Recent years have witnessed a great research boom in soft matter physics. By now, most advances, however, are of empirical results or purely mathematical extensions. The major obstacle is lacking of insights into fundamental physical laws underlying fractal mesostructures of soft matter. This study will use fractional mathematics, which consists of fractal, fractional calculus, fractional Brown...

In this paper, we explore modern methods and algorithms from fractal/chaotic systems theory for modeling speech signals in a multidimensional phase space and extracting characteristic invariant measures like generalized fractal dimensions and Lyapunov exponents. Such measures can capture valuable information for the characterisation of the multidimensional phase space which is closer to the tru...

This work proposes and study the concept of Functional Data Analysis transform, applying it to the performance improving of volumetric Bouligand-Minkowski fractal descriptors. The proposed transform consists essentially in changing the descriptors originally defined in the space of the calculus of fractal dimension into the space of coefficients used in the functional data representation of the...

A semigroup St of continuous operators in a Hilbert space H is considered. It is shown that the fractal dimension of a compact strictly invariant set X (X b H, StX = X) admits the same estimate as the Hausdorff dimension, namely, both are bounded from above by the Lyapunov dimension calculated in terms of the global Lyapunov exponents. Applications of the results so obtained to the two–dimensio...

The present work shows a novel fractal dimension method for shape analysis. The proposed technique extracts descriptors from a shape by applying a multi-scale approach to the calculus of the fractal dimension. The fractal dimension is estimated by applying the curvature scale-space technique to the original shape. By applying a multi-scale transform to the calculus, we obtain a set of descripto...

We introduce an algorithm for a search of extremal fractal curves in large curve classes. It heavily uses SAT-solvers—heuristic algorithms that find models CNF boolean formulas. Our was implemented and applied to the surjective $$\gamma :[0,1]\rightarrow [0,1]^d$$ with minimal dilation $$\begin{aligned} \sup _{t_1<t_2}\frac{\Vert \gamma (t_2)-\gamma (t_1)\Vert ^d}{t_2-t_1}. \end{aligned}$$ repo...

Comparative complexity analysis of EEGsignals registered before and after exposure to strong white light was performed using nonlinear quantifiers fractal dimension and cumulative pattern entropy of the signal. Some subjects are strongly influenced by exposure to light whereas others are unresponsive. Introduction The main analytical paradigm for EEG analysis has been its spectral decomposition...