Alice de Jesus Kozakevicius

Adaptive multiresolution WENO schemes for multi-species kinematic flow models

Multi-species kinematic flow models lead to strongly coupled, nonlinear systems of first-order, spatially one-dimensional conservation laws. The number of unknowns (the concentrations of the species) may be arbitrarily high. Models of this class include a multi-species generalization of the Lighthill-Whitham-Richards traffic model and a model for the sedimentation of polydisperse suspensions. Their solutions typically involve kinematic shocks separating areas of constancy, and should be approximated by high resolution schemes. A fifth-order weighted essentially non-oscillatory (WENO) scheme is combined with a multiresolution technique that adaptively generates a sparse point representation (SPR) of the evolving numerical solution. Thus, computational effort is concentrated on zones of strong variation near shocks. Numerical examples from the traffic and sedimentation models demonstrate the effectiveness of the resulting WENO multiresolution (WENO-MRS) scheme.

Automated drowsiness detection through wavelet packet analysis of a single EEG channel

Ratio indices computed from a single EEG channel used as drowsiness indicators.Delta and gamma brain rhythms successfully used for drowsiness detection.Wavelet packet transform as the main tool to localize specific brain frequency ranges.Transition from alert to drowsy state is taken as main event of interest.Wilcoxon signed rank test analysis pointed out the contribution of proposed indices. Advances in materials engineering, electronic circuits, sensors, signal processing and classification techniques have allowed computational systems to interpret biological quantities, recognizing physiological conditions. The next scientific challenge is to turn those technologies portable, wearable or even implantable, above all, being energy efficient. A prospective application for the next generation of portable electroencephalogram (EEG) signal processing systems is hazard prevention in attention-demanding activities. EEG keeps closest connection to the preoptic area where sleep is originated. In this paper, a methodology for assessing alertness level based on a single EEG channel (Pz-Oz) is proposed, allowing the reduction of the required hardware and the computational time of the algorithms, besides being more portable than multi-channel based ones. Two new spectral power-based indices (i) γ/? and (ii) ( γ + β )/( ? + α ) are computed from EEG rhythms through the normalized Haar discrete wavelet packet transform (WPT). The Haar WPT allows precisely resolving the brain rhythms into packets whilst demanding a relatively low computational cost. The effectiveness of the proposed indices in drowsiness detection is evaluated by comparison with five indices originally proposed for multi-channel processing. Statistical Wilcoxon signed rank test is applied to evaluate the performance of the entire set of indices, evidencing the significant changes in the alert-drowsy transitions of 20 subjects of a public database. The proposed indices (ii) and (i) presented the most and second more significant p-Values (p < 0.001 and p?=?0.001), respectively.

Splitting Wavelet Method for Solving 2D Conservation Laws

for which the grid adaptivity is controlled by the application of a wavelet transform to the numerical solution at each time step combined with a splitting method. Wavelet based adaptive schemes for uni-dimensional problems go back to Harten [4], who was one of the precursors in applying interpolating wavelet transforms to obtain a multiscale decomposition of the numerical solution. This multiresolution decomposition was used to decide whether the numerical flux function should be evaluated by an expensive high resolution scheme or it could be computed from a polynomial interpolation process in a multilevel fashion. For two-dimensional problems, the ideas proposed in [4] were extended in [6] where a two-dimensional wavelet transform is applied to the numerical divergence of (1). Again the multiresolution transform is used to analyze the smoothness of the numerical solution to decide where the numerical quantities can be obtained by interpolation or if they must be evaluated exactly by the numerical scheme. In reality, Martens approach provides a sensor to manage the flux (or divergence) computation but is far from being an adaptive mesh refinement technique since the numerical values on the highest resolution level (the finest dyadic grid of all multiresolution set) must be always available. An interesting alternative has been proposed by Holmstrom [2] in order to indeed produce an adaptive mesh refinement procedure based on a wavelet transform. Holmstrom introduced the concept of sparse point representation (SPR), which is a set of points obtained from the thresholded wavelet transform. The differential operator is then solved by a finite difference scheme over the sparse grid associated to the sparse point representation of the solution. For the SPR of uni-dimensional data the interpolating wavelet transform is considered and for the two-dimensional problems the basis for the bi-dimensional transform is obtained by the tensor product of one-dimensional wavelet and scaling function spaces [2]. The main idea proposed in this work is to avoid the application of a two-dimensional wavelet transform in order to construct an adaptive scheme for solving systems of type given by (1), keeping however the SPR approach. One possibihty for reducing the multidimensional problem to a sequence of one-dimensional problems is to consider a sphtting method (for example, here we have considered a time split MacCormack scheme [8]). Once the multidimensional problem is sphtted in many uni-dimensional sub-problems, each one, associated to a spatial direction, can be solved with an adaptive scheme in each slice of the spatial domain. The following section is reserved for presenting the wavelet time sphtting scheme, whose formulation is inspired by the standard MacCormack method [8]. The discretization is given with respect to a sparse grid per direction. In this sense, the adaptivity is performed for each spatial direction separately, meaning that no tensor product will be necessary to construct the wavelet transform. Each component of the sphtting method is solved by a Lax-Friedrichs scheme, in which numerical flux function is computed by an essentially non-oscillatory (ENO) reconstruction, as done for one-dimensional problems in [1]. The time evolution is done according to the time splitting formulation. Finally, in the last section some numerical simulations are presented.

