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