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)

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

Coupling between leg muscle activation and EEG during normal walking, intentional stops, and freezing of gait in Parkinson's disease

In this paper, we apply novel techniques for characterizing leg muscle activation patterns via electromyograms (EMGs) and for relating them to changes in electroencephalogram (EEG) activity during gait experiments. Specifically, we investigate changes of leg-muscle EMG amplitudes and EMG frequencies during walking, intentional stops, and unintended freezing-of-gait (FOG) episodes. FOG is a frequent paroxysmal gait disturbance occurring in many patients suffering from Parkinson's disease (PD). We find that EMG amplitudes and frequencies do not change significantly during FOG episodes with respect to walking, while drastic changes occur during intentional stops. Phase synchronization between EMG signals is most pronounced during walking in controls and reduced in PD patients. By analyzing cross-correlations between changes in EMG patterns and brain-wave amplitudes (from EEGs), we find an increase in EEG-EMG coupling at the beginning of stop and FOG episodes. Our results may help to better understand the enigmatic pathophysiology of FOG, to differentiate between FOG events and other gait disturbances, and ultimately to improve diagnostic procedures for patients suffering from PD. Copyright © 2019 Günther, Bartsch, Miron-Shahar, Hassin-Baer, Inzelberg, Kurths, Plotnik and Kantelhardt

Breathing during REM and non-REM sleep: correlated versus uncorrelated behaviour

Abstract Healthy sleep can be characterized by several stages: deep sleep, light sleep, and REM sleep. Here we show that these sleep stages lead to di erent autonomic regulation of breathing. Using the detrended uctuation analysis up to the fourth order we ÿnd that breath-to-breath intervals and breath volumes separated by several breaths are long-range correlated during the REM stages and during wake states. In contrast, in the non-REM stages (deep sleep and light sleep), long-range correlations are absent. This behaviour is very similar to the correlation behaviour of the heart rate during the night and may be related to the phase synchronization between heartbeat and breathing found recently. We speculate that the di erences are caused by di erent cortically in uenced control of the autonomic nervous system

Sublocalization, superlocalization, and violation of standard single parameter scaling in the Anderson model

We discuss the localization behavior of localized electronic wave functions in the one- and two-dimensional tight-binding Anderson model with diagonal disorder. We find that the distributions of the local wave function amplitudes at fixed distances from the localization center are well approximated by log-normal fits which become exact at large distances. These fits are consistent with the standard single parameter scaling theory for the Anderson model in 1d, but they suggest that a second parameter is required to describe the scaling behavior of the amplitude fluctuations in 2d. From the log-normal distributions we calculate analytically the decay of the mean wave functions. For short distances from the localization center we find stretched exponential localization ("sublocalization") in both, 1d and 2d. In 1d, for large distances, the mean wave functions depend on the number of configurations N used in the averaging procedure and decay faster that exponentially ("superlocalization") converging to simple exponential behavior only in the asymptotic limit. In 2d, in contrast, the localization length increases logarithmically with the distance from the localization center and sublocalization occurs also in the second regime. The N-dependence of the mean wave functions is weak. The analytical result agrees remarkably well with the numerical calculations.Comment: 12 pages with 9 figures and 1 tabl