A parallel wavelet adaptive WENO scheme for 2D conservation laws

Purpose The current work aims to present a parallel code using the open multi-processing (OpenMP) programming model for an adaptive multi-resolution high-order finite difference scheme for solving 2D conservation laws, comparing efficiencies obtained with a previous message passing interface formulation for the same serial scheme and considering the same type of 2D formulations laws. Design/methodology/approach The serial version of the code is naturally suitable for parallelization because the spatial operator formulation is based on a splitting scheme per direction for which the flux components are numerically computed by a Lax–Friedrichs factorization independently for each row or column. High-order approximations for numerical fluxes are computed by the third-order essentially non-oscillatory (ENO) and fifth-order weighted essentially non-oscillatory (WENO) interpolation schemes, assuming sparse grids in each direction. The grid adaptivity is obtained by a cubic interpolating wavelet transform applied in each space dimension, associated to a threshold operator. Time is evolved by a third order TVD Runge–Kutta method. Findings The parallel formulation is implemented automatically at compiling time by the OpenMP library routines, being virtually transparent to the programmer. This over simplifies any concerns about managing and/or updating the adaptive grid when compared to what is necessary to be done when other parallel approaches are considered. Numerical simulations results and the large speedups obtained for the Euler equations in gas dynamics highlight the efficiency of the OpenMP approach. Research limitations/implications The resulting speedups reflect the effectiveness of the OpenMP approach but are, to a large extension, limited by the hardware used (2 E5-2620 Intel Xeon processors, 6 cores, 2 threads/core, hyper-threading enabled). As the demand for OpenMP threads increases, the code starts to make explicit use of the second logical thread available in each E5-2620 processor core and efficiency drops. The speedup peak is reached near the possible maximum (24) at about 22, 23 threads. This peak reflects the hardware configuration and the true software limit should be located way beyond this value. Practical implications So far no attempts have been made to parallelize other possible code segments (for instance, the ENO|-WENO-TVD code lines that process the different data components which could potentially push the speed up limit to higher values even further. The fact that the speedup peak is located close to the present hardware limit reflects the scalability properties of the OpenMP programming and of the splitting scheme as well. Consequently, it is likely that the speedup peak with the OpenMP approach for this kind of problem formulation will be close to the physical (and/or logical) limit of the hardware used. Social implications This work is the result of a successful collaboration among researchers from two different institutions, one internationally well-known and with a long-term experience in applied mathematics for industrial applications and the other in a starting process of international academic insertion. In this way, this scientific partnership has the potential of promoting further knowledge exchange, involving students and other collaborators. Originality/value The proposed methodology (use of OpenMP programming model for the wavelet adaptive splitting scheme) is original and contributes to a very active research area in the past years, namely, adaptive methods for conservation laws and their parallel formulations, which is of great interest for the entire scientific community.

