Nicolas Bernard Garnier

Prenatal maternal stress alters maternal–fetal heart rate coupling, as demonstrated by the Fetal Stress Index derived from bivariate phase-rectified signal averaging. Here, we extend this framework using information-theoretical measures to elucidate underlying mechanisms. In 118 third-trimester pregnancies (59 stressed, 59 control), we computed entropy rate (ER), sample entropy (SE) and transfer entropy (TE) under multiple conditioning paradigms, employing mixed linear models for repeated measures. We identified dual coupling mechanisms at the short-term (0.5–2.5 s), but not long-term (2.5–5 s) time scales: (1) stress-invariant state-dependent synchronization, with maternal decelerations exerting approximately 60% coupling strength on fetal heart rate complexity—a fundamental coordination conserved across demographics; and (2) stress-sensitive temporal information transfer (TE), showing exploratory associations with maternal cortisol that require replication. A robust sex-by-stress interaction emerged in TE from mixed models, with exploratory female-specific coupling patterns absent in males. Universal acceleration predominance was observed in both maternal and fetal heart rates, stronger in fetuses and independent of sex or stress. We provide insight into the dependence of these findings on the sampling rate of the underlying data, identifying 4 Hz, commonly used for ultrasound-derived fetal heart rate recordings, as a sufficient sampling rate to capture the information flow. Information-theoretical analysis reveals that maternal–fetal coupling operates through complementary pathways with differential stress sensitivity, extending the Fetal Stress Index by elucidating causal foundations. Future studies should explore additional information-theoretical conditional approaches to resolve stress-specific and time-scale-specific differences in information flow.

The synchronization of biological activity with the alternation of day and night (circadian rhythm) is performed in the brain by a group of neurons, constituting the suprachiasmatic nucleus (SCN). The SCN is divided into two subgroups of oscillating cells: the ventro-lateral (VL) neurons, which are exposed to light (photic signal) and the dorso-medial (DM) neurons which are coupled to the VL cells. When the coupling between these neurons is strong enough, the system synchronizes with the photic period. Upon increasing the cell coupling, the entrainment of the DM cells has been recently shown to occur via a very sharp (jumping) transition when the period of the photic input is larger than the intrinsic period of the cells. Here, we characterize this transition with a simple realistic model. We show that two bifurcations possibly lead to the disappearance of the endogenous mode. Using a mean field model, we show that the jumping transition results from a supercritical Hopf-like bifurcation. This finding implies that both the period and strength of the stimulating photic signal, and the relative fraction of cells in the VL and DM compartments are crucial in determining the synchronization of the system.

We study the predictability of turbulent velocity signals using probabilistic analog forecasting. Here, predictability is defined by the accuracy of forecasts and the associated uncertainties. We study the Gledzer–Ohkitani–Yamada (GOY) shell model of turbulence as well as experimental measurements from a fully developed turbulent flow. In both cases, we identify the extreme values of velocity at small scales as localized unpredictable events that lead to a loss of predictability: worse mean predictions and an increase in their uncertainties. The GOY model, with its explicit scale separation, allows us to evaluate the prediction performance at individual scales to better relate the intensity of extreme events and the loss of forecast performance. Results show that predictability decreases systematically from large to small scales. These findings establish a statistical connection between predictability loss across scales and intermittency in turbulent flows.

Prenatal maternal stress (PS) is a risk factor for adverse offspring neurodevelopment. Heart rate variability (HRV) complexity provides a non-invasive marker of maternal autonomic regulation and may be influenced by mind--body interventions such as Yoga. In this quasi-randomized controlled trial, 28 chronically stressed pregnant women were followed from the second trimester until birth: 14 participated in weekly Hatha Yoga with electrocardiogram (ECG) recordings, and 14 received standard obstetric care with monthly ECGs. Group allocation was based on availability, with participants unaware of their assignment at enrollment. HRV complexity was assessed first with Sample Entropy and Entropy Rate and then expanded to 94 HRV metrics spanning temporal, frequency, nonlinear, and information-theoretical domains. All metrics were covariate-adjusted (maternal age, BMI, gestational age), standardized, and analyzed using timepoint-specific principal component analysis (PCA). From this, a unified HRV index was derived. Analyses revealed that HRV metric relationships changed dynamically across pregnancy, with PCA loadings shifting from frequency toward complexity measures in late gestation. The mixed effects model identified a significant time x group interaction effect (p = 0.041). These findings suggest a restructuring of HRV signal-analytical domains with advancing pregnancy attributable to Yoga and highlight the utility of advanced HRV analysis frameworks for future, larger trials.

