A new generation of instruments in astrophysics or vision now provide spherical data. These spherical data may present a selfsimilarity property while no spherical analysis tool is yet available to characterize this property. In this paper we present a first numerical study of the extension of multifractal analysis onto the sphere using spherical wavelet transforms. We use a model of multifract...

We define a large class of multifractal random measures and processes with arbitrary loginfinitely divisible exact or asymptotic scaling law. These processes generalize within a unified framework both the recently defined log-normal Multifractal Random Walk processes (MRW) [33, 3] and the log-Poisson “product of cynlindrical pulses” [7]. Their construction involves some “continuous stochastic m...

We use a recently developed a priori theory of diffusion-limited aggregation (DLA) to compute multifractal dimensions and their fluctuations, using methods analogous to field theoretical resummations. There are two regimes, depending upon n, the number of particles in the DLA cluster, as well as on the multifractal moment q. In the strongly fluctuating regime quenched and annealed dimensions di...

Irregularities in the amplitude and period are characteristic of both normal and pathological sustained vowels; they are a product of perturbations inherent in the phonation process. Their analysis provides useful diagnostic information for several vocal pathologies, and their accurate modelling has been shown to improve the quality of synthesized voice. In this work, we propose the application...

Ozone is a secondary pollutant that, at high concentrations in urban environment, affects human health. Thus, suitable knowledge of ozone dynamics is essential for avoiding undesirable effects on the population. Ten-minute ozone concentration time series recorded at Córdoba (southern Spain) in 2007, for January, April, July and October, have been analysed by using the strange attractor multifra...

This paper demonstrates that the Joint Probability Distribution (JPD) of a Bayesian network is a random multinomial multifractal. With sufficient asymmetry in individual prior and conditional probability distributions, the JPD is not only highly skewed as shown by Druzdzel [3], but also is stochastically self-similar and has clusters of highprobability instantiations at all scales. Based on the...

The large deviation multifractal spectrum is a function of central importance in multifractal analysis. It allows a ne description of the distribution of the singularities of a function over a given domain. The 2-microlocal spectrum, on the other hand, provides an extremely precise picture of the regularity of a distribution at a point. These two spectra display a number of similarities: their ...

In this work, we investigate the fine regularity of Lévy processes using the 2-microlocal formalism. This framework allows us to refine the multifractal spectrum determined by Jaffard and, in addition, study the oscillating singularities of Lévy processes. The fractal structure of the latter is proved to be more complex than the classic multifractal spectrum and is determined in the case of alp...

Separation of geochemical anomalies from background has always been a major concern of exploration geochemistry. The search for methods that can make this analysis quantitative and objective aims not only at the reduction of subjectiveness but also at providing an automatic routine in exploration, assisting the interpretation and production of geochemical maps. This report discusses two methodo...

Based on fractal theory and damage mechanics, the aim of this paper is to describe the monofractal and multifractal characteristics of corrosion morphology and develop a new approach to characterize the nonuniform corrosion degree of reinforcing bars. The relationship between fractal parameters and tensile strength of reinforcing bars are discussed. The results showed that corrosion mass loss r...