151
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Hong DC, Stanley HE. Cumulant renormalisation group and its application to the incipient infinite cluster in percolation. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/16/14/007] [Citation(s) in RCA: 42] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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152
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Nittmann J, Stanley HE. Role of fluctuations in viscous fingering and dendritic crystal growth: a noise-driven model with non-periodic sidebranching and no threshold for onset. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/20/15/009] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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153
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Herrmann HJ, Stanley HE. The fractal dimension of the minimum path in two- and three-dimensional percolation. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/21/17/003] [Citation(s) in RCA: 121] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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154
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Amaral LA, Goldberger AL, Stanley HE. Modeling heart rate variability by stochastic feedback. COMPUTER PHYSICS COMMUNICATIONS 1999; 121-122:126-128. [PMID: 11542688 DOI: 10.1016/s0010-4655(99)00295-7] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
We consider the question of how the cardiac rhythm spontaneously self-regulates and propose a new mechanism as a possible answer. We model the neuroautonomic regulation of the heart rate as a stochastic feedback system and find that the model successfully accounts for key characteristics of cardiac variability, including the 1/f power spectrum, the functional form and scaling of the distribution of variations of the interbeat intervals, and the correlations in the Fourier phases which indicate nonlinear dynamics.
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155
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Bunde A, Coniglio A, Hong DC, Stanley HE. Transport in a two-component randomly composite material: scaling theory and computer simulations of termite diffusion near the superconducting limit. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/18/3/007] [Citation(s) in RCA: 49] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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156
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Nittmann J, Stanley HE. Non-deterministic approach to anisotropic growth patterns with continuously tunable morphology: the fractal properties of some real snowflakes. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/20/17/010] [Citation(s) in RCA: 59] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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157
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Margolina A, Nakanishi H, Stauffer D, Stanley HE. Monte Carlo and series study of corrections to scaling in two-dimensional percolation. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/17/8/024] [Citation(s) in RCA: 41] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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158
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Milosevic S, Stassinopoulos D, Stanley HE. Asymptotic form of the spectral dimension at the fractal to lattice crossover. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/21/6/024] [Citation(s) in RCA: 22] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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159
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Jan N, Hong DC, Stanley HE. The fractal dimension and other percolation exponents in four and five dimensions. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/18/15/006] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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160
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Djordjevic ZV, Majid I, Stanley HE, Santos RJD. Correction-to-scaling exponents and amplitudes for the correlation length of linear polymers in two dimensions. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/16/14/006] [Citation(s) in RCA: 54] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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161
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Nakanishi H, Stanley HE. Scaling studies of percolation phenomena in systems of dimensionality two to seven. II. Equation of state. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/14/3/017] [Citation(s) in RCA: 21] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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162
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Nunes Amaral LA, Goldberger AL, Stanley HE. Scale-independent measures and pathologic cardiac dynamics. PHYSICAL REVIEW LETTERS 1998; 81:2388-2391. [PMID: 11542722 DOI: 10.1103/physrevlett.81.2388] [Citation(s) in RCA: 34] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
We study several scale-independent measures of cardiac interbeat interval dynamics defined through the application of the wavelet transform. We test their performance in detecting heart disease using a database consisting of records of interbeat intervals for a group of healthy individuals and subjects with congestive heart failure. We find that scale-independent measures effectively distinguish healthy from pathologic behavior and propose a new two-variable scale-independent measure that could be clinically useful. We compare the performance of a recently proposed scale-dependent measure and find that the results depend on the database analyzed and on the analyzing wavelet.
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163
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Nunes Amaral LA, Goldberger AL, Stanley HE. Stochastic feedback and the regulation of biological rhythms. EUROPHYSICS LETTERS 1998; 43:363-8. [PMID: 11542723 DOI: 10.1209/epl/i1998-00366-3] [Citation(s) in RCA: 98] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/19/2023]
Abstract
We propose a general approach to the question of how biological rhythms spontaneously self-regulate, based on the concept of "stochastic feedback". We illustrate this approach by considering at a coarse-grained level the neuroautonomic regulation of the heart rate. The model generates complex dynamics and successfully acounts for key characteristics of cardiac variability, including the l/f power spectrum, the functional form and scaling of the distribution of variations, and correlations in the Fourier phases indicating nonlinear dynamics.
