Resumo em Inglês:

ABSTRACT Inverse source reconstruction problems offer great potential for applications of interest to engineering, such as the identification of polluting sources, and to medicine, such as electroencephalography, to cite at least two relevant examples. From a mathematical point of view, the identification of a concentrated source (intensity and location) corresponds to the identification of the centroid (location) and size (intensity) of a distributed source. On the other hand, from a numerical point of view, it is observed that the use of domain discretization methods is intrinsically associated with the introduction of numerical noise in reconstruction algorithms, which is strongly inadvisable since inverse problems are reckoned to be ill-posed. The objective of this work is to explore, in the context of a Poisson problem and taking into account a numerical point of view, a new reconstruction algorithm based on the method of fundamental solutions, where a source point adequately represents the pointwise source within the domain. The inverse problem is reformulated as an optimization problem solved through a genetic algorithm. Finally, numerical examples are performed to analyze the accuracy of the proposed algorithm for two and three dimensions.

Resumo em Português:

RESUMO O Algoritmo Genético (AG) é caracterizado por ser uma meta-heurística mimetizada no processo genético de evolução natural baseada na Teoria dos Esquemas (TE) e pela Hipótese dos Blocos Construtivos (HBC). É fundamentado na busca por boas soluções mediante a ação de operadores genéticos que, se configurados indevidamente, podem inviabilizar a otimização devido ao funcionamento inadequado da TE e da HBC. As dificuldades em projetar designs de alta aptidão e as insuficientes provas teóricas sobre a TE e a HBC retratam o dilema fundamental do AG. Portanto, este artigo tem como objetivo prover uma melhor compreensão dos efeitos que a ação dos operadores genéticos exerce sobre a TE e a HBC. A partir de uma revisão tradicional da literatura, que explora o arcabouço teórico da TE e da HBC, apresentamos importantes reflexões sobre os principais gaps, trade-offs e perspectivas futuras sobre o AG.

Resumo em Inglês:

ABSTRACT The Genetic Algorithm (GA) is characterized by being a meta-heuristic mimicked in the process of natural evolution genetics based on Schema Theory (TE) and the Building Block Hypothesis (HBC). It is based on the search for good solutions through the action of genetic operators that, if improperly configured, can make the optimization unfeasible due to the improper functioning of the TE and HBC. Difficulties in designing high aptitude designs and insufficient theoretical evidence on TE and HBC portray the fundamental dilemma of AG. Therefore, this article aims to provide a better understanding of the effects that the action of genetic operators has on TE and HBC. From a traditional literature review, which explores the theoretical framework of TE and HBC, we present important reflections on the main gaps, trade-offs and future perspectives on GA.

Resumo em Inglês:

ABSTRACT This work presents the application of a CO2 emission estimation function for cargo vehicles on a Capacited Vehicle Routing Problems (CVRP) setting, considering route’s slopes variation. Comparisons were established with functions minimizing fuel consumption and route length in a case study about selective collection of recyclable waste at Sorocaba, state of São Paulo, Brazil. Routes with lower emissions have been achieved without significantly increasing fuel consumption or distance traveled.

Resumo em Português:

RESUMO Propomos duas variações do precondicionador de aproximação da inversa em blocos (BAINV), originalmente desenvolvido por Benzi, Kouhia e Tůma em 2001. A primeira variação, a aproximação da inversa em blocos estabilizada para matrizes não simétricas (SBAINV-NS), é válida para matrizes não simétricas e não singulares. A segunda variação, a aproximação da inversa em blocos estabilizada combinada (SBAINV-VAR), é baseada nas relações dos fatores da inversa aproximada em blocos com a fatoração LDU em blocos de A e na relação de aproximação da inversa de Neumann. Demonstramos a consistência matemática dessas novas versões e apresentamos os algoritmos referentes a cada uma delas, além de exibir experimentos numéricos onde comparamos a densidade dos precondicionadores e o número de iterações quando aplicados ao método estabilizado de gradientes bi-conjugados (Bi-CGSTAB). Os principais resultados numéricos obtidos indicam que o uso da estrutura de blocos pode aumentar o desempenho do método iterativo de Krylov em comparação com a versão escalar. Além disso, nos experimentos apresentados, o SBAINV-VAR produz, em geral, precondicionadores que realizam menos iterações do Bi-CGSTAB e são menos densos do que o SBAINV-NS.

Resumo em Inglês:

ABSTRACT We propose two variations of the block approximate inverse preconditioner (BAINV), presented by Benzi, Kouhia and Tůma in 2001. The first variation, the stabilized block approximate inverse for non-symmetric matrices (SBAINV-NS), is used for non-symmetric and non-singular matrices. The second variation, the combined stabilized block approximate inverse (SBAINV-VAR), is based on the relations between the block approximate inverse factors with the block LDU factors of A, as we will demonstrate, and on the relations between the approximate inverse and Neumann series. We prove the mathematical consistency of these new versions and present the algorithms for each one. We also present the numerical experiments, where we compare the density of the preconditioners and the number of iterations when applying the biconjugate gradient stabilized method (Bi-CGSTAB). The main numerical results indicate that the use of the block structure can increase the performance of the Krylov’s iterative method compared to the scalar version. Furthermore, the experiments show that SBAINV-VAR preconditioners, in general, perform less iterations of Bi-CGSTAB and are less dense than SBAINV-NS preconditioners.

