Biomedical subjects

Shlomo Havlin

Publications and source records attributed to Shlomo Havlin.

43 records · Page 3Linked to original sources

PubMed2002

Global climate models violate scaling of the observed atmospheric variability.

We test the scaling performance of seven leading global climate models by using detrended fluctuation analysis. We analyze temperature records of six representative sites around the globe simulated by the models, for two different scenarios: (i) with greenhouse gas forcing only and (ii) with greenhouse gas plus aerosol forcing. We find that the simulated records for both scenarios fail to reproduce the universal scaling behavior of the observed records and display wide performance differences. The deviations from the scaling behavior are more pronounced in the first scenario, where also the trends are clearly overestimated.

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PubMed2002

Fractal behavior of the shortest path between two lines in percolation systems.

Using Monte Carlo simulations, we determine the scaling form for the probability distribution of the shortest path l between two lines in a three-dimensional percolation system at criticality; the two lines can have arbitrary positions, orientations, and lengths. We find that the probability distributions can exhibit up to four distinct power-law regimes (separated by crossover regimes) with exponents depending on the relative orientations of the lines. We explain this rich fractal behavior with scaling arguments.

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PubMed2002

Universality classes for self-avoiding walks in a strongly disordered system.

We study the behavior of self-avoiding walks (SAWs) on square and cubic lattices in the presence of strong disorder. We simulate the disorder by assigning random energy epsilon taken from a probability distribution P(epsilon) to each site (or bond) of the lattice. We study the strong disorder limit for an extremely broad range of energies with P(epsilon) is proportional to 1/epsilon. For each configuration of disorder, we find by exact enumeration the optimal SAW of fixed length N and fixed origin that minimizes the sum of the energies of the visited sites (or bonds). We find the fractal dimension of the optimal path to be d(opt)=1.52+/-0.10 in two dimensions (2D) and d(opt)=1.82+/-0.08 in 3D. Our results imply that SAWs in strong disorder with fixed N are much more compact than SAWs in disordered media with a uniform distribution of energies, optimal paths in strong disorder with fixed end-to-end distance R, and SAWs on a percolation cluster. Our results are also consistent with the possibility that SAWs in strong disorder belong to the same universality class as the maximal SAW on a percolation cluster at criticality, for which we calculate the fractal dimension d(max)=1.64+/-0.02 for 2D and d(max)=1.87+/-0.05 for 3D, values very close to the fractal dimensions of the percolation backbone in 2D and 3D.

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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

Multifractal chaotic attractors in a system of delay-differential equations modeling road traffic.

We study a system of delay-differential equations modeling single-lane road traffic. The cars move in a closed circuit and the system's variables are each car's velocity and the distance to the car ahead. For low and high values of traffic density the system has a stable equilibrium solution, corresponding to the uniform flow. Gradually decreasing the density from high to intermediate values we observe a sequence of supercritical Hopf bifurcations forming multistable limit cycles, corresponding to flow regimes with periodically moving traffic jams. Using an asymptotic technique we find approximately small limit cycles born at Hopf bifurcations and numerically preform their global continuations with decreasing density. For sufficiently large delay the system passes to chaos following the Ruelle-Takens-Newhouse scenario (limit cycles-two-tori-three-tori-chaotic attractors). We find that chaotic and nonchaotic attractors coexist for the same parameter values and that chaotic attractors have a broad multifractal spectrum. (c) 2002 American Institute of Physics.

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PubMed2002

Scaling vs. nonscaling methods of assessing autonomic tone in streptozotocin-induced diabetic rats.

We studied heart rate variability in rats by power scaling spectral analysis (PSSA), autoregressive modeling (AR), and detrended fluctuation analysis (DFA), assessed stability by coefficient of variation between consecutive 6-h epochs, and then compared cross-correlation among techniques. These same parameters were checked from baseline conditions through acute and chronic disease states (streptozotocin-induced diabetes) followed by therapeutic intervention (insulin). Cross-correlation between methods over the entire time period was r = 0.94 (DFA and PSSA), r = 0.81 (DFA and AR), and r = 0.77 (AR and PSSA). Under baseline conditions the scaling parameter measured by DFA and PSSA and the high-frequency (HF) component measured by AR fluctuated around an average value, but these fluctuations were different for the three methods. After diabetes induction, a strong correlation was found between the HF power and the short-term scaling parameter. Despite their differences in methodology, DFA and PSSA assess changes in parasympathetic tone as detected by autoregressive modeling.

Animals↗

PubMed2001

From 1/f noise to multifractal cascades in heartbeat dynamics.

We explore the degree to which concepts developed in statistical physics can be usefully applied to physiological signals. We illustrate the problems related to physiologic signal analysis with representative examples of human heartbeat dynamics under healthy and pathologic conditions. We first review recent progress based on two analysis methods, power spectrum and detrended fluctuation analysis, used to quantify long-range power-law correlations in noisy heartbeat fluctuations. The finding of power-law correlations indicates presence of scale-invariant, fractal structures in the human heartbeat. These fractal structures are represented by self-affine cascades of beat-to-beat fluctuations revealed by wavelet decomposition at different time scales. We then describe very recent work that quantifies multifractal features in these cascades, and the discovery that the multifractal structure of healthy dynamics is lost with congestive heart failure. The analytic tools we discuss may be used on a wide range of physiologic signals. (c) 2001 American Institute of Physics.

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