Scaling of information in turbulence

Granero-Belinchon, Carlos; Roux, Stéphane; Garnier, Nicolas

doi:10.1209/0295-5075/115/58003

Cited by 21 publications

(13 citation statements)

References 23 publications

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“…Interestingly, this splits h (m,τ ) (X) into two contributions: H(X) only depends on the one-point statistics of X and is hence a static property. I (m,1,τ ) (X) gathers all information conveyed by linear and non linear temporal dynamics, irrespective of the variance of X [21]. For illustration, when X is a stationary jointly Gaussian process, hence fully defined by its variance σ 2 and normalized correlation function c(τ ) (such that c(τ = 0) = 1), one has:…”

Section: A Entropy Entropy Rate and Mutual Informationmentioning

confidence: 99%

Mutual information for intrapartum fetal heart rate analysis

Granero-Belinchon

Roux

Garnier

et al. 2017

2017 39th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC)

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The analysis of the temporal dynamics in intrapartum fetal heart rate (FHR), aiming at early detection of fetal acidosis, constitutes an intricate signal processing task, that continuously receives significant research efforts. Entropy and entropy rates, envisaged as measures of complexity, often computed via popular implementations referred to as Approximate Entropy (ApEn) or Sample Entropy (SampEn), have regularly been reported as significant features for intrapartum FHR analysis. The present contribution aims to show how mutual information enhances characterization of FHR temporal dynamics and improves fetal acidosis detection performance. To that end, mutual information is first connected to ApEn and SampEn both conceptually and with respect to estimation procedure. Second, mutual information, ApEn and SampEn are computed on a large (≃ 1000 subjects) and documented database of FHR data, collected in a French academic hospital. Reported results show that the use of mutual information permits to significantly outperform ApEn and SampEn for acidosis detection, during any stage of labor.

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Section: A Entropy Entropy Rate and Mutual Informationmentioning

confidence: 99%

Mutual information for intrapartum fetal heart rate analysis

Granero-Belinchon

Roux

Garnier

et al. 2017

2017 39th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC)

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“…The entropy rate h(τ) T evolution with the time scale τ (Figure 2a) reveals three different regimes, as would the power spectrum [24]. Between the small and the large scales, indicated by vertical dashed lines, the entropy rate evolves linearly in ln τ with a slope H = 1/3, just as it would have for a traditional fBm: this is the inertial regime.…”

Section: Regularized and Stationarized Fbmmentioning

confidence: 75%

“…For the fGn, these two quantities converge to a constant value when τ is increased, but it can be seen that the entropy of the increments converges from above when H < 1/2. For the fBm, the two quantities increase linearly in ln τ, with a slope that is exactly the Hurst exponent H [23,24]. For the time-integrated fBm, which has a generalized Hurst exponent larger than 1, the two quantities also evolve linearly in ln τ, but with a constant slope 1 independent on H. This indicates that neither the entropy of the increments nor the entropy rate can be used to estimate H ≥ 1.…”

Section: Numerical Observationsmentioning

confidence: 99%

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Quantifying Non-Stationarity with Information Theory

Granero-Belinchon

Roux

Garnier

2021

Entropy

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We introduce an index based on information theory to quantify the stationarity of a stochastic process. The index compares on the one hand the information contained in the increment at the time scale τ of the process at time t with, on the other hand, the extra information in the variable at time t that is not present at time t−τ. By varying the scale τ, the index can explore a full range of scales. We thus obtain a multi-scale quantity that is not restricted to the first two moments of the density distribution, nor to the covariance, but that probes the complete dependences in the process. This index indeed provides a measure of the regularity of the process at a given scale. Not only is this index able to indicate whether a realization of the process is stationary, but its evolution across scales also indicates how rough and non-stationary it is. We show how the index behaves for various synthetic processes proposed to model fluid turbulence, as well as on experimental fluid turbulence measurements.

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“…T evolution with the time scale τ (Figure 2a) reveals three different regimes, as would the power spectrum [24]. Between the small and the large scales, indicated by vertical dashed lines, the entropy rate evolves linearly in ln τ with a slope H = 1/3, just as it would have for a traditional fBm: this is the inertial regime.…”

Section: The Entropy Rate H(τ)mentioning

confidence: 78%

Quantifying Non-Stationarity with Information Theory

Granero-Belinchon,

Roux,

Garnier

2021

Preprint

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We introduce an index based on information theory to quantify the stationarity of a stochastic process. The index compares on the one hand the information contained in the increment at the time scale τ of the process at time t with, on the other hand, the extra information in the variable at time t that is not present at time t − τ . By varying the scale τ , the index can explore a full range of scales. We thus obtain a multi-scale quantity that is not restricted to the first two moments of the density distribution, nor to the covariance, but that probes the complete dependences in the process. This index indeed provides a measure of the regularity of the process at a given scale. Not only is this index able to indicate whether a realization of the process is stationary, but its evolution across scales also indicates how rough and non-stationary it is. We show how the index behaves for various synthetic processes proposed to model fluid turbulence, as well as on experimental fluid turbulence measurements.

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Scaling of information in turbulence

Cited by 21 publications

References 23 publications

Mutual information for intrapartum fetal heart rate analysis

Mutual information for intrapartum fetal heart rate analysis

Quantifying Non-Stationarity with Information Theory

Quantifying Non-Stationarity with Information Theory

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