The bidirectional selection between two classes widely emerges in various social lives, such as commercial trading and mate choosing. Until now, the discussions on bidirectional selection in structured human society are quite limited. We demonstrated
theoretically that the rate of successfully matching is affected greatly by individuals neighborhoods in social networks, regardless of the type of networks. Furthermore, it is found that the high average degree of networks contributes to increasing rates of successful matches. The matching performance in different types of networks has been quantitatively investigated, revealing that the small-world networks reinforces the matching rate more than scale-free networks at given average degree. In addition, our analysis is consistent with the modeling result, which provides the theoretical understanding of underlying mechanisms of matching in complex networks.
We propose a topological quantum phase transition for quantum states with different Berry phases in hole-doped III-V semiconductor quantum wells with bulk and structure inversion asymmetry. The Berry phase of the occupied Bloch states can be characte
ristic of topological metallic states. It is found that the adjustment of thickness of the quantum well may cause a transition of Berry phase in two-dimensional hole gas. Correspondingly, the jump of spin Hall conductivity accompanies the change of the Berry phase. This property is robust against the impurity potentials in the system. Experimental detection of this topological quantum phase transition is discussed.