Prenatal maternal stress (PS) is a risk factor for adverse offspring neurodevelopment. Heart rate variability (HRV) complexity provides a non-invasive marker of maternal autonomic regulation and may be influenced by mind–body interventions such as Yoga. In this quasi-randomized controlled trial, 28 chronically stressed pregnant women were followed from the second trimester until birth: 14 participated in weekly Hatha Yoga with electrocardiogram (ECG) recordings, and 14 received standard obstetric care with monthly ECGs. Group allocation was based on availability, with participants unaware of their assignment at enrollment. HRV complexity was assessed first with Sample Entropy and Entropy Rate and then expanded to 94 HRV metrics spanning temporal, frequency, nonlinear, and information-theoretical domains. All metrics were covariate-adjusted (maternal age, BMI, gestational age), standardized, and analyzed using timepoint-specific principal component analysis (PCA). From this, a unified HRV index was derived. Analyses revealed that HRV metric relationships changed dynamically across pregnancy, with PCA loadings shifting from frequency toward complexity measures in late gestation. The mixed effects model identified a significant time x group interaction effect (p = 0.041). These findings suggest a restructuring of HRV signal-analytical domains with advancing pregnancy attributable to Yoga and highlight the utility of advanced HRV analysis frameworks for future, larger trials.

In this paper, we present a multiscale characterization of the streamwise velocity of a turbulent channel flow. We study the second and fourth order structure functions and the flatness for scales ranging from the dissipative to the integral domains and for a wide range of distances to the walls spanning four distinct regions of the channel. We characterize the impact of the shear stress induced by the walls on these statistics. Far from the walls, in the outer layer, the impact of the boundaries on the flow is negligible, and the flow statistics follow the Kolmogorov–Obukhov theory. In the viscous, buffer, and logarithmic regions, the inertial domain can be split into two subdomains of scales with two different statistical behaviors. In the logarithmic region, the scaling of the structure functions agrees with the model of Davidson et al., J. Fluid Mech. 550, 51–60 (2006) but the scaling of the flatness seems to better correspond to the characterization of intermittency proposed by Kolmogorov and Obukhov in 1962. The structure functions and flatness of the streamwise velocity in the buffer and viscous regions are studied for the first time. We show the strong non-Gaussianity of the flow velocity at any scale in the viscous layer with strong intermittent events that may correspond to high shear-induced dissipation.

This article presents a multiscale, non-linear and directional statistical characterization of images based on the estimation of the skewness, flatness, entropy and distance from Gaussianity of the spatial increments. These increments are characterized by their magnitude and direction; they allow us to characterize the multiscale properties directionally and to explore anisotropy. To describe the evolution of the probability density function of the increments with their magnitude and direction, we use the skewness to probe the symmetry, the entropy to measure the complexity, and both the flatness and distance from Gaussianity to describe the shape. These four quantities allow us to explore the anisotropy of the linear correlations and non-linear dependencies of the field across scales. First, we validate the methodology on two-dimensional synthetic scale-invariant fields with different multiscale properties and anisotropic characteristics. Then, we apply it on two synthetic turbulent velocity fields: a perfectly isotropic and homogeneous one, and a channel flow where boundaries induce inhomogeneity and anisotropy. Our characterization unambiguously detects the anisotropy in the second case, where our quantities report scaling properties that depend on the direction of analysis. Furthermore, we show in both cases that turbulent velocity fluctuations are always isotropic, when the mean velocity profile is adequately removed.

This article presents a multiscale, non-linear and directional statistical characterization of images based on the estimation of the skewness, flatness, entropy and distance from Gaussianity of the spatial increments. These increments are characterized by their magnitude and direction; they allow us to characterize the multiscale properties directionally and to explore anisotropy. To describe the evolution of the probability density function of the increments with their magnitude and direction, we use the skewness to probe the symmetry, the entropy to measure the complexity, and both the flatness and distance from Gaussianity to describe the shape. These four quantities allow us to explore the anisotropy of the linear correlations and non-linear dependencies of the field across scales. First, we validate the methodology on two-dimensional synthetic scale-invariant fields with different multiscale properties and anisotropic characteristics. Then, we apply it on two synthetic turbulent velocity fields: a perfectly isotropic and homogeneous one, and a channel flow where boundaries induce inhomogeneity and anisotropy. Our characterization unambiguously detects the anisotropy in the second case, where our quantities report scaling properties that depend on the direction of analysis. Furthermore, we show in both cases that turbulent velocity fluctuations are always isotropic, when the mean velocity profile is adequately removed.