Limb dominance changes in walking evolution explored by asymmetric correlations in gait dynamics

Fluctuations in the stride interval time series of unconstrained walking are not random but seem to exhibit long-range correlations that decay as a power law (Hausdorff et al. (1995) [35]). Here, we examine whether asymmetries are present in the long-range correlations of different gait parameters (stride, swing and stance intervals) for the left and right limbs. Gait dynamics corresponding to 16 healthy subjects were obtained from the Physionet database, which contains stride, stance and swing intervals for both left and right limbs. Detrended Fluctuation Analysis (DFA) revealed the presence of asymmetric long-range correlations in all gait cycle variables investigated. A rich variety of scaling exponent dynamics was found, with the presence of synchronicity, decreased correlations and dominant correlations. The results are discussed in terms of the hypothesis that reduced strength of long-range correlations reflect both enhanced stability and adaptability.     

Statistical mechanics in biology: how ubiquitous are long-range correlations?

The purpose of this opening talk is to describe examples of recent progress in applying statistical mechanics to biological systems. We first briefly review several biological systems, and then focus on the fractal features characterized by the long-range correlations found recently in DNA sequences containing non-coding material. We discuss the evidence supporting the finding that for sequences containing only coding regions, there are no long-range correlations. We also discuss the recent finding that the exponent alpha characterizing the long-range correlations increases with evolution, and we discuss two related models, the insertion model and the insertion-deletion model, that may account for the presence of long-range correlations. Finally, we summarize the analysis of long-term data on human heartbeats (up to 10(4) heart beats) that supports the possibility that the successive increments in the cardiac beat-to-beat intervals of healthy subjects display scale-invariant, long-range "anti-correlations" (a tendency to beat faster is balanced by a tendency to beat slower later on). In contrast, for a group of subjects with severe heart disease, long-range correlations vanish. This finding suggests that the classical theory of homeostasis, according to which stable physiological processes seek to maintain "constancy," should be extended to account for this type of dynamical, far from equilibrium, behavior.     

Modeling long-range cross-correlations in two-component ARFIMA and FIARCH processes

We investigate how simultaneously recorded long-range power-law correlated multivariate signals cross-correlate. To this end we introduce a two-component ARFIMA stochastic process and a two-component FIARCH process to generate coupled fractal signals with long-range power-law correlations which are at the same time long-range cross-correlated. We study how the degree of cross-correlations between these signals depends on the scaling exponents characterizing the fractal correlations in each signal and on the coupling between the signals. Our findings have relevance when studying parallel outputs of multiple component of physical, physiological and social systems.     

Long-range strain correlations in sheared colloidal glasses

Glasses behave as solids on experimental time scales due to their slow relaxation. Growing dynamic length scales due to cooperative motion of particles are believed to be central to this slow response. For quiescent glasses, however, the size of the cooperatively rearranging regions has never been observed to exceed a few particle diameters, and the observation of long-range correlations has remained elusive. Here, we provide direct experimental evidence of long-range correlations during the deformation of a dense colloidal glass. By imposing an external stress, we force structural rearrangements, and we identify long-range correlations in the fluctuations of microscopic strain and elucidate their scaling and spatial symmetry. The applied shear induces a transition from homogeneous to inhomogeneous flow at a critical shear rate, and we investigate the role of strain correlations in this transition.     

Fluctuations in fluids out of thermal equilibrium

After a brief review of dynamic correlations in equilibrium fluids, we consider the long-range correlations between the fluctuations in a fluid subjected to a large stationary temperature gradient. These long-range correlations enhance and modify the Rayleigh spectrum of the fluid. We elucidate that the modifications of the Rayleigh line are determined by the coupling of the entropy fluctuations to the transverse velocity fluctuations. Recent attempts to test the theoretical predictions with the aid of light-scattering experiments are discussed.     

一维扩展量子罗盘模型的拓扑序和量子相变

应用矩阵乘积态表示的无限虚时间演化块算法,研究了扩展的量子罗盘模型.为了深入研究该模型的长程拓扑序和量子相变,基于奇数键和偶数键,引入了奇数弦关联和偶数弦关联,计算了保真度、奇数弦关联、偶数弦关联、奇数弦关联饱和性与序参量.弦关联表现出三种截然不同的行为:衰减为零、单调饱和与振荡饱和.基于弦关联的以上特征,给出了量子罗盘模型的基态序参量相图.在临界区,局域磁化强度和单调奇弦序参量的临界指数β=1/8表明:相变的普适类是Ising类型.此外,保真度探测到的相变点、连续性与非连续性和序参量的结果一致.     

