In this paper, we propose a new methodology for semisupervised acquisition of lexical taxonomies. Our approach is based on the theory of pretopology that offers a powerful formalism to model semantic relations and transforms a list of terms into a structured term space by combining different discriminant criteria. In order to learn a parameterized pretopological space, we define the Learning Pr...

For real projective spaces, (a) the Euclidean immersion dimension, (b) the existence of axial maps, and (c) the topological complexity are known to be three facets of the same problem. This paper describes the corresponding relationship between the symmetrized versions of (b) and (c) to the Euclidean embedding dimension of projective spaces. Extensions to the case of 2e torsion lens spaces and ...

As introduced by Weaver, (metric) derivations extend the notion of differential operators on Euclidean spaces and provide a linear differentiation theory that is well-defined on all metric spaces with Borel measures. The main result of this paper is a rigidity theorem for measures on Euclidean spaces that support a maximal number of derivations. The proof relies substantially on ideas from geom...

For inference on non-Euclidean data, ideally the data space is at least locally approx-imated by a Euclidean space; for a manifold by a chart, say. If suitable data descriptorslie asymptotically in such a common Euclidean neighborhood, one would expect a normalcentral limit theorem to hold. Already for locally flat spaces like the circle there are excep-tions causing smeariness....

Coxeter classified all discrete isometry groups generated by reflections that act on a Euclidean space or on a sphere of an arbitrary dimension (see [1]). His fundamental work became classical long ago. Lobachevsky spaces (classical hyperbolic spaces) are as symmetric as Euclidean spaces and spheres. However, discrete isometry groups generated by reflections, with fundamental polytopes of finit...

We define and study exact, efficient representations of realization spaces Euclidean Distance Constraint Systems (EDCS). These are graphs with distance assignments on the edges (frameworks) or graphs with distance interval assignments on the edges. Each representation corresponds to a choice of non-edges or Cayley parameters. The set of realizable distance assignments to the chosen parameters y...