Lipschitz extensions of maps between Heisenberg groups

Let $\H^n$ be the Heisenberg group of topological dimension 2n+1 . We prove that if n is odd, the pair of metric spaces $(\H^n, \H^n)$ does not have the Lipschitz extension property.

Fracture risk and zoledronic acid therapy in men with osteoporosis

Fractures in men are a major health issue, and data on the antifracture efficacy of therapies for osteoporosis in men are limited. We studied the effect of zoledronic acid on fracture risk among men with osteoporosis.

A high-resolution soil erosion risk map of Switzerland as strategic policy support system

Soil erosion models and soil erosion risk maps are often used as indicators to assess potential soil erosion in order to assist policy decisions. This paper shows the scientific basis of the soil erosion risk map of Switzerland and its application in policy and practice. Linking a USLE/RUSLE-based model approach (AVErosion) founded on multiple flow algorithms and the unit contributing area concept with an extremely precise and high-resolution digital terrain model (2 m × 2 m grid) using GIS allows for a realistic assessment of the potential soil erosion risk, on single plots, i.e. uniform and comprehensive for the agricultural area of Switzerland (862,579 ha in the valley area and the lower mountain regions). The national or small-scale soil erosion prognosis has thus reached a level heretofore possible only in smaller catchment areas or single plots. Validation was carried out using soil loss data from soil erosion damage mappings in the field from long-term monitoring in different test areas. 45% of the evaluated agricultural area of Switzerland was classified as low potential erosion risk, 12% as moderate potential erosion risk, and 43% as high potential erosion risk. However, many of the areas classified as high potential erosion risk are located at the transition from valley to mountain zone, where many areas are used as permanent grassland, which drastically lowers their current erosion risk. The present soil erosion risk map serves on the one hand to identify and prioritise the high-erosion risk areas, and on the other hand to promote awareness amongst farmers and authorities. It was published on the internet and will be made available to the authorities in digital form. It is intended as a tool for simplifying and standardising enforcement of the legal framework for soil erosion prevention in Switzerland. The work therefore provides a successful example of cooperation between science, policy and practice.

A Calculus of Evolving Objects

The demands of developing modern, highly dynamic applications have led to an increasing interest in dynamic programming languages and mechanisms. Not only applications must evolve over time, but the object models themselves may need to be adapted to the requirements of different run-time contexts. Class-based models and prototype-based models, for example, may need to co-exist to meet the demands of dynamically evolving applications. Multi-dimensional dispatch, fine-grained and dynamic software composition, and run-time evolution of behaviour are further examples of diverse mechanisms which may need to co-exist in a dynamically evolving run-time environment How can we model the semantics of these highly dynamic features, yet still offer some reasonable safety guarantees? To this end we present an original calculus in which objects can adapt their behaviour at run-time to changing contexts. Both objects and environments are represented by first-class mappings between variables and values. Message sends are dynamically resolved to method calls. Variables may be dynamically bound, making it possible to model a variety of dynamic mechanisms within the same calculus. Despite the highly dynamic nature of the calculus, safety properties are assured by a type assignment system.

A Calculus of Evolving Objects

The demands of developing modern, highly dynamic applications have led to an increasing interest in dynamic programming languages and mechanisms. Not only must applications evolve over time, but the object models themselves may need to be adapted to the requirements of different run-time contexts. Class-based models and prototype-based models, for example, may need to co-exist to meet the demands of dynamically evolving applications. Multi-dimensional dispatch, fine-grained and dynamic software composition, and run-time evolution of behaviour are further examples of diverse mechanisms which may need to co-exist in a dynamically evolving run-time environment. How can we model the semantics of these highly dynamic features, yet still offer some reasonable safety guarantees? To this end we present an original calculus in which objects can adapt their behaviour at run-time. Both objects and environments are represented by first-class mappings between variables and values. Message sends are dynamically resolved to method calls. Variables may be dynamically bound, making it possible to model a variety of dynamic mechanisms within the same calculus. Despite the highly dynamic nature of the calculus, safety properties are assured by a type assignment system.

Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems II: Strongly monotone quasi-Newtonian flows

In this article, we develop the a priori and a posteriori error analysis of hp-version interior penalty discontinuous Galerkin finite element methods for strongly monotone quasi-Newtonian fluid flows in a bounded Lipschitz domain Ω ⊂ ℝd, d = 2, 3. In the latter case, computable upper and lower bounds on the error are derived in terms of a natural energy norm, which are explicit in the local mesh size and local polynomial degree of the approximating finite element method. A series of numerical experiments illustrate the performance of the proposed a posteriori error indicators within an automatic hp-adaptive refinement algorithm.

The effect of projections on dimension in the Heisenberg group

We prove analogs of classical almost sure dimension theorems for Euclidean projection mappings in the first Heisenberg group, equipped with a sub-Riemannian metric.

Frequency of Sobolev and quasiconformal dimension distortion

We study Hausdorff and Minkowski dimension distortion for images of generic affine subspaces of Euclidean space under Sobolev and quasiconformal maps. For a supercritical Sobolev map f defined on a domain in RnRn, we estimate from above the Hausdorff dimension of the set of affine subspaces parallel to a fixed m-dimensional linear subspace, whose image under f has positive HαHα measure for some fixed α>mα>m. As a consequence, we obtain new dimension distortion and absolute continuity statements valid for almost every affine subspace. Our results hold for mappings taking values in arbitrary metric spaces, yet are new even for quasiconformal maps of the plane. We illustrate our results with numerous examples.

Implicit task sequence learning

Implicit task sequence learning (TSL) can be considered as an extension of implicit sequence learning which is typically tested with the classical serial reaction time task (SRTT). By design, in the SRTT there is a correlation between the sequence of stimuli to which participants must attend and the sequence of motor movements/key presses with which participants must respond. The TSL paradigm allows to disentangle this correlation and to separately manipulate the presences/absence of a sequence of tasks, a sequence of responses, and even other streams of information such as stimulus locations or stimulus-response mappings. Here I review the state of TSL research which seems to point at the critical role of the presence of correlated streams of information in implicit sequence learning. On a more general level, I propose that beyond correlated streams of information, a simple statistical learning mechanism may also be involved in implicit sequence learning, and that the relative contribution of these two explanations differ according to task requirements. With this differentiation, conflicting results can be integrated into a coherent framework.