We consider a recent model in which agents hold opinions about each other and influence other’s during random pair interactions. When the are initially close, on short term, all tend to increase over time. On contrary, when very unequal, of high status increase, but low stagnate without gossip decrease with gossip. derive moment approximation average opinion changes that explains these observat...

The conditional independences within a system of four discrete random variables are studied simultaneously. The problem where independences can occur at the same time, called the problem of probabilistic representability, is attacked by an analysis of cones of polymatroids. New results on the cone of all polymatroids satisfying Ingleton inequalities imply a substantial reduction of the problem ...

The contingency table literature on tests for dependence among discrete multi-category variables is extensive. Standard tests assume, however, that draws are independent and only limited results exist on the e¤ect of serial dependency a problem that is important in areas such as economics, …nance, medical trials and meteorology. This paper proposes new tests of independence based on canonical c...

Systems involving many variables are important in population and quantitative genetics, for example, in multi-trait prediction of breeding values and in exploration of multi-locus associations. We studied departures of the joint distribution of sets of genetic variables from independence. New measures of association based on notions of statistical distance between distributions are presented. T...

Numerous new properties of stochastic conditional independence are introduced. They are aimed, together with two surprisingly trivial examples, at a further reduction of the problem of probabilistic representability for four{element sets, i.e. of the problem which conditional independences within a system of four random variables can occur simultaneously. Proofs are based on fundamental propert...