We examine the detrended fluctuation analysis (DFA), which is a well-established method for the detection of long-range correlations in time series. We show that deviations from scaling which appear at small time scales become stronger in higher orders of DFA, and suggest a modified DFA method...

We study the effects of Parkinson's disease (PD) on the long-term fluctuation and phase synchronization properties of gait timing (series of interstride intervals) as well as gait force profiles (series characterizing the morphological changes between the steps). We find that the fluctuations in...

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 technique and obtain agreement within the error margins....

The persistence of the weather is a well-known phenomenon. If, for example, one day is sunny and warm, there is a high tendency that the next day remains similar. In this paper, we review recent results showing that the long-term persistence, characterized by the correlation C(s) of temperature...

The persistence of short term weather states is a well known phenomenon: A warm day is more likely to be followed by a warm day than by a cold one and vice versa. Using advanced methods from statistical physics that are able to distinguish between trends and persistence we have shown recently...

We study trends and temporal correlations in the monthly mean temperature data of Prague and Melbourne derived from four state-of-the-art general circulation models that are currently used in studies of anthropogenic effects on the atmosphere: GFDL-R15-a, CSIRO-Mk2, ECHAM4/OPYC3 and HADCM3. In...

We study two aspects of the detrended fluctuation analysis (DFA) method, namely the scaling behavior of the leading terms of the best-fit polynomials and the detection of trends. We show analytically and numerically that the standard deviation of the leading terms of the best-fit polynomials...

A method for embedding graphs in Euclidean space is suggested. The method connects nodes to their geographically closest neighbors and economizes on the total physical length of links. The topological and geometrical properties of scale-free networks embedded by the suggested algorithm are...

An explicit functional integral solution for the logistic map is presented. Furthermore, the discrete nature of this equation is used to explicitly calculate the corresponding Radon–Nikodym derivatives. This enables us to represent the solution as a multidimensional integral.

We study the localization of electronic wave functions in the one-dimensional Anderson model with diagonal disorder, where the site energies are long-range correlated. We find different behavior at the band edge and at the band center. Close to the band edge, the correlations lead to a decrease...