Highly structured distributions in artificial intelligence, cryptography and combinatorics

Modern applications of calculi for dealing with uncertainty and of multivariate statistics rely on highly structured distributions. The knowledge how to construct the distributions both from heterogeneous data comming from diferent sources and from expert knowledge in form of graphs, conditional independence constraints and entropic functions is crucial. We suggest to analyze related mathematical models using methodology of modern probability theory, statistics, combinatorics (graphs, matroids, polymatroids), and applied algebra. The expected results are to be encorporated into the secret sharing schemes of cryptography and in the probabilistics method known in combinatorics.