Multifunctions of Bounded Variation, Preliminary Version I

Consider control systems described by a differential equation with a control term or, more generally, by a differential inclusion with velocity set $F(t,x)$. Certain properties of state trajectories can be derived when, in addition to other hypotheses, it is assumed that $F(t,x)$ is merely measurable w.r.t. the time variable $t$. But sometimes a refined analysis requires the imposition of stronger hypotheses regarding the $t$ dependence of $F(t,x)$. Stronger forms of necessary conditions for state trajectories that minimize a cost can derived, for example, if it is hypothesized that $F(t,x)$ is Lipschitz continuous w.r.t. $t$. It has recently become apparent that interesting addition properties of state trajectories can still be derived, when the Lipschitz continuity hypothesis is replaced by the weaker requirement that $F(t,x)$ has bounded variation w.r.t. $t$. This paper introduces a new concept of multifunctions $F(t,x)$ that have bounded variation w.r.t. $t$ near a given state trajectory, of special relevance to control system analysis. Properties of such multifunctions are derived and their significance is illustrated by an application to sensitivity analysis.Comment: Preliminary version of a article which will submitted to a journal for publicatio

A decomposition technique for pursuit evasion games with many pursuers

Here we present a decomposition technique for a class of differential games. The technique consists in a decomposition of the target set which produces, for geometrical reasons, a decomposition in the dimensionality of the problem. Using some elements of Hamilton-Jacobi equations theory, we find a relation between the regularity of the solution and the possibility to decompose the problem. We use this technique to solve a pursuit evasion game with multiple agents

Minimax optimal control

Published versio

Regularity properties of optimal controls for problems with time-varying state and control constraints

Accepted versio

(Não) leituras de obras literárias em contexto escolar: um estudo de caso a partir de versão integral e adaptações de "O Cortiço", de Aluísio Azevedo

O presente trabalho se insere nas discussões do grupo de pesquisa Literatura e Educação e investigou, no contexto de uma escola pública de Ensino Fundamental e Médio do município de Guarapari (ES), como são as relações entre livros e leitores - por meio das contribuições teóricas e metodológicas da Nova História Cultural - a partir de três diferentes versões da obra O cortiço do autor Aluísio Azevedo: versão adaptada por Fabio Pinto da coleção É só o começo (2009); adaptação com roteiro de Ivan Jaf e arte de Rodrigo Rosa em história em quadrinhos (2010) distribuída pelo PNBE; e c) versão com texto integral (2014 [1890]); todas encontradas na biblioteca da escola campo. A pesquisa foi desenvolvida em dois momentos, sendo o primeiro de cunho bibliográfico-documental, que buscou perceber como se dão as relações entre livro, leitor e leitura e pensar o modo como algumas adaptações literárias são inseridas no mercado, inclusive as que integram programas de distribuição de livros como o PNBE. O segundo momento foi um estudo de caso com questionário e grupo focal, constituído por alunos de segundo e terceiro ano do Ensino Médio da escola campo, que, no âmbito do processo de educação literária, tentou responder às seguintes questões: a) como se dá a apropriação do texto integral e das diversas adaptações de uma obra pelos estudantes?; b) os textos adaptados despertam no leitor o desejo de conhecer o texto integral?; c) como os alunos agem para (não) realizar as leituras propostas pelo currículo escolar?: A pesquisa justifica-se em face: a) do interesse, nos campos da História e da Literatura, pelas práticas de leitores literários empíricos e pelos usos que são feitos de materiais impressos, em contextos institucionais, em tensão com orientações oficiais; b) da necessidade de se pensar as questões econômico-ideológicas que circundam a leitura em tensionamento com o mercado editorial; c) do nosso diagnóstico tomado aqui como pressuposto de que muitos alunos não leem obras literárias sugeridas pelo currículo escolar; d) da necessidade de se pensar as não leituras literárias para além da culpabilização discente. Com a investigação, conhecemos as formas de aquisição dos livros, algumas preferências, os principais mediadores de leitura, traçando assim um perfil de leitor de leitura literária da escola campo. Chegamos também à conclusão de que algumas adaptações podem ser instrumentos de mediação de leitura em sala de aula. Os autores que nortearam nosso estudo foram: Regina Zilberman (1999, 2013), Márcia Abreu (2001), Edmir Perrotti (1999) e João Wanderlei Geraldi (2010) (livro e leitura no contexto brasileiro); Annie Rouxel (2013), Maria Amélia Dalvi (2012, 2013, 2013a) e Neide Rezende (2013) (educação literária); Roger Chartier (1999, 2002, 2002a, 2010, 2013, 2013a) (práticas e representações, apropriação)

