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 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....

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...

We investigate the local cumulative phases at single sites of the lattice for time-dependent wave functions in the Anderson model in d=2 and 3. In addition to a local linear trend, the phases exhibit some fluctuations. We study the time correlations of these fluctuations using detrended...

Many natural records exhibit long-term correlations characterized by a power-law decay of the auto-correlation function, C(s)∼s−γ, with time lag s and correlation exponent 0γ1. We study, how the presence of such correlations affects the statistics of the return intervals rq for events...

We present an efficient technique for the study of quasi-periodic oscillations in noisy, non-stationary signals, which allows the assessment of system dynamics despite phase resetting and noise. It is based on the definition of anchor points in the signal (in the simplest case increases or...

We show that the method of level statistics can be applied successfully to investigate the localization behavior of vibrations and spin-wave states on the infinite percolation cluster for p⩾pc. The fluctuations of the density of states are well described within the framework of random matrix...

We study the performance of multifractal detrended fluctuation analysis (MF-DFA) applied to long-term correlated and multifractal data records in the presence of additive white noise, short-term memory and periodicities. Such additions and disturbances that can be typically found in the...

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...