We consider the discretized optimality system of a special class of elliptic optimal control problems and propose an all-at-once multigrid method for solving this discretized system. Under standard assumptions the convergence of the multigrid method and the robustness of the convergence rates with respect to the involved parameter are shown. Numerical experiments are presented for illustrating the theoretical results.

Objective. To assess the impact of a computerized system on physicians’ accuracy and agreement rate, as compared with unaided diagnosis. Methods. A set of 124 unilateral knee radiographs from the Osteoarthritis Initiative (OAI) study were analyzed by a computerized method with regard to Kellgren-Lawrence (KL) grade, as well as joint space narrowing, osteophytes, and sclerosis Osteoarthritis Research Society International (OARSI) grades. Physicians scored all images, with regard to osteophytes, sclerosis, joint space narrowing OARSI grades and KL grade, in 2 modalities: through a plain radiograph ( unaided) and a radiograph presented together with the report from the computer assisted detection system ( aided). Intraclass correlation between the physicians was calculated for both modalities. Furthermore, physicians’ performance was compared with the grading of the OAI study, and accuracy, sensitivity, and specificity were calculated in both modalities for each of the scored features. Results. Agreement rates for KL grade, sclerosis, and osteophyte OARSI grades, were statistically increased in the aided versus the unaided modality. Readings for joint space narrowing OARSI grade did not show a statistically difference between the 2 modalities. Readers’ accuracy and specificity for KL grade >0, KL >1, sclerosis OARSI grade >0, and osteophyte OARSI grade >0 was significantly increased in the aided modality. Reader sensitivity was high in both modalities. Conclusions. These results show that the use of an automated knee OA software increases consistency between physicians when grading radiographic features of OA. The use of the software also increased accuracy measures as compared with the OAI study, mostly through increases in specificity.

In this paper we consider a (one-shot) multigrid strategy for solving the discretized optimality system (KKT system) of a PDE-constrained optimization problem. In particular, we discuss the construction of an additive Schwarz-type smoother for a certain class of optimal control problems. A rigorous multigrid convergence analysis is presented. Numerical experiments are shown which confirm the theoretical results.

Reliabiliiy is a key concern in the current state of sofmare industry. Producing software without defects is still very difJicult. Therefore it is crucial to benefit from high-level language mechanisms such as assertions. Nevertheless contracts are mostly a specificity of the Eiffel language. This observation convinced ISE to build a new product, the Contract Wizard, which aims at providing .NET developers with the abiliiy to add contracts to a .NET assembly independently from the .NET language it was initially written in.This paper first gives an overview of the existing implementation of Design by Contract in various programming languages. It then explains how the new ISE Contract Wizard works by providing a guided tour of the product.

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