Phase transitions in Ising model induced by weight redistribution on weighted regular networks

In order to investigate the role of the weight in weighted networks, the collective behavior of the Ising system on weighted regular networks is studied by numerical simulation. In our model, the coupling strength between spins is inversely proportional to the corresponding weighted shortest distance. Disordering link weights can effectively affect the process of phase transition even though the underlying binary topological structure remains unchanged. Specifically, based on regular networks with homogeneous weights initially, randomly disordering link weights will change the critical temperature of phase transition. The results suggest that the redistribution of link weights may provide an additional approach to optimize the dynamical behaviors of the system.Comment: 6 pages, 5 figure

Logical gaps in the approximate solutions of the social learning game and an exact solution

After the social learning models were proposed, finding the solutions of the games becomes a well-defined mathematical question. However, almost all papers on the games and their applications are based on solutions built upon either an add-hoc argument or a twisted Bayesian analysis of the games. Here, we present logical gaps in those solutions and an exact solution of our own. We also introduced a minor extension to the original game such that not only logical difference but also difference in action outcomes among those solutions become visible.Comment: A major revisio

Games on graphs: A minor modification of payoff scheme makes a big difference

Various social dilemma games that follow different strategy updating rules have been studied on many networks.The reported results span the entire spectrum, from significantly boosting,to marginally affecting,to seriously decreasing the level of cooperation.Experimental results that are qualitatively different from theoretical prediction have also been reported.It is widely believed that the results are largely determined by three elements,including payoff matrices of the underlying 2*2 games,the way that the strategic states of the players are updated and the structure of the networks.Here we discuss the impact of a seemly non-essential mechanism -- what we refer to as a "payoff scheme". Specifically, in each round after the states of all of the players are determined,the payoff scheme is how each player's payoff is calculated.In addition to the two conventions in which either the accumulated or the averaged payoff is calculated from playing with all of the neighboring players,we here study the effects of calculating the payoff from pairing up with one random player from among the neighboring players. Based on probability theory, in a situation of uncorrelated events, the average payoff that involves all of the neighbors should,in principal,be equivalent to the payoff from pairing up with one neighbor.However,our simulation of games on graphs shows that, in many cases,the two payoff schemes lead to qualitatively different levels of cooperation.This finding appears to provide a possible explanation for a wide spectrum of observed behaviors in the literature.We have also observed that results from the randomly-pairing-one mechanism are more robust than the involving-all-neighbours mechanism because,in the former case, neither the other three main elements nor the initial states of the players have a large impact on the final level of cooperation compared with in the latter case.Comment: 23 pages,171 figure

Emergence of Global Preferential Attachment From Local Interaction

Global degree/strength based preferential attachment is widely used as an evolution mechanism of networks. But it is hard to believe that any individual can get global information and shape the network architecture based on it. In this paper, it is found that the global preferential attachment emerges from the local interaction models, including distance-dependent preferential attachment (DDPA) evolving model of weighted networks(M. Li et al, New Journal of Physics 8 (2006) 72), acquaintance network model(J. Davidsen et al, Phys. Rev. Lett. 88 (2002) 128701) and connecting nearest-neighbor(CNN) model(A. Vazquez, Phys. Rev. E 67 (2003) 056104). For DDPA model and CNN model, the attachment rate depends linearly on the degree or strength, while for acquaintance network model, the dependence follows a sublinear power law. It implies that for the evolution of social networks, local contact could be more fundamental than the presumed global preferential attachment. This is onsistent with the result observed in the evolution of empirical email networks.Comment: 9 pages, 5 figure