Recurring patterns in stationary intervals of abdominal uterine electromyograms during gestation

Abdominal uterine electromyograms (uEMG) studies have focused on uterine contractions to describe the evolution of uterine activity and preterm birth (PTB) prediction. Stationary, non-contracting uEMG has not been studied. The aim of the study was to investigate the recurring patterns in stationary uEMG, their relationship with gestation age and PTB, and PTB predictivity. A public database of 300 (38 PTB) three-channel (S1-S3) uEMG recordings of 30 min, collected between 22 and 35 weeks' gestation, was used. Motion and labour contraction-free intervals in uEMG were identified as 5-min weak-sense stationarity intervals in 268 (34 PTB) recordings. Sample entropy (SampEn), percentage recurrence (PR), percentage determinism (PD), entropy (ER), and maximum length (L MAX) of recurrence were calculated and analysed according to the time to delivery and PTB. Random time series were generated by random shuffle (RS) of actual data. Recurrence was present in actual data (p<0.001) but not RS. In S3, PR (p<0.005), PD (p<0.01), ER (p<0.005), and L MAX (p<0.05) were higher, and SampEn lower (p<0.005) in PTB. Recurrence indices increased (all p<0.001) and SampEn decreased (p<0.01) with decreasing time to delivery, suggesting increasingly regular and recurring patterns with gestation progression. All indices predicted PTB with AUC≥0.62 (p<0.05). Recurring patterns in stationary non-contracting uEMG were associated with time to delivery but were relatively poor predictors of PTB

M-furcations in coupled maps

We study the scaling behavior of $M$-furcation $(M\!=\!2, 3, 4,\dots)$ sequences of $M^n$-period $(n=1,2,\dots)$ orbits in two coupled one-dimensional (1D) maps. Using a renormalization method, how the scaling behavior depends on $M$ is particularly investigated in the zero-coupling case in which the two 1D maps become uncoupled. The zero-coupling fixed map of the $M$-furcation renormalization transformation is found to have three relevant eigenvalues $\delta$, $\alpha$, and $M$ ($\delta$ and $\alpha$ are the parameter and orbital scaling factors of 1D maps, respectively). Here the second and third ones, $\alpha$ and $M$, called the ``coupling eigenvalues'', govern the scaling behavior associated with coupling, while the first one $\delta$ governs the scaling behavior of the nonlinearity parameter like the case of 1D maps. The renormalization results are also confirmed by a direct numerical method.Comment: 18 pages + 2 figures (available upon request), Revtex 3.

Breathers in inhomogeneous nonlinear lattices: an analysis via centre manifold reduction

We consider an infinite chain of particles linearly coupled to their nearest neighbours and subject to an anharmonic local potential. The chain is assumed weakly inhomogeneous. We look for small amplitude discrete breathers. The problem is reformulated as a nonautonomous recurrence in a space of time-periodic functions, where the dynamics is considered along the discrete spatial coordinate. We show that small amplitude oscillations are determined by finite-dimensional nonautonomous mappings, whose dimension depends on the solutions frequency. We consider the case of two-dimensional reduced mappings, which occurs for frequencies close to the edges of the phonon band. For an homogeneous chain, the reduced map is autonomous and reversible, and bifurcations of reversible homoclinics or heteroclinic solutions are found for appropriate parameter values. These orbits correspond respectively to discrete breathers, or dark breathers superposed on a spatially extended standing wave. Breather existence is shown in some cases for any value of the coupling constant, which generalizes an existence result obtained by MacKay and Aubry at small coupling. For an inhomogeneous chain the study of the nonautonomous reduced map is in general far more involved. For the principal part of the reduced recurrence, using the assumption of weak inhomogeneity, we show that homoclinics to 0 exist when the image of the unstable manifold under a linear transformation intersects the stable manifold. This provides a geometrical understanding of tangent bifurcations of discrete breathers. The case of a mass impurity is studied in detail, and our geometrical analysis is successfully compared with direct numerical simulations

Surrogate-assisted network analysis of nonlinear time series

The performance of recurrence networks and symbolic networks to detect weak nonlinearities in time series is compared to the nonlinear prediction error. For the synthetic data of the Lorenz system, the network measures show a comparable performance. In the case of relatively short and noisy real-world data from active galactic nuclei, the nonlinear prediction error yields more robust results than the network measures. The tests are based on surrogate data sets. The correlations in the Fourier phases of data sets from some surrogate generating algorithms are also examined. The phase correlations are shown to have an impact on the performance of the tests for nonlinearity.Comment: 9 pages, 5 figures, Chaos (http://scitation.aip.org/content/aip/journal/chaos), corrected typo

Nonlinear time-series analysis revisited

In 1980 and 1981, two pioneering papers laid the foundation for what became known as nonlinear time-series analysis: the analysis of observed data---typically univariate---via dynamical systems theory. Based on the concept of state-space reconstruction, this set of methods allows us to compute characteristic quantities such as Lyapunov exponents and fractal dimensions, to predict the future course of the time series, and even to reconstruct the equations of motion in some cases. In practice, however, there are a number of issues that restrict the power of this approach: whether the signal accurately and thoroughly samples the dynamics, for instance, and whether it contains noise. Moreover, the numerical algorithms that we use to instantiate these ideas are not perfect; they involve approximations, scale parameters, and finite-precision arithmetic, among other things. Even so, nonlinear time-series analysis has been used to great advantage on thousands of real and synthetic data sets from a wide variety of systems ranging from roulette wheels to lasers to the human heart. Even in cases where the data do not meet the mathematical or algorithmic requirements to assure full topological conjugacy, the results of nonlinear time-series analysis can be helpful in understanding, characterizing, and predicting dynamical systems

Time series analysis for minority game simulations of financial markets

The minority game (MG) model introduced recently provides promising insights into the understanding of the evolution of prices, indices and rates in the financial markets. In this paper we perform a time series analysis of the model employing tools from statistics, dynamical systems theory and stochastic processes. Using benchmark systems and a financial index for comparison, several conclusions are obtained about the generating mechanism for this kind of evolut ion. The motion is deterministic, driven by occasional random external perturbation. When the interval between two successive perturbations is sufficiently large, one can find low dimensional chaos in this regime. However, the full motion of the MG model is found to be similar to that of the first differences of the SP500 index: stochastic, nonlinear and (unit root) stationary.Comment: LaTeX 2e (elsart), 17 pages, 3 EPS figures and 2 tables, accepted for publication in Physica

Statistical Mechanics and Information-Theoretic Perspectives on Complexity in the Earth System

Peer reviewedPublisher PD