Resumo em Inglês:

ABSTRACT A model is made for the dynamics of the transmission of the new SARS-CoV-2 coronavirus, which caused the COVID-19 pandemic. This model is based on the Susceptible-Infectious-Recovered model with heterogeneity in the susceptible population and in the infectious population. The susceptible population is divided into two subpopulations: individuals who are health professionals and individuals who are not. The infectious population is also divided into two subpopulations: individuals who are hospitalized and individuals who are not. A qualitative analysis of the theoretical model is performed, as well as simulations with official data regarding COVID-19 in the city of Manaus, Amazonas, Brazil, which corroborate the profile of the solution curves defined by the model.

Resumo em Inglês:

ABSTRACT In this work we identify the source in a 1D anomalous diffusion equation, from measurements of the concentration at a finite number of points. We use Caputo-Fabrizio time fractional derivative to model the phenomenon. Separating variables, we arrive to a linear system which provides approximate values for the Fourier coefficients of the unknown source. Numerical examples show the efficiency of the method, as well as some of its practical limitations.

Resumo em Inglês:

ABSTRACT In this work, we investigate the propagation of rotational solitary waves over a submerged obstacle in a vertically sheared shallow water channel with constant vorticity. In the weakly nonlinear, weakly dispersive regime the problem is formulated in the forced Korteweg-de Vries equation framework. The initial value problem for this equation is solved numerically using a Fourier pseudospectral method with an integrating factor. Solitary waves are taken as initial data and their interactions with an obstacle are analysed. We identify three types of regimes according to the intensity of the vorticity. A rotational solitary wave can bounce back and forth over the obstacle remaining trapped for large times, it can pass over the obstacle without reversing its direction or the wave can be blocked, i.e., it bounces back and forth above the obstacle until reaching a steady state. Such behaviour resembles the classical damped spring-mass system.

Resumo em Inglês:

ABSTRACT In this note, we consider the Complex Ginzburg-Landau equations with a bilinear control term in the real line. We prove well-posedness results concerned with the initial value problem for these equations in Zhidkov spaces using splitting methods.

Resumo em Inglês:

ABSTRACT In this paper, we describe an a posteriori error analysis for a conforming dual mixed scheme of the Poisson problem with non homogeneous Dirichlet boundary condition. As a result, we obtain an a posteriori error estimator, which is proven to be reliable and locally efficient with respect to the usual norm on Hdiv;Ω×L2Ω. We remark that the analysis relies on the standard Ritz projection of the error, and take into account a kind of a quasi-Helmholtz decomposition of functions in Hdiv;Ω, which we have established in this work. Finally, we present one numerical example that validates the well behavior of our estimator, being able to identify the numerical singularities when they exist.

Resumo em Inglês:

ABSTRACT In the present work a method for the detection of the cardiac pathology known as atrial fibrillation is proposed by calculating different information, statistics and other nonlinear measures over ECG signals. The original database contains records corresponding to patients who are diagnosed with this disease as well as healthy subjects. To formulate the dataset the Rényi permutation entropy, Fisher information measure, statistical complexity, Lyapunov exponent and fractal dimension were calculated, in order to determine how to combine this features to optimize the identification of the signals coming from ECG with the above mentioned cardiac pathology. With the aim to improve the results obtained in previous studies, a classification method based upon decision trees algorithms is implemented. Later a Montecarlo simulation of one thousand trials is performed with a seventy percent randomly selected from the dataset dedicated to train the classifier and the remaining thirty percent reserved to test in every trial. The quality of the classification is assessed through the computation of the area under the receiver operation characteristic curve (ROC), the F1-score and other classical performance metrics, such as the balanced accuracy, sensitivity, specificity, positive and negative predicted values. The results show that the incorporation of all these features to the dataset when are employed to train the classifier in the training task produces the best classification, in such a way that the largest quality parameter is achieved.

Resumo em Inglês:

ABSTRACT The covariance selection in Gaussian graphical models consists in selecting, based on a sample of a multivariate normal vector, all those pairs of variables that are conditionally dependent given the remaining variables. This problem is equivalent to estimate the graph identifying the nonzero elements on the off-diagonal entries of the precision matrix. There are different proposals to carry out covariance selection in high-dimensional Gaussian graphical models, such as neighborhood selection and Glasso, among others. In this paper we introduce a methodology for evaluating the performance of graph estimators, defining the notion of non-informative estimator. Through a simulation study, the empirical behavior of Glasso in different structures of the precision matrix is investigated and its performance is analyzed according to different degrees of density of the graph. Our proposal can be used for other covariance selection methods.

Resumo em Inglês:

ABSTRACT In this paper, a new method for supervised classification of hyperspectral images is proposed for the case in which the size of the training sample is small. It consists of replacing in the Mahalanobis distance the maximum likelihood estimator of the precision matrix by a sparse estimator. The method is compared with two other existing versions of LDA sparse, both in real and simulated images.