From complex networks, to language evolution, to musical compositions

摘要

Markov chains provide us with a powerful tool for studying the structure of graphs and databases in details. We review the method of generalized inverses for Markov chains and apply it for the analysis of urban structures, evolution of languages, and musical compositions. We also discuss a generalization of L′evy flights over large complex networks and study the interplay between the nonlinearity of diffusion process and the topological structure of the network.