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The spatial distribution of unvisited/persistent sites in $d=1$ $A+A\to\emptyset$ model is studied numerically. Over length scales smaller than a cut-off $\xi(t)\sim t^{z}$, the set of unvisited sites is found to be a fractal. The fractal…
We introduce a pipeline including multifractal detrended cross-correlation analysis (MF-DXA) modified by either singular value decomposition or the adaptive method to examine the statistical properties of the pulsar timing residual ($PTR$)…
We develop a technique for the multivariate data analysis of perturbed self-sustained oscillators. The approach is based on the reconstruction of the phase dynamics model from observations and on a subsequent exploration of this model. For…
The spectral dimension has been widely used to understand transport properties on regular and fractal lattices. Nevertheless, it has been little studied for complex networks such as scale-free and small world networks. Here we study the…
The length of minimal and maximal blocks equally distant on log-log scale versus fluctuation function considerably influences bias and variance of DFA. Through a number of extensive Monte Carlo simulations and different fractional Brownian…
It is ubiquitous in natural and social sciences that two variables, recorded temporally or spatially in a complex system, are cross-correlated and possess multifractal features. We propose a new method called multifractal detrended…
The fractal or Hausdorff dimension is a measure of roughness (or smoothness) for time series and spatial data. The graph of a smooth, differentiable surface indexed in $\mathbb{R}^d$ has topological and fractal dimension $d$. If the surface…
A new method for examining the possible space-time variation of the fine structure constant ($\alpha$) is proposed. The technique uses a relatively simple measurement with an optical resonator to compare atom-stabilized optical frequency…
Techniques such as detrended fluctuation analysis (DFA) and its extensions have been widely used to determine the nature of scaling in nucleotide sequences. In this brief communication we show that tandem repeats which are ubiquitous in…
As an objective measurement of spatial order in ventricular fibrillation (VF), spatial correlation functions and their characteristic lengths were estimated from epicardial electrograms of pigs in VF. The correlation length of the VF in…
The fluctuation properties of the human electroencephalogram (EEG) time series are studied using detrended fluctuation analysis. For all 128 channels in each of 18 subjects studied, it is found that the standard deviation of the…
This paper serves as a complementary material to a poster presented at the XXXVI Dynamics Days Europe in Corfu, Greece, on June 6th-10th in 2016. In this study, fractal dimension ($D$) of two types of self-affine signals were estimated with…
The Detrending Moving Average (DMA) algorithm has been widely used in its several variants for characterizing long-range correlations of random signals and sets (one-dimensional sequences or high-dimensional arrays) either over time or…
We analyze European temperature variability from station data with the method of detrended fluctuation analysis. This method is known to give a scaling exponent indicating long range correlations in time for temperature anomalies. However,…
In this letter we have analyzed the temporal correlations of the angle-of-arrival fluctuations of stellar images. Experimentally measured data were carefully examined by implementing multifractal detrended fluctuation analysis. This…
This paper extends the existing literature on empirical estimation of the confidence intervals associated to the Detrended Fluctuation Analysis (DFA). We used Montecarlo simulation to evaluate the confidence intervals. Varying the…
We describe an algorithm for simulating ultrasound propagation in random one-dimensional media, mimicking different microstructures by choosing physical properties such as domain sizes and mass densities from probability distributions. By…
Using detrended fluctuation analysis (DFA), we study the scaling properties of the volatility time series $V_i=| T_{i+1}-T_i|$ of daily temperatures $T_i$ for ten chosen sites around the globe. We find that the volatility is long range…
Waves propagating through a weakly scattering random medium show a pronounced branching of the flow accompanied by the formation of freak waves, i.e., extremely intense waves. Theory predicts that this strong fluctuation regime is…
Fractal/non-fractal morphological transitions allow for the systematic study of the physics behind fractal morphogenesis in nature. In these systems, the fractal dimension is considered a non-thermal order parameter, commonly and…