Michael Schneider

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Two-dimensional sparse grids contain only O(h ?1 log(h ?1)) grid points, in contrast to the usually used full O(h ?2)-grids, whereas for a suuciently smooth function the accuracy of the representation is only slightly deteriorated from O(h 2) to O(h 2 log(h ?1)). The combination technique presented in this paper uses the solutions of O(log(h ?1)) diierent,(More)
The OWL 2 Web Ontology Language, informally OWL 2, is an ontology language for the Semantic Web with formally defined meaning. OWL 2 ontologies provide classes, properties, individuals, and data values and are stored as Semantic Web documents. OWL 2 ontologies can be used along with information written in RDF, and OWL 2 ontologies themselves are primarily(More)
We discuss a few new results in the area of complex dynamics in higher dimension. We investigate generic properties of orbits of biholomorphic symplectomorphisms of C . In particular we show (Corollary 3.4) that for a dense Gδ set of maps, the set of points with bounded orbit has empty interior while the set of points with recurrent orbits nevertheless has(More)
We present both a hardware and a software implementation variant of the learning with errors (LWE) based cryptosystem presented by Lindner and Peikert. This work helps in assessing the practicality of lattice-based encryption. For the software implementation, we give a comparison between a matrix and polynomial based variant of the LWE scheme. This module(More)
Encryption and signature schemes based on worst-case lattice problems are promising candidates for the post-quantum era, where classic number-theoretic assumptions are rendered false. Although there have been many important results and breakthroughs in lattice cryptography, the questions of how to systematically evaluate their security in practice and how(More)
Lattice based cryptography is gaining more and more importance in the cryptographic community. It is a common approach to use a special class of lattices, so-called ideal lattices, as the basis of lattice based crypto systems. This speeds up computations and saves storage space for cryptographic keys. The most important underlying hard problem is the(More)
1. Basic properties of nef line bundles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . p. 5 1.A. Nef line bundles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . p. 5 1.B. Nef vector bundles . . . . . . . . . . . . . .(More)