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According to a well known theorem of Haussler and Welzl (1987), any range space of bounded VC-dimension admits an epsilon-net of size O (1/epsilon log 1/epsilon). Using probabilistic techniques, Pach and Woeginger (1990) showed that there exist range space ...
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This work is dedicated to the study of Borel equivalence relations acting on Borel fields of CAT(0) metric spaces over a standard probability space. In this new framework we get similar results to some theorems proved recently by S. Adams-W. Ballmann or N. ...
We consider the problem of determining the “closest”, or best Internet host to connect to, from a list of candidate servers. Most existing approaches rely on the use of metric, or more specifically Euclidean coordinates to infer network proximity. This is ...
The mathematical facet of modern crystallography is essentially based on analytical geometry, linear algebra as well as group theory. This study endeavours to approach the geometry and symmetry of crystals using the tools furnished by differential geometry ...
Our goal is to identify families of relations that are useful for reasoning about software. We describe such families using decidable quantifier-free classes of logical constraints with a rich set of operations. A key challenge is to define such classes of ...
We prove that the multiplier algebra of the Drury-Arveson Hardy space H-n(2) on the unit ball in C-n has no corona in its maximal ideal space, thus generalizing the corona theorem of L. Carleson to higher dimensions. This result is obtained as a corollary ...
The overlap number of a finite (d + 1)-uniform hypergraph H is the largest constant c(H) is an element of (0, 1] such that no matter how we map the vertices of H into R-d, there is a point covered by at least a c(H)-fraction of the simplices induced by the ...
Let P and Q be finite sets of points in the plane. In this note we consider the largest cardinality of a subset of the Minkowski sum S ⊆ P⊕Q which consist of convex independent points. We show that, if P and Q contain at most n points, then |S| = O(n^(4/3) ...
This interdisciplinary research project presents a corporation of architects, mathematicians and computer scientists. The team researches new methods for the efficient realization of complex architectural shapes. The present work investigates methods of it ...
