Marshall's Lemma for Convex Density Estimation

Marshall's (1970) lemma is an analytical result which implies root-n-consistency of the distribution function corresponding to the Grenander (1956) estimator of a non-decreasing probability density. The present paper derives analogous results for the setting of convex densities on [0,\infty).

Context-Oriented Programming

Context-dependent behavior is becoming increasingly important for a wide range of application domains, from pervasive computing to common business applications. Unfortunately, mainstream programming languages do not provide mechanisms that enable software entities to adapt their behavior dynamically to the current execution context. This leads developers to adopt convoluted designs to achieve the necessary runtime flexibility. We propose a new programming technique called Context-oriented Programming (COP) which addresses this problem. COP treats context explicitly, and provides mechanisms to dynamically adapt behavior in reaction to changes in context, even after system deployment at runtime. In this paper we lay the foundations of COP, show how dynamic layer activation enables multi-dimensional dispatch, illustrate the application of COP by examples in several language extensions, and demonstrate that COP is largely independent of other commitments to programming style.

Large deviations for heavy-tailed random elements in convex cones

We prove large deviation results for sums of heavy-tailed random elements in rather general convex cones being semigroups equipped with a rescaling operation by positive real numbers. In difference to previous results for the cone of convex sets, our technique does not use the embedding of cones in linear spaces. Examples include the cone of convex sets with the Minkowski addition, positive half-line with maximum operation and the family of square integrable functions with arithmetic addition and argument rescaling.

Fetal programming of pulmonary vascular dysfunction in mice: role of epigenetic mechanisms.

Insults during the fetal period predispose the offspring to systemic cardiovascular disease, but little is known about the pulmonary circulation and the underlying mechanisms. Maternal undernutrition during pregnancy may represent a model to investigate underlying mechanisms, because it is associated with systemic vascular dysfunction in the offspring in animals and humans. In rats, restrictive diet during pregnancy (RDP) increases oxidative stress in the placenta. Oxygen species are known to induce epigenetic alterations and may cross the placental barrier. We hypothesized that RDP in mice induces pulmonary vascular dysfunction in the offspring that is related to an epigenetic mechanism. To test this hypothesis, we assessed pulmonary vascular function and lung DNA methylation in offspring of RDP and in control mice at the end of a 2-wk exposure to hypoxia. We found that endothelium-dependent pulmonary artery vasodilation in vitro was impaired and hypoxia-induced pulmonary hypertension and right ventricular hypertrophy in vivo were exaggerated in offspring of RDP. This pulmonary vascular dysfunction was associated with altered lung DNA methylation. Administration of the histone deacetylase inhibitors butyrate and trichostatin A to offspring of RDP normalized pulmonary DNA methylation and vascular function. Finally, administration of the nitroxide Tempol to the mother during RDP prevented vascular dysfunction and dysmethylation in the offspring. These findings demonstrate that in mice undernutrition during gestation induces pulmonary vascular dysfunction in the offspring by an epigenetic mechanism. A similar mechanism may be involved in the fetal programming of vascular dysfunction in humans.

Local Stereology of Tensors of Convex Bodies

In this paper, we present local stereological estimators of Minkowski tensors defined on convex bodies in ℝ d . Special cases cover a number of well-known local stereological estimators of volume and surface area in ℝ3, but the general set-up also provides new local stereological estimators of various types of centres of gravity and tensors of rank two. Rank two tensors can be represented as ellipsoids and contain information about shape and orientation. The performance of some of the estimators of centres of gravity and volume tensors of rank two is investigated by simulation.