Effects of coarse-graining on the scaling behavior of long-range correlated and anti-correlated signals.

We investigate how various coarse-graining (signal quantization) methods affect the scaling properties of long-range power-law correlated and anti-correlated signals, quantified by the detrended fluctuation analysis. Specifically, for coarse-graining in the magnitude of a signal, we consider (i) the Floor, (ii) the Symmetry and (iii) the Centro-Symmetry coarse-graining methods. We find that for anti-correlated signals coarse-graining in the magnitude leads to a crossover to random behavior at large scales, and that with increasing the width of the coarse-graining partition interval Δ, this crossover moves to intermediate and small scales. In contrast, the scaling of positively correlated signals is less affected by the coarse-graining, with no observable changes when Δ < 1, while for Δ > 1 a crossover appears at small scales and moves to intermediate and large scales with increasing Δ. For very rough coarse-graining (Δ > 3) based on the Floor and Symmetry methods, the position of the crossover stabilizes, in contrast to the Centro-Symmetry method where the crossover continuously moves across scales and leads to a random behavior at all scales; thus indicating a much stronger effect of the Centro-Symmetry compared to the Floor and the Symmetry method. For coarse-graining in time, where data points are averaged in non-overlapping time windows, we find that the scaling for both anti-correlated and positively correlated signals is practically preserved. The results of our simulations are useful for the correct interpretation of the correlation and scaling properties of symbolic sequences.

Stratification pattern of static and scale-invariant dynamic measures of heartbeat fluctuations across sleep stages in young and elderly.

Cardiac dynamics exhibit complex variability characterized by scale-invariant and nonlinear temporal organization related to the mechanism of neuroautonomic control, which changes with physiologic states and pathologic conditions. Changes in sleep regulation during sleep stages are also related to fluctuations in autonomic nervous activity. However, the interaction between sleep regulation and cardiac autonomic control remains not well understood. Even less is known how this interaction changes with age, as aspects of both cardiac dynamics and sleep regulation differ in healthy elderly compared to young subjects. We hypothesize that because of the neuroautonomic responsiveness in young subjects, fractal and nonlinear features of cardiac dynamics exhibit a pronounced stratification pattern across sleep stages, while in elderly these features will remain unchanged due to age-related loss of cardiac variability and decline of neuroautonomic responsiveness. We analyze the variability and the temporal fractal organization of heartbeat fluctuations across sleep stages in both young and elderly. We find that independent linear and nonlinear measures of cardiac control consistently exhibit the same ordering in their values across sleep stages, forming a robust stratification pattern. Despite changes in sleep architecture and reduced heart rate variability in elderly subjects, this stratification surprisingly does not break down with advanced age. Moreover, the difference between sleep stages for some linear, fractal, and nonlinear measures exceeds the difference between young and elderly, suggesting that the effect of sleep regulation on cardiac dynamics is significantly stronger than the effect of healthy aging. Quantifying changes in this stratification pattern may provide insights into how alterations in sleep regulation contribute to increased cardiac risk.

Fractal scale-invariant and nonlinear properties of cardiac dynamics remain stable with advanced age: a new mechanistic picture of cardiac control in healthy elderly.

Heart beat fluctuations exhibit temporal structure with robust long-range correlations, fractal and nonlinear features, which have been found to break down with pathologic conditions, reflecting changes in the mechanism of neuroautonomic control. It has been hypothesized that these features change and even break down also with advanced age, suggesting fundamental alterations in cardiac control with aging. Here we test this hypothesis. We analyze heart beat interval recordings from the following two independent databases: 1) 19 healthy young (average age 25.7 yr) and 16 healthy elderly subjects (average age 73.8 yr) during 2 h under resting conditions from the Fantasia database; and 2) 29 healthy elderly subjects (average age 75.9 yr) during approximately 8 h of sleep from the sleep heart health study (SHHS) database, and the same subjects recorded 5 yr later. We quantify: 1) the average heart rate (); 2) the SD sigma(R-R) and sigma(DeltaR-R) of the heart beat intervals R-R and their increments DeltaR-R; 3) the long-range correlations in R-R as measured by the scaling exponent alpha(R-R) using the Detrended Fluctuation Analysis; 4) fractal linear and nonlinear properties as represented by the scaling exponents alpha(sgn) and alpha(mag) for the time series of the sign and magnitude of DeltaR-R; and 5) the nonlinear fractal dimension D(k) of R-R using the fractal dimension analysis. We find: 1) No significant difference in (P > 0.05); 2) a significant difference in sigma(R-R) and sigma(DeltaR-R) for the Fantasia groups (P < 10(-4)) but no significant change with age between the elderly SHHS groups (P > 0.5); and 3) no significant change in the fractal measures alpha(R-R) (P > 0.15), alpha(sgn) (P > 0.2), alpha(mag) (P > 0.3), and D(k) with age. Our findings do not support the hypothesis that fractal linear and nonlinear characteristics of heart beat dynamics break down with advanced age in healthy subjects. Although our results indeed show a reduced SD of heart beat fluctuations with advanced age, the inherent temporal fractal and nonlinear organization of these fluctuations remains stable. This indicates that the coupled cascade of nonlinear feedback loops, which are believed to underlie cardiac neuroautonomic regulation, remains intact with advanced age.

Mori-Zwanzig memory analysis in single-molecule spectroscopy.

We study the dynamical behavior of the Rhodospirillum molischianum LH2 complex based on intensity time series obtained from single-molecule spectroscopy experiments. This is achieved by reconstructing the memory function describing the time-dependent fluctuations of the excited states. We conclude that the apparent stochastic evolution of the dynamics is controlled by at least two different non-Markovian main processes.

Analyzing memory effects of complex systems from time series.

A numerical algorithm is presented in order to determine all coefficients of the Mori-Zwanzig equation from a given finite time series. The algorithm is applicable to observables of arbitrary complex systems. Meteorological and financial systems are investigated. By analyzing directional variables and amplitudes we are able to observe and discuss memory effects on different time scales. We show that analyzing the memory kernel provides important insights into the dynamics of a complex system.