback function has changed; it means
only that you're presenting the same function with different input
patterns, so naturally you get different output patterns.

has to be independent of the input, since it just represents a piece of
non-adaptive apparatus with fixed characteristics. This physical device
can't vary its physical properties as the input pattern changes. The
same feedback function has to apply as long as you're using the same
schedule.

In engineering, this subject is called "transfer functions." A transfer
function is a way of describing a physical input-output device in a way
that allows calculating its output for ANY pattern of inputs (in the
domain in which inputs and outputs are being measured).

···

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I will be ordering the rats this week.

Hooray!
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Chris Kitzke 960221.0800 --
Rick Marken 960213.2100 --

pretty sure) in the sense of "insanity," not "anger."
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Shannon Williams (960221.08:30) --

A thinking creature pauses in one goal to pursue another. A
thinking creature can delay or inhibit the behavior indicated by
'E'. A thinking creature can change his 'R', etc. It seems to me
that the behavior generating mechanism in a thinking creature has
evolved to be quite different from the behavior generating
mechanism in an insect.

Well, I'll leave it up to you. How would you apply hierarchical PCT to