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ABSTRACT Fuzzy systems that include Takagi-Sugeno inference method with linear outputs, are widely known to have the ability to uniformly approximate any polynomial with high precision and, as a consequence, any continuous function, by applying the approximation theorem of Weierstrass. There is one more advantage for these methods which is to obtain an explicit expression of the defuzzified output as a function of the system’s inputs. The purpose of this study is to describe the dynamics of a data set collected through the behavior of the tangential envelope and the local concavity of a curve to be adjusted. The functions that define the envelope and its concavity are identified by means of a hybrid system that combines a fuzzy clustering with the qualities of the Takagi-Sugeno inference method. The analyzed data set represents the world population of confirmed infected people by the infectious disease caused by the coronavirus of severe acute respiratory syndrome, named COVID-19. The proposed fuzzy method, in two versions, first and second order, are compared with curves built through the least square method with the maximum of the absolute value of the difference between the fit values and the data, normalized at each instant. In these comparisons, both fuzzy approaches proposed in this study are the ones that best match the data collected, being the fuzzy approximation of second order the best of all.Resumo em Português:
RESUMO Neste trabalho propomos e analisamos medidas de relaxamento do distanciamento social, e seus impactos no sentido epidemiológico, a partir das simulações de um modelo matemático compartimental do tipo SEIRD (Suscetível-Exposto-Infectado-Recuperado-Morto) generalizado, que implicitamente leva em conta medidas de quarentena, considerando a estimativa da dinâmica de espalhamento da doença do coronavírus (COVID-19) sob perturbações/incertezas. O objetivo principal é avaliar os efeitos nas projeções da epidemia da COVID-19 no Brasil e, em particular, no estado do Rio de Janeiro. Diferentes estratégias de relaxamento das medidas de distanciamento social são investigadas para determinar quais delas são viáveis e menos perigosas para a população. Os resultados destacam a necessidade de manter políticas de distanciamento social para controlar a propagação da doença. Especificamente, o cenário de relaxamento abrupto do distanciamento social, implementado após a ocorrência do pico de casos diagnosticados positivamente, pode prolongar a epidemia, com um aumento significativo do número previsto de casos confirmados e de mortes. Um cenário ainda pior pode ocorrer se a política de relaxamento do distanciamento social é implementada antes da evidência do controle epidêmico, indicando a importância da escolha adequada de quando parar e começar a relaxar as medidas de distanciamento social. A abordagem empregada aqui, e as análises subsequentes aplicadas no Brasil e Rio de Janeiro, pode ser usada para outros locais.Resumo em Inglês:
ABSTRACT In this work, we propose and analyze social distancing relaxation measures and their epidemiological impacts through simulations of a compartmental mathematical model. Our generalized SEIRD model implicitly takes into account social distancing measures, considering the estimate of the spreading dynamics of COVID-19 under disturbances/uncertainties. The main objective is to assess the effects on the projections of the COVID-19 epidemic in Brazil and, in particular, in the state of Rio de Janeiro. Different relaxation strategies of social distancing measures are investigated to determine which ones are viable and less dangerous for the population. The results highlight the need to maintain social distancing policies to control the spread of the disease. Specifically, the scenario considered as abrupt relaxation measures, implemented after the peak of positively diagnosed cases has occurred, can prolong the epidemic, with a significant increase in the expected number of confirmed and death cases. An even worse scenario can occur if the relaxation policy is implemented prior to the evidence of epidemiological control, indicating the importance of the proper choice of when to stop and start to relax social distancing measures. The approach employed here, and the subsequent analyzes applied to Brazil and Rio de Janeiro, can be used for other locations.Resumo em Português:
RESUMO O presente trabalho analisa e desenvolve um método para resolver equações diferenciais fracionárias utilizando o Método de Monte Carlo. Uma simulação numérica é realizada para algumas equações diferenciais, comparando os resultados com o que existe na literatura matemática. A linguagem Python é usada para criar modelos computacionais.Resumo em Inglês:
ABSTRACT This article analyzes and develops a method to solve fractional ordinary differential equations using the Monte Carlo Method. A numerical simulation is performed for some differential equations, comparing the results with what exists in the mathematical literature. The Python language is used to create computational models.Resumo em Inglês:
