Direct test for determinism in a time series

Kaplan, Daniel T.; Glass, Leon

doi:10.1103/physrevlett.68.427

Cited by 364 publications

(168 citation statements)

References 13 publications

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“…The two steps can be iterated several times (presently 10), whereby the resulting surrogates approach the original recording both in the spectrum as well as the distribution. As above, we have We used the method originally proposed by Kaplan and Glass [49], which is based on measuring average directional vectors in a coarse-grained phase space. The idea is that, in case of a deterministic solution, neighboring trajectories in a small portion of the phase space should all point in the same direction, i.e.…”

Section: Time Series Analysis Methods and Resultsmentioning

confidence: 99%

Establishing the stochastic nature of intracellular calcium oscillations from experimental data

Perc

Green

Dixon

et al. 2008

Biophysical Chemistry

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Calcium has been established as a key messenger in both intra-and intercellular signaling. Experimentally observed intracellular calcium responses to different agonists show a variety of behaviors from simple spiking to complex oscillatory regimes. Here we study typical experimental traces of calcium oscillations in hepatocytes obtained in response to phenylephrine and ATP. The traces were analyzed with methods of nonlinear time series analysis in order to determine the stochastic/deterministic nature of the intracellular calcium oscillations. Despite the fact that the oscillations appear, visually, to be deterministic yet perturbed by noise, our analyses provide strong evidence that the measured calcium traces in hepatocytes are prevalently of stochastic nature. In particular, bursting calcium oscillations are temporally correlated Gaussian series distorted by a monotonic, instantaneous, timeindependent function, whilst the spiking behavior appears to have a dynamical nonlinear component whereby the overall determinism level is still low. The biological importance of this finding is discussed in relation to the mechanisms incorporated in mathematical models as well as the role of stochasticity and determinism at cellular and tissue levels which resemble typical statistical and thermodynamic effects in physics.

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Section: Time Series Analysis Methods and Resultsmentioning

confidence: 99%

Establishing the stochastic nature of intracellular calcium oscillations from experimental data

Perc

Green

Dixon

et al. 2008

Biophysical Chemistry

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“…Kaplan & Glass (1992) developed a direct test for determinism in a time series. This method is based on the fact that the tangent of the trajectory of a deterministic system is a function of the region in the phase space.…”

Section: The Deterministic Test Of a Time Series·mentioning

confidence: 99%

“…As a first step, it is possible to estimate the determinism inherent in a given time series. Kaplan & Glass (1992) developed a direct test for determinism in a given time series. This article introduces this method for analyzing EEG and MEG and presents comparisons with other nonlinear measures such as the fractal dimension.…”

Section: Introductionmentioning

confidence: 99%

Testing the determinism of EEG and MEG

Mühlnickel

Rendtorff

Kowalik

et al. 1994

Integrative Physiological and Behavioral Science

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“…Two major difficulties for solving this issue are (i) chaos can be induced by noise [1][2][3][4][5][6][7][8], and (ii) standard Brownian motions may have a deterministic origin [8,9]. Although many methods have been proposed to distinguish chaos from noise [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27], it is generally difficult to fully sort out the capabilities and limitations of a particular method.…”

Section: Introductionmentioning

confidence: 99%

Detecting low-dimensional chaos by the “noise titration” technique: Possible problems and remedies

Gao¹,

Hu²,

Mao³

et al. 2012

Chaos, Solitons & Fractals

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a b s t r a c tDistinguishing low-dimensional chaos from noise is an important issue in time series analysis. Among the many methods proposed for this purpose is the noise titration technique, which quantifies the amount of noise that needs to be added to the signal to fully destroy its nonlinearity. Two groups of researchers recently have questioned the validity of the technique. In this paper, we report a broad range of situations where the noise titration technique fails, and offer solutions to fix the problems identified.

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Direct test for determinism in a time series

Cited by 364 publications

References 13 publications

Establishing the stochastic nature of intracellular calcium oscillations from experimental data

Establishing the stochastic nature of intracellular calcium oscillations from experimental data

Testing the determinism of EEG and MEG

Detecting low-dimensional chaos by the “noise titration” technique: Possible problems and remedies

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