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.
Illustration of the hopping model. The random walk selects successively the variables δj +1, δj +3, δj +5, δj +2, δj +7, and δj +6. The dashed boxes indicate the size (here r = 4) of the correlated zones.
Example series produced by the hopping model (N = 1024). From top to bottom, γ = 10, γ = 50, γ = 100, and γ = 200.
Fractal properties of the series produced by the model, as a function of degeneracy (γ) and of the width of the correlation window (r). Left: Percentage of series best modeled by ARMIFA models, as a function of γ. Median panel: Mean sum of ARFIMA weights, as a function of γ. Right panel: Evolution of the mean α exponent with γ. Error bars represent 95% confidence intervals.
Article metrics loading...
Full text loading...