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Register a new userFluctuations in network dynamics
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Added by
Marcio Argollo de Menezes
Publication date
2003
fields
Physics
and research's language is
English
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Most complex networks serve as conduits for various dynamical processes, ranging from mass transfer by chemical reactions in the cell to packet transfer on the Internet. We collected data on the time dependent activity of five natural and technological networks, finding that for each the coupling of the flux fluctuations with the total flux on individual nodes obeys a unique scaling law. We show that the observed scaling can explain the competition between the systems internal collective dynamics and changes in the external environment, allowing us to predict the relevant scaling exponents.
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The parallel dynamics of the fully connected Blume-Emery-Griffiths neural network model is studied for arbitrary temperature. By employing a probabilistic signal-to-noise approach, a recursive scheme is found determining the time evolution of the distribution of the local fields and, hence, the evolution of the order parameters. A comparison of this approach is made with the generating functional method, allowing to calculate any physical relevant quantity as a function of time. Explicit analytic formula are given in both methods for the first few time steps of the dynamics. Up to the third time step the results are identical. Some arguments are presented why beyond the third time step the results differ for certain values of the model parameters. Furthermore, fixed-point equations are derived in the stationary limit. Numerical simulations confirm our theoretical findings.
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We employ a functional renormalization group to study interfaces in the presence of a pinning potential in $d=4-epsilon$ dimensions. In contrast to a previous approach [D.S. Fisher, Phys. Rev. Lett. {bf 56}, 1964 (1986)] we use a soft-cutoff scheme. With the method developed here we confirm the value of the roughness exponent $zeta approx 0.2083 epsilon$ in order $epsilon$. Going beyond previous work, we demonstrate that this exponent is universal. In addition, we analyze the generation of higher cumulants in the disorder distribution and the role of temperature as a dangerously irrelevant variable.
We review three studies of information flow in social networks that help reveal their underlying social structure, how information spreads through them and why small world experiments work.
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