Uniform generation in trace monoids

We consider the problem of random uniform generation of traces (the elements of a free partially commutative monoid) in light of the uniform measure on the boundary at infinity of the associated monoid. We obtain a product decomposition of the uniform measure at infinity if the trace monoid has several irreducible components-a case where other notions such as Parry measures, are not defined. Random generation algorithms are then examined.Comment: Full version of the paper in MFCS 2015 with the same titl

Cycle-centrality in complex networks

Networks are versatile representations of the interactions between entities in complex systems. Cycles on such networks represent feedback processes which play a central role in system dynamics. In this work, we introduce a measure of the importance of any individual cycle, as the fraction of the total information flow of the network passing through the cycle. This measure is computationally cheap, numerically well-conditioned, induces a centrality measure on arbitrary subgraphs and reduces to the eigenvector centrality on vertices. We demonstrate that this measure accurately reflects the impact of events on strategic ensembles of economic sectors, notably in the US economy. As a second example, we show that in the protein-interaction network of the plant Arabidopsis thaliana, a model based on cycle-centrality better accounts for pathogen activity than the state-of-art one. This translates into pathogen-targeted-proteins being concentrated in a small number of triads with high cycle-centrality. Algorithms for computing the centrality of cycles and subgraphs are available for download

Number of Prefixes in Trace Monoids: Clique Polynomials and Dependency Graphs

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