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Plamen Ch Ivanov

Publications and source records attributed to Plamen Ch Ivanov.

18 recordsLinked to original sources
PubMed2006

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. We find that for identical coupling strengths, oscillators with broader power spectra exhibit weaker synchronization. Further, we find that within a broad bandwidth range, bandpass filtering reduces the effect of noise but can lead to a spurious increase in the degree of phase synchronization with narrowing bandwidth, even when the coupling between the two oscillators remains the same.

Biophysics↗
PubMed2006

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. We propose an approach based on the cross-correlation of the instantaneous phase increments to quantify the coupling between BP and BFV signals. We find that the maximum correlation strength is different for the two groups and for the different conditions. For healthy subjects the amplitude of the cross-correlation between the instantaneous phase increments of BP and BFV is small and attenuates within 3-5 heartbeats. In contrast, for post-stroke subjects, this amplitude is significantly larger and cross-correlations persist up to 20 heartbeats. Further, we show that the instantaneous phase increments of BP and BFV are cross-correlated even within a single heartbeat cycle. We compare the results of our approach with three complementary methods: direct BP-BFV cross-correlation, transfer function analysis, and phase synchronization analysis. Our findings provide insight into the mechanism of cerebral vascular control in healthy subjects, suggesting that this control mechanism may involve rapid adjustments (within a heartbeat) of the cerebral vessels, so that BFV remains steady in response to changes in peripheral BP.

Blood Flow Velocity↗
PubMed2005

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.

Algorithms↗
PubMed2005

Quantifying signals with power-law correlations: a comparative study of detrended fluctuation analysis and detrended moving average techniques.

Detrended fluctuation analysis (DFA) and detrended moving average (DMA) are two scaling analysis methods designed to quantify correlations in noisy nonstationary signals. We systematically study the performance of different variants of the DMA method when applied to artificially generated long-range power-law correlated signals with an a priori known scaling exponent alpha(0) and compare them with the DFA method. We find that the scaling results obtained from different variants of the DMA method strongly depend on the type of the moving average filter. Further, we investigate the optimal scaling regime where the DFA and DMA methods accurately quantify the scaling exponent alpha(0) , and how this regime depends on the correlations in the signal. Finally, we develop a three-dimensional representation to determine how the stability of the scaling curves obtained from the DFA and DMA methods depends on the scale of analysis, the order of detrending, and the order of the moving average we use, as well as on the type of correlations in the signal.

Journal Article↗
PubMed2005

Power-law correlated processes with asymmetric distributions.

Motivated by the fact that many physical systems display (i) power-law correlations together with (ii) an asymmetry in the probability distribution, we propose a stochastic process that can model both properties. The process depends on only two parameters, where one controls the scaling exponent of the power-law correlations, and the other controls the degree of asymmetry in the distributions leaving the correlations unaffected. We apply the process to air humidity data and find that the statistical properties of the process are in a good agreement with those observed in the data.

Algorithms↗
PubMed2005

Effect of nonlinear filters on detrended fluctuation analysis.

When investigating the dynamical properties of complex multiple-component physical and physiological systems, it is often the case that the measurable system's output does not directly represent the quantity we want to probe in order to understand the underlying mechanisms. Instead, the output signal is often a linear or nonlinear function of the quantity of interest. Here, we investigate how various linear and nonlinear transformations affect the correlation and scaling properties of a signal, using the detrended fluctuation analysis (DFA) which has been shown to accurately quantify power-law correlations in nonstationary signals. Specifically, we study the effect of three types of transforms: (i) linear ( y(i) =a x(i) +b) , (ii) nonlinear polynomial ( y(i) =a x(k)(i) ) , and (iii) nonlinear logarithmic [ y(i) =log ( x(i) +Delta) ] filters. We compare the correlation and scaling properties of signals before and after the transform. We find that linear filters do not change the correlation properties, while the effect of nonlinear polynomial and logarithmic filters strongly depends on (a) the strength of correlations in the original signal, (b) the power k of the polynomial filter, and (c) the offset Delta in the logarithmic filter. We further apply the DFA method to investigate the "apparent" scaling of three analytic functions: (i) exponential [exp (+/-x+a) ] , (ii) logarithmic [log (x+a) ] , and (iii) power law [ (x+a)(lambda) ] , which are often encountered as trends in physical and biological processes. While these three functions have different characteristics, we find that there is a broad range of values for parameter a common for all three functions, where the slope of the DFA curves is identical. We further note that the DFA results obtained for a class of other analytic functions can be reduced to these three typical cases. We systematically test the performance of the DFA method when estimating long-range power-law correlations in the output signals for different parameter values in the three types of filters and the three analytic functions we consider.

