Assessment of Singularities in the EEG During A-Phases of Sleep Based on Wavelet Decomposition.

Electroencephalography (EEG) signals convey information related to different processes that take place in the brain. From the EEG fluctuations during sleep, it is possible to establish the sleep stages and identify short events, commonly related to a specific physiological process or pathology. Some of these short events (called A-phases) present an organization and build up the concept of the Cyclic Alternating Pattern (CAP) phenomenon. In general, the A-phases abruptly modify the EEG fluctuations, and a singular behavior could occur. With the aim to quantify the abrupt changes during A-phases, in this work the wavelet analysis is considered to compute Hölder exponents, which measure the singularity strength. We considered time windows of 2s outside and 5s inside A-phases onset (or offset). A total number of 5121 A-phases from 9 healthy participants and 10 patients with periodic leg movements were analyzed. Within an A-phase the Hölder numerical value tends to be 0.6, which implies a less abrupt singularity. Whereas outside of A-phases, it is observed that the Hölder value is approximately equal to 0.3, which implies stronger singularities, i.e., a more evident discontinuity in the signal behavior. In addition, it seems that the number of singularities increases inside of A-phases. The numerical results suggest that the EEG naturally conveys singularities modified by the A-phase occurrence, and this information could help to conceptualize the CAP phenomenon from a new perspective based on the sharpness of the EEG instead of the oscillatory way.

Scaling Analysis of an Image Encryption Scheme Based on Chaotic Dynamical Systems.

Despite that many image encryption systems based on chaotic or hyperchaotic systems have been proposed to protect different kinds of information, it has been crucial to achieve as much security as possible in such systems. In this sense, we numerically implement a known image encryption system with some variants, making special emphasis when two operations are considered in the scrambling stage. The variants of such an encryption system are based on some hyperchaotic systems, which generated some substitution boxes and the keys of the system. With the aim to have a more complete evaluation, some internal stages of the image encryption scheme have been evaluated by using common statistical tests, and also the scaling behavior of the encrypted images has been calculated by means of a two-dimensional detrended fluctuation analysis (2D-DFA). Our results show that the image encryption systems that include two operations or transformations in the scrambling stage present a better performance than those encryption systems that consider just one operation. In fact, the 2D-DFA approach was more sensitive than some common statistical tests to determine more clearly the impact of multiple operations in the scrambling process, confirming that this scaling method can be used as a perceptual security metric, and it may contribute to having better image encryption systems.

Relation between heart beat fluctuations and cyclic alternating pattern during sleep in insomnia patients.

Insomnia is a condition that affects the nervous and muscular system. Thirty percent of the population between 18 and 60 years suffers from insomnia. The effects of this disorder involve problems such as poor school or job performance and traffic accidents. In addition, patients with insomnia present changes in the cardiac function during sleep. Furthermore, the structure of electroencephalographic A-phases, which builds up the Cyclic Alternating Pattern during sleep, is related to the insomnia events. Therefore, the relationship between these brain activations (A-phases) and the autonomic nervous system would be of interest, revealing the interplay of central and autonomic activity during insomnia. With this goal, a study of the relationship between A-phases and heart rate fluctuations is presented. Polysomnography recording of five healthy subjects, five sleep misperception patients and five patients with psychophysiological insomnia were used in the study. Detrended Fluctuation Analysis (DFA) was used in order to evaluate the heart rate dynamics and this was correlated with the number of A-phases. The results suggest that pathological patients present changes in the dynamics of the heart rate. This is reflected in the modification of A-phases dynamics, which seems to modify of heart rate dynamics.

On the wavelet formalism for multifractal analysis.

It is proved that the multifractal characterizations of diametrically regular measures that are provided by the wavelet and by the Hentschel-Procaccia formalisms are identical. (c) 2001 American Institute of Physics.