Search PubMed⌕ Search

Biomedical subjects

H E Stanley

Publications and source records attributed to H E Stanley.

At least 19 recordsLinked to original sources
PubMed2001

Scale invariance in the nonstationarity of human heart rate.

We introduce a segmentation algorithm to probe the temporal organization of heterogeneities in human heartbeat interval time series. We find that the lengths of segments with different local mean heart rates follow a power-law distribution and show that this scale-invariant structure is not a simple consequence of the long-range correlations present in the data. The differences in mean heart rates between consecutive segments display a common functional form, but with different parameters for healthy individuals and for heart-failure patients. These findings suggest that there is relevant physiological information hidden in the heterogeneities of the heartbeat time series.

Algorithms↗
PubMed2001

Average time spent by Lévy flights and walks on an interval with absorbing boundaries.

We consider a Lévy flyer of order alpha that starts from a point x(0) on an interval [O,L] with absorbing boundaries. We find a closed-form expression for the average number of flights the flyer takes and the total length of the flights it travels before it is absorbed. These two quantities are equivalent to the mean first passage times for Lévy flights and Lévy walks, respectively. Using fractional differential equations with a Riesz kernel, we find exact analytical expressions for both quantities in the continuous limit. We show that numerical solutions for the discrete Lévy processes converge to the continuous approximations in all cases except the case of alpha-->2, and the cases of x(0)-->0 and x(0)-->L. For alpha>2, when the second moment of the flight length distribution exists, our result is replaced by known results of classical diffusion. We show that if x(0) is placed in the vicinity of absorbing boundaries, the average total length has a minimum at alpha=1, corresponding to the Cauchy distribution. We discuss the relevance of this result to the problem of foraging, which has received recent attention in the statistical physics literature.

Journal Article↗
PubMed2001

Quantifying and interpreting collective behavior in financial markets.

Firms having similar business activities are correlated. We analyze two different cross-correlation matrices C constructed from (i) 30-min price fluctuations of 1000 US stocks for the two-year period 1994-95 and (ii) one-day price fluctuations of 422 US stocks for the 35-year period 1962-96. We find that the eigenvectors of C corresponding to the largest eigenvalues allow us to partition the set of all stocks into distinct subsets. These subsets are similar to business sectors, and are stable for extended periods of time. We find that price fluctuations of these subsets are characterized by power-law decaying time correlations, reminiscent of strongly interacting systems.

Journal Article↗
PubMed2001

Dynamics of supercooled water in configuration space.

We study the potential energy surface (PES) sampled by a liquid modeled via the widely studied extended simple point charge (SPC/E) model for water. We characterize the curvature of the PES by calculating the instantaneous normal mode (INM) spectrum for a wide range of densities and temperatures. We discuss the information contained in the INM density of states, which requires additional processing to be unambiguously associated with the long-time dynamics. For the SPC/E model, we find that the slowing down of the dynamics in the supercooled region-where the ideal mode coupling theory has been used to describe the dynamics-is controlled by the reduction in the number of directions in configuration space that allow a structural change. We find that the fraction f(dw) of the double-well directions in configuration space determines the value of the diffusion constant D, thereby relating a property of the PES to a macroscopic dynamic quantity; specifically, it appears that square root D is approximately linear in f(dw). Our findings are consistent with the hypothesis that, at the mode coupling crossover temperature, dynamical processes based on the free exploration of configuration space vanish, and processes requiring activation dominate. Hence, the reduction of the number of directions allowing free exploration of configuration space is the mechanism of diffusion implicitly implemented in the ideal mode coupling theory. Additionally, we find a direct relationship between the number of basins sampled by the system and the number of free directions. In this picture, diffusion appears to be related to geometrical properties of the PES, and to be entropic in origin.

Journal Article↗
PubMed2001

Avalanche dynamics of crackle sound in the lung.

We analyze a sequence of short transient sound waves, called "crackles," which are associated with explosive openings of airways during lung inflation. The distribution of time intervals between consecutive crackles Delta(t) shows two regimes of power law behavior. We develop an avalanche model which fits the data over five decades of Delta(t). We find that the regime for large Delta(t) is related to the dynamics of distinct avalanches in a Cayley tree, and the regime for small Delta(t) is determined by the dynamics of crackle propagation within a single avalanche. We also obtain a mean-field solution of the model which provides information about lung inflation.

Acoustics↗
PubMed2001

Noise effects on the complex patterns of abnormal heartbeats.

Patients at high risk for sudden death often exhibit complex heart rhythms in which abnormal heartbeats are interspersed with normal heartbeats. We analyze such a complex rhythm in a single patient over a 12-h period and show that the rhythm can be described by a theoretical model consisting of two interacting oscillators with stochastic elements. By varying the magnitude of the noise, we show that for an intermediate level of noise, the model gives best agreement with key statistical features of the dynamics.

