The nil Hecke ring and singularity of Schubert varieties

We give a criterion for smoothness of a point in any Schubert variety in any G/B in terms of the nil Hecke ring.Comment: AMSTE

"Paremmin tässä yhteiskunnassa kiinni" : kokemuksia Jyväskylän sosiaalitoimen työllistämisprojektista

Software verification is recognized as an important and difficult problem. We present a norel framework, based on symbolic execution, for the automated verification of software. The framework uses annotations in the form of method specifications an3 loop invariants. We present a novel iterative technique that uses invariant strengthening and approximation for discovering these loop invariants automatically. The technique handles different types of data (e.g. boolean and numeric constraints, dynamically allocated structures and arrays) and it allows for checking universally quantified formulas. Our framework is built on top of the Java PathFinder model checking toolset and it was used for the verification of several non-trivial Java programs

Extended temporal logic revisited

vardi Abstract. A key issue in the design of a model-checking tool is the choice of the formal language with which properties are specified. It is now recognized that a good language should extend linear temporal logic with the ability to specify all-regular properties. Also, designers, who are familiar with finite-state machines, prefer extensions based on automata than these based on fixed points or propositional quantification. Early extensions of linear temporal logic with automata use nondeterministic Büchi automata. Their drawback has been inability to refer to the past and the asymmetrical structure of nondeterministic automata. In this work we study an extension of linear temporal logic, called ETL ©� � , that uses two-way alternating automata as temporal connectives. Two-way automata can traverse the input word back and forth and they are exponentially more succinct than one-way automata. Alternating automata combine existential and universal branching and they are exponentially more succinct than nondeterministic automata. The rich structure of two-way alternating automata makes ETL ©� � a very powerful and convenient logic. We show that ETL ©� � formulas can be translated to nondeterministic Büchi automata with an exponential blow up. It follows that the satisfiability and model-checking problems for ETL ©� � are PSPACEcomplete, as are the ones for LTL and its earlier extensions with automata. So, in spite of the succinctness of two-way and alternating automata, the advantages of ETL ©� � are obtained without a major increase in space complexity. The recent acceptance of alternating automata by the industry and the development of symbolic procedures for handling them make us optimistic about the practicality of ETL ©� �.

Cardiovascular events associated with rofecoxib : final analysis of the APPROVe trial

Background: Selective inhibition of cyclo-oxygenase-2 has been associated with an increased risk of cardiovascular events in several clinical trials. The Adenomatous Polyp Prevention on Vioxx (APPROVe) study assessed the effect of 3-year treatment with a cyclo-oxygenase-2 inhibitor, rofecoxib (25 mg), on recurrence of neoplastic polyps of the large bowel. We report the cardiovascular outcomes of a long-term follow-up of participants in the trial. Methods: The APPROVe study is a multicentre, randomised, placebo-controlled, double-blind trial. 2587 patients with a history of colorectal adenomas were recruited at 108 centres worldwide during 2000 and 2001. Participants were followed for adverse events while on treatment and during the following 14 days. However, after early termination of treatment because of cardiovascular toxicity, we attempted to follow up all randomised patients for at least 1 year after stopping study treatment. External committees blindly assessed potential serious cardiovascular events. The focus of the analysis was the combined incidence of non-fatal myocardial infarction, non-fatal stroke, and death from cardiovascular, haemorrhagic, and unknown causes (Antiplatelet Trialists' Collaboration [APTC] combined endpoint). We used Cox proportional hazards regression to calculate endpoint hazard ratios. The study is registered with ClinicalTrials.gov, number NCT0282386. Findings: We obtained extended post-treatment cardiovascular follow-up data from 84% of participants, and extended mortality follow-up from 95%. In total, 59 individuals had an APTC endpoint in the rofecoxib group and 34 in the placebo group (hazard ratio 1.79, 95% CI 1.17-2.73; p=0.006). In the first year after cessation of treatment, there was a non-significant increase in the risks of APTC endpoints. The APTC hazard ratio did not substantially change over time. Interpretation: Use of rofecoxib is associated with increased rates of APTC events. Study data are compatible with an early increase in risk that persists for one year after stopping treatment