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Degeneracy and long-range correlations
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View: Figures


Image of FIG. 1.
FIG. 1.

Redundancy and degeneracy in networks models. These two panels represent hypothetical networks performing a function by transmitting information from the upper level to the lower one. The left panel illustrates a redundant system, in which several distinct pathways perform the same function. The right panel corresponds to a degenerate network: components could belong to several pathways, and then neighbor pathways share common components.

Image of FIG. 2.
FIG. 2.

Illustration of the hopping model. The random walk selects successively the variables , , , , , and . The dashed boxes indicate the size (here  = 4) of the correlated zones.

Image of FIG. 3.
FIG. 3.

Example series produced by the hopping model ( = 1024). From top to bottom,  = 10,  = 50,  = 100, and  = 200.

Image of FIG. 4.
FIG. 4.

Fractal properties of the series produced by the model, as a function of degeneracy () and of the width of the correlation window (). Left: Percentage of series best modeled by ARMIFA models, as a function of . Median panel: Mean sum of ARFIMA weights, as a function of . Right panel: Evolution of the mean α exponent with . Error bars represent 95% confidence intervals.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Degeneracy and long-range correlations