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MULTIFRACTAL PROPERTIES OF THE SETS OF ZEROES OF BROWNIAN PATHS
independent random variables Brownian motion local time Hausdor
2015/9/29
In this paper we study Brownian zeroes in the neighborhood of which one can observe non-typical growth
rate of Brownian excursions. We interprete the multifractal curve for the Brownian zeroes calcul...
Multifractal analysis of some multiple ergodic averages for the systems with non-constant Lyapunov exponents
Multifractal analysis of some multiple ergodic averages non-constant Lyapunov exponents Dynamical Systems
2012/6/27
We study certain multiple ergodic averages of an iterated functions system generated by two contractions on the unit interval. By using the dynamical coding ${0,1}^{\mathbb{N}}$ of the attractor, we c...
Geometrical exponents of contour loops on synthetic multifractal rough surfaces: multiplicative hierarchical cascade p-model
Geometrical exponents contour loops multiplicative hierarchical cascade p-model
2011/8/18
Abstract: In this paper, we study many geometrical properties of the contour loops to characterize the morphology of typical synthetic multifractal surfaces following multiplicative hierarchical casca...
Probing Tissue Multifractality Using Wavelet based Multifractal Detrended Fluctuation Analysis: Applications in Precancer Detection
Fractal Multifractal detrended fluctuation analysis Phase contrast imaging Refractive index Cancer diagnosis
2011/8/4
Abstract: The refractive index fluctuations in the connective tissue layer (stroma) of human cervical tissues having different grades of precancers (dysplasia) was quantified using a wavelet-based mul...
Perturbation approach to multifractal dimensions for certain critical random matrix ensembles
multifractal dimensions Perturbation random matrix ensembles
2011/7/6
Fractal dimensions of eigenfunctions for various critical random matrix ensembles are investigated in perturbation series in the regimes of strong and weak multifractality. In both regimes we obtain e...
Computational approach to multifractal music
Fractal, Fractal dimension, Mulifractality, Singularity spectrum
2011/9/1
In this work we perform a fractal analysis of 160 pieces of music belonging to six different genres. We show that the majority of the pieces reveal characteristics that allow us to classify them as ph...
Discrete to continuum transition in multifractal spacetimes
multifractal spacetimes continuum transition High Energy Physics - Theory
2011/7/27
Abstract: We outline a field theory on a multifractal spacetime. The measure in the action is characterized by a varying Hausdorff dimension and logarithmic oscillations governed by a fundamental phys...
Linearization effect in multifractal analysis: Insights from Random Energy Model analysis
Multifractal analysis linearization effect compound Poisson motion
2011/3/3
The analysis of the linearization effect in multifractal analysis, and hence of the estimation of moments for multifractal processes, is revisited borrowing concepts from the statistical physics of di...
Linearization effect in multifractal analysis: Insights from Random Energy Model analysis
Linearization effect multifractal analysis Random Energy Model analysis
2011/1/4
The analysis of the linearization effect in multifractal analysis, and hence of the estimation of moments for multifractal processes, is revisited borrowing concepts from the statistical physics of di...
Multifractal structure of Bernoulli convolutions
Multifractal structure Bernoulli convolutions
2010/11/15
Let $\nu_\lambda^p$ be the distribution of the random series $\sum_{n=1}^\infty i_n \lambda^n$, where $i_n$ is a sequence of i.i.d. random variables taking the values 0,1 with probabilities $p,1-p$. T...
Optimal transport for multifractal random measures. Applications
Random measures multifractal processes optimal transport metric KPZ
2010/11/26
In this paper, we study optimal transportation problems for multifractal random measures. Since these measures are much less regular than optimal transportation theory requires, we introduce a new not...
Typical Borel measures on $[0,1]d$ satisfy a multifractal formalism
Borel measures Hausdorff dimension Multifractal anal-ysis Baire categories
2010/11/29
In this article, we prove that in the Baire category sense, measures supported by the unit cube of Rd typically satisfy a multifractal formalism. To achieve this, we compute explicitly the multifracta...
Spectral and multifractal study of electroseismic time series associated to the Mw=6.5 earthquake of 24 October 1993 in Mexico
Spectral and multifractal study electroseismic time series
2009/12/14
In this work we present a spectral and multifractal study of the electric self-potential fluctuations registered in an electroseismic station located at 100km from the epicenter of an earthquake (EQ) ...
Dynamics of multifractal and correlation characteristics of the spatio-temporal distribution of regional seismicity before the strong earthquakes
multifractal and correlation characteristics spatio-temporal distribution regional seismicity
2009/12/11
Investigations of the distribution of regional seismicity and the results of numerical simulations of the seismic process show the increase of inhomogenity in spatio-temporal distribution of the seism...
Monofractal or multifractal:a case study of spatial distribution of mining-induced seismic activity
spatial distribution mining-induced seismic activity
2009/11/16
Using finite data sets and limited size of study volumes may result in significant spurious effects when estimating the scaling properties of various physical processes. These effects are examined wit...