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A Babloyantz

Publications and source records attributed to A Babloyantz.

14 recordsLinked to original sources
PubMed1991

Predictability of human EEG: a dynamical approach.

The electroencephalogram recordings from human scalp are analysed in the framework of recent methods of nonlinear dynamics. Three stages of brain activity are considered: the alpha waves (eyes closed), the deep sleep (stage four) and the Creutzfeld-Jakob coma. Two dynamical parameters of the attractors are evaluated. These are the Lyapunov exponents, which measure the divergence or convergence of trajectories in phase space and the Kolmogorov or metric entropy, whose inverse gives the mean predicting time of a given EEG signal. In all the stages considered, the results reveal the presence of at least two positive Lyapunov exponents, which are the footprints of chaos. This number increases to three positive exponents in the case of alpha waves, indicating that although for very short episodes the alpha waves seem extremely coherent, the variability of the brain increases markedly over larger periods of activity. The degree of entropy/chaos increases from coma to deep sleep and then to alpha waves. The large predicting time observed for deep sleep suggests that these waves are related to a slow rate of information processing. The predicting time of the alpha waves is much smaller, indicating a rapid loss of information. Finally, with the help of the Lyapunov exponents, the attractor's dimensions are evaluated using two different conjectures and compared to values obtained previously by the Grassberger-Procaccia algorithm.

Brain↗
PubMed1991

Evidence for slow brain waves: a dynamical approach.

Various techniques of non-linear dynamics have been applied with success to EEG data and have provided a new insight into brain dynamics. Among these the 'recurrence plot' is a powerful tool for revealing the presence of drift or periodicities and is easily obtained in the framework of a non-linear dynamical analysis. When this analysis is applied to the EEG recorded from a patient suffering from Creutzfeldt-Jakob disease one observes the presence of slow periodicities of the order of 58 sec. We suggest that the recurrence plots are powerful tools for discovering hidden periodicities of EEG as well as the degree of stationarity of brain activity.

Brain↗
PubMed1988

Is the normal heart a periodic oscillator?

With the help of several independent methods of nonlinear dynamics, the electrocardiograms (ECG) of four normal human hearts are studied qualitatively and quantitatively. A total of 36 leads were tested. The power spectrum, the autocorrelation function, the phase portrait, the Poincaré section, the correlation dimension, the Lyapunov exponent and the Kolmogorov entropy all point to the fact that the normal heart is not a perfect oscillator. The cardiac activity stems from deterministic dynamics of chaotic nature characterized by correlation dimensions D2 ranging from 3.6 to 5.2. Two different phase spaces are constructed for the evaluation of D2: the introduction of time lags and the direct use of space vectors give similar results. It is shown that the variabilities in interbeat intervals are not random but exhibit short range correlations governed by deterministic laws. These correlations may be related to the accelerating and decelerating physiological processes. This new approach to the cardiac activity may be used in clinical diagnosis. Also they are valuable tools for the evaluation of mathematical models which describe cardiac activity in terms of evolution equations.

Electrocardiography↗
PubMed1986

Low-dimensional chaos in an instance of epilepsy.

Using a time series obtained from the electroencephalogram recording of a human epileptic seizure, we show the existence of a chaotic attractor, the latter being the direct consequence of the deterministic nature of brain activity. This result is compared with other attractors seen in normal human brain dynamics. A sudden jump is observed between the dimensionalities of these brain attractors (4.05 +/- 0.05 for deep sleep) and the very low dimensionality of the epileptic state (2.05 +/- 0.09). The evaluation of the autocorrelation function and of the largest Lyapunov exponent allows us to sharpen further the main features of underlying dynamics. Possible implications in biological and medical research are briefly discussed.

Brain↗
PubMed1976

A model for competing polymers leading to their spatial separation.

A model for a prebiotic polymer synthesis in a gradient of monomer is presented. In the absence of mutations the synthesis of the polymer proceeds in the region where the monomer concentration is the highest. However if a favorable mutation occurs, the latter accumulates in the high concentration zone and the initial polymer is restricted to a poorer monomer concentration region.

Biological Evolution↗
PubMed1974

Models for positional information and positional differentiation.

It is commonly thought that the formation of patterns in developing organisms is due to the existence of a gradient of a morphogen that determines the fate of cells as a function of position in the organism. A model is presented based on a molecular mechanism where the gradient is established by the active transport of a morphogen between source and sink. The cellular differentiation and the subsequent spatial pattern formation results from the interaction of this morphogen with the genetic regulatory mechanisms of cells. Some properties of the model are given and discussed in relation to grafting experiments in hydra.

Animals↗