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164
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Suki B, Andrade JS, Coughlin MF, Stamenović D, Stanley HE, Sujeer M, Zapperi S. Mathematical modeling of the first inflation of degassed lungs. Ann Biomed Eng 1998; 26:608-17. [PMID: 9662153 DOI: 10.1114/1.126] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
Abstract
The pressure-volume (P-V) relationship of degassed lungs during the first inflation is different from that in consecutive inflations. We developed a mathematical model of the P-V curve of the first inflation by assuming that (1) central airways are open leading to many subtrees of n generations that are initially closed; (2) an airway opens when inflation pressure reaches the opening threshold pressure of that segment; and (3) the opening threshold pressures do not depend on airway generation. In this model, airway opening occurs in cascades or avalanches. To test the model which contains only two parameters, n and a pressure, P(low), at which at least one subtree completely opens, we measured the first inflation P-V curves of 15 excised and degassed rabbit lungs. By fitting these data, we found that n=17+/-5, P(low)=23+/-4 cmH2O, and that there is a wide distribution of threshold pressures for airways with diameters <2 mm. Analysis of the P-V curve in a lung which was lavaged with a liquid of constant surface tension and in which airways are presumably open demonstrated that the distribution of threshold pressures is narrow, and hence no avalanches occur during inflation. We conclude that in normal lungs the first inflation is dominated by avalanche behavior of airway opening providing information on the global distribution of threshold pressures and the average site of airway closure.
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165
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Suki B, Alencar AM, Sujeer MK, Lutchen KR, Collins JJ, Andrade JS, Ingenito EP, Zapperi S, Stanley HE. Life-support system benefits from noise. Nature 1998; 393:127-8. [PMID: 9603516 DOI: 10.1038/30130] [Citation(s) in RCA: 164] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
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166
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Rosenblum MG, Peng CK, Mietus JE, Havlin S, Stanley HE, Goldberger AL. Scaling and universality in heart rate variability distributions. PHYSICA A 1998; 249:587-593. [PMID: 11541514 DOI: 10.1016/s0378-4371(97)00522-0] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
We find that a universal homogeneous scaling form describes the distribution of cardiac variations for a group of healthy subjects, which is stable over a wide range of time scales. However, a similar scaling function does not exist for a group with a common cardiopulmonary instability associated with sleep apnea. Subtle differences in the distributions for the day- and night-phase dynamics for healthy subjects are detected.
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167
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Peng CK, Hausdorff JM, Havlin S, Mietus JE, Stanley HE, Goldberger AL. Multiple-time scales analysis of physiological time series under neural control. PHYSICA A 1998; 249:491-500. [PMID: 11541513 DOI: 10.1016/s0378-4371(97)00508-6] [Citation(s) in RCA: 24] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
Abstract
We discuss multiple-time scale properties of neurophysiological control mechanisms, using heart rate and gait regulation as model systems. We find that scaling exponents can be used as prognostic indicators. Furthermore, detection of more subtle degradation of scaling properties may provide a novel early warning system in subjects with a variety of pathologies including those at high risk of sudden death.
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168
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Cruz L, Urbanc B, Buldyrev SV, Christie R, Gómez-Isla T, Havlin S, McNamara M, Stanley HE, Hyman BT. Aggregation and disaggregation of senile plaques in Alzheimer disease. Proc Natl Acad Sci U S A 1997; 94:7612-6. [PMID: 9207140 PMCID: PMC23870 DOI: 10.1073/pnas.94.14.7612] [Citation(s) in RCA: 78] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023] Open
Abstract
We quantitatively analyzed, using laser scanning confocal microscopy, the three-dimensional structure of individual senile plaques in Alzheimer disease. We carried out the quantitative analysis using statistical methods to gain insights about the processes that govern Abeta peptide deposition. Our results show that plaques are complex porous structures with characteristic pore sizes. We interpret plaque morphology in the context of a new dynamical model based on competing aggregation and disaggregation processes in kinetic steady-state equilibrium with an additional diffusion process allowing Abeta deposits to diffuse over the surface of plaques.
