1. INTRODUCTION. Hypergraphs. Information Theory. Cauchy-Schwarz. It seems reasonable to assume that most mathematicians would be puzzled to find these three terms as, say, key words for the same mathematical paper. (Just in case this puzzlement is a result of being unfamiliar with the term " hypergraph " : a hypergraph is nothing other than a family of sets, and will be defined formally later....

In studies of discrete structures, functions are frequently used that express the proximity of objects but do not belong to the family of metrics. We consider a class of such functions that is characterized by a normalization condition and an inequality that plays the same role as the triangle inequality does for metrics. We show that the introduced functions, named Σ-proximities (" sigma-proxi...

Video signatures are compact representations of video sequences designed for efficient similarity measurement. In this paper, we propose a feature extraction technique to support fast similarity search on large databases of video signatures. Our proposed technique transforms the high dimensional video signatures into low dimensional vectors where similarity search can be efficiently performed. ...