Detection of nonlinear dynamics in short, noisy time series

Barahona, Mauricio; Poon, Chi Sang

doi:10.1038/381215a0

Cited by 229 publications

(155 citation statements)

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“…2). Oversampling can introduce linearities in the data (Barahona and Poon, 1996). With a sampling frequency of 50 Hz, we failed to detect nonlinearities in several cases and the average noise limit values were significantly smaller than with a 5 Hz sampling rate.…”

Section: Technical Issuesmentioning

confidence: 99%

“…The best nonlinear model is obtained by sequentially increasing K values with d > 1. Both models are then compared and the null hypothesis (linearity) is tested against the alternate hypothesis (non-linearity) using parametric (F-test) and nonparametric (Whitney-Mann) statistics (Barahona and Poon, 1996). If the null hypothesis is rejected with an alpha risk of 1%, namely if the experimental series is best described with a non-linear model, the titration process itself can be started.…”

Section: Non-linear Analysismentioning

confidence: 99%

“…The noise titration procedure was applied as described by Poon et al (2001). Figure 1 provides a graphical explanation of the principle of the technique; a detailed mathematical description that can be found elsewhere (Barahona and Poon, 1996;Poon and Merrill, 1997;Poon and Barahona, 2001). In brief, this technique begins by an identification process capable of a robust and highly sensitive detection of deterministic dynamics (including chaos) within a given time series, even when it is noisy and of short duration (Barahona and Poon, 1996;Poon and Merrill, 1997).…”

Section: Non-linear Analysismentioning

confidence: 99%

“…This procedure was first performed on the signal as acquired, namely without filtering and at a 50 Hz sampling rate. Then, because oversampling can introduce co-linearities in the signal (Barahona and Poon, 1996), the data were subsampled at 5 Hz (Fig.2) and the full noise titration process was repeated to evaluate the impact of the sampling rate on the results.…”

Section: Non-linear Analysismentioning

confidence: 99%

“…However, such descriptors are typically highly sensitive to noise, making them particularly misleading when applied to short and noisy biological time series (Barahona and Poon, 1996;Bruce, 1996). One strategy to infer the presence of nonlinear determinism in a noisy signal is by statistical comparison with randomly generated "surrogate" data (Theiler et al, 1992).…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Chaotic dynamics of resting ventilatory flow in humans assessed through noise titration

Wysocki

Fiamma

Straus

et al. 2006

Respiratory Physiology & Neurobiology

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The mammalian ventilatory behaviour exhibits nonlinear dynamics as reflected by certain nonlinearity or complexity indicators (e.g. correlation dimension, approximate entropy, Lyapunov exponents...) but this is not sufficient to determine its possible chaotic nature. To address this, we applied the noise titration technique, previously shown to discern and quantify chaos in short and noisy time series, to ventilatory flow recordings obtained in quietly breathing normal humans. Nine subjects (8 men and 1 woman, 24-42 yrs) were studied during 15-minute epochs of ventilatory steadystate (10.1±3.0 breaths/minute, tidal volume 0.63±0.2L). Noise titration applied to the unfiltered signals subsampled at 5 Hz detected nonlinearity in all cases (noise limit 20.2±12.5%). Noise limit values were weakly correlated to the correlation dimension and the largest Lyapunov exponent of the signals. This study shows that the noise titration approach evidences a chaotic dimension to the behavior of ventilatory flow over time in normal humans during tidal breathing.

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Section: Technical Issuesmentioning

confidence: 99%

Section: Non-linear Analysismentioning

confidence: 99%