Foi aceito, e se tornou palestra convidada:
XXX Encontro Nacional de Física da Matéria Condensada
Copy-mutate processes for growth of bipartite networks: an application to cultural evolution
Osame Kinouchi, Adriano J. Holanda, Antônio Carlos Roque, Rosa Wanda Diez Garcia
Universidade de São Paulo
We propose a copy-mutate stochastic process for growth of bipartite networks. We find that its non-equilibrium stationary state, which has scale-free statistics, presents also strong memory effects ("founder effect"). We examine the performance of several algorithm variants, and find that the inclusion of node fitness and competitive selection is essential to reproduce empirical data concerning the bipartite network of culinary recipes and ingredients. The empirical database has been collected from traditional cookbooks from Brazil, England, France and Medieval Europe. We present rank-plots for ingredients and ingredients pairs and study rank-plot entropies. We determine power-law exponents from complementary accumulated distributions and find that all books have similar exponents (with exception of a medieval culinary book). We also examine the temporal evolution of the average recipe fitness and find an asymptotical power law with very low exponent, indicating that the historical process represented by the model is very far from equilibrium. More general applications to cultural evolution ("memetics") are discussed.