Semantics and Syntactic Representations

Harry Erwin erwin at trwacs.fp.trw.com
Mon Dec 6 13:56:24 EST 1993

Dr. Freeman indicates that the paper covering the material presented at
the recent Society for Neuroscience is in preparation and should be
available in preprint form later this month. 

The best definition of the Kn notation I've encountered is in Mass Action
in the Nervous System, by Walter J. Freeman, Academic Press, 1975, page
26. 'K' is named for the late A. Katchalsky. A K0 set is 10^3 to 10^8
neurons with a common source of input, a common sign of output, and no
functional interconnections. A KI set adds dense interconnections among
the neurons. A KII set is formed by dense functional interconnections
between two KI sets. Only inhibitory/excitatory systems were known at the
time of book publication. A network of KII sets is a KIII set if there is

Francisco Varela spoke at the Second Radford Conference. One area of
difference between him and Freeman is the nature of the carrier waveform
that (when synchronized) carries the association between channels. Freeman
believes it to be chaotic and there are reasons to believe that may be so
based both on function and the nature of the data. Varela believes it to
be periodic, with compact support. Freeman points out that the quality of
the biological data is such that chaos cannot be proven or disproven.
When I asked him, Bernardo Huberman indicated that he regarded Freeman's
work as solid, especially given the non-linear dynamics involved. (Note he
made the initial prediction that neural nets would be chaotic.) In my
simulation work, it appears chaotic, although I haven't tested the data
beyond verifying mixing (which is clear). The dynamics are not well-
understood. They appear to be some form of perturbed quasi-periodicity,
with the perturbation creating near-limit-cycles into which the system can
be thrown when the pattern of coupling strengths between oscillators
matches the pattern of strong and weak signals well. It's similar to the
dynamics I've seen in certain types of computer systems, and I've been told
there is unpublished Russian work that is very relevant. 

Harry Erwin
Internet: herwin at cs.gmu.edu or erwin at trwacs.fp.trw.com
Working on Freeman nets....

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