2,389 research outputs found
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
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