We examine several recently suggested methods for the detection of long-range correlations in data series based on similar ideas as the well-established Detrended Fluctuation Analysis (DFA). In particular, we present a detailed comparison between the regular DFA and two recently suggested...

Healthy sleep can be characterized by several stages: deep sleep, light sleep, and REM sleep. Here we show that these sleep stages lead to different autonomic regulation of breathing. Using the detrended fluctuation analysis up to the fourth order we find that breath-to-breath intervals and...

We develop a method for the multifractal characterization of nonstationary time series, which is based on a generalization of the detrended fluctuation analysis (DFA). We relate our multifractal DFA method to the standard partition function-based multifractal formalism, and prove that both...

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...