ABSTRACT On 30 January 2020, the World Health Organization (WHO) officially declared the epidemic of Coronavirus (COVID-19), which is a highly contagious virus that has been causing deaths worldwide. Early treatment was proven to be inefficient and social isolation became the main factor inhibiting the disease, before vaccination. In this article, we evaluate the efficiency of this isolation as a control, through numerical simulations of mathematical model of the SEIR type (Susceptible-Exposed-Infectious-Removed) with population heterogeneity, in which the susceptible population was distributed according to the age group (children / youth, adults and elderly) and the infectious population was categorized according to the severity of symptoms (severe, mild and asymptomatic). The results suggest that the isolation of only one of the susceptible subpopulations is inefficient to control the spread of the virus, which indicates that vertical isolation is not enough to contain the proliferation of COVID-19. Furthermore, the disease does not have the strength to invade the population when there is sufficient social isolation composed of susceptible subpopulations and the epidemiological scenario improves when there is awareness of the importance of the quarantine of infectious individuals with mild symptoms.Resumo em Inglês:
ABSTRACT Nonlinear steady rotational waves in a low-pressure region are investigated. The problem is formulated in a simplified canonical domain through the use of a conformal mapping, which flattens the free surface. Steady waves are computed numerically using a Newton’s method and classified into three types. Besides, our results indicate that there is a region in which steady waves do not exist. The thickness of this region is compared with the one predicted by the weakly nonlinear, weakly dispersive regime.Resumo em Português:
RESUMO O presente artigo avaliou a interferência da quantidade de defasagens utilizadas no resultado do valor-p associado à estatística utilizada no teste de Dickey-Fuller aumentado (ADF), bem como identificou algumas propriedades das séries estudadas que interferem em seu resultado. Foram realizados três experimentos com séries de diferentes amplitudes, considerando estrutura do modelo em relação à presença ou não de constante e/ou tendência, e quantidade de defasagens como fatores. Modelos autorregressivos do tipo AR(1) foram considerados para a geração de dados pelo método de Monte Carlo, que poderiam apresentar diferentes intensidades para o coeficiente associado à primeira defasagem. Depois da aplicação do teste ADF, foram determinadas as proporções de rejeição da hipótese nula em cada condição experimental, sendo utilizada uma análise de variância com a estatística qui-quadrado para verificar a influência da quantidade de defasagens no valor-p. Os resultados mostram que se houver raiz unitária, o teste apresenta bons resultados, independentemente da quantidade de defasagens considerada. Entretanto, o mesmo não foi observado nos casos em que a série temporal não apresenta raiz unitária.Resumo em Inglês:
ABSTRACT In this paper we evaluate how much influence the number of selected lags has in the p-value obtained from the statistic considered in an augmented Dickey-Fuller test (ADF). Three experiments with different series sizes were carried out considering the presence (or not) of a constant and/or trend, and also different number of lags. Autoregressive models (AR1) are used in the data generating process through the Monte Carlo method, considering different values for the coefficient associated with the first lag. After the application of the ADF test, we calculate the proportion of times when the null hypothesis was rejected in each scenario, and perform an analysis of variance (considering chi-square statistic) to verify the influence of the number of selected lags in the p-value. Results show that if a unit root is verified, then the test presents a good performance, regardless of the number of lags. However, the same was not observed in cases where the time series does not present a unit root.Resumo em Inglês:
ABSTRACT The present work has as main objective to investigate the use of fractional calculus in the modeling of epidemic outbreaks of interacting populations. In particular, we propose a generalization of the SIR model with fractional derivatives to describe the dynamics of the COVID-19 epidemic outbreak in two cities with interacting populations. In special, we consider the dynamics of COVID-19 in the municipalities of Pelotas and Rio Grande, which are neighboring cities and are relatively geographically isolated from the rest of the state of Rio Grande do Sul.Resumo em Inglês:
ABSTRACT In this work, a nodal and iterative technique to evaluate the effective multiplication factor as well as the neutron flux, in multigroup diffusion problems, is presented. An iterative scheme, similar to the source iteration method, is implemented to decouple the system of differential equations which is the fundamental mathematical model. Then, analytical solutions are derived for the one-dimensional transverse integrated equations, of each energy group, resulting from a nodal approach. Constant approximations are assumed for the unknown transverse leakage terms in the contours of the nodes. In addition, constant and linear representations are investigated to express the fluxes in the source term to be updated in the iterative process. Numerical results for the effective multiplication factor were obtained for a series of twodimensional multigroup problems with upscattering and downscattering. The procedure is simple, fast, the analysis of the results indicated a satisfactory agreement with results available in the literature and the use of different approximations to the source term seems to be a good alternative, instead of using higher-order approximations on the contour of the nodes, to improve accuracy.Resumo em Português:
RESUMO A combinação entre cirurgias de emparelhamentos de arestas de polígonos regulares e a troca de arestas do grafo de emparelhamentos sobre a superfície, permite determinar de forma mais eficiente as famílias de grafos de emparelhamentos sobre superfícies fechadas e orientadas com gênero g≥2.Resumo em Inglês:
