English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The robustness of two widespread multifractal analysis methods, one based ondetrended fluctuation analysis and one on wavelet leaders, is discussed in thecontext of time-series containing non-uniform structures with only isolatedsingularities. Signals generated by simulated and experimentally-realized chaosgenerators, together with synthetic data addressing particular aspects, aretaken into consideration. The results reveal essential limitations affectingthe ability of both methods to correctly infer the non-multifractal nature ofsignals devoid of a cascade-like hierarchy of singularities. Namely, signalsharboring only isolated singularities are found to artefactually give rise tobroad multifractal spectra, resembling those expected in the presence of awell-developed underlying multifractal structure. Hence, there is a real riskof incorrectly inferring multifractality due to isolated singularities. Thecareful consideration of local scaling properties and the distribution ofH\"older exponent obtained, for example, through wavelet analysis, isindispensable for rigorously assessing the presence or absence ofmultifractality.

Wavelet-based discrimination of isolated singularities masquerading as multifractals in detrended fluctuation analyses