M.T. Martín

EEG analysis using wavelet-based information tools

Wavelet-based informational tools for quantitative electroencephalogram (EEG) record analysis are reviewed. Relative wavelet energies, wavelet entropies and wavelet statistical complexities are used in the characterization of scalp EEG records corresponding to secondary generalized tonic-clonic epileptic seizures. In particular, we show that the epileptic recruitment rhythm observed during seizure development is well described in terms of the relative wavelet energies. In addition, during the concomitant time-period the entropy diminishes while complexity grows. This is construed as evidence supporting the conjecture that an epileptic focus, for this kind of seizures, triggers a self-organized brain state characterized by both order and maximal complexity.

Brain electrical activity analysis using wavelet-based informational tools

The traditional way of analyzing brain electrical activity, on the basis of Electroencephalography (EEG) records, relies mainly on visual inspection and years of training. Although it is quite useful, of course, one has to acknowledge its subjective nature that hardly allows for a systematic protocol. In order to overcome this undesirable feature, a quantitative EEG analysis has been developed over the years that introduces objective measures, reflecting not only the characteristics of the brain activity itself but also giving clues concerning the underlying associated neural dynamics. The processing of information by the brain is reflected in dynamical changes of the electrical activity in (i) time, (ii) frequency, and (iii) space. Therefore, the concomitant studies require methods capable of describing the qualitative variation of the signal in both time and frequency. In the present work we introduce new information tools based on the wavelet transform for the assessment of EEG data as adapted to a non-extensive scenario.

Wootters’ distance revisited: a new distinguishability criterium

Abstract.The notion of distinguishability between quantum states has shown to be fundamental in the frame of quantum information theory. In this paper we present a new distinguishability criterium by using a information theoretic quantity: the Jensen-Shannon divergence (JSD). This quantity has several interesting properties, both from a conceptual and a formal point of view. Previous to define this distinguishability criterium, we review some of the most frequently used distances defined over quantum mechanics’ Hilbert space. In this point our main claim is that the JSD can be taken as a unifying distance between quantum states.

Distances in Probability Space and the Statistical Complexity Setup

Statistical complexity measures (SCM) are the composition of two ingredients: (i) entropies and (ii) distances in probability-space. In consequence, SCMs provide a simultaneous quantification of the randomness and the correlational structures present in the system under study. We address in this review important topics underlying the SCM structure, viz., (a) a good choice of probability metric space and (b) how to assess the best distance-choice, which in this context is called a “disequilibrium” and is denoted with the letter Q. Q, indeed the crucial SCM ingredient, is cast in terms of an associated distance D. Since out input data consists of time-series, we also discuss the best way of extracting from the time series a probability distribution P. As an illustration, we show just how these issues affect the description of the classical limit of quantum mechanics.

ENTROPIC NON-TRIVIALITY, THE CLASSICAL LIMIT AND GEOMETRY-DYNAMICS CORRELATIONS

The quantum-classical limit together with the associated onset of chaos is employed here in order to illustrate the importance of a proper choice of distance in probability space if one wishes to describe dynamical properties from the information theory viewpoint.

On extracting probability distribution information from time series

Time-series (TS) are employed in a variety of academic disciplines. In this paper we focus on extracting probability density functions (PDFs) from TS to gain an insight into the underlying dynamic processes. On discussing this “extraction” problem, we consider two popular approaches that we identify as histograms and Bandt–Pompe. We use an information-theoretic method to objectively compare the information content of the concomitant PDFs.

A hybrid method using wavelets for the numerical solution of boundary value problems on the interval

Abstract In this work, various aspects of wavelet-based methods for second order boundary value problems under Galerkin framework are investigated. Based on the B-spline multiresolution analysis (MRA) on the line we propose a hybrid method on the interval which combines different treatments for interior and boundary splines. By using this procedure, the MRA structure was conserved and hierarchical representations of the solution at different scales were obtained without much computational effort. Numerical examples are given to verify the effectiveness of the proposed method and the comparison with other techniques is presented.

A Maximum Entropy Approach for Predicting Epileptic Tonic-Clonic Seizure

The development of methods for time series analysis and prediction has always been and continues to be an active area of research. In this work, we develop a technique for modelling chaotic time series in parametric fashion. In the case of tonic-clonic epileptic electroencephalographic (EEG) analysis, we show that appropriate information theory tools provide valuable insights into the dynamics of neural activity. Our purpose is to demonstrate the feasibility of the maximum entropy principle to anticipate tonic-clonic seizure in patients with epilepsy.

A NEW REFINEMENT WAVELET–GALERKIN METHOD IN A SPLINE LOCAL MULTIRESOLUTION ANALYSIS SCHEME FOR BOUNDARY VALUE PROBLEMS

In this work, a new Wavelet–Galerkin method for boundary value problems is presented. It improves the approximation in terms of scaling functions obtained through a collocation scheme combined with variational equations. A B-spline multiresolution structure on the interval is designed in order to refine the solution recursively and efficiently using wavelets. Numerical examples are given to verify good convergence properties of the proposed method.

Impairment of Erythrocytes Incubated in Glucose Medium: A Wavelet-Information Theory Analysis

This study investigates the effects produced by an increased concentration of glucose in a suspending medium on the erythrocytes Information Theory quantifiers. Erythrocytes, which were obtained from eight healthy volunteers, were washed and incubated in vitro with glucose solutions at different concentrations. The measured Wavelet-based Information Theory quantifiers include the Relative Wavelet Energy (RWE), the Normalized Total Wavelet Shannon Entropy (NTWS), MPR-Statistical Complexity Measure (SCM) and entropy–complexity plane. The results show that the increase in glucose concentration does not produce significant changes on the RWE, while significant ones on the NTSE, which combined with SCM values allow to identify different behaviour for all the different populations in the entropy–complexity plane. Modification in the hemorheological properties of cells could be clearly detected with these Wavelet-based Information Theory quantifiers.