Regensburg 2007 – wissenschaftliches Programm
Bereiche | Tage | Auswahl | Suche | Downloads | Hilfe
DY: Fachverband Dynamik und Statistische Physik
DY 6: Statistical physics of complex networks II
DY 6.4: Vortrag
Montag, 26. März 2007, 15:15–15:30, H3
Scaling and criticality in finite dynamical networks at the SP limit — •Thimo Rohlf1, Natali Gulbahce2, and Christof Teuscher3 — 1Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA — 2LANL, Center for Nonlinear Studies, MS B258, Los Alamos, NM 87545, USA — 3LANL, Advanced Computing Laboratory, MS B287, Los Alamos, NM 87545, USA
It has been shown that both Random Boolean Networks (RBN) and Random Threshold Networks (RTN) exhibit a order-disorder transition at a critical average connectivity Kc in the thermodynamical limit [1,2]. Looking at the statistical distributions of damage spreading for both RBN and RTN, we go beyond this mean-field approximation.
We study the scaling properties of damage size distributions as a function of system size N and initial perturbation size d(t=0) in the sparse percolation (SP) limit (i.e. d(t=0)/N → 0 for large N). We present evidence that another characteristic point, Ks exists for finite systems, where the expectation value of damage spreading in the network is independent of N. We find that damage distributions strongly depend on the order of averages taken over dynamics and network ensembles, possibly limiting the validity of mean-field predictions.
Finally, we discuss the implications of our findings for evolutionary processes and learning applied to networks which solve specific computational tasks.
[1] Derrida, B. and Pomeau, Y. (1986), Europhys. Lett., 1, 45-49
[2] Rohlf, T. and Bornholdt, S. (2002), Physica A 310, 245-259