An Elimination Method for Solving Bivariate Polynomial Systems: Eliminating the Usual Drawbacks

We present an exact and complete algorithm to isolate the real solutions of a zero-dimensional bivariate polynomial system. The proposed algorithm constitutes an elimination method which improves upon existing approaches in a number of points. First, the amount of purely symbolic operations is significantly reduced, that is, only resultant computation and square-free factorization is still needed. Second, our algorithm neither assumes generic position of the input system nor demands for any change of the coordinate system. The latter is due to a novel inclusion predicate to certify that a certain region is isolating for a solution. Our implementation exploits graphics hardware to expedite the resultant computation. Furthermore, we integrate a number of filtering techniques to improve the overall performance. Efficiency of the proposed method is proven by a comparison of our implementation with two state-of-the-art implementations, that is, LPG and Maple's isolate. For a series of challenging benchmark instances, experiments show that our implementation outperforms both contestants.Comment: 16 pages with appendix, 1 figure, submitted to ALENEX 201

Deconstructing Approximate Offsets

We consider the offset-deconstruction problem: Given a polygonal shape Q with n vertices, can it be expressed, up to a tolerance \eps in Hausdorff distance, as the Minkowski sum of another polygonal shape P with a disk of fixed radius? If it does, we also seek a preferably simple-looking solution P; then, P's offset constitutes an accurate, vertex-reduced, and smoothened approximation of Q. We give an O(n log n)-time exact decision algorithm that handles any polygonal shape, assuming the real-RAM model of computation. A variant of the algorithm, which we have implemented using CGAL, is based on rational arithmetic and answers the same deconstruction problem up to an uncertainty parameter \delta; its running time additionally depends on \delta. If the input shape is found to be approximable, this algorithm also computes an approximate solution for the problem. It also allows us to solve parameter-optimization problems induced by the offset-deconstruction problem. For convex shapes, the complexity of the exact decision algorithm drops to O(n), which is also the time required to compute a solution P with at most one more vertex than a vertex-minimal one.Comment: 18 pages, 11 figures, previous version accepted at SoCG 2011, submitted to DC

Landesrestaurierungsprogramm und Universitätsbibliothek: Bestandserhaltung und kundenorientierte Dienstleistung für Forschung und Lehre

Die aktuellen Herausforderungen durch die Bestände selbst, die Kunden und die ökonomischen Bedingungen werden geschildert, ebenso werden die angewendeten Maßnahmen und Verfahren der Bestandserhaltung skizziert

Consistency of Loop Regularization Method and Divergence Structure of QFTs Beyond One-Loop Order

We study the problem how to deal with tensor-type two-loop integrals in the Loop Regularization (LORE) scheme. We use the two-loop photon vacuum polarization in the massless Quantum Electrodynamics (QED) as the example to present the general procedure. In the processes, we find a new divergence structure: the regulated result for each two-loop diagram contains a gauge-violating quadratic harmful divergent term even combined with their corresponding counterterm insertion diagrams. Only when we sum up over all the relevant diagrams do these quadratic harmful divergences cancel, recovering the gauge invariance and locality.Comment: 33 pages, 5 figures, Sub-section IIIE removed, to be published in EPJ

PACRR: A Position-Aware Neural IR Model for Relevance Matching

In order to adopt deep learning for information retrieval, models are needed that can capture all relevant information required to assess the relevance of a document to a given user query. While previous works have successfully captured unigram term matches, how to fully employ position-dependent information such as proximity and term dependencies has been insufficiently explored. In this work, we propose a novel neural IR model named PACRR aiming at better modeling position-dependent interactions between a query and a document. Extensive experiments on six years' TREC Web Track data confirm that the proposed model yields better results under multiple benchmarks.Comment: To appear in EMNLP201