Related papers: A case study of stratus cloud base height multifra…
The unsupervised and principled diagnosis of multi-scale data is a fundamental obstacle in modern scientific problems from, for instance, weather and climate prediction, neurology, epidemiology, and turbulence. Multi-scale data is…
A fractal is in essence a hierarchy with cascade structure, which can be described with a set of exponential functions. From these exponential functions, a set of power laws indicative of scaling can be derived. Hierarchy structure and…
We show that it can be considered some of Bach pitches series as a stochastic process with scaling behavior. Using multifractal deterend fluctuation analysis (MF-DFA) method, frequency series of Bach pitches have been analyzed. In this view…
In this paper, a systematic analysis of hourly wind speed data obtained from four potential wind generation sites in North Dakota is conducted. The power spectra of the data exhibited a power law decay characteristic of $1/f^{\alpha}$…
We consider two sequential models of deposition and aggregation for particles. The first model (No Diffusion) simulates surface diffusion through a deterministic capture area, while the second (Sequential Diffusion) allows the atoms to…
We examine the scaling regime for the detrended fluctuation analysis (DFA) - the most popular method used to detect the presence of long memory in data and the fractal structure of time series. First, the scaling range for DFA is studied…
Recently, fractional derivatives have been employed to analyze various systems in engineering, physics, finance and hidrology. For instance, they have been used to investigate anomalous diffusion processes which are present in different…
We consider a broad class of Continuous Time Random Walks with large fluctuations effects in space and time distributions: a random walk with trapping, describing subdiffusion in disordered and glassy materials, and a L\'evy walk process,…
Fluctuations in small biological systems can be crucial for their function. Large-deviation theory characterizes such rare events from the perspective of stochastic processes. In most cases it is very difficult to directly determine the…
On microscopic and mesoscopic scales, plastic flow of crystals is characterized by large intrinsic fluctuations. Deformation by crystallographic slip occurs in a sequence of intermittent bursts ('slip avalanches') with power-law size…
Some years ago we proposed a new approach to the analysis of galaxy and cluster correlations based on the concepts and methods of modern statistical Physics. This led to the surprising result that galaxy correlations are fractal and not…
We study the nature of fluctuations in variety of price indices involving companies listed on the New York Stock Exchange. The fluctuations at multiple scales are extracted through the use of wavelets belonging to Daubechies basis. The fact…
Zonal jets manifest themselves as bands with sharp interfaces in the vorticity configuration. We develop an algorithm to track these fluctuating vorticity interfaces and systematically investigate their characteristic spatio-temporal…
Based on the Multifractal Detrended Fluctuation Analysis (MFDFA) and on the Wavelet Transform Modulus Maxima (WTMM) methods we investigate the origin of multifractality in the time series. Series fluctuating according to a qGaussian…
This is a short note on the spatiotemporal complexity of the dynamical state(s) of the universe at subhorizon scales (up to 300 Mpc). There are reasons, based mainly on infrared radiative divergences, to believe that one can encounter a…
Recently the statistical characterizations of financial markets based on physics concepts and methods attract considerable attentions. We used two possible procedures of analyzing multifractal properties of a time series. The first one uses…
This paper establishes the consistency of spectral approaches to data clustering. We consider clustering of point clouds obtained as samples of a ground-truth measure. A graph representing the point cloud is obtained by assigning weights to…
The numerical experiments of turbulence conducted by Gotoh et al. are analyzed precisely with the help of the formulae for the scaling exponents of velocity structure function and for the probability density function (PDF) of velocity…
This article illustrates the application of multiple scales analysis to two archetypal quasilinear systems; i.e. to systems involving fast dynamical modes, called fluctuations, that are not directly influenced by fluctuation--fluctuation…
We show that the daily average air humidity fluctuations exhibit non-trivial $1/f^{\alpha}$ behaviour which different from the spectral properties of other meteorological quantities. This feature and the fractal spatial strucure found in…