Algorithms↗
PubMed2004

Endogenous circadian rhythm in an index of cardiac vulnerability independent of changes in behavior.

There exists a robust day/night pattern in the incidence of adverse cardiac events with a peak at approximately 10 a.m. This peak traditionally has been attributed to day/night patterns in behaviors affecting cardiac function in vulnerable individuals. However, influences from the endogenous circadian pacemaker independent from behaviors may also affect cardiac control. Heartbeat dynamics under healthy conditions exhibit robust complex fluctuations characterized by self-similar temporal structures, which break down under pathologic conditions. We hypothesize that these dynamical features of the healthy human heartbeat have an endogenous circadian rhythm that brings the features closer to those observed under pathologic conditions at the endogenous circadian phase corresponding to approximately 10 a.m. We investigate heartbeat dynamics in healthy subjects recorded throughout a 10-day protocol wherein the sleep/wake and behavior cycles are desynchronized from the endogenous circadian cycle, enabling assessment of circadian factors while controlling for behavior-related factors. We demonstrate that the scaling exponent characterizing temporal correlations in heartbeat dynamics does exhibit a significant circadian rhythm (with a sharp peak at the circadian phase corresponding to approximately 10 a.m.), which is independent from scheduled behaviors and mean heart rate. Cardiac dynamics under pathologic conditions such as congestive heart failure also are associated with a larger value of the scaling exponent of the interbeat interval. Thus, the sharp peak in the scaling exponent at the circadian phase coinciding with the period of highest cardiac vulnerability observed in epidemiological studies suggests that endogenous circadian-mediated influences on cardiac control may be involved in the day/night pattern of adverse cardiac events in vulnerable individuals.

Adult↗
PubMed2004

Common scale-invariant patterns of sleep-wake transitions across mammalian species.

Although mammals of different species have different sleep patterns, brief sleep-wake transitions commonly are observed across species and appear to occur randomly throughout the sleeping period. The dynamical patterns and functions of these brief awakenings from sleep are not well understood, and they often are viewed as disruptions (random or pathologic) of the sleep process. In this article, we hypothesize that brief awakenings from sleep may reflect aspects of the endogenous sleep control mechanism and thus may exhibit certain robust dynamical patterns across species. We analyze sleep recordings from mice, rats, cats, and humans, and we compare the distributions of sleep and wake episode durations. For all four species, we find that durations of brief wake episodes during the sleep period exhibit a scale-free power-law behavior with an exponent alpha that remains the same for all species (alpha approximately equal to 2.2). In contrast, sleep episode durations for all four species follow exponential distributions with characteristic time scales, which change across species in relation to body mass and metabolic rate. Our findings suggest common dynamical features of brief awakenings and sleep durations across species and may provide insights into the dynamics of the neural circuits controlling sleep.

Animals↗
PubMed2004

New class of level statistics in correlated disordered chains.

We study the properties of the level statistics of 1D disordered systems with long-range spatial correlations. We find a threshold value in the degree of correlations below which in the limit of large system size the level statistics follows a Poisson distribution (as expected for 1D uncorrelated-disordered systems), and above which the level statistics is described by a new class of distribution functions. At the threshold, we find that with increasing system size, the standard deviation of the function describing the level statistics converges to the standard deviation of the Poissonian distribution as a power law. Above the threshold we find that the level statistics is characterized by different functional forms for different degrees of correlations.

Journal Article↗
PubMed2004

Common scaling patterns in intertrade times of U. S. stocks.

