Related papers: On Multifractal Structure in Non-Representational …
This paper proposes a novel algorithm for the problem of structural image segmentation through an interactive model-based approach. Interaction is expressed in the model creation, which is done according to user traces drawn over a given…
The concept of multifractality offers a powerful formal tool to filter out multitude of the most relevant characteristics of complex time series. The related studies thus far presented in the scientific literature typically limit themselves…
We present a statistical analysis of music scores from different composers using detrended fluctuation analysis. We find different fluctuation profiles that correspond to distinct auto-correlation structures of the musical pieces. Further,…
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 expressions similar to those of the…
The epitaxial growth of complex oxide thin films provide three avenues to generate unique properties: the ability to influence the 3-dimensional structure of the film, the presence of a surface, and the generation of an interface. In all…
Multifractal analysis studies signals, functions, images or fields via the fluctuations of their local regularity along time or space, which capture crucial features of their temporal/spatial dynamics. It has become a standard signal and…
Multifractal scaling (MFS) refers to structures that can be described as a collection of interwoven fractal subsets which exhibit power-law spatial scaling behavior with a range of scaling exponents (concentration, or singularity,…
A matrix pattern is often either a sign pattern with entries in {0,+,-} or, more simply, a nonzero pattern with entries in {0,*}. A matrix pattern A is spectrally arbitrary if for any choice of a real matrix spectrum, there is a real matrix…
A multi-scale approach to the inverse reconstruction of a pattern's microstructure is reported. Instead of a correlation function, a pair of entropic descriptors (EDs) is proposed for stochastic optimization method. The first of them…
The coupling space of perceptrons with continuous as well as with binary weights gets partitioned into a disordered multifractal by a set of $p=\gamma N$ random input patterns. The multifractal spectrum $f(\alpha)$ can be calculated…
A method for estimating the relative content of crystalline phases of a multiphase sample, based on probabilistic analysis of the intensities of the diffraction pattern reflexes, has been developed. The method is based on the introduction…
We analyze invariant measures of two coupled piecewise linear and everywhere expanding maps on the synchronization manifold. We observe that though the individual maps have simple and smooth functions as their stationary densities, they…
The diversity of painting styles represents a rich visual vocabulary for the construction of an image. The degree to which one may learn and parsimoniously capture this visual vocabulary measures our understanding of the higher level…
Dark-field x-ray microscopy utilizes Bragg diffraction to collect full-field x-ray images of "mesoscale" structure of ordered materials. Information regarding the structural heterogeneities and their physical implications is gleaned through…
Patterns, which are collections of elements arranged in regular or near-regular arrangements, are an important graphic art form and widely used due to their elegant simplicity and aesthetic appeal. When a pattern is encoded as a flat image…
We present a novel method for determining multi-fractal properties from experimental data. It is based on maximising the likelihood that the given finite data set comes from a particular set of parameters in a multi-parameter family of well…
We present a formalism that leads very naturally to a hierarchical description of the different contrast structures in images, providing precise definitions of sharp edges and other texture components. Within this formalism, we achieve a…
Many fluctuating systems consist of macroscopic structures in addition to noisy signals. Thus, for this class of fluctuating systems, the scaling behaviors are very complicated. Such phenomena are quite commonly observed in Nature, ranging…
We develop a method for the multifractal characterization of nonstationary time series, which is based on a generalization of the detrended fluctuation analysis (DFA). We relate our multifractal DFA method to the standard partition…
In the first section we review recent results on the harmonic analysis of fractals generated by iterated function systems with emphasis on spectral duality. Classical harmonic analysis is typically based on groups whereas the fractals are…