Sistemas dinâmicos com simetrias e anti-simetrias
Palestrante: Iris de Oliveira (ICMC-USP)
Quando: quarta-feira, 21 de setembro, às 13h
Onde:: Sala 3-012
Resumo: Num sistema dinâmico, a presença de simetrias ou anti-simetrias leva à ocorrência de múltiplas soluções: simetrias levam trajetórias em trajetórias, preservando a direção com o tempo, ao passo que anti-simetrias levam trajetórias em trajetórias, revertendo a direção com o tempo. Quando ambas ocorrem simultaneamente, o sistema é chamado reversível-equivariante e o conjunto destes objetos tem estrutura de grupo, o grupo das simetrias e anti-simetrias do sistema. A formulação matemática para tal ocorrência pode simplificar significamente o estudo sistemático de tais sistemas e é feita através da teoria de representação de grupos. Vamos fazer uma introdução ao estudo de sistemas reversíveis-equivariantes e apresentar alguns resultados interessante.
--------------------Seminários de Singularidades
Topological properties of finitely determined map germs from R^3 to R^3
Palestrante: Juan Antonio Moya Pérez (Universitat de València)
Quando: quinta-feira, 22 de setembro, às 10h
Onde: Sala 3-102
Resumo: The link of a real analytic map germ f : (R3; 0) ! (R3; 0) is obtained by taking the intersection of the image with a small enough sphere S2 centered at the origin in 3. If f is nitely determined, then we can ensure that the link is a stable map from S2 to S2. We de ne Gauss words which contains all the topological information of the link in the case that the singular set S() is connected. As an application, we give a classi cation of nitely determined weighted homogeneous map germs with 2-jet equivalent to (x; y; xz) in a special case and of all the ruled map germs from R3 to R3.
--------------------Seminário de Coisas Legais
Pense positivo!!!
Palestrante: Daniel Smania (ICMC-USP)
Quando: Quinta-feira, 22 de setembro, às 13h
Onde: Sala 5-001
Resumo: Vários problemas em Matemática envolvem matrizes positivas, isto é, matrizes cujas entradas são todas positivas. Por exemplo, sabendo as taxas de imigração e emigração entre certas cidades, e que tais taxas permanecem constantes ao longo do tempo, é possível deduzir as populações das cidades em um futuro longínquo com extraordinária precisão, mesmo sem saber quase nada sobre a população atual! Este resultado envolve o estudo de matrizes positivas, utilizando o chamado Teorema de Perron-Frobenius. A demonstração deste resultado é também fascinante, pois faz uso e tem conexões com várias áreas da matemática, como espaços métricos (Princípio de Contração de Banach) e Geometria (geometrias não euclidianas).
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Seminário de Geometria Algébrica
Local-global principles for integral points on curves
Palestrante: José Felipe Voloch (University of Texas at Austin)
Quando: Quinta-feira, 22 de setembro, às 14h
Onde: Sala 4-124 (Videoteca)
Resumo: We will discuss how to state a local-global principle for existence of integral and rational points on curves using Galois covers. This leads to a number of related conjectures and we will also present some results towards them.
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Seminários de Estatística - ICMC/UFSCar
Approximate inferences for skew-normal independent nonlinear mixed-effects models with application to AIDS studies
Palestrante: Prof. Dr. Victor Hugo Lachos Davila (IMECC-UNICAMP)
Quando: sexta-feira, 23 de setembro, às 14h
Onde: Sala de seminários DEs-UFSCar
Resumo: Nonlinear mixed-effects models have received a great deal of attention in the statistical literature in recent years because of the flexibility in handling longitudinal studies, including human immunodeficiency virus viral dynamics, pharmacokinetic analyses, and studies of growth and decay. A standard assumption in nonlinear mixed-effects models for continuous responses is the normal distribution for the random effects and the within-subject errors, making it sensitive to outliers. We present a novel class of asymmetric nonlinear mixed-effects models that provides for an efficient estimation of the parameters in the analysis of longitudinal data. We assume that, marginally, the random effects follow a multivariate skew–normal/independent distribution and that the random errors follow a symmetric normal/independent distribution providing an appealing robust alternative to the usual normal distribution in nonlinear mixed-effects models. We propose an approximate likelihood analysis for maximum likelihood estimation based on the EM-type algorithm that produce accurate maximum likelihood estimates and significantly reduces the numerical difficulty associated with the exact maximum likelihood estimation. Techniques for prediction of future responses under this class of distributions are also briefly investigated. Simulation studies indicate that our proposed methods work well for small, medium and large variability of the random effects. The newly developed procedures are illustrated with a HIV case study that was initially analyzed using normal nonlinear mixed-effects models.
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Seminários de Estatística - ICMC/UFSCar
Approximate inferences for skew-normal independent nonlinear mixed-effects models with application to AIDS studies
Palestrante: Prof. Dr. Victor Hugo Lachos Davila (IMECC-UNICAMP)
Quando: sexta-feira, 23 de setembro, às 14h
Onde: Sala de seminários DEs-UFSCar
Resumo: Nonlinear mixed-effects models have received a great deal of attention in the statistical literature in recent years because of the flexibility in handling longitudinal studies, including human immunodeficiency virus viral dynamics, pharmacokinetic analyses, and studies of growth and decay. A standard assumption in nonlinear mixed-effects models for continuous responses is the normal distribution for the random effects and the within-subject errors, making it sensitive to outliers. We present a novel class of asymmetric nonlinear mixed-effects models that provides for an efficient estimation of the parameters in the analysis of longitudinal data. We assume that, marginally, the random effects follow a multivariate skew–normal/independent distribution and that the random errors follow a symmetric normal/independent distribution providing an appealing robust alternative to the usual normal distribution in nonlinear mixed-effects models. We propose an approximate likelihood analysis for maximum likelihood estimation based on the EM-type algorithm that produce accurate maximum likelihood estimates and significantly reduces the numerical difficulty associated with the exact maximum likelihood estimation. Techniques for prediction of future responses under this class of distributions are also briefly investigated. Simulation studies indicate that our proposed methods work well for small, medium and large variability of the random effects. The newly developed procedures are illustrated with a HIV case study that was initially analyzed using normal nonlinear mixed-effects models.
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Informações:
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