Multifractal analysis based on the weak scaling exponent and applications to MEG recordings in neuroscience

Abstract

We develop the mathematical properties of a multifractal analysis of data based on the weak scaling exponent. The advantage of this analysis is that it does not require any a priori global regularity assumption on the analyzed signal, in contrast with the previously used H\"older or p-exponents. As an illustration, we show that this technique allows one to perform a multifractal analysis of MEG signals, which records electromagnetic brain activity, that was not theoretically valid using the formerly introduced methods based on H\"older or p-exponents.

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Reproductions