ABSTRACT The combination between surgeries of the pairing of edges of regular polygons (over on a closed and orientable surface) and the exchange of edges of the graph on the surface, allows more efficiently the families of graphs pairing on surfaces with genus g≥2.Resumo em Inglês:
ABSTRACT In this paper, we present the results of a new approach to the splitting factor preconditioner, which is a preconditioner based on the Incomplete Cholesky factorization and the splitting preconditioner. In previous work for small linear programming problems, the preconditioner was applied in all iterations of the interior point method and compared with the splitting preconditioner also applied in all iterations. In this paper, we will do a hybrid approach, in which in the first iterations the preconditioner is the Incomplete Cholesky Factorization, and in the last iterations, the preconditioner used is the splitting factor preconditioner or the splitting preconditioner. The results obtained show that even in the hybrid approach, the splitting factor preconditioner achieved better performance.Resumo em Português:
RESUMO Nesta contribuição analisaremos o problema inverso de identificação do coeficiente de rigidez em vigas modeladas pela equação de Euler-Bernoulli, a partir de medidas da deflexão. Apresentaremos o problema na forma de uma equação de operador parâmetro-para-medidas, para o qual, provaremos propriedades importantes, como compacidade e continuidade. Mostraremos ainda que o operador parâmetropara-medidas é Fréchet diferenciável e que satisfaz a condição do cone tangente. Essas propriedades são suficientes para recuperarmos de forma estável e convergente (método de regularização) o coeficiente de rigidez através de métodos iterativos como Landweber e Steepest descent. Por fim, apresentamos os efeitos de estabilidade das soluções aproximadas com relação as medidas com diferentes níveis de ruídos, através de exemplos numéricos.Resumo em Inglês:
ABSTRACT In this contribution, we analyze the identifiability of the stiffness coefficient inverse problem in beams modeled by the Euler-Bernoulli equation, from measurements of the beam deflection. We present the problem in the form of a parameter-to-measure operator equation, for which we prove important properties, such as compactness and continuity. We also show that the parameter-to-measure operator is Fréchet differentiable and that it satisfies the tangential cone condition. These properties are sufficient to recover in a stable and convergent way (regularization method) the stiffness coefficient through iterative methods such as Landweber and Steepest descent. Finally, we present the stability effects of the approximate solutions concerning measurements with different noise levels through numerical examples.Resumo em Português:
RESUMO A extensão da malha rodoviária brasileira tanto em pistas simples quanto em pistas duplas ou alargamento de rodovias, tem aumentado significativamente junto ao crescimento populacional, e os impactos causados em função das construções e reformas vêm sendo constantemente discutidos sob o ponto de vista de suas consequências ambientais. Rodovias nunca deixarão de existir, tampouco novas construções, contudo, a implantação de medidas de controle e monitoramento ambiental podem reduzir os impactos negativos evitando danos irreversíveis ao meio ambiente. Este trabalho apresenta o desenvolvimento de uma metodologia para classificação de regiões em imagens do entorno de rodovias com base em Processamento Digital de Imagens (PDI) e Lógica Fuzzy a partir do uso dos descritores de cor e textura que melhor caracterizam os variados tipos de cobertura do solo. Para isso foram extraídas 600 amostras (recortes de imagens) de dimensões 29×29 pixels do entorno da rodovia Raposo Tavares, sendo 100 amostras para cada grupo de cobertura do solo considerados neste trabalho: residências, indústrias, rodovias, solo exposto, vegetação rasteira (gramíneas) e vegetação arbórea (matas). A partir dessas amostras foi construído um SIF (Sistema de Inferência Fuzzy) para classificação dos tipos de cobertura do solo. Ao se aplicar este sistema nas 600 amostras obteve-se uma matriz de confusão dos resultados e um índice kappa igual a 0,9197, que mostra a eficiência da metodologia desenvolvida.Resumo em Inglês:
ABSTRACT The extension of the Brazilian road network, both in simple and multiple lanes and in widening of highways, has increased along with population growth, and the impacts caused by important constructions and reforms are constantly discussed from the point of view of their consequences environmental issues. Highways will never cease to exist, nor will new construction. However, the implementation of control and environmental monitoring measures can reduce negative impacts by avoiding irreversible damage to the environment. This work, aims to develop a methodology for classifying and replacing images of highways around based on Digital Image Processing and Fuzzy Logic to extract color and texture descriptors from various types of soil cover. For this, 600 (29×29 pixels) dimensions (image clippings) were collected from the surroundings of the Raposo Tavares highway, 100 for each ground cover group, forming the basis of the thesis study: residences, industries, highways, exposed soil, undergrowth (grasses) and tree vegetation (forests). From these samples, a FIS (Fuzzy Inference System) was built to classify the types of soil cover. When applying this system to the 600 samples, a confusing matrix was obtained and a calculated kappa index equal to 0.9197, which shows the efficiency of the developed methodology.