Forwarded with permission:
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From: Society for chaos theory in psychology on behalf of Robert A Gregson
Sent: Thursday, July 03, 1997 7:46 PM
To: CHAOPSYC at LIST.UVM.EDU
Subject: information transmission stability
The classic work on information transmission
and its stability in time was developed
by the Russian mathematician Pinsker (1960/1964)
and may be found in translation (into English)
by Feinstein, publ Holden Day, San Francisco.
However, all that meticulous work is
strictly about stationary processes with
gaussian noise, I don't know of reworking
the existence theorems to deal with only locally
dynamically stationary proceses, and abandoning
completely the gaussian restrictions, which
obviously have value if one wants to use
Fisherian information measures on inverse
variances.
It has increasingly seemed to me that something
along those lines would be required to link more
firmly nonlinear dynamics to observable
psychological response processes, in the micro-
as opposed to the macro- levels.
Whilst I am musing, may I draw attention to a very
recent paper by Luce in Jnl Math Psych this year,
in which he laments the non-progress of math
psych in its mainstream form in the USA, and indeed
acknowledges the existence of NDPLS.
There is also in press now in JMP a paper by a
group at Amsterdam, headed by Cees van Leeuwen,
on
Stability and Intermittency in large scale
coupled oscillator models for Perceptual Segmentation
which draws on work by Kaneko. I think their actual choice
of model is wrong for psychophysiology, you can
compare what they have done with what I did in my
1992 book (specifically re Kaneko), and a forthcoming
Australian conference paper which I can send to
anyone as a Postcript file if they want it.
For those who are going, have a nice conference.
Robert A. M. Gregson
Emeritus Professor
Division of Psychology
School of Life Sciences
Australian National University
Canberra ACT 0200
