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Tony Smith
Meme Media
Melbourne, Australia

Registered: Oct 2003
Posts: 168

Stu Kauffman returns to the Edge of Chaos

Actually, like me, he seems to have never given up on it.

According to a new interview with Suzan Mazur in Scoop, Stu has some important new results showing that cells are critical (at the edge):

I have ever since 1987 believed that cells are poised on the edge of chaos. You’ll find it in my first two books.
(...)
So there’s this poised edge of chaos state between order and chaos. Here’s what we’re beginning to know now, 20 years later. There’s evidence that cells are at the edge of chaos. The mathematical term is critical. Ordered, chaotic and critical. Edge of chaos will do.

So two main papers have been published. One came out just a couple of weeks ago and I’m one of the authors on it . . It is the first direct evidence that maybe cells are at the edge of chaos. There’s really dramatic evidence. It’s gorgeous. But it’s only one example.
A quick Google for that recent paper came up empty, so I can only guess it really is too current.

(The Edge of Chaos is closely related to Wolfram's 1983 Class 4 categorisation of simple cellular automata, but with an implication of further narrowing which is antithetical to Wolfram's 2002 Principle of Computational Equivalence.)

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Old Post 05-05-2008 12:50 PM
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Lawrence J. Thaden


Registered: Jan 2004
Posts: 357

Tony,

Are the categories themselves "ordered" as chaotic, critical, and ordered?

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Jason Cawley
Wolfram Science Group
Phoenix, AZ USA

Registered: Aug 2003
Posts: 712

I think he is actually talking about this one -

http://www.sciencedirect.com/scienc...352bb30e77999ce

Here is the abstract -

In a previous study it was shown that a simple random Boolean network model, with two input connections per node, can describe with a good approximation (with the exception of the smallest avalanches) the distribution of perturbations in gene expression levels induced by the knock-out of single genes in Saccharomyces cerevisiae. Here we address the reason why such a simple model actually works: we present a theoretical study of the distribution of avalanches and show that, in the case of a Poissonian distribution of outgoing links, their distribution is determined by the value of the Derrida exponent. This explains why the simulations based on the simple model have been effective, in spite of the unrealistic hypothesis about the number of input connections per node. Moreover, we consider here the problem of the choice of an optimal threshold for binarizing continuous data, and we show that tuning its value provides an even better agreement between model and data, valuable also in the important case of the smallest avalanches. Finally, we also discuss the choice of an optimal value of the Derrida parameter in order to match the experimental distributions: our results indicate a value slightly below the critical value 1.

Here is another, more recent paper of this group, in the same vein, doing formal experiments on random boolean networks trying to simulate the effect of single node knock outs -

http://aimsciences.org/journals/pdf...=3282&mode=full

I hope this helps.

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Old Post 05-05-2008 08:34 PM
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