We consider the multifractal spectrum of harmonic measure of a Brownian motion path in two or three dimensions. We show that the multifractal spectrum is nontrivial and relate the spectrum to the intersection exponent. As a corollary we show that harmonic measure on a three dimension Brownian motion path is carried on a set of Hausdorr dimension strictly less than two.

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.

Background Recent studies suggest that time series of healthy human interbeat intervals belong to a special class of bio-signals displaying multifractal properties. The breakdown of multifractality was observed in congestive heart failure and angina pectoris; however, there has been no attempt to evaluate multifractal behavior before and after beating heart myocardial revascularization (off-pum...

This paper deals with multifractal theory applied to image analysis. Multifractals show many interesting peculiarities in the characterization of textured surfaces. In the paper, a method for the computation of multifractal parameters is proposed, together with some application results. Moreover, results are shown that depict the exploitation of such features in a data-fusion environment for SA...

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...

Physiological processes-such as, the brain's resting-state electrical activity or hemodynamic fluctuations-exhibit scale-free temporal structuring. However, impacts common in biological systems such as, noise, multiple signal generators, or filtering by transport function, result in multimodal scaling that cannot be reliably assessed by standard analytical tools that assume unimodal scaling. He...