Discovering Informative Connection Subgraphs in Multi-Relational Graphs

Discovering patterns in graphs has long been an area of interest. In most approaches to such pattern discovery either quantitative anomalies, frequency of substructure or maximum flow is used to measure the interestingness of a pattern. In this paper we introduce heuristics that guide a subgraph discovery algorithm away from banal paths towards more informative ones. Given an RDF graph a user might pose a question of the form: What are the most relevant ways in which entity X is related to entity Y? the response to which is a subgraph connecting X to Y. We use our heuristics to discover informative subgraphs within RDF graphs. Our heuristics are based on weighting mechanisms derived from edge semantics suggested by the RDF schema. We present an analysis of the quality of the subgraphs generated with respect to path ranking metrics. We then conclude presenting intuitions about which of our weighting schemes and heuristics produce higher quality subgraphs

Overview of (pro-)Lie group structures on Hopf algebra character groups

Character groups of Hopf algebras appear in a variety of mathematical and physical contexts. To name just a few, they arise in non-commutative geometry, renormalisation of quantum field theory, and numerical analysis. In the present article we review recent results on the structure of character groups of Hopf algebras as infinite-dimensional (pro-)Lie groups. It turns out that under mild assumptions on the Hopf algebra or the target algebra the character groups possess strong structural properties. Moreover, these properties are of interest in applications of these groups outside of Lie theory. We emphasise this point in the context of two main examples: The Butcher group from numerical analysis and character groups which arise from the Connes--Kreimer theory of renormalisation of quantum field theories.Comment: 31 pages, precursor and companion to arXiv:1704.01099, Workshop on "New Developments in Discrete Mechanics, Geometric Integration and Lie-Butcher Series", May 25-28, 2015, ICMAT, Madrid, Spai

Notes on a paper of Mess

These notes are a companion to the article "Lorentz spacetimes of constant curvature" by Geoffrey Mess, which was first written in 1990 but never published. Mess' paper will appear together with these notes in a forthcoming issue of Geometriae Dedicata.Comment: 26 page

Amenability of groups and GG-sets

This text surveys classical and recent results in the field of amenability of groups, from a combinatorial standpoint. It has served as the support of courses at the University of G\"ottingen and the \'Ecole Normale Sup\'erieure. The goals of the text are (1) to be as self-contained as possible, so as to serve as a good introduction for newcomers to the field; (2) to stress the use of combinatorial tools, in collaboration with functional analysis, probability etc., with discrete groups in focus; (3) to consider from the beginning the more general notion of amenable actions; (4) to describe recent classes of examples, and in particular groups acting on Cantor sets and topological full groups

Hemodynamics

xii, 419 p. : ill.; 25 cm