Quantifying Non-Stationarity with Information Theory.

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.

Distance to Healthy Metabolic and Cardiovascular Dynamics From Fetal Heart Rate Scale-Dependent Features in Pregnant Sheep Model of Human Labor Predicts the Evolution of Acidemia and Cardiovascular Decompensation.

The overarching goal of the present work is to contribute to the understanding of the relations between fetal heart rate (FHR) temporal dynamics and the well-being of the fetus, notably in terms of predicting the evolution of lactate, pH and cardiovascular decompensation (CVD). It makes uses of an established animal model of human labor, where 14 near-term ovine fetuses subjected to umbilical cord occlusions (UCO) were instrumented to permit regular intermittent measurements of metabolites lactate and base excess, pH, and continuous recording of electrocardiogram (ECG) and systemic arterial blood pressure (to identify CVD) during UCO. ECG-derived FHR was digitized at the sampling rate of 1,000 Hz and resampled to 4 Hz, as used in clinical routine. We focused on four FHR variability features which are tunable to temporal scales of FHR dynamics, robustly computable from FHR sampled at 4 Hz and within short-time sliding windows, hence permitting a time-dependent, or local, analysis of FHR which helps dealing with signal noise. Results show the sensitivity of the proposed features for early detection of CVD, correlation to metabolites and pH, useful for early acidosis detection and the importance of coarse time scales (2.5-8 s) which are not disturbed by the low FHR sampling rate. Further, we introduce the performance of an individualized self-referencing metric of the distance to healthy state, based on a combination of the four features. We demonstrate that this novel metric, applied to clinically available FHR temporal dynamics alone, accurately predicts the time occurrence of CVD which heralds a clinically significant degradation of the fetal health reserve to tolerate the trial of labor.

Kullback-Leibler divergence measure of intermittency: Application to turbulence.

For generic systems exhibiting power law behaviors, and hence multiscale dependencies, we propose a simple tool to analyze multifractality and intermittency, after noticing that these concepts are directly related to the deformation of a probability density function from Gaussian at large scales to non-Gaussian at smaller scales. Our framework is based on information theory and uses Shannon entropy and Kullback-Leibler divergence. We provide an extensive application to three-dimensional fully developed turbulence, seen here as a paradigmatic complex system where intermittency was historically defined and the concepts of scale invariance and multifractality were extensively studied and benchmarked. We compute our quantity on experimental Eulerian velocity measurements, as well as on synthetic processes and phenomenological models of fluid turbulence. Our approach is very general and does not require any underlying model of the system, although it can probe the relevance of such a model.

Mutual information for intrapartum fetal heart rate analysis.

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.

Continuous and discontinuous transitions to synchronization.

We describe how the transition to synchronization in a system of globally coupled Stuart-Landau oscillators changes from continuous to discontinuous when the nature of the coupling is moved from diffusive to reactive. We explain this drastic qualitative change as resulting from the co-existence of a particular synchronized macrostate together with the trivial incoherent macrostate, in a range of parameter values for which the latter is linearly stable. In contrast to the paradigmatic Kuramoto model, this particular state observed at the synchronization transition contains a finite, non-vanishing number of synchronized oscillators, which results in a discontinuous transition. We consider successively two situations where either a fully synchronized state or a partially synchronized state exists at the transition. Thermodynamic limit and finite size effects are briefly discussed, as well as connections with recently observed discontinuous transitions.

The role of cellular coupling in the spontaneous generation of electrical activity in uterine tissue.

The spontaneous emergence of contraction-inducing electrical activity in the uterus at the beginning of labor remains poorly understood, partly due to the seemingly contradictory observation that isolated uterine cells are not spontaneously active. It is known, however, that the expression of gap junctions increases dramatically in the approach to parturition, by more than one order of magnitude, which results in a significant increase in inter-cellular electrical coupling. In this paper, we build upon previous studies of the activity of electrically excitable smooth muscle cells (myocytes) and investigate the mechanism through which the coupling of these cells to electrically passive cells results in the generation of spontaneous activity in the uterus. Using a recently developed, realistic model of uterine muscle cell dynamics, we investigate a system consisting of a myocyte coupled to passive cells. We then extend our analysis to a simple two-dimensional lattice model of the tissue, with each myocyte being coupled to its neighbors, as well as to a random number of passive cells. We observe that different dynamical regimes can be observed over a range of gap junction conductances: at low coupling strength, corresponding to values measured long before delivery, the activity is confined to cell clusters, while the activity for high coupling, compatible with values measured shortly before delivery, may spread across the entire tissue. Additionally, we find that the system supports the spontaneous generation of spiral wave activity. Our results are both qualitatively and quantitatively consistent with observations from in vitro experiments. In particular, we demonstrate that the increase in inter-cellular electrical coupling observed experimentally strongly facilitates the appearance of spontaneous action potentials that may eventually lead to parturition.

Spatiotemporal chaos: the microscopic perspective.

Extended nonequilibrium systems can be studied in the framework of field theory or from the dynamical systems perspective. Here we report numerical evidence that the sum of a well-defined number of instantaneous Lyapunov exponents for the complex Ginzburg-Landau equation is given by a simple function of the space average of the square of the macroscopic field. This relationship follows from an explicit formula for the time-dependent values of almost all the exponents.