Conexão entre as redes complexas e estatística de Kaniadakis e busca eficiente das propriedades críticas do processo epidêmico difusivo 1D

In this work we study a connection between a non-Gaussian statistics, the Kaniadakis statistics, and Complex Networks. We show that the degree distribution P(k)of a scale free-network, can be calculated using a maximization of information entropy in the context of non-gaussian statistics. As an example, a numerical analysis based on the preferential attachment growth model is discussed, as well as a numerical behavior of the Kaniadakis and Tsallis degree distribution is compared. We also analyze the diffusive epidemic process (DEP) on a regular lattice one-dimensional. The model is composed of A (healthy) and B (sick) species that independently diffusive on lattice with diffusion rates DA and DB for which the probabilistic dynamical rule A + B → 2B and B → A. This model belongs to the category of non-equilibrium systems with an absorbing state and a phase transition between active an inactive states. We investigate the critical behavior of the DEP using an auto-adaptive algorithm to find critical points: the method of automatic searching for critical points (MASCP). We compare our results with the literature and we find that the MASCP successfully finds the critical exponents 1/ѵ and 1/zѵ in all the cases DA =DB, DA DB. The simulations show that the DEP has the same critical exponents as are expected from field-theoretical arguments. Moreover, we find that, contrary to a renormalization group prediction, the system does not show a discontinuous phase transition in the regime o DA >DB.

Dinâmica e estrutura de redes complexas no modelo de afinidade

In this work we elaborate and discuss a Complex Network model which presents connectivity scale free probability distribution (power-law degree distribution). In order to do that, we modify the rule of the preferential attachment of the Bianconi-Barabasi model, including a factor which represents the similarity of the sites. The term that corresponds to this similarity is called the affinity, and is obtained by the modulus of the difference between the fitness (or quality) of the sites. This variation in the preferential attachment generates very interesting results, by instance the time evolution of the connectivity, which follows a power-law distribution ki / ( t t0 )fi, where fi indicates the rate to the site gain connections. Certainly this depends on the affinity with other sites. Besides, we will show by numerical simulations results for the average path length and for the clustering coefficient