Independent coordinates for strange attractors from mutual information

Fraser, Andrew M.; Swinney, Harry L.

doi:10.1103/physreva.33.1134

Cited by 4,003 publications

(2,266 citation statements)

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“…Identical time delay was used for all subjects and tasks, because variations in the chosen time delay may diminish the reliability of resulting LDS [19]. To determine the delay, we used estimates of the minimum of the average mutual information on the velocity time series [20]. The delay was set to 44 samples, the median of these estimates over all subjects, markers and tasks.…”

Section: State Space Reconstructionmentioning

confidence: 99%

Precision of estimates of local stability of repetitive trunk movements

et al. 2013

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Purpose Local dynamic stability of trunk movements quantified by means of the maximum Lyapunov exponent (k max ) can provide information on trunk motor control and might offer a measure of trunk control in low-back pain patients. It is unknown how many repetitions are necessary to obtain sufficiently precise estimates of k max and whether fatigue effects on k max can be avoided while increasing the number of repetitions. Method Ten healthy subjects performed 100 repetitions of trunk movements in flexion, of trunk rotation and of a task combining these movement directions. k max was calculated from thorax, pelvis and trunk (thorax relative to pelvis) kinematics. Data series were analyzed using a bootstrap procedure; ICC and coefficient of variation were used to quantify precision as a function of the number of cycles analyzed. ANOVA was used to compare movement tasks and to test for effects of time.Results Trunk local stability reached acceptable precision level after 30 repetitions. k max was higher (indicating lower stability) in flexion, compared to rotation and combined tasks. There was no time effect (fatigue). k max of trunk movement was lower and less variable than that of thorax and pelvis movements. Conclusions The data provided allow for an informed choice of the number of repetitions in assessing local dynamic stability of trunk movements, weighting the gain in precision against the increase in measurement effort. Within the 100 repetitions tested, fatigue did not affect results. We suggest that increased stability during asymmetric movement may be explained by higher co-activation of trunk muscles.

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Section: State Space Reconstructionmentioning

confidence: 99%

Precision of estimates of local stability of repetitive trunk movements

et al. 2013

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“…MI is a metric derived from Shannon's information theory to estimate the information gained from observations of one random event on another [15], [38], [47]. MI measures both linear and nonlinear dependences between two time series [15], [38].…”

Section: Auto Mutual Information (Ami)mentioning

confidence: 99%

“…MI measures both linear and nonlinear dependences between two time series [15], [38]. Hence, it can be regarded as a non-linear equivalent of the correlation function [20], [38].…”

Section: Auto Mutual Information (Ami)mentioning

confidence: 99%

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Approximate entropy and auto mutual information analysis of the electroencephalogram in Alzheimer’s disease patients

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Hornero

et al. 2008

Med Biol Eng Comput

126

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We analysed the electroencephalogram (EEG) from Alzheimer's disease (AD) patients with two non-linear methods: Approximate Entropy (ApEn) and Auto Mutual Information (AMI). ApEn quantifies regularity in data, while AMI detects linear and non-linear dependencies in time series. EEGs from 11 AD patients and 11 age-matched controls were analysed. ApEn was significantly lower in AD patients at electrodes O1, O2, P3 and P4 (p < 0.01). The EEG AMI decreased more slowly with time delays in patients than in controls, with significant differences at electrodes T5, T6, O1, O2, P3 and P4 (p < 0.01). The strong correlation between results from both methods shows that the AMI rate of decrease can be used to estimate the regularity in time series. Our work suggests that non-linear EEG analysis may contribute to increase the insight into brain dysfunction in AD, especially when different time scales are inspected, as is the case with AMI.

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“…Time series consisting of approximately 4 000 points were obtained using an 8-bit analog-to-digital converter at a sampling frequency of 1 000 Hz. The time lag for the reconstruction of phase space was determined by the mutual information criterion (Fraser and Swinney, 1986), which yielded l= 21. See Fig.…”

Section: Simulations Using Time Seriesmentioning

confidence: 99%