URL query string anomaly sensor designed with the bidimensional Haar wavelet transform

In this paper, the 2D Haar wavelet transform is the proposed analysis technique for HTTP traffic data. Web attacks are detected by two threshold operations applied to the wavelet coefficients of the 2D transform: one based on their median and the other on the best approximation method. The two proposed algorithms are validated through an extensive number of simulations, including comparisons with well-established techniques, confirming the effectiveness of the designed sensor.

A parallel splitting wavelet method for 2D conservation laws

The current work presents a parallel formulation using the MPI protocol for an adaptive high order finite difference scheme to solve 2D conservation laws. Adaptivity is achieved at each time iteration by the application of an interpolating wavelet transform in each space dimension. High order approximations for the numerical fluxes are computed by ENO and WENO schemes. Since time evolution is made by a TVD Runge-Kutta space splitting scheme, the problem is naturally suitable for parallelization. Numerical simulations and speedup results are presented for Euler equations in gas dynamics problems.

Drowsiness detection for single channel EEG by DWT best m-term approximation

Introduction In this paper we propose a promising new technique for drowsiness detection. It consists of applying the best m-term approximation on a single-channel electroencephalography (EEG) signal preprocessed through a discrete wavelet transform. Methods In order to classify EEG epochs as awake or drowsy states, the most significant m terms from the wavelet expansion of an EEG signal are selected according to the magnitude of their coefficients related to the alpha and beta rhythms. Results By using a simple thresholding strategy it provides hit rates comparable to those using more complex techniques. It was tested on a set of 6 hours and 50 minutes EEG drowsiness signals from PhysioNet Sleep Database yielding an overall sensitivity (TPR) of 84.98% and 98.65% of precision (PPV). Conclusion The method has proved itself efficient at separating data from different brain rhythms, thus alleviating the requirement for complex post-processing classification algorithms.

Classificação de estágios de sono através da aplicação de DWT sobre um único canal de EEG

Este trabalho apresenta uma nova metodologia de apoio a decisao para a classificacao de estagios de sono. No metodo proposto, uma transformada wavelet discreta (DWT) e aplicada a um unico canal de eletroencefalograma (EEG) e sao extraidas, dos coeficientes da DWT, caracteristicas estatisticas de ritmos cerebrais relacionados ao sono que, posteriormente, alimentam um classificador. Diversos algoritmos para classificacao, incluindo florestas aleatorias, sao avaliados em um conjunto de mais de 100.000 instâncias disponiveis em uma base de dados publica. Obtem-se acuracias superiores a 90% e coeficientes kappa maiores que 0.8 para as classificacoes de 2 a 6 estados de estagios de sono. O resultados obtidos sao comparaveis aos de trabalhos no estado da arte.

WENO wavelet method for a hyperbolic model of two-phase flow in conservative form

The current work presents a WENO wavelet adaptive method for solving multiphase flow problems. The grid adaptivity in each time step is obtained by the application of a thresholded interpolating wavelet transform, which allows the construction of a small yet effective sparse point representation of the solution. The spatial operator is solved by the Lax-Friedrich flux splitting approach in which the flux derivatives are approximated by the WENO scheme. Hyperbolic models of two-phase flow in conservative form are efficiently solved since shocks and rarefaction waves are precisely captured by the chosen methodology. Substantial computational gains are obtained through the grid reduction feature while maintaining the quality of the solutions.

Classificador de imagens de pulmão utilizando wavelets de Haar e distância de Mahalanobis

Um metodo de extracao de caracteristicas e reconhecimento de padroes de imagens de tomografia de pulmao e proposto a partir da aplicacao da transformada wavelet de Haar 2D. Como medida de similaridade, a distância de Mahalanobis e utilizada por considerar a correlacao entre os dados, o que se torna relevante, uma vez que a distincao visual entre as imagens e pequena. O algoritmo foi testado utilizando-se diferentes vetores de caracteristicas, bem como diferentes agrupamentos de imagens. Foi obtida uma taxa de acerto superior a 85% ao se considerar duas classes.