Magnitude and sign of long-range correlated time series: Decomposition and surrogate signal generation.

We systematically study the scaling properties of the magnitude and sign of the fluctuations in correlated time series, which is a simple and useful approach to distinguish between systems with different dynamical properties but the same linear correlations. First, we decompose artificial long-range power-law linearly correlated time series into magnitude and sign series derived from the consecutive increments in the original series, and we study their correlation properties. We find analytical expressions for the correlation exponent of the sign series as a function of the exponent of the original series.

Delay-correlation landscape reveals characteristic time delays of brain rhythms and heart interactions.

Within the framework of 'Network Physiology', we ask a fundamental question of how modulations in cardiac dynamics emerge from networked brain-heart interactions. We propose a generalized time-delay approach to identify and quantify dynamical interactions between physiologically relevant brain rhythms and the heart rate. We perform empirical analysis of synchronized continuous EEG and ECG recordings from 34 healthy subjects during night-time sleep.

Plasticity of brain wave network interactions and evolution across physiologic states.

Neural plasticity transcends a range of spatio-temporal scales and serves as the basis of various brain activities and physiologic functions. At the microscopic level, it enables the emergence of brain waves with complex temporal dynamics. At the macroscopic level, presence and dominance of specific brain waves is associated with important brain functions.

Network Physiology: How Organ Systems Dynamically Interact.

We systematically study how diverse physiologic systems in the human organism dynamically interact and collectively behave to produce distinct physiologic states and functions. This is a fundamental question in the new interdisciplinary field of Network Physiology, and has not been previously explored. Introducing the novel concept of Time Delay Stability (TDS), we develop a computational approach to identify and quantify networks of physiologic interactions from long-term continuous, multi-channel physiological recordings.

Impact of stock market structure on intertrade time and price dynamics.

We analyse times between consecutive transactions for a diverse group of stocks registered on the NYSE and NASDAQ markets, and we relate the dynamical properties of the intertrade times with those of the corresponding price fluctuations. We report that market structure strongly impacts the scale-invariant temporal organisation in the transaction timing of stocks, which we have observed to have long-range power-law correlations. Specifically, we find that, compared to NYSE stocks, stocks registered on the NASDAQ exhibit significantly stronger correlations in their transaction timing on scales within a trading day.

Dynamical patterns of human postural responses to emotional stimuli.

Postural displacements in response to emotional activation have recently been proposed as a direct and objective index of approach-avoidance behavior in humans. Here, we present the results of an experiment designed to assess spontaneous postural responses to discrete affective pictures, briefly presented in random order of valence. Our findings question the interpretation of phasic postural responses to emotional stimuli as approach-avoidance behavior.

Phase transitions in physiologic coupling.

Integrated physiological systems, such as the cardiac and the respiratory system, exhibit complex dynamics that are further influenced by intrinsic feedback mechanisms controlling their interaction. To probe how the cardiac and the respiratory system adjust their rhythms, despite continuous fluctuations in their dynamics, we study the phase synchronization of heartbeat intervals and respiratory cycles. The nature of this interaction, its physiological and clinical relevance, and its relation to mechanisms of neural control is not well understood.

Network physiology reveals relations between network topology and physiological function.

The human organism is an integrated network where complex physiological systems, each with its own regulatory mechanisms, continuously interact, and where failure of one system can trigger a breakdown of the entire network. Identifying and quantifying dynamical networks of diverse systems with different types of interactions is a challenge. Here we develop a framework to probe interactions among diverse systems, and we identify a physiological network.

Phase transitions in the first-passage time of scale-invariant correlated processes.

A key quantity describing the dynamics of complex systems is the first-passage time (FPT). The statistical properties of FPT depend on the specifics of the underlying system dynamics. We present a unified approach to account for the diversity of statistical behaviors of FPT observed in real-world systems.

Aging effects on cardiac and respiratory dynamics in healthy subjects across sleep stages.

Study Objectives: Respiratory and heart rate variability exhibit fractal scaling behavior on certain time scales. We studied the short-term and long-term correlation properties of heartbeat and breathing-interval data from disease-free subjects focusing on the age-dependent fractal organization. We also studied differences across sleep stages and night-time wake and investigated quasi-periodic variations associated with cardiac risk.

Effect of extreme data loss on long-range correlated and anticorrelated signals quantified by detrended fluctuation analysis.

Detrended fluctuation analysis (DFA) is an improved method of classical fluctuation analysis for nonstationary signals where embedded polynomial trends mask the intrinsic correlation properties of the fluctuations. To better identify the intrinsic correlation properties of real-world signals where a large amount of data is missing or removed due to artifacts, we investigate how extreme data loss affects the scaling behavior of long-range power-law correlated and anticorrelated signals. We introduce a segmentation approach to generate surrogate signals by randomly removing data segments from stationary signals with different types of long-range correlations.

