Related papers: Detrended fluctuation analysis for fractals and mu…
We provide an alternative method for analysis of multifractal properties of time series. The new approach takes into account the behaviour of the whole multifractal profile of the generalized Hurst exponent $h(q)$ for all moment orders $q$,…
The blasting of brittle materials with sharp particles is an important fabrication technology in many industrial processes. In particular, for micro-systems, it allows the production of devices with feature sizes down to few tens of…
Stock markets can become inefficient due to calendar anomalies known as day-of-the-week effect. Calendar anomalies are well-known in financial literature, but the phenomena remain to be explored in econophysics. In this paper we use…
A dynamic scaling of a diffusion process involving the Langmuir type adsorption is studied. We find dynamic scaling functions in one and two dimensions and compare them with direct numerical simulations, and we further study the dynamic…
In this paper, we present an assortment of both standard and advanced Fourier techniques that are useful in the analysis of astrophysical time series of very long duration -- where the observation time is much greater than the time…
It is the purpose of the paper to describe the virtues of time-frequency methods for signal processing applications, having astronomical time series in mind. Different methods are considered and their potential usefulness respectively…
Multifractal analysis techniques are applied to patterns in several abstract expressionist artworks, paintined by various artists. The analysis is carried out on two distinct types of structures: the physical patterns formed by a specific…
We present a topology optimization (TO) method for a 1D dielectric metasurface, coupling the classical trend-fluctuations analysis (FTA) and the diamond-square-algorithm (DSA). In the classical FTA, a couple of device distributions termed…
A theory of time and space with fractional dimensions (FD) of time and space ($d_{\alpha}, \alpha=t,{\bf r})$ defined on multifractal sets is proposed. The FD is determined (using principle of minimum the functionals of FD) by the energy…
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…
Multifractality is ubiquitously observed in complex natural and socioeconomic systems. Multifractal analysis provides powerful tools to understand the complex nonlinear nature of time series in diverse fields. Inspired by its striking…
We provide a rigorous study on dimensions of fractal interpolation function defined on a closed and bounded interval of $\mathbb{R}$ which is associated to a continuous function with respect to a base function, scaling functions and a…
Multifractal analysis has become a powerful signal processing tool that characterizes signals or images via the fluctuations of their pointwise regularity, quantified theoretically by the so-called multifractal spectrum. The practical…
Fractal grids generate turbulence by exciting many length scales of different sizes simultaneously rather than using the nonlinear cascade mechanism to obtain multi-scale structures, as it is the case for regular grids. The interest in…
The harmonic measure (or diffusion field or electrostatic potential) near a percolation cluster in two dimensions is considered. Its moments, summed over the accessible external hull, exhibit a multifractal spectrum, which I calculate…
Many multi-dimensional signals appear in the real world, such as digital images and data that has spatial and temporal dimensions. How to show the spectrum of these multi-dimensional signals correctly is a key challenge in the field of…
Complex networks have recently attracted much attention in diverse areas of science and technology. Many networks such as the WWW and biological networks are known to display spatial heterogeneity which can be characterized by their fractal…
Eigenstate multifractality is of significant interest with potential applications in various fields of quantum physics. Most of the previous studies concentrated on fine-tuned quantum models to realize multifractality which is generally…
We study the multifractal temporal scaling properties of river discharge and precipitation records. We compare the results for the multifractal detrended fluctuation analysis method with the results for the wavelet transform modulus maxima…
For a long time, many methods are developed to make temporal signal analyses based on time series. However, for geographical systems, spatial signal analyses are as important as temporal signal analyses. Nonstationary spatial and temporal…