We analyze the sequence of time intervals between consecutive stock trades of thirty companies representing eight sectors of the U.S. economy over a period of 4 yrs. For all companies we find that: (i) the probability density function of intertrade times may be fit by a Weibull distribution, (ii) when appropriately rescaled the probability densities of all companies collapse onto a single curve implying a universal functional form, (iii) the intertrade times exhibit power-law correlated behavior within a trading day and a consistently greater degree of correlation over larger time scales, in agreement with the correlation behavior of the absolute price returns for the corresponding company, and (iv) the magnitude series of intertrade time increments is characterized by long-range power-law correlations suggesting the presence of nonlinear features in the trading dynamics, while the sign series is anticorrelated at small scales. Our results suggest that independent of industry sector, market capitalization and average level of trading activity, the series of intertrade times exhibit possibly universal scaling patterns, which may relate to a common mechanism underlying the trading dynamics of diverse companies. Further, our observation of long-range power-law correlations and a parallel with the crossover in the scaling of absolute price returns for each individual stock, support the hypothesis that the dynamics of transaction times may play a role in the process of price formation.

Journal Article↗
PubMed2004

Non-random fluctuations and multi-scale dynamics regulation of human activity.

We investigate if known extrinsic and intrinsic factors fully account for the complex features observed in recordings of human activity as measured from forearm motion in subjects undergoing their regular daily routine. We demonstrate that the apparently random forearm motion possesses dynamic patterns characterized by robust scale-invariant and nonlinear features. These patterns remain stable from one subject to another and are unaffected by changes in the average activity level that occur within individual subjects throughout the day and on different days of the week, since they persist during daily routine and when the same subjects undergo time-isolation laboratory experiments designed to account for the circadian phase and to control the known extrinsic factors. Further, by modeling the scheduled events imposed throughout the laboratory protocols, we demonstrate that they cannot account for the observed scaling patterns in activity fluctuations. We attribute these patterns to a previously unrecognized intrinsic nonlinear multi-scale control mechanism of human activity that is independent of known extrinsic factors such as random and scheduled events, as well as the known intrinsic factors which possess a single characteristic time scale such as circadian and ultradian rhythms.

Adult↗
PubMed2002

Correlation differences in heartbeat fluctuations during rest and exercise.

We study the heartbeat activity of healthy individuals at rest and during exercise. We focus on correlation properties of the intervals formed by successive peaks in the pulse wave and find significant scaling differences between rest and exercise. For exercise the interval series is anticorrelated at short-time scales and correlated at intermediate-time scales, while for rest we observe the opposite crossover pattern--from strong correlations in the short-time regime to weaker correlations at larger scales. We also suggest a physiologically motivated stochastic scenario to provide an intuitive explanation of the scaling differences between rest and exercise.

Biophysical Phenomena↗
PubMed2002

Complex patterns of abnormal heartbeats.

Individuals having frequent abnormal heartbeats interspersed with normal heartbeats may be at an increased risk of sudden cardiac death. However, mechanistic understanding of such cardiac arrhythmias is limited. We present a visual and qualitative method to display statistical properties of abnormal heartbeats. We introduce dynamical "heartprints" which reveal characteristic patterns in long clinical records encompassing approximately 10(5) heartbeats and may provide information about underlying mechanisms. We test if these dynamics can be reproduced by model simulations in which abnormal heartbeats are generated (i) randomly, (ii) at a fixed time interval following a preceding normal heartbeat, or (iii) by an independent oscillator that may or may not interact with the normal heartbeat. We compare the results of these three models and test their limitations to comprehensively simulate the statistical features of selected clinical records. This work introduces methods that can be used to test mathematical models of arrhythmogenesis and to develop a new understanding of underlying electrophysiologic mechanisms of cardiac arrhythmia.

Arrhythmias, Cardiac↗
PubMed2002

Metal-insulator transition in chains with correlated disorder.