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169
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Viswanathan GM, Buldyrev SV, Havlin S, Stanley HE. Quantification of DNA patchiness using long-range correlation measures. Biophys J 1997; 72:866-75. [PMID: 9017212 PMCID: PMC1185610 DOI: 10.1016/s0006-3495(97)78721-6] [Citation(s) in RCA: 39] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023] Open
Abstract
We introduce and develop new techniques to quantify DNA patchiness, and to quantify characteristics of its mosaic structure. These techniques, which involve calculating two functions, alpha(l) and beta(l), measure correlations at length scale l and detect distinct characteristic patch sizes embedded in scale-invariant patch size distributions. Using these new methods, we address a number of issues relating to the mosaic structure of genomic DNA. We find several distinct characteristic patch sizes in certain genomic sequences, and compare, contrast, and quantify the correlation properties of different sequences, including a number of yeast, human, and prokaryotic sequences. We exclude the possibility that the correlation properties and the known mosaic structure of DNA can be explained either by simple Markov processes or by tandem repeats of dinucleotides. We find that the distinct patch sizes in all 16 yeast chromosomes are similar. Furthermore, we test the hypothesis that, for yeast, patchiness is caused by the alternation of coding and noncoding regions, and the hypothesis that in human sequences patchiness is related to repetitive sequences. We find that, by themselves, neither the alternation of coding and noncoding regions, nor repetitive sequences, can fully explain the long-range correlation properties of DNA.
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170
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Grübel P, Bhaskar KR, Cave DR, Garik P, Stanley HE, Lamont JT. Interaction of an aluminum-magnesium containing antacid and gastric mucus: possible contribution to the cytoprotective function of antacids. Aliment Pharmacol Ther 1997; 11:139-45. [PMID: 9042986 DOI: 10.1046/j.1365-2036.1997.104275000.x] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 02/03/2023]
Abstract
BACKGROUND Antacids are generally thought to protect the gastric mucosa from damage primarily by their ability to neutralize hydrochloric acid, but recently other mechanisms of antacid cytoprotection have been suggested. The aim of our study was to determine if the antacid hydrotalcit (Mg6Al2(OH)16CO3 x 4H2O) and its clinical formulations Talcid (suspension and tablet) can influence the acid barrier properties of pig gastric mucus (PGM). METHODS Viscosities, flow patterns of injected HCl, and permeability to HCl were assayed in solutions of PGM with and without added antacid. RESULTS Talcid-suspension markedly increased mucin viscosity between pH 2 and 7. In contrast, powdered Talcid-tablet and hydrotalcit noticeably reduced mucin viscosity at pH 5 and below. HCl barely diffused through PGM-Talcid-suspension, whereas the acid was able to quickly penetrate a PGM-Talcid-tablet powder or PGM-hydrotalcit mixture. When injected into a mixture of PGM-Talcid-suspension, HCl travelled in a single distinct channel whereas in both PGM-Talcid-tablet powder or PGM-hydrotalcit mixtures, the acid mixed irregularly throughout. Experiments with antacids alone revealed that Talcid-suspension, but not Talcid-tablet nor hydrotalcit, had barrier properties similar to PGM. CONCLUSION Talcid-suspension has viscoelastic features similar to gastric mucin and may afford mucosal protection by its ability to maintain or mimic the barrier properties of gastric mucus gel. In contrast, powdered Talcid-tablets and hydrotalcit reduce the barrier function of gastric mucus.
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171
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Viswanathan GM, Peng CK, Stanley HE, Goldberger AL. Deviations from uniform power law scaling in nonstationary time series. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1997; 55:845-9. [PMID: 11541831 DOI: 10.1103/physreve.55.845] [Citation(s) in RCA: 80] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Abstract
A classic problem in physics is the analysis of highly nonstationary time series that typically exhibit long-range correlations. Here we test the hypothesis that the scaling properties of the dynamics of healthy physiological systems are more stable than those of pathological systems by studying beat-to-beat fluctuations in the human heart rate. We develop techniques based on the Fano factor and Allan factor functions, as well as on detrended fluctuation analysis, for quantifying deviations from uniform power-law scaling in nonstationary time series. By analyzing extremely long data sets of up to N = 10(5) beats for 11 healthy subjects, we find that the fluctuations in the heart rate scale approximately uniformly over several temporal orders of magnitude. By contrast, we find that in data sets of comparable length for 14 subjects with heart disease, the fluctuations grow erratically, indicating a loss of scaling stability.
