Comparison of models and lattice-gas simulations for Liesegang patterns

For more than a century Liesegang patterns -- self-organized, quasi-periodic structures occurring in diffusion-limited chemical reactions with two components -- have been attracting scientists. The pattern formation can be described by four basic empirical laws. In addition to many experiments, several models have been devised to understand the formation of the bands and rings. Here we review the most important models and complement them with detailed three-dimensional lattice-gas simulations. We show how the mean-field predictions can be reconciled with experimental data by a redefinition of the distances suggested by our lattice-gas simulations.Comment: 21 pages, 9 figures, accepted for publication in EPJ Special Topic

Modulations of Heart Rate, ECG, and Cardio-Respiratory Coupling Observed in Polysomnography

The cardiac component of cardio-respiratory polysomnography is covered by ECG and heart rate recordings. However their evaluation is often underrepresented in summarizing reports. As complements to EEG, EOG, and EMG, these signals provide diagnostic information for autonomic nervous activity during sleep. This review presents major methodological developments in sleep research regarding heart rate, ECG and cardio-respiratory couplings in a chronological (historical) sequence. It presents physiological and pathophysiological insights related to sleep medicine obtained by new technical developments. Recorded nocturnal ECG facilitates conventional heart rate variability analysis, studies of cyclical variations of heart rate, and analysis of ECG waveform. In healthy adults, the autonomous nervous system is regulated in totally different ways during wakefulness, slow-wave sleep, and REM sleep. Analysis of beat-to-beat heart-rate variations with statistical methods enables us to estimate sleep stages based on the differences in autonomic nervous system regulation. Furthermore, up to some degree, it is possible to track transitions from wakefulness to sleep by analysis of heart-rate variations. ECG and heart rate analysis allow assessment of selected sleep disorders as well. Sleep disordered breathing can be detected reliably by studying cyclical variation of heart rate combined with respiration-modulated changes in ECG morphology (amplitude of R wave and T wave)

Bivariate phase-rectified signal averaging

Phase-Rectified Signal Averaging (PRSA) was shown to be a powerful tool for the study of quasi-periodic oscillations and nonlinear effects in non-stationary signals. Here we present a bivariate PRSA technique for the study of the inter-relationship between two simultaneous data recordings. Its performance is compared with traditional cross-correlation analysis, which, however, does not work well for non-stationary data and cannot distinguish the coupling directions in complex nonlinear situations. We show that bivariate PRSA allows the analysis of events in one signal at times where the other signal is in a certain phase or state; it is stable in the presence of noise and impassible to non-stationarities.Comment: 19 pages, 6 figures, revised version submitted to Physica

Multifractal detrended fluctuation analysis of nonstationary time series

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 approaches are equivalent for stationary signals with compact support. By analyzing several examples we show that the new method can reliably determine the multifractal scaling behavior of time series. By comparing the multifractal DFA results for original series to those for shuffled series we can distinguish multifractality due to long-range correlations from multifractality due to a broad probability density function. We also compare our results with the wavelet transform modulus maxima (WTMM) method, and show that the results are equivalent.Comment: 14 pages (RevTex) with 10 figures (eps

Detecting Long-range Correlations with Detrended Fluctuation Analysis

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 that appear at small time scales become stronger in higher orders of DFA, and suggest a modified DFA method to remove them. The improvement is necessary especially for short records that are affected by non-stationarities. Furthermore, we describe how crossovers in the correlation behavior can be detected reliably and determined quantitatively and show how several types of trends in the data affect the different orders of DFA.Comment: 10 pages, including 8 figure