04401 Abstracts Collection -- Algorithms and Complexity for Continuous

From 26.09.04 to 01.10.04, the Dagstuhl Seminar ``Algorithms and Complexity for Continuous Problems\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Leapfrog and Related Operations on Toroidal Fullerenes

A 4-valent square tiled toroid is transformed into 3-valent hexagonal (and other polygonal) lattices either by simple cutting procedures or by some more elaborated operations such as leapfrog and related transformations. Tiling or embedding isomers can be interchanged by means of such operations on toroidal maps, for which rigorous definitions and some theorems are given. Parents and products of most important operations are illustrated

David Hilbert and the foundations of the theory of plane area

This paper provides a detailed study of David Hilbert’s axiomatization of the theory of plane area, in the classical monograph Foundation of Geometry (1899). On the one hand, we offer a precise contextualization of this theory by considering it against its nineteenth-century geometrical background. Specifically, we examine some crucial steps in the emergence of the modern theory of geometrical equivalence. On the other hand, we analyze from a more conceptual perspective the significance of Hilbert’s theory of area for the foundational program pursued in Foundations. We argue that this theory played a fundamental role in the general attempt to provide a new independent basis for Euclidean geometry. Furthermore, we contend that our examination proves relevant for understanding the requirement of “purity of the method” in the tradition of modern synthetic geometry.Fil: Giovannini, Eduardo Nicolás. Universidad Nacional del Litoral. Instituto de Humanidades y Ciencias Sociales del Litoral. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Humanidades y Ciencias Sociales del Litoral; Argentin

Diffusion in the Lorentz gas

The Lorentz gas, a point particle making mirror-like reflections from an extended collection of scatterers, has been a useful model of deterministic diffusion and related statistical properties for over a century. This survey summarises recent results, including periodic and aperiodic models, finite and infinite horizon, external fields, smooth or polygonal obstacles, and in the Boltzmann-Grad limit. New results are given for several moving particles and for obstacles with flat points. Finally, a variety of applications are presented.Comment: 28 pages, 5 figure

Siegel measures

The goals of this paper are first to describe and then to apply an ergodic-theoretic generalization of the Siegel integral formula from the geometry of numbers. The general formula will be seen to serve both as a guide and as a tool for questions concerning the distribution, in senses to be made precise, of the set of closed leaves of measured foliations subordinate to meromorphic quadratic differentials on closed Riemann surfaces.Comment: 50 pages, published versio

Bats of the Monongahela National Forest

Populations of bats across the eastern United States have experienced significant declines in recent years. Insight into their distributions and habitat associations, as well as understanding population trends, will aid in conservation efforts. In this study, the geographic distributions of the 10 species of bats found in the Monongahela National Forest of West Virginia were analyzed, using maximum entropy modeling and mist-netting data from 1997 through 2012. Forest type, hydrologic features, elevation, land-cover type, and distance to caves were typically the most important explanatory variables within these models, although results varied among species. By understanding these foraging habitat associations and locations of bats, forest personnel will be able to use these localized data to guide their management decisions. Trends in species diversity and abundance also were examined. Species diversity remained mostly stable and although not significant, a decline in abundance over time indicated decreases in some populations of bats, particularly by those species affected by white-nose syndrome