Arrhythmias, Cardiac↗
PubMed2001

Percolation threshold, Fisher exponent, and shortest path exponent for four and five dimensions.

We develop a method of constructing percolation clusters that allows us to build very large clusters using very little computer memory by limiting the maximum number of sites for which we maintain state information to a number of the order of the number of sites in the largest chemical shell of the cluster being created. The memory required to grow a cluster of mass s is of the order of s(straight theta) bytes where straight theta ranges from 0.4 for two-dimensional (2D) lattices to 0.5 for six (or higher)-dimensional lattices. We use this method to estimate d(min), the exponent relating the minimum path l to the Euclidean distance r, for 4D and 5D hypercubic lattices. Analyzing both site and bond percolation, we find d(min)=1.607+/-0.005 (4D) and d(min)=1.812+/-0.006 (5D). In order to determine d(min) to high precision, and without bias, it was necessary to first find precise values for the percolation threshold, p(c): p(c)=0.196889+/-0.000003 (4D) and p(c)=0.14081+/-0.00001 (5D) for site and p(c)=0.160130+/-0.000003 (4D) and p(c)=0.118174+/-0.000004 (5D) for bond percolation. We also calculate the Fisher exponent tau determined in the course of calculating the values of p(c): tau=2.313+/-0.003 (4D) and tau=2.412+/-0.004 (5D).

Journal Article↗
PubMed2001

Characterization of the branching structure of the lung from "macroscopic" pressure-volume measurements.

We analyze the problem of fluid flow in a bifurcating structure containing random blockages that can be removed by fluid pressure. We introduce an asymmetric tree model and find that the predicted pressure-volume relation is connected to the distribution Pi(n) of the generation number n of the tree's terminal segments. We use this relation to explore the branching structure of the lung by analyzing experimental pressure-volume data from dog lungs. The Pi(n) extracted from the data using the model agrees well with experimental data on the branching structure. We can thus obtain information about the asymmetric structure of the lung from macroscopic, noninvasive pressure-volume measurements.

Animals↗
PubMed2001

Effect of trends on detrended fluctuation analysis.

Detrended fluctuation analysis (DFA) is a scaling analysis method used to estimate long-range power-law correlation exponents in noisy signals. Many noisy signals in real systems display trends, so that the scaling results obtained from the DFA method become difficult to analyze. We systematically study the effects of three types of trends--linear, periodic, and power-law trends, and offer examples where these trends are likely to occur in real data. We compare the difference between the scaling results for artificially generated correlated noise and correlated noise with a trend, and study how trends lead to the appearance of crossovers in the scaling behavior. We find that crossovers result from the competition between the scaling of the noise and the "apparent" scaling of the trend. We study how the characteristics of these crossovers depend on (i) the slope of the linear trend; (ii) the amplitude and period of the periodic trend; (iii) the amplitude and power of the power-law trend, and (iv) the length as well as the correlation properties of the noise. Surprisingly, we find that the crossovers in the scaling of noisy signals with trends also follow scaling laws--i.e., long-range power-law dependence of the position of the crossover on the parameters of the trends. We show that the DFA result of noise with a trend can be exactly determined by the superposition of the separate results of the DFA on the noise and on the trend, assuming that the noise and the trend are not correlated. If this superposition rule is not followed, this is an indication that the noise and the superposed trend are not independent, so that removing the trend could lead to changes in the correlation properties of the noise. In addition, we show how to use DFA appropriately to minimize the effects of trends, how to recognize if a crossover indicates indeed a transition from one type to a different type of underlying correlation, or if the crossover is due to a trend without any transition in the dynamical properties of the noise.

Analysis of Variance↗
PubMed2001

Behavioral-independent features of complex heartbeat dynamics.

We test whether the complexity of the cardiac interbeat interval time series is simply a consequence of the wide range of scales characterizing human behavior, especially physical activity, by analyzing data taken from healthy adult subjects under three conditions with controls: (i) a "constant routine" protocol where physical activity and postural changes are kept to a minimum, (ii) sympathetic blockade, and (iii) parasympathetic blockade. We find that when fluctuations in physical activity and other behavioral modifiers are minimized, a remarkable level of complexity of heartbeat dynamics remains, while for neuroautonomic blockade the multifractal complexity decreases.

Activities of Daily Living↗
PubMed2001

Dynamics of viscous penetration in percolation porous media.

