Data e horário: 15/09, 2a feira, 11:00 às 11:30h
Local: Auditórios Centro Cultural e 12o andar
Chair: Leandro Bezerra de Lima
Título: Kac's lemma for Furstenberg recurrences
Resumo: O teorema de recorrência de Poincaré garante que, em sistemas dinâmicos com medida invariante finita, um conjunto de medida positiva é visitado infinitas vezes. O lema de Kac estabelece que o tempo médio de retorno a tal conjunto é inversamente proporcional à sua medida. Neste trabalho, propomos uma extensão do lema de Kac para o caso de recorrências múltiplas em progressões aritméticas, introduzidas por Furstenberg. Focamos em sistemas dinâmicos discretos, com ênfase em cadeias de Markov, e desenvolvemos um algoritmo combinatório e probabilístico para calcular tempos de recorrência múltipla. Por meio de estimadores de Monte Carlo e testes de hipótese, observamos convergência consistente das médias desses tempos, o que dá suporte à generalização.
Data e horário: 15/09, 2a feira, 11:30 às 12:00h
Local: Auditórios Centro Cultural e 12o andar
Chair: Fernanda de Bastiani
Título: On the computation of sparse reflexive generalized inverses
Resumo: The well-known Moore-Penrose (M-P) pseudoinverse is used in several linear-algebra applications; for example, to compute least-squares solutions of inconsistent systems of linear equations. Irrespective of whether a given matrix is sparse, its M-P pseudoinverse can be completely dense, potentially leading to high computational burden and numerical difficulties, especially when we are dealing with high-dimensional matrices. The M-P pseudoinverse is uniquely characterized by four properties, but not all of them need to be satisfied for some applications. In this work, we apply mathematical optimization to induce general sparsity and structured sparsity on generalized inverses of a given matrix, which satisfy only specific subsets of the M-P properties. We use 1-norm (vector) minimization to induce (unstructured) sparsity and 2,1-norm minimization to induce (structured) row-sparsity. Structured sparsity is useful, not only because of computational efficiency, but also for explainability. In the context of the least-squares application it is desirable to have row-sparsity, i.e., to have few non-zero rows on the generalized inverse, as then the associated linear model is more explainable. More specifically, least-squares theory connects explanatory variables to predicted variables (observations), through a linear regression model in which the unknown parameters of the linear relation are estimated by the least-squares solution. Row-sparsity corresponds to the selection of a small number of explanatory variables to determine a linear model. We also consider local-search procedures that produce generalized inverses with guaranteed structured sparsity, low rank, and magnitude of the entries under control.
Data e horário: 15/09, 2a feira, 12:00 às 12:45h
Local: Auditórios Centro Cultural e 12o andar
Chair: Gabriel Haeser
Título: Modeling nanoparticle-stabilized foam flow in porous media: Mathematical analysis and uncertainty quantification
Resumo: Foams have potential applications as mobility-control agents to optimize gas flooding in several subsurface processes such as aquifer remediation, greenhouse carbon storage, and enhanced oil recovery. Experimental studies indicate that their stability and resistance can be enhanced by adding nanoparticles. In this work, we present two new mathematical models for nanoparticle-stabilized foam flow in porous media. The first assumes foam at local equilibrium and is governed by a non-strictly hyperbolic system of conservation laws, for which we provide a global analytical solution, enabling efficient sensitivity and uncertainty analyses. We also discuss the most favorable conditions for observing nanoparticle effects in laboratory experiments. The second model incorporates foam texture, nanoparticle retention, and the resulting permeability reduction. For this more complex case, we present a steady-state semi-analytical solution, used to investigate how suspended nanoparticle loss and reduced permeability influence foam flow.