According to Bloch's theorem, electronic wavefunctions in perfectly ordered crystals are extended, which implies that the probability of finding an electron is the same over the entire crystal. Such extended states can lead to metallic behaviour. But when disorder is introduced in the crystal, electron states can become localized, and the system can undergo a metal-insulator transition (also known as an Anderson transition). Here we theoretically investigate the effect on the physical properties of the electron wavefunctions of introducing long-range correlations in the disorder in one-dimensional binary solids, and find a correlation-induced metal-insulator transition. We perform numerical simulations using a one-dimensional tight-binding model, and find a threshold value for the exponent characterizing the long-range correlations of the system. Above this threshold, and in the thermodynamic limit, the system behaves as a conductor within a broad energy band; below threshold, the system behaves as an insulator. We discuss the possible relevance of this result for electronic transport in DNA, which displays long-range correlations and has recently been reported to be a one-dimensional disordered conductor.

Crystallization↗
PubMed2002

Characterization of sleep stages by correlations in the magnitude and sign of heartbeat increments.

We study correlation properties of the magnitude and the sign of the increments in the time intervals between successive heartbeats during light sleep, deep sleep, and rapid eye movement (REM) sleep using the detrended fluctuation analysis method. We find short-range anticorrelations in the sign time series, which are strong during deep sleep, weaker during light sleep, and even weaker during REM sleep. In contrast, we find long-range positive correlations in the magnitude time series, which are strong during REM sleep and weaker during light sleep. We observe uncorrelated behavior for the magnitude during deep sleep. Since the magnitude series relates to the nonlinear properties of the original time series, while the sign series relates to the linear properties, our findings suggest that the nonlinear properties of the heartbeat dynamics are more pronounced during REM sleep. Thus, the sign and the magnitude series provide information which is useful in distinguishing between the sleep stages.

Biophysics↗
PubMed2002

Effect of nonstationarities on detrended fluctuation analysis.

Detrended fluctuation analysis (DFA) is a scaling analysis method used to quantify long-range power-law correlations in signals. Many physical and biological signals are "noisy," heterogeneous, and exhibit different types of nonstationarities, which can affect the correlation properties of these signals. We systematically study the effects of three types of nonstationarities often encountered in real data. Specifically, we consider nonstationary sequences formed in three ways: (i) stitching together segments of data obtained from discontinuous experimental recordings, or removing some noisy and unreliable parts from continuous recordings and stitching together the remaining parts-a "cutting" procedure commonly used in preparing data prior to signal analysis; (ii) adding to a signal with known correlations a tunable concentration of random outliers or spikes with different amplitudes; and (iii) generating a signal comprised of segments with different properties-e.g., different standard deviations or different correlation exponents. We compare the difference between the scaling results obtained for stationary correlated signals and correlated signals with these three types of nonstationarities. We find that introducing nonstationarities to stationary correlated signals leads to the appearance of crossovers in the scaling behavior and we study how the characteristics of these crossovers depend on (a) the fraction and size of the parts cut out from the signal, (b) the concentration of spikes and their amplitudes (c) the proportion between segments with different standard deviations or different correlations and (d) the correlation properties of the stationary signal. We show how to develop strategies for preprocessing "raw" data prior to analysis, which will minimize the effects of nonstationarities on the scaling properties of the data, and how to interpret the results of DFA for complex signals with different local characteristics.

Computer Simulation↗
PubMed2002

Fractal dynamics in physiology: alterations with disease and aging.

According to classical concepts of physiologic control, healthy systems are self-regulated to reduce variability and maintain physiologic constancy. Contrary to the predictions of homeostasis, however, the output of a wide variety of systems, such as the normal human heartbeat, fluctuates in a complex manner, even under resting conditions. Scaling techniques adapted from statistical physics reveal the presence of long-range, power-law correlations, as part of multifractal cascades operating over a wide range of time scales. These scaling properties suggest that the nonlinear regulatory systems are operating far from equilibrium, and that maintaining constancy is not the goal of physiologic control. In contrast, for subjects at high risk of sudden death (including those with heart failure), fractal organization, along with certain nonlinear interactions, breaks down. Application of fractal analysis may provide new approaches to assessing cardiac risk and forecasting sudden cardiac death, as well as to monitoring the aging process. Similar approaches show promise in assessing other regulatory systems, such as human gait control in health and disease. Elucidating the fractal and nonlinear mechanisms involved in physiologic control and complex signaling networks is emerging as a major challenge in the postgenomic era.

Aging↗