1,700 research outputs found
Computing commons interval of K permutations, with applications to modular decomposition of graphs
International audienceWe introduce a new way to compute common intervals of K permutations based on a very simple and general notion of generators of common intervals. This formalism leads to simple and efficient algorithms to compute the set of all common intervals of K permutations, that can contain a quadratic number of intervals, as well as a linear space basis of this set of common intervals. Finally, we show how our results on permutations can be used for computing the modular decomposition of graphs in linear time
Connected Floer homology of covering involutions
Using the covering involution on the double branched cover of the
three-sphere branched along a knot, and adapting ideas of Hendricks-Manolescu
and Hendricks-Hom-Lidman, we define new knot invariants and apply them to
deduce novel linear independence results in the smooth concordance group of
knots.Comment: 21 pages, 5 figure
Triangular bases of integral closures
In this work, we consider the problem of computing triangular bases of
integral closures of one-dimensional local rings.
Let be a discrete valued field with valuation ring and
let be the maximal ideal. We take , a
monic irreducible polynomial of degree and consider the extension as well as the integral closure of
in , which we suppose to be finitely generated as an -module.
The algorithm , presented in this paper, computes
triangular bases of fractional ideals of . The theoretical
complexity is equivalent to current state of the art methods and in practice is
almost always faster. It is also considerably faster than the routines found in
standard computer algebra systems, excepting some cases involving very small
field extensions
Event generation with SHERPA 1.1
In this paper the current release of the Monte Carlo event generator Sherpa,
version 1.1, is presented. Sherpa is a general-purpose tool for the simulation
of particle collisions at high-energy colliders. It contains a very flexible
tree-level matrix-element generator for the calculation of hard scattering
processes within the Standard Model and various new physics models. The
emission of additional QCD partons off the initial and final states is
described through a parton-shower model. To consistently combine multi-parton
matrix elements with the QCD parton cascades the approach of Catani, Krauss,
Kuhn and Webber is employed. A simple model of multiple interactions is used to
account for underlying events in hadron--hadron collisions. The fragmentation
of partons into primary hadrons is described using a phenomenological
cluster-hadronisation model. A comprehensive library for simulating tau-lepton
and hadron decays is provided. Where available form-factor models and matrix
elements are used, allowing for the inclusion of spin correlations; effects of
virtual and real QED corrections are included using the approach of Yennie,
Frautschi and Suura.Comment: 47 pages, 21 figure
CORADD: Correlation Aware Database Designer for Materialized Views and Indexes
We describe an automatic database design tool that exploits correlations between attributes when recommending materialized views (MVs) and indexes. Although there is a substantial body of related work exploring how to select an appropriate set of MVs and indexes for a given workload, none of this work has explored the effect of correlated attributes (e.g., attributes encoding related geographic information) on designs. Our tool identifies a set of MVs and secondary indexes such that correlations between the clustered attributes of the MVs and the secondary indexes are enhanced, which can dramatically improve query performance. It uses a form of Integer Linear Programming (ILP) called ILP Feedback to pick the best set of MVs and indexes for given database size constraints. We compare our tool with a state-of-the-art commercial database designer on two workloads, APB-1 and SSB (Star Schema Benchmark---similar to TPC-H). Our results show that a correlation-aware database designer can improve query performance up to 6 times within the same space budget when compared to a commercial database designer.National Science Foundation (U.S.) (Grant IIS-0704424)SAP Corporation (Grant
A survey of Heegaard Floer homology
This work has two goals. The first is to provide a conceptual introduction to
Heegaard Floer homology, the second is to survey the current state of the
field, without aiming for completeness. After reviewing the structure of
Heegaard Floer homology, we list some of its most important applications. Many
of these are purely topological results, not referring to Heegaard Floer
homology itself. Then, we briefly outline the construction of Lagrangian
intersection Floer homology. We construct the Heegaard Floer chain complex as a
special case of the above, and try to motivate the role of the various
seemingly ad hoc features such as admissibility, the choice of basepoint, and
Spin^c-structures. We also discuss the proof of invariance of the homology up
to isomorphism under all the choices made, and how to define Heegaard Floer
homology using this in a functorial way (naturality). Next, we explain why
Heegaard Floer homology is computable, and how it lends itself to the various
combinatorial descriptions. The last chapter gives an overview of the
definition and applications of sutured Floer homology, which includes sketches
of some of the key proofs. Throughout, we have tried to collect some of the
important open conjectures in the area. For example, a positive answer to two
of these would give a new proof of the Poincar\'e conjecture.Comment: 38 pages, 1 figure, a few minor correction
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