17,552 research outputs found
Evaluating Datalog via Tree Automata and Cycluits
We investigate parameterizations of both database instances and queries that
make query evaluation fixed-parameter tractable in combined complexity. We show
that clique-frontier-guarded Datalog with stratified negation (CFG-Datalog)
enjoys bilinear-time evaluation on structures of bounded treewidth for programs
of bounded rule size. Such programs capture in particular conjunctive queries
with simplicial decompositions of bounded width, guarded negation fragment
queries of bounded CQ-rank, or two-way regular path queries. Our result is
shown by translating to alternating two-way automata, whose semantics is
defined via cyclic provenance circuits (cycluits) that can be tractably
evaluated.Comment: 56 pages, 63 references. Journal version of "Combined Tractability of
Query Evaluation via Tree Automata and Cycluits (Extended Version)" at
arXiv:1612.04203. Up to the stylesheet, page/environment numbering, and
possible minor publisher-induced changes, this is the exact content of the
journal paper that will appear in Theory of Computing Systems. Update wrt
version 1: latest reviewer feedbac
Note on the Origin of the Highest Energy Cosmic Rays
In this note we argue that the galactic model chosen by E.-J. Ahn, G.
Medina-Tanco, P.L. Bierman and T. Stanev in their paper discussing the origin
of the highest energy cosmic rays, is alone responsible for the focussing of
positive particles towards the North galactic pole. We discuss the validity of
this model, in particular in terms of field reversals and radial extensions. We
conclude that with such a model one cannot retreive any directional information
from the observed direction of the cosmic rays. In particular one cannot
identify point sources at least up to energies of about 200 EeV. Therefore the
apparent clustering of the back-traced highest energy cosmic rays observed to
date cannot be interpreted as an evidence for a point source nor for the
identification of M87, which happens to be close to the North pole, as being
such a source.Comment: 3 pages, 2 figure
Reproducing pairs of measurable functions and partial inner product spaces
We continue the analysis of reproducing pairs of weakly measurable functions,
which generalize continuous frames. More precisely, we examine the case where
the defining measurable functions take their values in a partial inner product
space (PIP spaces). Several examples, both discrete and continuous, are
presented.Comment: 20 pages, 1 figure. arXiv admin note: substantial text overlap with
arXiv:1505.0418
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