[From Bill Powers (2010.09.24.0752 MDT)]
Hg:
I'm having some trouble finding an elegant way to model the
following problem.
Say I have two CS working in parallel. Now a higher order CS
sets the reference signal for both of them. There are situations
in which one of the lower CS has to be disabled, e.g. it should
not take any action, not even controlling for a zero set point.
BP: Hello, Hannes, and welcome.
There are several possible answers that might be right -- there are almost no systematic data to support them yet.
1. Fact: Neural signals are positive only: that is, the frequency of firing of a neuron can't go negative. This means that error signals are generated only if the positive input to a neuron serving as a comparator is greater than the negative input.
If the positive input receives the reference signal, the negative input receives the perceptual signal. The error signal will be nonzero only if the inhibitory perceptual signal is less than the excitatory reference signal. If the reference signal is zero, the error signal will be zero no matter how large the perceptual signal is. Setting the reference signal to zero will therefore turn the comparator completely off and no output will ever be generated by the associated control system. That turns the control system off.
If reference and perceptual signals are interchanged, an error signal will be nonzero only if the perceptual signal is greater than the reference signal. The reference signal sets the threshold of error. Setting the reference signal to zero will not turn this kind of system off. With zero reference signal, any perceptual signal at all generates an error signal. However, in the absence of any perceptual signal, no reference signal however large can create an error signal and generate output.
Combining the above two types of comparator produces a composite comparator that will produce one error signal (a positive signal) for one sign of error, and a different error signal (also positive) for the opposite sign of error. This is probably how agonist and antagonist muscles are operated to achieve bidirectional output forces. The basal ganglia are known to operate in this way.
2. A higher control system can alter the behavior of a lower-order system, in principle, by sending modulating signals to the output function of the lower system. Some synapses work this way; instead of contributing directly to the firing rate of another neuron, one incoming signal varies the responsiveness of a synapse to another incoming signal. It acts like a gain or attenuation control. This could work on any function in the lower system: input function, comparator, or output function. To turn a control system off, the gain of the function would be turned down to zero.
I haven't tried modeling -- that is, simulating on a computer -- this kind of system at all. All my models assume bidirection control by varying the reference signal. So the field is wide open, Hannes. Be my guest.
In a strict hierarchy, this can be done by setting the reference
signal to what the input signal currently is (a higher order CS
thus has to emulate the input function), so that the comparator
is zero and therefore no action is done.
Yes, but that's very much the hard way to do it. Something would have to sense both signals, perceive the difference in magnitudes, and adjust one of them to make the difference be zero. And if one signal varied, the "something" would have to make the other sign track it. This doesn't sound likely to me.
Does this make sense to you?
Best,
Bill P.
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At 09:18 AM 9/24/2010 +0200, Hannes Gr�uler wrote: