Complex determinantal processes and noise.
The class of componentwise concave copulas is considered, with particular emphasis on its closure under some constructions of copulas (e.g., ordinal sum) and its relations with other classes of copulas characterized by some notions of concavity and/or convexity. Then, a sharp upper bound is given for the -measure of non-exchangeability for copulas belonging to this class.
Compositional models are used to construct probability distributions from lower-order probability distributions. On the other hand, Bayesian models are used to represent probability distributions that factorize according to acyclic digraphs. We introduce a class of models, called recursive factorization models, to represent probability distributions that recursively factorize according to sequences of sets of variables, and prove that they have the same representation power as both compositional...
Compositions and partitions of positive integers are often studied in separate frameworks where partitions are given by q-series generating functions and compositions exhibiting specific patterns are designated by generating functions for these patterns. Here, we view compositions as alternating sequences of weakly increasing and strictly decreasing partitions (i.e. alternating blocks). We obtain generating functions for the number of such partitions in terms of the size of the composition, the...