The Necessity for a Time Local Dimension in Systems with Time Varying Attractors

We show that a simple non-linear system of ordinary differential equations may possess a time varying attractor dimension. This indicates that it is infeasible to characterize EEG and MEG time series with a single time global dimension. We suggest another measure for the description of non-stationary attractors.Comment: 13 Postscript pages, 12 Postscript figures (figures 3b and 4 by request from Y. Ashkenazy: [email protected]

Non-linear Analysis of Single Electroencephalography (EEG) for Sleep-Related Healthcare Applications

OBJECTIVES: Soft-computing techniques are commonly used to detect medical phenomena and to help with clinical diagnoses and treatment. The purpose of this paper is to analyze the single electroencephalography (EEG) signal with the chaotic methods in order to identify the sleep stages. METHODS: Data acquisition (polysomnography) was performed on four healthy young adults (all males with a mean age of 27.5 years). The evaluated algorithm was designed with a correlation dimension and Lyapunov's exponent using a single EEG signal that detects differences in chaotic characteristics. RESULTS: The change of the correlation dimension and the largest Lyapunov exponent over the whole night sleep EEG was performed. The results show that the correlation dimension and largest Lyapunov exponent decreased from light sleep to deep sleep and they increased during the rapid eye movement stage. CONCLUSIONS: These results suggest that chaotic analysis may be a useful adjunct to linear (spectral) analysis for identifying sleep stages. The single EEG based nonlinear analysis is suitable for u-healthcare applications for monitoring sleepope

Analysis of electroencephalograms in Alzheimer's disease patients with multiscale entropy

The aim of this study was to analyse the electroencephalogram (EEG) background activity of Alzheimer’s disease (AD) patients using the Multiscale Entropy (MSE). The MSE is a recently developed method that quantifies the regularity of a signal on different time scales. These time scales are inspected by means of several coarse-grained sequences formed from the analysed signals. We recorded the EEGs from 19 scalp electrodes in 11 AD patients and 11 age-matched controls and estimated the MSE profile for each epoch of the EEG recordings. The shape of the MSE profiles reveals the EEG complexity, and it suggests that the EEG contains information in deeper scales than the smallest one. Moreover, the results showed that the EEG background activity is less complex in AD patients than control subjects. We found significant difference

Extended Recurrence Plot Analysis and its Application to ERP Data

We present new measures of complexity and their application to event related potential data. The new measures base on structures of recurrence plots and makes the identification of chaos-chaos transitions possible. The application of these measures to data from single-trials of the Oddball experiment can identify laminar states therein. This offers a new way of analyzing event-related activity on a single-trial basis.Comment: 21 pages, 8 figures; article for the workshop ''Analyzing and Modelling Event-Related Brain Potentials: Cognitive and Neural Approaches`` at November 29 - December 01, 2001 in Potsdam, German

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.Comment: 4 pages,late

Wavelet analysis of epileptic spikes

Interictal spikes and sharp waves in human EEG are characteristic signatures of epilepsy. These potentials originate as a result of synchronous, pathological discharge of many neurons. The reliable detection of such potentials has been the long standing problem in EEG analysis, especially after long-term monitoring became common in investigation of epileptic patients. The traditional definition of a spike is based on its amplitude, duration, sharpness, and emergence from its background. However, spike detection systems built solely around this definition are not reliable due to the presence of numerous transients and artifacts. We use wavelet transform to analyze the properties of EEG manifestations of epilepsy. We demonstrate that the behavior of wavelet transform of epileptic spikes across scales can constitute the foundation of a relatively simple yet effective detection algorithm.Comment: 4 pages, 3 figure

Regular and stochastic behavior of Parkinsonian pathological tremor signals

Regular and stochastic behavior in the time series of Parkinsonian pathological tremor velocity is studied on the basis of the statistical theory of discrete non-Markov stochastic processes and flicker-noise spectroscopy. We have developed a new method of analyzing and diagnosing Parkinson's disease (PD) by taking into consideration discreteness, fluctuations, long- and short-range correlations, regular and stochastic behavior, Markov and non-Markov effects and dynamic alternation of relaxation modes in the initial time signals. The spectrum of the statistical non-Markovity parameter reflects Markovity and non-Markovity in the initial time series of tremor. The relaxation and kinetic parameters used in the method allow us to estimate the relaxation scales of diverse scenarios of the time signals produced by the patient in various dynamic states. The local time behavior of the initial time correlation function and the first point of the non-Markovity parameter give detailed information about the variation of pathological tremor in the local regions of the time series. The obtained results can be used to find the most effective method of reducing or suppressing pathological tremor in each individual case of a PD patient. Generally, the method allows one to assess the efficacy of the medical treatment for a group of PD patients.Comment: 39 pages, 10 figures, 1 table Physica A, in pres

