Nonlinear Measures for Characterizing Rough Surface Morphologies

We develop a new approach to characterizing the morphology of rough surfaces based on the analysis of the scaling properties of contour loops, i.e. loops of constant height. Given a height profile of the surface we perform independent measurements of the fractal dimension of contour loops, and the exponent that characterizes their size distribution. Scaling formulas are derived and used to relate these two geometrical exponents to the roughness exponent of a self-affine surface, thus providing independent measurements of this important quantity. Furthermore, we define the scale dependent curvature and demonstrate that by measuring its third moment departures of the height fluctuations from Gaussian behavior can be ascertained. These nonlinear measures are used to characterize the morphology of computer generated Gaussian rough surfaces, surfaces obtained in numerical simulations of a simple growth model, and surfaces observed by scanning-tunneling-microscopes. For experimentally realized surfaces the self-affine scaling is cut off by a correlation length, and we generalize our theory of contour loops to take this into account.Comment: 39 pages and 18 figures included; comments to [email protected]

Linear and Nonlinear Measures Predict Swimming in the Leech

Stimulation of a trigger interneuron of an isolated nerve cord preparation of the medicinal leech, Hirudo medicinalis, sometimes leads to swimming; sometimes it does not. We investigate signals transmitted in the ventral cord of the leech after stimulation and seek quantitative measures that would make it possible to distinguish signals that predict swimming from those that do not. We find that a number of linear as well as nonlinear measures provide statistically significant distinctions between the two kinds of signals. The linear measures are the time dependence of (i) the standard deviation and (ii) the autocorrelation function at a small time delay. The nonlinear measures are (i) a measure of nonlinear predictability and (ii) the time dependence of a measure of the size of the embedded signal trajectory. Calculations using surrogate data suggest that the differences between the two classes of signals are dynamical as well as statistical

Linear and Nonlinear Measures Predict Swimming in the Leech

Stimulation of a trigger interneuron of an isolated nerve cord preparation of the medicinal leech, Hirudo medicinalis, sometimes leads to swimming; sometimes it does not. We investigate signals transmitted in the ventral cord of the leech after stimulation and seek quantitative measures that would make it possible to distinguish signals that predict swimming from those that do not. We find that a number of linear as well as nonlinear measures provide statistically significant distinctions between the two kinds of signals. The linear measures are the time dependence of (i) the standard deviation and (ii) the autocorrelation function at a small time delay. The nonlinear measures are (i) a measure of nonlinear predictability and (ii) the time dependence of a measure of the size of the embedded signal trajectory. Calculations using surrogate data suggest that the differences between the two classes of signals are dynamical as well as statistical

USE OF NONLINEAR MEASURES TO COMPARE ATHLETE POSTURAL SWAY DYNAMICS

The purpose of this study was to examine the use of nonlinear analysis as a tool to evaluate postural sway patterns in athletes and physically active non-athletes. Balance is an integral part of many sports but seems to be task specific. Data collection occurred for 30 seconds during eyes open condition on Double Leg and Single Left and Right Leg trials. Analysis of the data using Transfer Entropy (TE) and Fractal Dimension (FD) yielded Ice Hockey and Football players having distinctly different postural dynamic control from each other and physically active non-players in only a couple conditions for TE and multiple conditions for FD. These balance measures support the idea of sports requiring different postural sway dynamics

Postural control: learning to balance and responses to mechanical and sensory perturbations

The purpose of the current research was to examine how a novel balance task is learnt by individuals with a mature neurological system, and to investigate the responses of experienced hand balancers to mechanical and sensory perturbations. Balance in each posture was assessed by various techniques, including: traditional measures of centre of pressure, nonlinear time series analysis of centre of pressure, estimates of feedback time delay from cross correlations and delayed regression models, and calculation of small, medium, and large movement corrections. Data from this study suggests that the best balance metric for distinguishing between each of the balance conditions was the traditional balance measure of sway velocity. However, sway velocity cannot provide any further information on the underlying process of balance. Nonlinear measures of balance offer insight into the underlying deterministic processes that control balance, offering measures of system determinism, complexity, and predictability. Assessments of feedback time delay and movement corrections provide both an insight into the control of posture and help distinguish one condition from another. Both feedback time delay and movement corrections and magnitudes may be used simultaneously to delve further into the control of posture. Delayed regression models seem to be an appropriate and useful tool for estimating feedback time delays during balance. Findings support the use of the third term in the adapted regression model as a means of estimating the effect of passive stiffness on feedback time delay. Generally, with increased duration in handstand subjects displayed reduced sway as measured by traditional measures of balance. A more marked change in nonlinear measures of balance can be seen, with quicker reductions in variance for some nonlinear measures of balance than in the traditional measures. It may be that more pronounced changes in nonlinear measures represent changes in the subjects underlying process of postural control, whereas less pronounced changes in traditional measures relate more to their general ability or performance in the balance task

Nonlinear aspects of the EEG during sleep in children

Electroencephalograph (EEG) analysis enables the neuronal behavior of a section of the brain to be examined. If the behavior is nonlinear then nonlinear tools can be used to glean information on brain behavior, and aid in the diagnosis of sleep abnormalities such as obstructive sleep apnea syndrome (OSAS). In this paper the sleep EEGs of a set of normal and mild OSAS children are evaluated for nonlinear behaviour. We consider how the behaviour of the brain changes with sleep stage and between normal and OSAS children.Comment: 9 pages, 2 figures, 4 table

Fractal Measures and Nonlinear Dynamics of Overcontact Binaries

Overcontact binary stars are systems of two stars where the component stars are in contact with each other. This implies that they share a common envelope of gas. In this work we seek signatures of nonlinearity and chaos in these stars by using time series analysis techniques. We use three main techniques, namely the correlation dimension,f (\alpha) spectrum and the bicoherence. The former two are calculated from the reconstructed dynamics, while the latter is calculated from the Fourier transforms of the time series of intensity variations(light curves) of these stars. Our dataset consists of data from 463 overcontact binary stars in the Kepler field of view [1]. Our analysis indicates nonlinearity and signatures of chaos in almost all the light curves. We also explore whether the underlying nonlinear properties of the stars are related to their physical properties like fill-out-factor, a measure of the extend of contact between the components of an overcontact binary system . We observe that significant correlations exist between the fill out factor and the nonlinear quantifiers. This correlation is more pronounced in specific subcategories constructed based on the mass ratios and effective temperatures of the binaries. The correlations observed can be indicative of variations in the nonlinear properties of the star as it ages. We believe that this study relating nonlinear and astrophysical properties of binary stars is the first of its kind and is an important starting point for such studies in other astrophysical objects displaying nonlinear dynamical behaviour.Comment: 17 pages, 12 figures, submitted to Communications in Nonlinear Science and Numerical Simulatio