Application of statistical physics to heartbeat diagnosis.

We present several recent studies based on statistical physics concepts that can be used as diagnostic tools for heart failure. We describe the scaling exponent characterizing the long-range correlations in heartbeat time series as well as the multifractal features recently discovered in heartbeat rhythm. It is found that both features, the long-range correlations and the multifractility, are weaker in cases of heart failure.     

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.     

The pairing correlations in the phased t－U Hubbard model

In this paper we have studied the phased t－U Hubbard model. Using the constrained path Monte Carlo method, we investigated the effects of phase factor on pairing correlation functions in the ground state, and we found that the long-range correlations are dependent on the choice of phase factor, and for some special values of phase factor there exist long-range pairing correlations only in the strong coupling region.     

Nucleotide composition effects on the long-range correlations in human genes

We use the wavelet transform to investigate the fractal scaling properties of coding and noncoding human DNA sequences. We find that the strength of the long-range correlations observed in the introns increases with the guanine-cytosine (GC) content, while coding sequences show no such correlations at any GC content. However, we demonstrate that long-range correlations can be detected when the coding sequences are undersampled by retaining the third base of each codon only. This strongly suggests that the observed correlations are not likely to be due to insertion-deletion mechanisms. We comment about the origin of these correlations in terms of putative dynamical processes that could produce the isochore structure of the human genome. Received: 18 August 1997 / Accepted: 29 October 1997     

Fractal landscape analysis of DNA walks

By mapping nucleotide sequences onto a "DNA walk", we uncovered remarkably long-range power law correlations [Nature 356 (1992) 168] that imply a new scale invariant property of DNA. We found such long-range correlations in intron-containing genes and in non-transcribed regulatory DNA sequences, but not in cDNA sequences or intron-less genes. In this paper, we present more explicit evidences to support our findings.     

Experiments to detect long-range heteronuclear shift correlations: LR-J-HSMQC

The utility of the J-HSMQC experiment to detect long-range CH correlations was investigated. Two new long-range J-compensated pulse sequences, LR-J-HSMQC(80,27) and LR-J-HSMQC(27,80), were developed using the (3beta(x))beta(y) composite 90 degrees pulse sequence. These two experiments were shown to be effective for long-range coupling constants, (n)J(CH), that were greater than 3 Hz. Although the overall sensitivities of the long-range J-HSMQC experiments were slightly lower than that of the conventional decoupled HMBC experiment, their 2D maps showed additional cross peaks that could be useful in structure elucidation. LR-J-HSMQC(27,80) was very efficient in yielding two- and four-bond relay correlations. The utility of the new sequences is demonstrated with strychnine as the sample.     

Current-voltage characteristics of double-strand DNA sequences

We use a tight-binding formulation to investigate the transmissivity and the current-voltage (I-V) characteristics of sequences of double-strand DNA molecules. In order to reveal the relevance of the underlying correlations in the nucleotides distribution, we compare the results for the genomic DNA sequence with those of artificial sequences (the long-range correlated Fibonacci and Rudin-Shapiro one) and a random sequence, which is a kind of prototype of a short-range correlated system. The random sequence is presented here with the same first neighbors pair correlations of the human DNA sequence. We found that the long-range character of the correlations is important to the transmissivity spectra, although the I-V curves seem to be mostly influenced by the short-range correlations.     

Evidence of long-distance correlation of fluctuations during edge transitions to improved-confinement regimes in the TJ-II stellarator

Long-distance coupling between edge parameters' fluctuations has been investigated in the TJ-II stellarator. Results show long-range correlations in potential fluctuations, which are amplified by the development of radial electric fields during transitions to improved-confinement regimes, whereas there is no correlation between ion saturation current signals. These experimental findings suggest the importance of long-range correlations as a new fingerprint of the plasma behavior during the development of edge shear flows and the key role of electric fields to amplify them.     

