Isospectral Alexandrov Spaces

We construct the first non-trivial examples of compact non-isometric Alexandrov spaces which are isospectral with respect to the Laplacian and not isometric to Riemannian orbifolds. This construction generalizes independent earlier results by the authors based on Schueth's version of the torus method.Comment: 15 pages, no figures; minor clarification

Development of an agroforestry system for chicken production

This report was presented at the UK Organic Research 2002 Conference. Because conventional production of chickens has gone further than any other animal production system towards complete control of the animal’s brief lives, development of effective silvo-poultry systems seems particularly necessary for these essentially woodland birds. The objective is to develop a production system that closely matches the physiological and behavioural needs of the animals being reared. For the example of chickens, this means trying to mimic a woodland/forest-clearing environment. By providing a wide range of trees, shrubs and herbs, it should be possible to provide shelter, nutrition and medicinal benefits for the birds. At the same time, the system needs to fulfil other functions in terms of biodiversity and community assets for the farm, together with profitable organic chicken production

Factors determining the occurrence of Flat Bugs (Aradidae) in beech dominated forests

The habitat requirements of most Aradidae and the decisive factors that influence their occurrence are still poorly understood. To reduce this lack of knowledge a standardised survey of Aradidae in two large beech forest areas of Bavaria (northern Steigerwald and High Spessart) was conducted. The following hypotheses were tested: 1) With increasing habitat tradition (temporal continuity), population densities of Aradidae increase, 2) Increasing dead wood supply supports higher abundance of Aradidae, 3) There are key structures for particular species with respect to type of dead wood, diameter and exposure to sunlight, and 4) The occurrence of particular fungi species determines the occurrence of Aradidae. In our study, Aradidae were sampled in point sample plots by flight-interception traps and time-standardised hand collection. To analyse specific habitat requirements additional sampling was performed to increase the sample size. Four species of Aradidae were observed in the two forest areas: Aneurus avenius, Aradus betulae, A. conspicuus and A. depressus. The results demonstrate that all species have different and specific habitat requirements. Especially for A. betulae habitat tradition of standing dead wood of large dimensions infested by Fomes fomentarius seems to be crucial. Hence, A. betulae was only observed in the Spessart and only at the sites with habitat tradition.Die Habitatansprüche der meisten Aradidae sowie die entscheidenden Faktoren die ihr Auftreten bedingen werden immer noch wenig verstanden. Um diese Wissenslücke zu verringern wurde eine standardisierte Aufnahme der Aradidae in zwei großen Buchenwaldgebieten Bayerns (nördlicher Steigerwald, Hochspessart) durchgeführt. Dabei wurden folgende Hypothesen ge-testet: 1) Die Populationsdichten der Aradidae steigen mit zunehmender Totholztradition, 2) erhöhte Verfügbarkeit an Totholz fördert eine höhere Abundanz der Aradidae, 3) es gibt Schlüsselstrukturen für bestimmte Arten in Bezug auf Totholztyp, -durchmesser und Sonnen-Exposition und 4) das Auftreten bestimmter Pilzarten bestimmt das Vorkommen der Aradidae. Zu diesem Zweck wurden Aradidae im Probekreisen mit Hilfe von Lufteklektoren und zeitnormierte Handaufsammlungen erfasst. Zur Analyse von spezifischen Habitatansprüchen wurden zusätzliche Fänge durchgeführt um die Stichprobengröße zu erhöhen. Vier Arten der Aradidae wurden in den bei-den Gebieten festgestellt: Aneurus avenius, Aradus betulae, A. conspicuus und A. depressus. Die Ergebnisse zeigen, dass alle Arten unterschiedliche und spezifische Habitatansprüche haben. Besonders für A. betulae scheint die Totholztradition, von starkem, von Fomes fomentarius besiedeltem, stehendem Totholz, eine entscheidende Rolle zu spielen. Folglich wurde sie Art nur am Totholz-traditionsreicheren Waldstandort, dem Spessart, gefunden

Incremental Network Design with Minimum Spanning Trees

Given an edge-weighted graph $G=(V,E)$ and a set $E_0\subset E$, the incremental network design problem with minimum spanning trees asks for a sequence of edges $e'_1,\ldots,e'_T\in E\setminus E_0$ minimizing $\sum_{t=1}^Tw(X_t)$ where $w(X_t)$ is the weight of a minimum spanning tree $X_t$ for the subgraph $(V,E_0\cup\{e'_1,\ldots,e'_t\})$ and $T=\lvert E\setminus E_0\rvert$. We prove that this problem can be solved by a greedy algorithm.Comment: 9 pages, minor revision based on reviewer comment

Big Cities. Big Water. Big Challenges: Water in an Urbanizing World.

This paper applies the water footprint methodology to six megacities across Africa, Asia, and Latin America to explore the effect of urbanization on water use and demand and determine what measures need to be taken to meet this demand. Key threats to water resources in many or all of the cities studied include: water stress or scarcity, pollution and decreasing water quality, and vulnerability to extreme weather caused by climate change

A Multigrid Method for the Efficient Numerical Solution of Optimization Problems Constrained by Partial Differential Equations

We study the minimization of a quadratic functional subject to constraints given by a linear or semilinear elliptic partial differential equation with distributed control. Further, pointwise inequality constraints on the control are accounted for. In the linear-quadratic case, the discretized optimality conditions yield a large, sparse, and indefinite system with saddle point structure. One main contribution of this thesis consists in devising a coupled multigrid solver which avoids full constraint elimination. To this end, we define a smoothing iteration incorporating elements from constraint preconditioning. A local mode analysis shows that for discrete optimality systems, we can expect smoothing rates close to those obtained with respect to the underlying constraint PDE. Our numerical experiments include problems with constraints where standard pointwise smoothing is known to fail for the underlying PDE. In particular, we consider anisotropic diffusion and convection-diffusion problems. The framework of our method allows to include line smoothers or ILU-factorizations, which are suitable for such problems. In all cases, numerical experiments show that convergence rates do not depend on the mesh size of the finest level and discrete optimality systems can be solved with a small multiple of the computational cost which is required to solve the underlying constraint PDE. Employing the full multigrid approach, the computational cost is proportional to the number of unknowns on the finest grid level. We discuss the role of the regularization parameter in the cost functional and show that the convergence rates are robust with respect to both the fine grid mesh size and the regularization parameter under a mild restriction on the next to coarsest mesh size. Incorporating spectral filtering for the reduced Hessian in the control smoothing step allows us to weaken the mesh size restriction. As a result, problems with near-vanishing regularization parameter can be treated efficiently with a negligible amount of additional computational work. For fine discretizations, robust convergence is obtained with rates which are independent of the regularization parameter, the coarsest mesh size, and the number of levels. In order to treat linear-quadratic problems with pointwise inequality constraints on the control, the multigrid approach is modified to solve subproblems generated by a primal-dual active set strategy (PDAS). Numerical experiments demonstrate the high efficiency of this approach due to mesh-independent convergence of both the outer PDAS method and the inner multigrid solver. The PDAS-multigrid method is incorporated in the sequential quadratic programming (SQP) framework. Inexact Newton techniques further enhance the computational efficiency. Globalization is implemented with a line search based on the augmented Lagrangian merit function. Numerical experiments highlight the efficiency of the resulting SQP-multigrid approach. In all cases, locally superlinear convergence of the SQP method is observed. In combination with the mesh-independent convergence rate of the inner solver, a solution method with optimal efficiency is obtained

Against False Settlement: Designing Efficient Consumer Rights Enforcement Systems in Europe

Published in cooperation with the American Bar Association Section of Dispute Resolutio