From: samodena@csemail.cropsci.ncsu.edu (S. A. Modena)
Subject: Anisotropic Voting Rules
Summary: A model for inherent noise-induced error correction in proteins?
Keywords: noise entropy complexity error correction information theory
Organization: Crop Science Dept., NCSU, Raleigh, NC 27695-7620
Date: Sun, 16 Aug 1992 08:35:08 GMT

What follows below is a quote from:
	"How to Define Complexity in Physics, and Why"
     	by Charles H. Bennet

which is an article in the book:

		"Complexity, Entropy, and the Physics of Information"
		Edited by W. H. Zurek
		Addison-Weslet, The Advanced Book Program, 
			Redwood City, CA  1990
		ISBN 0-201-51509-1
		QC39.S48  1991

The following should be read in light of TD Schneider, JTB 148:125-137 1991,
who cites earlier works of Bennet, among others.

"ERROR-CORRECTING COMPUTATION

"What collective phenomena suffice to allow error-correcting
computation  and/or the generation of complexity to proceed despite 
the locally destructive effects of noise?  In particular,
how does dissipation favor the generation and maintenance of
complexity in noisy systems?

"*  Dissipation allows error-correction, a many-to-one mapping
in phase space.

"*   Dissipative systems are exempt from the Gibbs phase rule.
In typical d-dimensional equilibrium systems with short-ranged
 interactions, barring symmetries or accidental degeneracy of 
parameters such as occurs on a coexistance line, there is a unique 
thermodynamic phase of lowest free energy.  This renders equilibrium 
systems ergodic and unable to store information reliably in the presence 
of "hostile" (i.e., symmetry-breaking) noise.  Analogous dissipative 
systems, because they have no defined free energy in d dimensions, 
are exempt from this rule.  A (d+1)-dimensional free energy can be 
defined, but varying the parameters of the d-dimensional model does not 
in general destabilize a new phase relative to another.

"*   What other properties besides irreversibility does a system need 
to take advantage of the exemption from the Gibbs phase rule?  In 
general the problem is to correct erroneous regions, in which data 
computation locally differs from that originally stored or programmed 
into the system.  These regions, which may be of finite size, arise 
spontaneuosly due to noise and to subsequent propagation of errors 
through the system's normal dynamics.  Local majority voting over a 
symmetric neighborhood, as in the Ising model at low temperature, in 
insufficient to suppress islands when the noise favors their growth.  
Instead of true stability, one has a metastable situation in which 
small islands are suppressed by surface tension, but large islands grow.  
Two methods are known for achieving absolute stability in the presence 
of symmetry-breaking noise.

"Anisotropic Voting Rules in two or more dimensions contrive to shrink 
arbitrarily large islands by differential motion of their boundaries.  
The rule is such that any island, while it may grow in some directions, 
shrinks in others; eventually the island becomes surrounded by shrinking 
facets only and disappears (figures not included in this post).  The 
requisite anisotropy need not be present initially, but may arise through 
spontaneous symmetry breaking.

"Hierarchial Voting Rules.  These comlex rules, in one or more 
dimensions, correct errors by a programmed heirarchy of blockwise 
majority voting.  The complexity arises from the need of the rule to 
mainain the heirarchial structure, which exists only in software."

I haven't had a chance to read Bennet's self-citations yet.  I think
Bennet's Anisotropic Voting Rules would seem to apply to
folded proteins nicely.

Steve
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