Solvable sequence evolution models and genomic correlations

We study a minimal model for genome evolution whose elementary processes are single site mutation, duplication and deletion of sequence regions, and insertion of random segments. These processes are found to generate long-range correlations in the composition of letters as long as the sequence length is growing; i.e., the combined rates of duplications and insertions are higher than the deletion rate. For constant sequence length, on the other hand, all initial correlations decay exponentially. These results are obtained analytically and by simulations. They are compared with the long-range correlations observed in genomic DNA, and the implications for genome evolution are discussed.     

Pressure-Induced Crossover From Two- to Three-Dimensional Magnetic Correlations in La 1.4 Sr 1.6 Mn 2 O 7 Manganite

Magnetic pressure-temperature phase diagram of La 1.4 Sr 1.6 Mn 2 O 7 layered manganese oxide has been studied by neutron diffraction. Three phases have been found in this compound at ambient pressure: high-temperature phase with quasi two-dimensional correlations of the magnetic moments on Mn sites and two low-temperature phases with long-range order - antiferromagnetic and ferromagnetic. Under hydrostatic pressure the antiferromagnetic phase is favoured with respect to the two-dimensional and long-range ferromagnetic phases. The magnetic phase with two-dimensional correlations is thus suppressed by the antiferromagnetic phase with long-range order. We discuss this result in terms of the pressure-induced electron transfer and compare our conclusions with predictions given by theoretical calculations.     

Density functional theory for polyelectrolytes near oppositely charged surfaces

We report a nonlocal density functional theory of polyelectrolyte solutions that faithfully accounts for both short- and long-range correlations neglected in a typical mean-field method. It is shown that for systems with strong electrostatic interactions, the long-range correlations are subdued by direct Coulomb attractions, thereby manifesting strong local excluded-volume effects. The theory has also been used to describe the influence of the polyion chain length and small ion valence on charge inversion due to the adsorption of polyelectrolytes at an oppositely charged surface.     

Fractal landscapes in biological systems: long-range correlations in DNA and interbeat heart intervals

Here we discuss recent advances in applying ideas of fractals and disordered systems to two topics of biological interest, both topics having common the appearance of scale-free phenomena, i.e., correlations that have no characteristic length scale, typically exhibited by physical systems near a critical point and dynamical systems far from equilibrium. (i) DNA nucleotide sequences have traditionally been analyzed using models which incorporate the possibility of short-range nucleotide correlations. We found, instead, a remarkably long-range power law correlation. We found such long-range correlations in intron-containing genes and in non-transcribed regulatory DNA sequences as well as intragenomic DNA, but not in cDNA sequences or intron-less genes. We also found that the myosin heavy chain family gene evolution increases the fractal complexity of the DNA landscapes, consistent with the intron-late hypothesis of gene evolution. (ii) The healthy heartbeat is traditionally thought to be regulated according to the classical principle of homeostasis, whereby physiologic systems operate to reduce variability and achieve an equilibrium-like state. We found, however, that under normal conditions, beat-to-beat fluctuations in heart rate display long-range power law correlations.     

Joint multifractal analysis based on wavelet leaders

Mutually interacting components form complex systems and these components usually have long-range cross-correlated outputs. Using wavelet leaders, we propose a method for characterizing the joint multifractal nature of these long-range cross correlations; we call this method joint multifractal analysis based on wavelet leaders (MF-X-WL). We test the validity of the MF-X-WL method by performing extensive numerical experiments on dual binomial measures with multifractal cross correlations and bivariate fractional Brownian motions (bFBMs) with monofractal cross correlations. Both experiments indicate that MF-X-WL is capable of detecting cross correlations in synthetic data with acceptable estimating errors. We also apply the MF-X-WL method to pairs of series from financial markets (returns and volatilities) and online worlds (online numbers of different genders and different societies) and determine intriguing joint multifractal behavior.     

Long-range correlations in hadron-nucleus interactions

An analysis of correlations in rapidity of charged particles produced in proton and antiproton interactions on hydrogen, argon and xenon at 200 GeV is presented. Positive long-range correlations are observed in interactions on heavy targets. The dependence of rapidity correlations between the forward and backward hemisphere on the number of projectile collisions is discussed.