Eduardo Serrano

Analysis of wavelet-filtered tonic-clonic electroencephalogram recordings.

EEG signals obtained during tonic-clonic epileptic seizures can be severely contaminated by muscle and physiological noise. Heavily contaminated EEG signals are hard to analyse quantitatively and also are usually rejected for visual inspection by physicians, resulting in a considerable loss of collected information. The aim of this work was to develop a computer-based method of time series analysis for such EEGs. A method is presented for filtering those frequencies associated with muscle activity using a wavelet transform. One of the advantages of this method over traditional filtering is that wavelet filtering of some frequency bands does not modify the pattern of the remaining ones. In consequence, the dynamics associated with them do not change. After generation of a ‘noise free’ signal by removal of the muscle artifacts using wavelets, a dynamic analysis was performed using non-linear dynamics metric tools. The characteristic parameters evaluated (correlation dimension D2 and largest Lyapunov exponent λ1) were compatible with those obtained in previous works. The average values obtained were: D2=4.25 and λ1=3.27 for the pre-ictal stage; D2=4.03 and λ1=2.68 for the tonic seizure stage; D2=4.11 and λ1=2.46 for the clonic seizure stage.

Study of EEG Brain Maturation Signals with Multifractal Detrended Fluctuation Analysis

In this work, we have study the EEG signals of birds during the first 6 weeks of life. The aim of the article is to perform a quantitative analysis of the dynamical changes observed in these signals due to the brain maturation effects. The signals’ long scaling behaviour is study by Multifractal Detrended Fluctuation Analysis (MFDFA). This method allows the multifractal characterization of these EEG nonstationary time series and characterize the different stage of bird brain maturation.

ABOUT THE EFFECTIVENESS OF DIFFERENT METHODS FOR THE ESTIMATION OF THE MULTIFRACTAL SPECTRUM OF NATURAL SERIES

Complex natural systems present characteristics of scalar invariance. This behavior has been experimentally verified and a large related bibliography has been reported. Multifractal Formalism is a ...

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.

Active Tangent Link System for Transverse Support of Large Thin Meniscus Mirrors

An active tangent link system was developed to provide transverse support for large thin meniscus mirrors. The support system uses six tangent links to control position and distribute compensating force to the mirror. Each of the six tangent links utilizes an electromechanical actuator and an imbedded lever system working through a load cell and flexure. The lever system reduces the stiffness, strength and force resolution requirements of the electromechanical actuator and allows more compact packaging. Although all six actuators are essentially identical, three of them are operated quasi statically, and are only used to position the optic. The other three are actively operated to produce an optimal and repeatable distribution of the transverse load. This repeatable load distribution allows for a more effective application of a look up table and reduces the demands on the active optics system. A control system was developed to manage the quasi static force equilibrium servo loop using a control matrix that computes the displacements needed to correct any force imbalance with good convergence and stability. This system was successfully retrofitted to the 4.3 meter diameter, 100 mm thick SOAR primary mirror to allow for more expeditious convergence of the mirror figure control system. This system is also intended for use as the transverse support system for the LSST 3.4 meter diameter thin meniscus secondary mirror.

A Quantitative Analysis of an EEG Epileptic Record Based on MultiresolutionWavelet Coefficients

The characterization of the dynamics associated with electroencephalogram (EEG) signal combining an orthogonal discrete wavelet transform analysis with quantifiers originated from information theory is reviewed. In addition, an extension of this methodology based on multiresolution quantities, called wavelet leaders, is presented. In particular, the temporal evolution of Shannon entropy and the statistical complexity evaluated with different sets of multiresolution wavelet coefficients are considered. Both methodologies are applied to the quantitative EEG time series analysis of a tonic-clonic epileptic seizure, and comparative results are presented. In particular, even when both methods describe the dynamical changes of the EEG time series, the one based on wavelet leaders presents a better time resolution.

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.

Wavelet projection methods for solving pseudodifferential inverse problems

We consider the Inverse Problem (IP) associated to an equation of the form Af = g, where A is a pseudodifferential operator with symbol. It consists in finding a solution f for given data g. When the operator A is not strongly invertible and the data is perturbed with noise, the IP may be ill-posed and the solution must be approximate carefully. For the present application we regard a particular orthonormal wavelet basis and perform a wavelet projection method to construct a solution to the Forward Problem (FP). The approximate solution to the IP is achieved based on the decomposition of the perturbed data calculating the elementary solutions that are nearly the preimages of the wavelets. Based on properties of both, the basis and the operator, and taking into account the energy of the data, we can handle the error that arises from the partial knowledge of the data and from the non-exact inversion of each element of the wavelet basis. We estimate the error of the approximation and discuss the advantages of the proposed scheme.

AN ENTROPY BASED IN WAVELET LEADERS TO QUANTIFY THE LOCAL REGULARITY OF A SIGNAL AND ITS APPLICATION TO ANALIZE THE DOW JONES INDEX

Local regularity analysis is useful in many fields, such as financial analysis, fluid mechanics, PDE theory, signal and image processing. Different quantifiers have been proposed to measure the local regularity of a function. In this paper we present a new quantifier of local regularity of a signal: the pointwise wavelet leaders entropy. We define this new measure of regularity by combining the concept of entropy, coming from the information theory and statistical mechanics, with the wavelet leaders coefficients. Also we establish its inverse relation with one of the well-known regularity exponents, the pointwise Holder exponent. Finally, we apply this methodology to the financial data series of the Dow Jones Industrial Average Index, registered in the period 1928–2011, in order to compare the temporal evolution of the pointwise Holder exponent and the pointwise wavelet leaders entropy. The analysis reveals that temporal variation of these quantifiers reflects the evolution of the Dow Jones Industrial Ave...

Brain Maturation Changes Characterized by Algorithmic Complexity (Lempel and Ziv Complexity)

Recent experimental results suggest that basal electroencephalogram (EEG)changes reflect the widespread functional evolution in neuronal circuits, occurring in chicken brain during the “synapse maturation” period, between 3 and 8 weeks’ posthatch. In present work a quantitative analysis based on the Algorithmic Complexity (Lempel and Ziv Complexity) is performed. It is shown that this complexity presents a peak at week 2 posthatch 2, and a tendency to stabilize its values after the week 5 posthatch.