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172
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Kutnjak-Urbanc B, Havlin S, Stanley HE. Temporal correlations in a one-dimensional sandpile model. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 54:6109-6113. [PMID: 9965829 DOI: 10.1103/physreve.54.6109] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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173
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Starr FW, Harrington ST, Boghosian BM, Stanley HE. Interface Roughening in a Hydrodynamic Lattice-Gas Model with Surfactant. PHYSICAL REVIEW LETTERS 1996; 77:3363-3366. [PMID: 10062201 DOI: 10.1103/physrevlett.77.3363] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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174
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Makse HA, Davies GW, Havlin S, Ivanov PC, King PR, Stanley HE. Long-range correlations in permeability fluctuations in porous rock. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 54:3129-3134. [PMID: 9965453 DOI: 10.1103/physreve.54.3129] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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175
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Ivanov PC, Rosenblum MG, Peng CK, Mietus J, Havlin S, Stanley HE, Goldberger AL. Scaling behaviour of heartbeat intervals obtained by wavelet-based time-series analysis. Nature 1996; 383:323-7. [PMID: 8848043 DOI: 10.1038/383323a0] [Citation(s) in RCA: 416] [Impact Index Per Article: 14.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023]
Abstract
Biological time-series analysis is used to identify hidden dynamical patterns which could yield important insights into underlying physiological mechanisms. Such analysis is complicated by the fact that biological signals are typically both highly irregular and non-stationary, that is, their statistical character changes slowly or intermittently as a result of variations in background influences. Previous statistical analyses of heartbeat dynamics have identified long-range correlations and power-law scaling in the normal heartbeat, but not the phase interactions between the different frequency components of the signal. Here we introduce a new approach, based on the wavelet transform and an analytic signal approach, which can characterize non-stationary behaviour and elucidate such phase interactions. We find that, when suitably rescaled, the distributions of the variations in the beat-to-beat intervals for all healthy subjects are described by a single function stable over a wide range of timescales. However, a similar scaling function does not exist for a group with cardiopulmonary instability caused by sleep apnoea. We attribute the functional form of the scaling observed in the healthy subjects to underlying nonlinear dynamics, which seem to be essential to normal heart function. The approach introduced here should be useful in the analysis of other nonstationary biological signals.
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176
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Zapperi S, Stanley HE. Self-organized branching processes: Avalanche models with dissipation. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 54:2483-2488. [PMID: 9965358 DOI: 10.1103/physreve.54.2483] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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177
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Spasojevic D, Bukvic S, Milosevic S, Stanley HE. Barkhausen noise: Elementary signals, power laws, and scaling relations. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 54:2531-2546. [PMID: 9965364 DOI: 10.1103/physreve.54.2531] [Citation(s) in RCA: 154] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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178
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Kutnjak-Urbanc B, Zapperi S, Milosevic S, Stanley HE. Sandpile model on the Sierpinski gasket fractal. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 54:272-277. [PMID: 9965069 DOI: 10.1103/physreve.54.272] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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179
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Sastry S, Debenedetti PG, Sciortino F, Stanley HE. Singularity-free interpretation of the thermodynamics of supercooled water. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 53:6144-6154. [PMID: 9964976 DOI: 10.1103/physreve.53.6144] [Citation(s) in RCA: 275] [Impact Index Per Article: 9.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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180
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Czirók A, Stanley HE, Vicsek T. Possible origin of power-law behavior in n-tuple Zipf analysis. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 53:6371-6375. [PMID: 9964996 DOI: 10.1103/physreve.53.6371] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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181
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Makse HA, Barabási AL, Stanley HE. Elastic string in a random medium. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 53:6573-6576. [PMID: 9965025 DOI: 10.1103/physreve.53.6573] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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182
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Makse HA, Havlin S, Schwartz M, Stanley HE. Method for generating long-range correlations for large systems. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 53:5445-5449. [PMID: 9964877 DOI: 10.1103/physreve.53.5445] [Citation(s) in RCA: 71] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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183