Research on the relation of EEG signal chaos characteristics with high-level intelligence activity of human brain

Using phase space reconstruct technique from one-dimensional and multi-dimensional time series and the quantitative criterion rule of system chaos, and combining the neural network; analyses, computations and sort are conducted on electroencephalogram (EEG) signals of five kinds of human consciousness activities (relaxation, mental arithmetic of multiplication, mental composition of a letter, visualizing a 3-dimensional object being revolved about an axis, and visualizing numbers being written or erased on a blackboard). Through comparative studies on the determinacy, the phase graph, the power spectra, the approximate entropy, the correlation dimension and the Lyapunov exponent of EEG signals of 5 kinds of consciousness activities, the following conclusions are shown: (1) The statistic results of the deterministic computation indicate that chaos characteristic may lie in human consciousness activities, and central tendency measure (CTM) is consistent with phase graph, so it can be used as a division way of EEG attractor. (2) The analyses of power spectra show that ideology of single subject is almost identical but the frequency channels of different consciousness activities have slight difference. (3) The approximate entropy between different subjects exist discrepancy. Under the same conditions, the larger the approximate entropy of subject is, the better the subject's innovation is. (4) The results of the correlation dimension and the Lyapunov exponent indicate that activities of human brain exist in attractors with fractional dimensions. (5) Nonlinear quantitative criterion rule, which unites the neural network, can classify different kinds of consciousness activities well. In this paper, the results of classification indicate that the consciousness activity of arithmetic has better differentiation degree than that of abstract

Chaos in neural networks with a nonmonotonic transfer function

Time evolution of diluted neural networks with a nonmonotonic transfer function is analitically described by flow equations for macroscopic variables. The macroscopic dynamics shows a rich variety of behaviours: fixed-point, periodicity and chaos. We examine in detail the structure of the strange attractor and in particular we study the main features of the stable and unstable manifolds, the hyperbolicity of the attractor and the existence of homoclinic intersections. We also discuss the problem of the robustness of the chaos and we prove that in the present model chaotic behaviour is fragile (chaotic regions are densely intercalated with periodicity windows), according to a recently discussed conjecture. Finally we perform an analysis of the microscopic behaviour and in particular we examine the occurrence of damage spreading by studying the time evolution of two almost identical initial configurations. We show that for any choice of the parameters the two initial states remain microscopically distinct.Comment: 12 pages, 11 figures. Accepted for publication in Physical Review E. Originally submitted to the neuro-sys archive which was never publicly announced (was 9905001

Rhythmic dynamics and synchronization via dimensionality reduction : application to human gait

Reliable characterization of locomotor dynamics of human walking is vital to understanding the neuromuscular control of human locomotion and disease diagnosis. However, the inherent oscillation and ubiquity of noise in such non-strictly periodic signals pose great challenges to current methodologies. To this end, we exploit the state-of-the-art technology in pattern recognition and, specifically, dimensionality reduction techniques, and propose to reconstruct and characterize the dynamics accurately on the cycle scale of the signal. This is achieved by deriving a low-dimensional representation of the cycles through global optimization, which effectively preserves the topology of the cycles that are embedded in a high-dimensional Euclidian space. Our approach demonstrates a clear advantage in capturing the intrinsic dynamics and probing the subtle synchronization patterns from uni/bivariate oscillatory signals over traditional methods. Application to human gait data for healthy subjects and diabetics reveals a significant difference in the dynamics of ankle movements and ankle-knee coordination, but not in knee movements. These results indicate that the impaired sensory feedback from the feet due to diabetes does not influence the knee movement in general, and that normal human walking is not critically dependent on the feedback from the peripheral nervous system