Optimal Control Problems with Mixed and Pure State Constraints

This paper provides necessary conditions of optimality for optimal control problems, in which the pathwise constraints comprise both “pure” constraints on the state variable and “mixed” constraints on control and state variables. The proofs are along the lines of earlier analysis for mixed constraint problems, according to which Clarke's theory of “stratified” necessary conditions is applied to a modified optimal control problem resulting from absorbing the mixed constraint into the dynamics; the difference here is that necessary conditions which now take into account the presence of pure state constraints are applied to the modified problem. Necessary conditions are given for a rather general formulation of the problem containing both forms of the constraints, and then these are specialized to problems having special structure. While combined pure state and mixed control/state problems have been previously treated in the literature, the necessary conditions in this paper are proved under less restrictive hypotheses and for novel formulations of the constraints

Just-In-Time Compilation of NumPy Vector Operations

In this paper, we introduce JIT compilation for thehigh-productivity framework Python/NumPy in order to boost theperformance significantly. The JIT compilation of Python/NumPyis completely transparent to the user – the runtime system willautomatically JIT compile and execute the NumPy instructionsencountered in a Python application. In other words, we introducea framework that provides the high-productivity from Pythonwhile maintaining the high-performance of a low-level, compiledlanguage.We transforms NumPy vector instruction into an AbstractSyntax Tree representation that creates the basis for furtheroptimizations. From the AST we auto-generate C code whichwe compile into computational kernels and execute. These incorporatetemporary array removal and loop-fusion which are mainbenefactors in the achieved speedups. In order to amortize theoverhead of creation, we also implement a cache for the compiledkernels.We evaluate the JIT compilation by executing several scientificcomputing benchmarks on an AMD. Compared to NumPy, weachieve speedups of a factor 4.72 for a N-Body application and7.51 for a Jacobi Stencil application executing on a single CPUcore

Towards two-dimensional metallic behavior at LaAlO3/SrTiO3 interfaces

Using a low-temperature conductive-tip atomic force microscope in cross-section geometry we have characterized the local transport properties of the metallic electron gas that forms at the interface between LaAlO3 and SrTiO3. At low temperature, we find that the carriers do not spread away from the interface but are confined within ~10 nm, just like at room temperature. Simulations taking into account both the large temperature and electric-field dependence of the permittivity of SrTiO3 predict a confinement over a few nm for sheet carrier densities larger than ~6 10^13 cm-2. We discuss the experimental and simulations results in terms of a multi-band carrier system. Remarkably, the Fermi wavelength estimated from Hall measurements is ~16 nm, indicating that the electron gas in on the verge of two-dimensionality.Comment: Accepted for publication in Physical Review Letter

Plasmon-pole approximation for semiconductor quantum wire electrons

We develop the plasmon-pole approximation for an interacting electron gas confined in a semiconductor quantum wire. We argue that the plasmon-pole approximation becomes a more accurate approach in quantum wire systems than in higher dimensional systems because of severe phase-space restrictions on particle-hole excitations in one dimension. As examples, we use the plasmon-pole approximation to calculate the electron self-energy due to the Coulomb interaction and the hot-electron energy relaxation rate due to LO-phonon emission in GaAs quantum wires. We find that the plasmon-pole approximation works extremely well as compared with more complete many-body calculations.Comment: 16 pages, RevTex, figures included. Also available at http://www-cmg.physics.umd.edu/~lzheng