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Barabási AL, Buldyrev SV, Stanley HE, Suki B. Avalanches in the lung: A statistical mechanical model. PHYSICAL REVIEW LETTERS 1996; 76:2192-2195. [PMID: 10060629 DOI: 10.1103/physrevlett.76.2192] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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184
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Mantegna RN, Buldyrev SV, Goldberger AL, Havlin S, Peng C, Simons M, Stanley HE. Mantegna et al. reply. PHYSICAL REVIEW LETTERS 1996; 76:1979-1981. [PMID: 10060574 DOI: 10.1103/physrevlett.76.1979] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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185
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Schwarzer S, Havlin S, Ossadnik P, Stanley HE. Number of branches in diffusion-limited aggregates: The skeleton. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 53:1795-1804. [PMID: 9964441 DOI: 10.1103/physreve.53.1795] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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186
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Peng CK, Havlin S, Stanley HE, Goldberger AL. Fractal scaling properties in nonstationary heartbeat time series. ACTA ACUST UNITED AC 1996. [DOI: 10.1063/1.51000] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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187
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Cuerno R, Makse HA, Tomassone S, Harrington ST, Stanley HE. Stochastic model for surface erosion via ion sputtering: Dynamical evolution from ripple morphology to rough morphology. PHYSICAL REVIEW LETTERS 1995; 75:4464-4467. [PMID: 10059915 DOI: 10.1103/physrevlett.75.4464] [Citation(s) in RCA: 25] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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188
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Sciortino F, Essmann U, Stanley HE, Hemmati M, Shao J, Wolf GH, Angell CA. Crystal stability limits at positive and negative pressures, and crystal-to-glass transitions. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995; 52:6484-6491. [PMID: 9964167 DOI: 10.1103/physreve.52.6484] [Citation(s) in RCA: 21] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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189
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Zapperi S, Stanley HE. Self-organized branching processes: Mean-field theory for avalanches. PHYSICAL REVIEW LETTERS 1995; 75:4071-4074. [PMID: 10059807 DOI: 10.1103/physrevlett.75.4071] [Citation(s) in RCA: 120] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/21/2023]
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190
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Horváth VK, Stanley HE. Temporal scaling of interfaces propagating in porous media. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995; 52:5166-5169. [PMID: 9964016 DOI: 10.1103/physreve.52.5166] [Citation(s) in RCA: 66] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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191
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Gyure MF, Harrington ST, Strilka R, Stanley HE. Scaling in late stage spinodal decomposition with quenched disorder. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995; 52:4632-4639. [PMID: 9963955 DOI: 10.1103/physreve.52.4632] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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192
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Amaral LA, Barabási AL, Makse HA, Stanley HE. Scaling properties of driven interfaces in disordered media. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995; 52:4087-4104. [PMID: 9963882 DOI: 10.1103/physreve.52.4087] [Citation(s) in RCA: 62] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Araujo M, Larralde H, Havlin S, Stanley HE. Araujo et al. reply. PHYSICAL REVIEW LETTERS 1995; 75:2251. [PMID: 10059254 DOI: 10.1103/physrevlett.75.2251] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Mantegna RN, Buldyrev SV, Goldberger AL, Havlin S, Peng CK, Simons M, Stanley HE. Systematic analysis of coding and noncoding DNA sequences using methods of statistical linguistics. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995; 52:2939-50. [PMID: 9963739 DOI: 10.1103/physreve.52.2939] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/16/2023]
Abstract
We compare the statistical properties of coding and noncoding regions in eukaryotic and viral DNA sequences by adapting two tests developed for the analysis of natural languages and symbolic sequences. The data set comprises all 30 sequences of length above 50 000 base pairs in GenBank Release No. 81.0, as well as the recently published sequences of C. elegans chromosome III (2.2 Mbp) and yeast chromosome XI (661 Kbp). We find that for the three chromosomes we studied the statistical properties of noncoding regions appear to be closer to those observed in natural languages than those of coding regions. In particular, (i) a n-tuple Zipf analysis of noncoding regions reveals a regime close to power-law behavior while the coding regions show logarithmic behavior over a wide interval, while (ii) an n-gram entropy measurement shows that the noncoding regions have a lower n-gram entropy (and hence a larger "n-gram redundancy") than the coding regions. In contrast to the three chromosomes, we find that for vertebrates such as primates and rodents and for viral DNA, the difference between the statistical properties of coding and noncoding regions is not pronounced and therefore the results of the analyses of the investigated sequences are less conclusive. After noting the intrinsic limitations of the n-gram redundancy analysis, we also briefly discuss the failure of the zeroth- and first-order Markovian models or simple nucleotide repeats to account fully for these "linguistic" features of DNA. Finally, we emphasize that our results by no means prove the existence of a "language" in noncoding DNA.
