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Extreme fluctuations in noisy task-completion landscapes on scale-free networks
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10.1063/1.2735446
/content/aip/journal/chaos/17/2/10.1063/1.2735446
http://aip.metastore.ingenta.com/content/aip/journal/chaos/17/2/10.1063/1.2735446

Figures

Image of FIG. 1.
FIG. 1.

(a) The scaled distribution of the width of task-completion landscapes on a one-dimensional regular network. The inset is the same graph in log-linear scale. The dashed curve is the scaled width distribution of the KPZ/EW surface (Ref. 86 ). (b) The scaled distribution of the maximum fluctuations in the same network. The inset is in log-linear scale and the dashed curve is the appropriately scaled Airy distribution function (Refs. 53 and 54 ).

Image of FIG. 2.
FIG. 2.

Steady-state width of the EW synchronization landscape from exact numerical diagonalization using Eq. (29) . (a) For the BA network, as a function of for various values of the minimum degree . The inset shows the same data on log-linear scales. (b) For the BA network, as a function of for different system sizes . The inset shows the behavior of the width vs ; the solid straight line represents the MF result [Eq. (28) ]. (c) For the BA and CM networks (with and ) as a function of , where is the average degree, for two system sizes. The bold straight solid and dashed lines correspond to the MF result [Eq. (28) ] with and , respectively.

Image of FIG. 3.
FIG. 3.

Average maximum fluctuations and average width for SF networks generated by the BA model. The data points are obtained by averaging over ten different network realizations. (a) Maximum fluctuations vs . (b) Maximum fluctuations vs system size. (c) Width vs . (d) Width vs system size.

Image of FIG. 4.
FIG. 4.

Average maximum fluctuations and the width for SF CM networks with . The data points are obtained by averaging over ten different network realizations. (a) Maximum fluctuations vs . (b) Maximum fluctuations vs system size. (c) Width vs . (d) Width vs system size.

Image of FIG. 5.
FIG. 5.

Distributions of (a) individual fluctuations, (b) maximum fluctuations, and (c) the width for the BA model with . The different individual fluctuations distributions in (a) are for different degree values ranging from the maximum to the minimum. The insets in (b) and (c) show the same distributions of the main graph but scaled to zero mean and unit variance in a log-linear scale. The dashed curves in the insets represent the Gumbel pdf [Eq. (16) ] in (b) and Gaussian pdf in (c) scaled in the same way. The system size is .

Image of FIG. 6.
FIG. 6.

Same as Fig. 5 for the CM network with and .

Tables

Generic image for table
Table I.

Domain of attractions of the most common distributions for the maximum of iid random variables.

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/content/aip/journal/chaos/17/2/10.1063/1.2735446
2007-06-28
2014-04-16
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Extreme fluctuations in noisy task-completion landscapes on scale-free networks
http://aip.metastore.ingenta.com/content/aip/journal/chaos/17/2/10.1063/1.2735446
10.1063/1.2735446
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