Search results for "Correlation dimension"
showing 10 items of 24 documents
Neural net classification of REM sleep based on spectral measures as compared to nonlinear measures
2001
In various studies the implementation of nonlinear and nonconventional measures has significantly improved EEG (electroencephalogram) analyses as compared to using conventional parameters alone. A neural network algorithm well approved in our laboratory for the automatic recognition of rapid eye movement (REM) sleep was investigated in this regard. Originally based on a broad range of spectral power inputs, we additionally supplied the nonlinear measures of the largest Lyapunov exponent and correlation dimension as well as the nonconventional stochastic measures of spectral entropy and entropy of amplitudes. No improvement in the detection of REM sleep could be achieved by the inclusion of …
Nonlinear analysis of continuous ECG during sleep II. Dynamical measures
2000
The hypothesis that cardiac rhythms are associated with chaotic dynamics implicating a healthy flexibility has motivated the investigation of continuous ECG with methods of nonlinear system theory. Sleep is known to be associated with modulations of the sympathetic and parasympathetic control of cardiac dynamics. Thus, the differentiation of ECG signals recorded during different sleep stages can serve to determine the usefulness of nonlinear measures in discriminating ECG states in general. For this purpose the following six nonlinear measures were implemented: correlation dimension D2, Lyapunov exponent L1. Kolmogorov entropy K2, as well as three measures derived from the analysis of unsta…
Surrogate data analysis of sleep electroencephalograms reveals evidence for nonlinearity
1996
We tested the hypothesis of whether sleep electroencephalographic (EEG) signals of different time windows (164 s, 82 s, 41 s and 20.5 s) are in accordance with linear stochastic models. For this purpose we analyzed the all-night sleep electroencephalogram of a healthy subject and corresponding Gaussian-rescaled phase randomized surrogates with a battery of five non-linear measures. The following nonlinear measures were implemented: largest Lyapunov exponent L1, correlation dimension D2, and the Green-Savit measures delta 2, delta 4 and delta 6. The hypothesis of linear stochastic data was rejected with high statistical significance. L1 and D2 yielded the most pronounced effects, while the G…
The dimensionality of human's electroencephalogram during sleep.
1991
In order to perform an analysis of nonlinear EEG-dynamics we investigated the EEG of ten male probands during sleep. According to Rechtschaffen and Kales (1968) we scored the sleep-EEG and applied an algorithm, proposed by Grassberger and Proccaccia (1983) to compute the correlation dimension of different sleep stages. The correlation dimension characterizes the dynamics of the EEG signal and estimates the degrees of freedom of the signal under study. We could demonstrate, that the EEG of slow wave sleep stages depicts a dimensionality, which is two units smaller than that of light or REM sleep.
Nonlinear analysis of continuous ECG during sleep I. Reconstruction.
2000
In recent years evidence has accumulated that ECG signals are of a nonlinear nature. It has been recognized that strictly periodic cardiac rhythms are not accompanied by healthy conditions but, on the contrary, by pathological states. Therefore, the application of methods from nonlinear system theory for the analysis of ECG signals has gained increasing interest. Crucial for the application of nonlinear methods is the reconstruction (embedding) of the time series in a phase space with appropriate dimension. In this study continuous ECG signals of 12 healthy subjects recorded during different sleep stages were analysed. Proper embedding dimension was determined by application of two techniqu…
A Nonlinear Approach to Brain Function: Deterministic Chaos and Sleep EEG
1992
In order to perform a nonlinear dimensional analysis of the sleep electroencephalogram (EEG), we applied an algorithm proposed by Grassberger and Procaccia to calculate the correlation dimension D2 of different sleep stages under Lorazepam medication versus placebo. This correlation dimension characterizes the dynamics of the sleep EEG and it estimates the degrees of freedom of the signal under study. We demonstrate that slow-wave sleep depicts a much smaller dimensionality than light or rapid eye movement (REM) sleep, and that Lorazepam does not alter the EEG's dimensionality except in stage II and REM.
Strange Attractors, Chaotic Behavior and Informational Aspects of Sleep EEG Data
1992
In order to perform a nonlinear dimensional analysis of the sleep EEG, we applied an algorithm proposed to calculate the correlation dimension D2 of different sleep stages. D2 characterizes the dynamics of the sleep EEG, estimates the degrees of freedom, and describes the complexity of the signal under study. An attempt is made to correlate dimensionality analysis and informational aspects of the sleep EEG. Information processing by the brain during different sleep stages of healthy subjects under the influence of lorazepam and in unmedicated acute schizophrenics is estimated.
Alterations of Continuous MEG Measures during Mental Activities
2000
In a pilot study, we investigated the topography of 11 continuous MEG measures for the eyes-opened and eyes-closed condition together with three simple mental tasks (mental arithmetic, visual imagery, word generation). One-minute recordings for each condition from 16 right-handed subjects were analyzed. The electrophysiological measures consisted of 6 spectral band measures together with spectral edge frequency and spectral entropy, plus the time-domain-based entropy of amplitudes (ENA) and the nonlinear measures correlation dimension D2 and Lyapunov exponent L1. In summary, our results indicate a pronounced task-dependent difference between the anterior and the posterior region, but no lat…
Nonlinear EEG dynamics during sleep in depression and schizophrenia.
1994
The article deals with the question, whether nonlinear analysis of the sleep EEG may give clues to understanding of disturbed information processing in psychiatric diseases. We point out how the nonlinear approach to EEG dynamics is motivated and review recent investigations concerning nonlinear dynamical properties of physiological systems. We present calculations of the correlation dimension D2 and the principal Lyapunov-exponent lambda 1 for sleep EEG data from 9 depressive and 11 schizophrenic inpatients compared to healthy controls. Combining the findings for D2 and lambda 1 our results point to altered nonlinear brain dynamics mainly during slow wave sleep in depression and during REM…
Connectivity Influences on Nonlinear Dynamics in Weakly-Synchronized Networks: Insights from Rössler Systems, Electronic Chaotic Oscillators, Model a…
2019
Natural and engineered networks, such as interconnected neurons, ecological and social networks, coupled oscillators, wireless terminals and power loads, are characterized by an appreciable heterogeneity in the local connectivity around each node. For instance, in both elementary structures such as stars and complex graphs having scale-free topology, a minority of elements are linked to the rest of the network disproportionately strongly. While the effect of the arrangement of structural connections on the emergent synchronization pattern has been studied extensively, considerably less is known about its influence on the temporal dynamics unfolding within each node. Here, we present a compr…