A Posteriori analysis of discontinuous Galerkin schemes for systems of hyperbolic conservation laws

In this work we construct reliable a posteriori estimates for some semi- (spatially) discrete discontinuous Galerkin schemes applied to nonlinear systems of hyperbolic conservation laws. We make use of appropriate reconstructions of the discrete solution together with the relative entropy stability framework, which leads to error control in the case of smooth solutions. The methodology we use is quite general and allows for a posteriori control of discontinuous Galerkin schemes with standard flux choices which appear in the approximation of conservation laws. In addition to the analysis, we conduct some numerical benchmarking to test the robustness of the resultant estimator.

A comparison of duality and energy a posteriori estimates for $\mathrm {L}_{\infty }(0,T;\mathrm {L}_2(\varOmega ))$ in parabolic problems

We use the elliptic reconstruction technique in combination with a duality approach to prove a posteriori error estimates for fully discrete backward Euler scheme for linear parabolic equations. As an application, we combine our result with the residual based estimators from the a posteriori estimation for elliptic problems to derive space-error indicators and thus a fully practical version of the estimators bounding the error in the $ \mathrm {L}_{\infty }(0,T;\mathrm {L}_2(\varOmega ))$ norm. These estimators, which are of optimal order, extend those introduced by Eriksson and Johnson in 1991 by taking into account the error induced by the mesh changes and allowing for a more flexible use of the elliptic estimators. For comparison with previous results we derive also an energy-based a posteriori estimate for the $ \mathrm {L}_{\infty }(0,T;\mathrm {L}_2(\varOmega ))$-error which simplifies a previous one given by Lakkis and Makridakis in 2006. We then compare both estimators (duality vs. energy) in practical situations and draw conclusions.

Reduced relative entropy techniques for a posteriori analysis of multiphase problems in elastodynamics

We give an a posteriori analysis of a semidiscrete discontinuous Galerkin scheme approximating solutions to a model of multiphase elastodynamics, which involves an energy density depending not only on the strain but also the strain gradient. A key component in the analysis is the reduced relative entropy stability framework developed in Giesselmann (2014, SIAM J. Math. Anal., 46, 3518–3539). This framework allows energy-type arguments to be applied to continuous functions. Since we advocate the use of discontinuous Galerkin methods we make use of two families of reconstructions, one set of discrete reconstructions and a set of elliptic reconstructions to apply the reduced relative entropy framework in this setting.

Fundamentos jurídicos e econômicos da OPA a posteriori (tag along) e a questão sob a ótica de empresas que praticam boas práticas de governança corporativa

O texto trata da oferta pública de alienação de controle, atualmente prevista pelo artigo 254-a da lei societária n. 6404/76, e regulada pela instrução cvm n. 361. Trata da questão sobre “a quem deve pertencer o ágio pago pelo poder de controle”, elencando fundamentos jurídicos invocados por autores estrangeiros e nacionais, e fundamentos econômicos levantados e demonstrados em pesquisas empíricas, por autores estrangeiros. Ao final, busca demonstrar que, em alguns aspectos, o fundamento econômico se sobressai quando a questão é vista por empresários que buscam capitalizar-se via mercado de capitais e, para tanto, oferecem a seus investidores normas tidas como “boas práticas de governança corporativa”.

Localization of the optimal solution and a posteriori bounds for aggregation

After an aggregated problem has been solved, it is often desirable to estimate the accuracy loss due to the fact that a simpler problem than the original one has been solved. One way of measuring this loss in accuracy is the difference in objective function values. To get the bounds for this difference, Zipkin (Operations Research 1980;28:406) has assumed, that a simple (knapsack-type) localization of an original optimal solution is known. Since then various extensions of Zipkin's bound have been proposed, but under the same assumption. A method to compute the bounds for variable aggregation for convex problems, based on general localization of the original solution is proposed. For some classes of the original problem it is shown how to construct the localization. Examples are given to illustrate the main constructions and a small numerical study is presented.

Estudo da viabilidade do emprego da técnica de subtração radiográfica digital em radiografias periapicais com registro a posteriori

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Avaliação de reabsorções radiculares apicais externas decorrentes de movimentação ortodôntica em radiografias periapicais com registro a posteriori

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Acute respiratory syndrome after inhalation of waterproofing sprays: a posteriori exposure-response assessment in 102 cases

Waterproofing agents are widely used to protect leather and textiles in both domestic and occupational activities. An outbreak of acute respiratory syndrome following exposure to waterproofing sprays occurred during the winter 2002-2003 in Switzerland. About 180 cases were reported by the Swiss Toxicological Information Centre between October 2002 and March 2003, whereas fewer than 10 cases per year had been recorded previously. The reported cases involved three brands of sprays containing a common waterproofing mixture, that had undergone a formulation change in the months preceding the outbreak. A retrospective analysis was undertaken in collaboration with the Swiss Toxicological Information Centre and the Swiss Registries for Interstitial and Orphan Lung Diseases to clarify the circumstances and possible causes of the observed health effects. Individual exposure data were generated with questionnaires and experimental emission measurements. The collected data was used to conduct numeric simulation for 102 cases of exposure. A classical two-zone model was used to assess the aerosol dispersion in the near- and far-field during spraying. The resulting assessed dose and exposure levels obtained were spread on large scales, of several orders of magnitude. No dose-response relationship was found between exposure indicators and health effects indicators (perceived severity and clinical indicators). Weak relationships were found between unspecific inflammatory response indicators (leukocytes, C-reactive protein) and the maximal exposure concentration. The results obtained disclose a high interindividual response variability and suggest that some indirect mechanism(s) predominates in the respiratory disease occurrence. Furthermore, no threshold could be found to define a safe level of exposure. These findings suggest that the improvement of environmental exposure conditions during spraying alone does not constitute a sufficient measure to prevent future outbreaks of waterproofing spray toxicity. More efficient preventive measures are needed prior to the marketing and distribution of new waterproofing agents.

A posteriori registration and subtraction of panoramic compared with intraoral radiography

OBJECTIVES: To demonstrate the feasibility of panoramic image subtraction for implant assessment. STUDY DESIGN: Three titanium implants were inserted into a fresh pig mandible. One intraoral and 2 panoramic images were obtained at baseline and after each of 6 incremental (0.3, 0.6, 1.0, 1.5, 2.0, 2.5 mm) removals of bone. For each incremental removal of bone, the mandible was removed from and replaced in the holding device. Images representing incremental bone removals were registered by computer with the baseline images and subtracted. Assessment of the subtraction images was based on visual inspection and analysis of structured noise. RESULTS: Incremental bone removals were more visible in intraoral than in panoramic subtraction images; however, computer-based registration of panoramic images reduced the structured noise and enhanced the visibility of incremental removals. CONCLUSION: The feasibility of panoramic image subtraction for implant assessment was demonstrated.

Estimación bayesiana de características en robots móviles mediante muestreo de la densidad a posteriori

Comunicación presentada en el I Congrés Català d’Intel·ligència Artificial, Tarragona, Octubre de 1998.