(Quantum) Space-Time as a Statistical Geometry of Lumps in Random Networks

In the following we undertake to describe how macroscopic space-time (or rather, a microscopic protoform of it) is supposed to emerge as a superstructure of a web of lumps in a stochastic discrete network structure. As in preceding work (mentioned below), our analysis is based on the working philosophy that both physics and the corresponding mathematics have to be genuinely discrete on the primordial (Planck scale) level. This strategy is concretely implemented in the form of \tit{cellular networks} and \tit{random graphs}. One of our main themes is the development of the concept of \tit{physical (proto)points} or \tit{lumps} as densely entangled subcomplexes of the network and their respective web, establishing something like \tit{(proto)causality}. It may perhaps be said that certain parts of our programme are realisations of some early ideas of Menger and more recent ones sketched by Smolin a couple of years ago. We briefly indicate how this \tit{two-story-concept} of \tit{quantum} space-time can be used to encode the (at least in our view) existing non-local aspects of quantum theory without violating macroscopic space-time causality.Comment: 35 pages, Latex, under consideration by CQ

Frequent Itemset Border Approximation by Dualization

International audienceThe approach FIBAD is introduced with the purpose of computing approximate borders of frequent itemsets by leveraging dualization and computation of approximate minimal transversals of hypergraphs. The distinctiveness of the FIBAD's theoretical foundations s the approximate dualization where a new function ~f is defined to compute the approximate negative border. From a methodological point of view, the function ~f is implemented by the method AMTHR that consists of a reduction of the hypergraph and a computation of its minimal transversals. For evaluation purposes, we study the sensibility of FIBAD to AMTHR by replacing this latter by two other algorithms that compute approximate minimal transversals. We also compare our approximate dualization-based method with an existing approach that computes directly, without dualization, the approximate borders. The experimental results show that our method outperforms the other methods as it produces borders that have the highest quality