Physics of brain dynamics: Fokker-Planck analysis reveals changes in EEG delta and theta activity during anaesthesia.

We use drift and diffusion coefficients to reveal interactions between different oscillatory processes underlying a complex signal and apply the method to EEG delta and theta frequencies in the brain. By analysis of data recorded from rats during anaesthesia we consider the stability and basins of attraction of fixed points in the phase portrait of the deterministic part of the retrieved stochastic process. We show that different classes of dynamics are associated with deep and light anaesthesia, and we demonstrate that the predominant directionality of the interaction is such that theta drives delta.

The effect of low-frequency oscillations on cardio-respiratory synchronization: Observations during rest and exercise.

We show that the transitions which occur between close orders of synchronization in the cardio-respiratory system are mainly due to modulation of the cardiac and respiratory processes by low-frequency components. The experimental evidence is derived from recordings on healthy subjects at rest and during exercise. Exercise acts as a perturbation of the system that alters the mean cardiac and respiratory frequencies and changes the amount of their modulation by low-frequency oscillations.

Taylor's frozen-flow hypothesis in Burgers turbulence.

By detailed analytical treatment of the shock dynamics in the Burgers turbulence with large scale forcing we calculate the velocity structure functions between pairs of points displaced both in time and space. Our analytical treatment verifies the so-called Taylor's frozen-flow hypothesis without relying on any closure and under very general assumptions. We discuss the limitation of the hypothesis and show that it is valid up to time scales smaller than the correlation time scale of temporal velocity correlation function.

Direction of coupling from phases of interacting oscillators: a permutation information approach.

We introduce a directionality index for a time series based on a comparison of neighboring values. It can distinguish unidirectional from bidirectional coupling, as well as reveal and quantify asymmetry in bidirectional coupling. It is tested on a numerical model of coupled van der Pol oscillators, and applied to cardiorespiratory data from healthy subjects.

Phase coupling in the cardiorespiratory interaction.

Markovian analysis is applied to derive nonlinear stochastic equations for the reconstruction of heart rate and respiration rate variability data. A model of their 'phase' interactions is obtained for the first time, thereby gaining new insights into the strength and direction of the cardiorespiratory phase coupling. The reconstructed model can reproduce synchronisation phenomena between the cardiac and the respiratory systems, including switches in synchronisation ratio.