Scaling in a general class of critical random Boolean networks

Physics – Condensed Matter – Disordered Systems and Neural Networks

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

11 pages

Scientific paper

10.1103/PhysRevE.74.046101

We derive analytically the scaling behavior in the thermodynamic limit of the number of nonfrozen and relevant nodes in the most general class of critical Kauffman networks for any number of inputs per node, and for any choice of the probability distribution for the Boolean functions. By defining and analyzing a stochastic process that determines the frozen core we can prove that the mean number of nonfrozen nodes in any critical network with more than one input per node scales with the network size $N$ as $N^{2/3}$, with only $N^{1/3}$ nonfrozen nodes having two nonfrozen inputs and the number of nonfrozen nodes with more than two inputs being finite in the thermodynamic limit. Using these results we can conclude that the mean number of relevant nodes increases for large $N$ as $N^{1/3}$, with only a finite number of relevant nodes having two relevant inputs, and a vanishing fraction of nodes having more than three of them. It follows that all relevant components apart from a finite number are simple loops, and that the mean number and length of attractors increases faster than any power law with network size.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Scaling in a general class of critical random Boolean networks does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Scaling in a general class of critical random Boolean networks, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Scaling in a general class of critical random Boolean networks will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-529046

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.