Multifractal Analysis for Nutritional Assessment

Multifractal Analysis for Nutritional Assessment

The concept of multifractality is currently used to describe self-similar and complex scaling properties observed in numerous biological signals. Fractals are geometric objects or dynamic variations which exhibit some degree of similarity (irregularity) to the original object in a wide range of scales. This approach determines irregularity of biologic signal as an indicator of adaptability, the...

Multifractal analysis for all

Multifractal formalism and analysis have been described many times (Lopes and Betrouni, 2009). There are several approaches to the implementation of multifractal analysis and there numerous ways to present these (Olsen, 1995; Wendt et al., 2009; Ihlen, 2012). Ihlen’s article, in the June 4th 2012 issue of Frontiers of Physiology, entitled “Introduction to multifractal detrended fluctuation anal...

Multifractal Analysis for Multimodal Maps

Given a multimodal interval map f : I → I and a Hölder potential ' : I → R, we study the dimension spectrum for equilibrium states of '. The main tool here is inducing schemes, used to overcome the presence of critical points. The key issue is to show that enough points are ‘seen’ by a class of inducing schemes. We also compute the Lyapunov spectrum. We obtain the strongest results when f is a ...

Box-counting multifractal analysis.

Local Multifractal Analysis

We introduce a local multifractal formalism adapted to functions, measures or distributions which display multifractal characteristics that can change with time, or location. We develop this formalism in a general framework and we work out several examples of measures and functions where this setting is relevant.