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Displaying 361 –
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Social networks representing one or more relationships between individuals and one or more categorical characteristics of the individuals exhibit both structure and composition. Probabilistic models of such networks can be used for analyzing the interrelations between structural and compositional variables, for instance in order to find how structure can be explained by composition or how structure explains composition. Different models are discussed and different statistical methods are employed...
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...
We shall compute the exact value of rigidity of the triangular matrix with entries 0 and 1.
A simple idea used in many combinatorial algorithms is the idea of pivoting. Originally, it comes from the method proposed by Gauss in the 19th century for solving systems of linear equations. This method had been extended in 1947 by Dantzig for the famous simplex algorithm used for solving linear programs. From since, a pivoting algorithm is a method exploring subsets of a ground set and going from one subset σ to a new one σ′ by deleting an element inside σ and adding an element outside σ: σ′ = σv} ∪ {u},...
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