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Buldyrev SV, Havlin S, Kertész J, Sadr-Lahijany R, Shehter A, Stanley HE. Surface roughening with quenched disorder in high dimensions: Exact results for the Cayley tree. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995; 52:373-388. [PMID: 9963441 DOI: 10.1103/physreve.52.373] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Czirók A, Mantegna RN, Havlin S, Stanley HE. Correlations in binary sequences and a generalized Zipf analysis. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995; 52:446-452. [PMID: 9963447 DOI: 10.1103/physreve.52.446] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Havlin S, Buldyrev SV, Goldberger AL, Mantegna RN, Peng CK, Simons M, Stanley HE. Statistical and linguistic features of DNA sequences. FRACTALS 1995; 3:269-284. [PMID: 11539281 DOI: 10.1142/s0218348x95000229] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
We present evidence supporting the idea that the DNA sequence in genes containing noncoding regions is correlated, and that the correlation is remarkably long range--indeed, base pairs thousands of base pairs distant are correlated. We do not find such a long-range correlation in the coding regions of the gene. We resolve the problem of the "non-stationary" feature of the sequence of base pairs by applying a new algorithm called Detrended Fluctuation Analysis (DFA). We address the claim of Voss that there is no difference in the statistical properties of coding and noncoding regions of DNA by systematically applying the DFA algorithm, as well as standard FFT analysis, to all eukaryotic DNA sequences (33 301 coding and 29 453 noncoding) in the entire GenBank database. We describe a simple model to account for the presence of long-range power-law correlations which is based upon a generalization of the classic Levy walk. Finally, we describe briefly some recent work showing that the noncoding sequences have certain statistical features in common with natural languages. Specifically, we adapt to DNA the Zipf approach to analyzing linguistic texts, and the Shannon approach to quantifying the "redundancy" of a linguistic text in terms of a measurable entropy function. We suggest that noncoding regions in plants and invertebrates may display a smaller entropy and larger redundancy than coding regions, further supporting the possibility that noncoding regions of DNA may carry biological information.
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Havlin S, Amaral LA, Buldyrev SV, Harrington ST, Stanley HE. Dynamics of surface roughening with quenched disorder. PHYSICAL REVIEW LETTERS 1995; 74:4205-4208. [PMID: 10058442 DOI: 10.1103/physrevlett.74.4205] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Buldyrev SV, Goldberger AL, Havlin S, Mantegna RN, Matsa ME, Peng CK, Simons M, Stanley HE. Long-range correlation properties of coding and noncoding DNA sequences: GenBank analysis. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995; 51:5084-91. [PMID: 9963221 DOI: 10.1103/physreve.51.5084] [Citation(s) in RCA: 476] [Impact Index Per Article: 16.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Abstract
An open question in computational molecular biology is whether long-range correlations are present in both coding and noncoding DNA or only in the latter. To answer this question, we consider all 33301 coding and all 29453 noncoding eukaryotic sequences--each of length larger than 512 base pairs (bp)--in the present release of the GenBank to dtermine whether there is any statistically significant distinction in their long-range correlation properties. Standard fast Fourier transform (FFT) analysis indicates that coding sequences have practically no correlations in the range from 10 bp to 100 bp (spectral exponent beta=0.00 +/- 0.04, where the uncertainty is two standard deviations). In contrast, for noncoding sequences, the average value of the spectral exponent beta is positive (0.16 +/- 0.05) which unambiguously shows the presence of long-range correlations. We also separately analyze the 874 coding and the 1157 noncoding sequences that have more than 4096 bp and find a larger region of power-law behavior. We calculate the probability that these two data sets (coding and noncoding) were drawn from the same distribution and we find that it is less than 10(-10). We obtain independent confirmation of these findings using the method of detrended fluctuation analysis (DFA), which is designed to treat sequences with statistical heterogeneity, such as DNA's known mosaic structure ("patchiness") arising from the nonstationarity of nucleotide concentration. The near-perfect agreement between the two independent analysis methods, FFT and DFA, increases the confidence in the reliability of our conclusion.
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Amaral LA, Barabási A, Buldyrev SV, Harrington ST, Havlin S, Sadr-Lahijany R, Stanley HE. Avalanches and the directed percolation depinning model: Experiments, simulations, and theory. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995; 51:4655-4673. [PMID: 9963178 DOI: 10.1103/physreve.51.4655] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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