Certain time domain, frequency domain and a nonlinear measure of heart rate variability are studied in women following a meditative practice called cyclic meditation. The nonlinear measure studied is the sampling entropy. We show that there is an increase in the sampling entropy in the meditative group as compared to the control group. The time domain measure called pNNx is shown to be useful i...

Oscillations of heart rate and blood pressure are related to the activity of the underlying control mechanism. They have been investigated mostly with linear methods in the time and frequency domains. Also, in recent years, many different nonlinear analysis methods have been applied for the evaluation of cardiovascular variability. This review presents the most commonly used nonlinear methods. ...

The choice of the input signals has impact on the nonparametric frequency response function (FRF) measurements of a nonlinear MIMO system. It is shown that Gaussian noise, periodic noise, and random multisines are equivalent, yielding in the limit the same linear approximation to a nonlinear MIMO system. Even in the noiseless case, variability of the FRF is observed due to the presence of the n...

An original homogenization method was used to analyze the nonlinear elastic properties of epithelial cells probed by magnetic twisting cytometry. In this approach, the apparent rigidity of a cell with nonlinear mechanical properties is deduced from the mechanical response of the entire population of adherent cells. The proposed hyperelastic cell model successfully accounts for the variability i...

Two diverse complexity metrics quantifying time irreversibility and local prediction, in connection with a surrogate data approach, were utilized to detect nonlinear dynamics in short heart period (HP) variability series recorded in fetuses, as a function of the gestational period, and in healthy humans, as a function of the magnitude of the orthostatic challenge. The metrics indicated the pres...

When considering human neuroimaging data, an appreciation of signal variability represents a fundamental innovation in the way we think about brain signal. Typically, researchers represent the brain's response as the mean across repeated experimental trials and disregard signal fluctuations over time as "noise". However, it is becoming clear that brain signal variability conveys meaningful func...

This paper presents a statistical diagnostic to interpret the dynamics of nonlinear variability in models. It consists in applying the Multichannel Singular Spectrum Analysis to the variability of a suitable equation of a dynamical system. This method enables us to evaluate the sensitivity of the oscillatory features of a physical model to tendencies in its mathematical formulation. Hence, resp...

Stability certification and identification of a safe stabilizing initial set are two important concerns in ensuring operational safety, stability, robustness dynamical systems. With the advent machine-learning tools, these issues need to be addressed for systems with machine-learned components feedback loop. To develop general theory stability stabilizability neural network (NN)-controlled nonl...