Levels of complexity in scale-invariant neural signals.

Many physical and physiological signals exhibit complex scale-invariant features characterized by 1/f scaling and long-range power-law correlations, indicating a possibly common control mechanism. Specifically, it has been suggested that dynamical processes, influenced by inputs and feedback on multiple time scales, may be sufficient to give rise to 1/f scaling and scale invariance. Two examples of physiologic signals that are the output of hierarchical multiscale physiologic systems under neural control are the human heartbeat and human gait.

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.

Endogenous circadian rhythm in human motor activity uncoupled from circadian influences on cardiac dynamics.

The endogenous circadian pacemaker influences key physiologic functions, such as body temperature and heart rate, and is normally synchronized with the sleep/wake cycle. Epidemiological studies demonstrate a 24-h pattern in adverse cardiovascular events with a peak at approximately 10 a.m.

Scale-invariant aspects of cardiac dynamics across sleep stages and circadian phases.

We review recent attempts to understand the influence of sleep and wake states, sleep-stage transitions during sleep and the endogenous circadian rhythms on the neuroautonomic regulation of cardiac dynamics as represented by the scale-invariant organization of heartbeat fluctuations. We find that the probability distribution, the long-range temporal correlations as well as the nonlinear properties of the heartbeat fluctuations are significantly altered with transition from sleep to wake state, across sleep-stages and circadian phases. These sleep and circadian mediated changes in cardiac dynamics occur simultaneously over a broad range of time scales, suggesting a more complex then previously known interaction between the neural systems of sleep and circadian regulation with the neuroautonomic cardiac control, beyond rhythmic modulation at a characteristic time scale.

The suprachiasmatic nucleus functions beyond circadian rhythm generation.

We recently discovered that human activity possesses a complex temporal organization characterized by scale-invariant/self-similar fluctuations from seconds to approximately 4 h-(statistical properties of fluctuations remain the same at different time scales). Here, we show that scale-invariant activity patterns are essentially identical in humans and rats, and exist for up to approximately 24 h: six-times longer than previously reported. Theoretically, such scale-invariant patterns can be produced by a neural network of interacting control nodes-system components with feedback loops-operating at different time scales.

Patterns of phase-dependent spiral wave attenuation in excitable media.

We show that introducing periodic planar fronts with long excitation duration can lead to spiral attenuation. The attenuation occurs periodically over cycles of several planar fronts, forming a variety of complex spatiotemporal patterns. We find that these attenuation patterns occur only at specific phases of the descending fronts relative to the rotational phase of the spiral.

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.

Patterns of spiral wave attenuation by low-frequency periodic planar fronts.

There is evidence that spiral waves and their breakup underlie mechanisms related to a wide spectrum of phenomena ranging from spatially extended chemical reactions to fatal cardiac arrhythmias [A. T. Winfree, The Geometry of Biological Time (Springer-Verlag, New York, 2001); J.

Spurious detection of phase synchronization in coupled nonlinear oscillators.

Coupled nonlinear systems under certain conditions exhibit phase synchronization, which may change for different frequency bands or with the presence of additive system noise. In both cases, Fourier filtering is traditionally used to preprocess data. We investigate to what extent the phase synchronization of two coupled Rössler oscillators depends on (1) the broadness of their power spectrum, (2) the width of the bandpass filter, and (3) the level of added noise.

Cross-correlation of instantaneous phase increments in pressure-flow fluctuations: applications to cerebral autoregulation.

We investigate the relationship between the blood flow velocities (BFV) in the middle cerebral arteries and beat-to-beat blood pressure (BP) recorded from a finger in healthy and post-stroke subjects during the quasisteady state after perturbation for four different physiologic conditions: supine rest, head-up tilt, hyperventilation, and CO2 rebreathing in upright position. To evaluate whether instantaneous BP changes in the steady state are coupled with instantaneous changes in the BFV, we compare dynamical patterns in the instantaneous phases of these signals, obtained from the Hilbert transform, as a function of time. We find that in post-stroke subjects the instantaneous phase increments of BP and BFV exhibit well-pronounced patterns that remain stable in time for all four physiologic conditions, while in healthy subjects these patterns are different, less pronounced, and more variable.

Fractionally integrated process with power-law correlations in variables and magnitudes.

Motivated by the fact that many empirical time series--including changes of heartbeat intervals, physical activity levels, intertrade times in finance, and river flux values--exhibit power-law anticorrelations in the variables and power-law correlations in their magnitudes, we propose a simple stochastic process that can account for both types of correlations. The process depends on only two parameters, where one controls the correlations in the variables and the other controls the correlations in their magnitudes. We apply the process to time series of heartbeat interval changes and air temperature changes and find that the statistical properties of the modeled time series are in agreement with those observed in the data.