We investigate the dynamics of viscous penetration in two-dimensional percolation networks at criticality for the case in which the ratio between the viscosities of displaced and injected fluids is very large. We report extensive numerical simulations that indicate that the scaling exponents for the breakthrough time distribution are the same as the previously reported values computed for the case of unit viscosity ratio. Our results are consistent with the possibility that viscous displacement through critical percolation networks constitutes a single universality class, independent of the viscosity ratio. We also find that the distributions of mass and breakthrough time of the invaded clusters have the same scaling form, but with different critical exponents.

Journal Article↗
PubMed2001

Waterlike anomalies for core-softened models of fluids: two-dimensional systems.

We use molecular-dynamics simulations in two dimensions to investigate the possibility that a core-softened potential can reproduce static and dynamic anomalies found experimentally in liquid water: (i) the increase in specific volume upon cooling, (ii) the increase in isothermal compressibility upon cooling, and (iii) the increase in the diffusion coefficient with pressure. We relate these anomalies to the shape of the potential. We obtain the phase diagram of the system and identify two solid phases: a square crystal (high-density phase) and a triangular crystal (low-density phase). We also discuss the relation between the anomalies observed and the polymorphism of the solid. Finally, we compare the phase diagram of our model system with experimental data, noting especially the line of temperatures of maximum density, the line of pressures of maximum diffusion constant, and the line of temperatures of minimum isothermal compressibility.

Journal Article↗
PubMed2001

Thermodynamic and structural aspects of the potential energy surface of simulated water.

Relations between the thermodynamics and dynamics of supercooled liquids approaching a glass transition is a topic of considerable interest. The potential energy surface of model liquids has been increasingly studied, since it provides a connection between the configurational component of the partition function on the one hand, and the system dynamics on the other. This connection is most obvious at low temperatures, where the motion of the system can be partitioned into vibrations within a basin of attraction and infrequent interbasin transitions. In this work, we present a description of the potential energy surface properties of supercooled liquid water. The dynamics of this model have been studied in great detail in recent years. We locate the minima sampled by the liquid by "quenches" from equilibrium configurations generated via molecular dynamics simulations, and then calculate the temperature and density dependence of the basin energy, degeneracy, and shape. The temperature dependence of the energy of the minima is qualitatively similar to simple liquids, but has anomalous density dependence. The unusual density dependence is also reflected in the configurational entropy, the thermodynamic measure of degeneracy. Finally, we study the structure of simulated water at the minima, which provides insight on the progressive tetrahedral ordering of the liquid on cooling.

Journal Article↗
PubMed2001

Magnitude and sign correlations in heartbeat fluctuations.

We propose an approach for analyzing signals with long-range correlations by decomposing the signal increment series into magnitude and sign series and analyzing their scaling properties. We show that signals with identical long-range correlations can exhibit different time organization for the magnitude and sign. We find that the magnitude series relates to the nonlinear properties of the original time series, while the sign series relates to the linear properties. We apply our approach to the heartbeat interval series and find that the magnitude series is long-range correlated, while the sign series is anticorrelated and that both magnitude and sign series may have clinical applications.

Algorithms↗
PubMed2001

Thermodynamically important contacts in folding of model proteins.

We introduce a quantity, the entropic susceptibility, that measures the thermodynamic importance-for the folding transition-of the contacts between amino acids in model proteins. Using this quantity, we find that only one equilibrium run of a computer simulation of a model protein is sufficient to select a subset of contacts that give rise to the peak in the specific heat observed at the folding transition. To illustrate the method, we identify thermodynamically important contacts in a model 46-mer. We show that only about 50% of all contacts present in the protein native state are responsible for the sharp peak in the specific heat at the folding transition temperature, while the remaining 50% of contacts do not affect the specific heat.

Amino Acids↗
PubMed2001

Generic mechanism for generating a liquid-liquid phase transition.

Recent experimental results indicate that phosphorus--a single-component system--can have a high-density liquid (HDL) and a low-density liquid (LDL) phase. A first-order transition between two liquids of different densities is consistent with experimental data for a variety of materials, including single-component systems such as water, silica and carbon. Molecular dynamics simulations of very specific models for supercooled water, liquid carbon and supercooled silica predict a LDL-HDL critical point, but a coherent and general interpretation of the LDL-HDL transition is lacking. Here we show that the presence of a LDL and a HDL can be directly related to an interaction potential with an attractive part and two characteristic short-range repulsive distances. This kind of interaction is common to other single-component materials in the liquid state (in particular, liquid metals), and such potentials are often used to describe systems that exhibit a density anomaly. However, our results show that the LDL and HDL phases can occur in systems with no density anomaly. Our results therefore present an experimental challenge to uncover a liquid-liquid transition in systems like liquid metals, regardless of the presence of a density anomaly.

Journal Article↗