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A mathematical method for constructing fractal curves and surfaces, termed the $p\lambda n$ fractal decomposition, is presented. It allows any function to be split into a finite set of fractal discontinuous functions whose sum is equal…
This paper is concerned mainly with the macroscopic fractal behavior of various random sets that arise in modern and classical probability theory. Among other things, it is shown here that the macroscopic behavior of Boolean coverage…
We present a theoretical and numerical study on the motion of isotropic helicoids in complex flows. These are particles whose motion is invariant under rotations but not under mirror reflections of the particle. This is the simplest, yet…
If our aesthetic preferences are affected by fractal geometry of nature, scaling regularities would be expected to appear in all art forms, including music. While a variety of statistical tools have been proposed to analyze time series in…
A gray-level image texture descriptors based on fractal dimension estimation is proposed in this work. The proposed method estimates the fractal dimension using probability (Voss) method. The descriptors are computed applying a multiscale…
Most of the known methods for estimating the fractal dimension of fractal sets are based on the evaluation of a single geometric characteristic, e.g. the volume of its parallel sets. We propose a method involving the evaluation of several…
Fluid flows such as gases or liquids exhibit space-time fluctuations on all scales extending down to molecular scales. Such broadband continuum fluctuations characterise all dynamical systems in nature and are identified as selfsimilar…
In the last few years, new insights have permitted unexpected progress in the study of fractal shapes in two dimensions. A new approach, called Schramm-Loewner evolution, or SLE, has arisen through analytic function theory and probability…
We employed the method of virial expansion in order to compute the retarded density correlation function (generalized diffusion propagator) in the critical random matrix ensemble in the limit of strong multifractality. We found that the…
Leaky waves are an important class of waves, particularly for guiding waves along structures embedded within another medium; a mismatch in wavespeeds often leads to leakage of energy from the waveguide, or interface, into the medium, which…
Analysis and modeling of networked objects are fundamental pieces of modern data mining. Most real-world networks, from biological to social ones, are known to have common structural properties. These properties allow us to model the growth…
I report the results of the test, where the takers had to tell true masterpieces of abstract art from the fakes, produced by me. I describe each picture by the fraction of the test takers, who selected it as a masterpiece. When I compare…
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…
We introduce a large class of random Young diagrams which can be regarded as a natural one-parameter deformation of some classical Young diagram ensembles; a deformation which is related to Jack polynomials and Jack characters. We show that…
Fabricating experimental pictures in research work is a serious academic misconduct, which should better be detected in the reviewing process. However, due to large number of submissions, the detection whether a picture is fabricated or…
We consider an ideal invisibility cloak which is illuminated by monochromatic light and which moves in vacuum at constant relativistic velocity with respect to the common inertial frame of light source and observer. We show that, in…
Multiple scattering is a process in which a particle is repeatedly deflected by other particles. In an overwhelming majority of cases, the ensuing random walk can successfully be described through Gaussian, or normal, statistics. However,…
When an ensemble of particles interact hydrodynamically, they generically display large-scale transient structures such as swirls in sedimenting particles [1], or colloidal strings in sheared suspensions [2]. Understanding these…
The fractal nature of complex networks has received a great deal of research interest in the last two decades. Similarly to geometric fractals, the fractality of networks can also be defined with the so-called box-covering method. A network…
It was demonstrated that there is a geometrical order in the structure of literature. Fractal geometry as a modern mathematical approach and a new geometrical viewpoint on natural objects including both processes and structures was employed…