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

Minimax optimal control

Published 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

Veros v0.1 – a fast and versatile ocean simulator in pure Python

A general circulation ocean model is translated from Fortran to Python. Its code structure is optimized to exploit available Python utilities, remove simulation bottlenecks, and comply with modern best practices. Furthermore, support for Bohrium is added, a framework that provides a just-in-time compiler for array operations and that supports parallel execution on both CPU and GPU targets.For applications containing more than a million grid elements, such as a typical 1° × 1° horizontal resolution global ocean model, Veros is approximately half as fast as the MPI-parallelized Fortran base code on 24 CPUs and as fast as the Fortran reference when running on a high-end GPU. By replacing the original conjugate gradient stream function solver with a solver from the pyAMG Python package, this particular subroutine outperforms the corresponding Fortran version by up to 1 order of magnitude.The study is concluded with a simple application in which the North Atlantic wave response to a Southern Ocean wind perturbation is investigated. It is found that even in a realistic setting the phase speeds of boundary waves matched the expectations based on theory and idealized models.</p

An effective mass theorem for the bidimensional electron gas in a strong magnetic field

We study the limiting behavior of a singularly perturbed Schr\"odinger-Poisson system describing a 3-dimensional electron gas strongly confined in the vicinity of a plane $(x,y)$ and subject to a strong uniform magnetic field in the plane of the gas. The coupled effects of the confinement and of the magnetic field induce fast oscillations in time that need to be averaged out. We obtain at the limit a system of 2-dimensional Schr\"odinger equations in the plane $(x,y)$, coupled through an effective selfconsistent electrical potential. In the direction perpendicular to the magnetic field, the electron mass is modified by the field, as the result of an averaging of the cyclotron motion. The main tools of the analysis are the adaptation of the second order long-time averaging theory of ODEs to our PDEs context, and the use of a Sobolev scale adapted to the confinement operator

Inelastic Coulomb scattering rates due to acoustic and optical plasmon modes in coupled quantum wires

We report a theoretical study on the inelastic Coulomb scattering rate of an injected electron in two coupled quantum wires in quasi-one-dimensional doped semiconductors. Two peaks appear in the scattering spectrum due to the optical and the acoustic plasmon scattering in the system. We find that the scattering rate due to the optical plasmon mode is similar to that in a single wire but the acoustic plasmon scattering depends crucially on its dispersion relation at small $q$. Furthermore, the effects of tunneling between the two wires are studied on the inelastic Coulomb scattering rate. We show that a weak tunneling can strongly affect the acoustic plasmon scattering.Comment: 6 Postscript figure

Intrasubband and Intersubband Electron Relaxation in Semiconductor Quantum Wire Structures

We calculate the intersubband and intrasubband many-body inelastic Coulomb scattering rates due to electron-electron interaction in two-subband semiconductor quantum wire structures. We analyze our relaxation rates in terms of contributions from inter- and intrasubband charge-density excitations separately. We show that the intersubband (intrasubband) charge-density excitations are primarily responsible for intersubband (intrasubband) inelastic scattering. We identify the contributions to the inelastic scattering rate coming from the emission of the single-particle and the collective excitations individually. We obtain the lifetime of hot electrons injected in each subband as a function of the total charge density in the wire.Comment: Submitted to PRB. 20 pages, Latex file, and 7 postscript files with Figure

Towards A Census of Earth-mass Exo-planets with Gravitational Microlensing

Thirteen exo-planets have been discovered using the gravitational microlensing technique (out of which 7 have been published). These planets already demonstrate that super-Earths (with mass up to ~10 Earth masses) beyond the snow line are common and multiple planet systems are not rare. In this White Paper we introduce the basic concepts of the gravitational microlensing technique, summarise the current mode of discovery and outline future steps towards a complete census of planets including Earth-mass planets. In the near-term (over the next 5 years) we advocate a strategy of automated follow-up with existing and upgraded telescopes which will significantly increase the current planet detection efficiency. In the medium 5-10 year term, we envision an international network of wide-field 2m class telescopes to discover Earth-mass and free-floating exo-planets. In the long (10-15 year) term, we strongly advocate a space microlensing telescope which, when combined with Kepler, will provide a complete census of planets down to Earth mass at almost all separations. Such a survey could be undertaken as a science programme on Euclid, a dark energy probe with a wide-field imager which has been proposed to ESA's Cosmic Vision Programme.Comment: 10 pages. White Paper submission to the ESA Exo-Planet Roadmap Advisory Team. See also "Inferring statistics of planet populations by means of automated microlensing searches" by M. Dominik et al. (arXiv:0808.0004