Mapping problems for quasiregular mappings

We study images of the unit ball under certain special classes of quasiregular mappings. For homeomorphic, i.e., quasiconformal mappings problems of this type have been studied extensively in the literature. In this paper we also consider non-homeomorphic quasiregular mappings. In particular, we study (topologically) closed quasiregular mappings originating from the work of J. V\"ais\"al\"a and M. Vuorinen in 1970's. Such mappings need not be one-to-one but they still share many properties of quasiconformal mappings. The global behavior of closed quasiregular mappings is similar to the local behavior of quasiregular mappings restricted to a so-called normal domain.Comment: 16 pages, 1 figur

Harmonic Shears of Slit and Polygonal Mappings

In this paper, we study harmonic mappings by using the shear construction, introduced by Clunie and Sheil-Small in 1984. We consider two classes of conformal mappings, each of which maps the unit disk D univalently onto a domain which is convex in the horizontal direction, and shear these mappings with suitable dilatations \omega. Mappings of the first class map the unit disk D onto four-slit domains and mappings of the second class take D onto regular n-gons. In addition, we discuss the minimal surfaces associated with such harmonic mappings. Furthermore, illustrations of mappings and associated minimal surfaces are given by using Mathematica.Comment: 17 pages, 6 figures, 2 table

A Local to Global Principle for the Complexity of Riemann Mappings (Extended Abstract)

We show that the computational complexity of Riemann mappings can be bounded by the complexity needed to compute conformal mappings locally at boundary points. As a consequence we get first formally proven upper bounds for Schwarz-Christoffel mappings and, more generally, Riemann mappings of domains with piecewise analytic boundaries

How do Ontology Mappings Change in the Life Sciences?

Mappings between related ontologies are increasingly used to support data integration and analysis tasks. Changes in the ontologies also require the adaptation of ontology mappings. So far the evolution of ontology mappings has received little attention albeit ontologies change continuously especially in the life sciences. We therefore analyze how mappings between popular life science ontologies evolve for different match algorithms. We also evaluate which semantic ontology changes primarily affect the mappings. We further investigate alternatives to predict or estimate the degree of future mapping changes based on previous ontology and mapping transitions.Comment: Keywords: mapping evolution, ontology matching, ontology evolutio