Networks and link data

[David E. Wojick]

Sylvan,

I did not know about it, but percolation theory looks like a promising marriage between network analysis and statistical fluid flow. (I am new to network analysis.) The question then becomes how can it be applied to the diffusion of ideas in science? 

We opted for a contagion model rather than a fluid diffusion or percolation model because ideas are not conserved, as mass flows are. The idea does not move from you to me but rather is replicated in me. That is, when you get me to think about percolation theory you do not lose any thought in the process.

On the other hand, there are important processes in the congitive flow system that are conserved. Funding for example, and the flow of funds to various ideas greatly determines which ideas get thought about by whom. My client, OSTI, is part of the DOE Office of Science which funds about $4 billion a year of basic research. Which ideas get funded is their chief concern.

This leads to a broader concept which is conserved, which I call "attention." Rather than looking at the movement of an idea from person to person, look at the movement of attention from idea to idea. If we assume that one can only think about one topic at a time then attention is conserved. Thinking about percolation thoery precludes thinking about some other theory (unless one is thinking about the combination of course). Even for groups of scientists, which can think about more than one topic at once, there is an allocation of attention at any given time.

As with any applied math, the question is how to apply it to the thing or process under study. For the diffusion of scientific ideas this is a hard problem, because the science of ideas is poorly developed. But I think we are making headway. Thanks for your interest.

David

>
>David
>
>> seems to me to be an important question. I think a similar problem arises
>> in statistical mechanics.
>
>Are you thinking of Percolation Theory?
>
><http://en.wikipedia.org/wiki/Percolation_theory>
>
>Albert, R. and A. L. Barabasi, 2002: Statistical mechanics of complex networks. Reviews of Modern Physics, 74, 47-97.
><http://www.nd.edu/~networks/Publication%20Categories/01%20Review%20Articles/StatisticalMechanics_Rev%20of%20Modern%20Physics%2074,%2047%20(2002).pdf>
>
>Newman, M. E. J. and D. J. Watts, 1999: Scaling and percolation in the small-world network model. Physical Review E, 60, 7332 LP  - 7342
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>Essam, J. W., 1980: Percolation theory. Reports on Progress in Physics, 43, 833-912.
>
>
>Sylvan
>
>
>Dr. J. Sylvan Katz, Visiting Fellow
>SPRU, University of Sussex
>http://www.sussex.ac.uk/Users/sylvank
>
>Adjunct Professor
>Mathematics & Statistics, University of Saskatchewan
>
>Associate Researcher
>Institut national de la recherche scientifique, University of Quebec

-- 

"David E. Wojick, Ph.D." <WojickD at osti.gov>
Senior Consultant -- The DOE Science Accelerator http://www.osti.gov/innovation/scienceaccelerator.pdf
http://www.osti.gov/innovation/
A strategic initiative of the Office of Scientific and Technical Information, US Department of Energy

(540) 858-3150 
391 Flickertail Lane, Star Tannery, VA 22654 USA
http://www.bydesign.com/powervision/resume.html provides my bio and client list. 
http://www.bydesign.com/powervision/Mathematics_Philosophy_Science/ presents some of my own research on information structure and dynamics.