Opinion diversity and community formation in adaptive networks

It is interesting and of significant importance to investigate how network structures co-evolve with opinions. The existing models of such co-evolution typically lead to the final states where network nodes either reach a global consensus or break into separated communities, each of which holding its own community consensus. Such results, however, can hardly explain the richness of real-life observations that opinions are always diversified with no global or even community consensus, and people seldom, if not never, totally cut off themselves from dissenters. In this article, we show that, a simple model integrating consensus formation, link rewiring and opinion change allows complex system dynamics to emerge, driving the system into a dynamic equilibrium with co-existence of diversified opinions. Specifically, similar opinion holders may form into communities yet with no strict community consensus; and rather than being separated into disconnected communities, different communities remain to be interconnected by non-trivial proportion of inter-community links. More importantly, we show that the complex dynamics may lead to different numbers of communities at steady state with a given tolerance between different opinion holders. We construct a framework for theoretically analyzing the co-evolution process. Theoretical analysis and extensive simulation results reveal some useful insights into the complex co-evolution process, including the formation of dynamic equilibrium, the phase transition between different steady states with different numbers of communities, and the dynamics between opinion distribution and network modularity, etc.Comment: 12 pages, 8 figures, Journa

Calculations of spin induced transport in ferromagnets

Based on first-principles density functional calculations, a general approach for determining and analyzing the degree of spin polarization (P) in ferromagnets is presented. The approach employs the so-called tetrahedron method to evaluate the Fermi surface integrations of P in both ballistic and diffusive regimes. The validity of the method is examined by comparing the calculated P values for Fe and Ni with the experiment. The method is shown to yield highly accurate results with minimal computational effort. Within our approach, it is also possible to systematically analyze the contributions of various types of electronic states to the spin induced transport. As a case study, the transport properties of the soft-ferromagnet CeMnNi4 are investigated in order to explain the origin of the existing difference between the experimental and theoretical values of P in this intermetallic compound.Comment: 6 pages, 4 figures; to appear in Physical Review B 75 (2007