We propose a mechanism to suppress proton decay induced by dimension-5 operators in a supersymmetric SO(10) model. Proton lifetime is directly connected with the intermediate vacuum expectation value which is responsible for the seesaw mechanism. The
model shows many consistencies with the present theoretical results such as the components of the two Higgs doublets in the minimal supersymmetric standard model.
The extended supersymmetric SO(10) model with missing partner mechanism is studied. An intermediate vacuum expectation value is incorporated which corresponds to the see-saw scale. Gauge coupling unification is not broken explicitly. Proton decay is
found to satisfy the present experimental limits at the cost of fine-tuning some parameters.
Many real-world networks display a natural bipartite structure. It is necessary and important to study the bipartite networks by using the bipartite structure of the data. Here we propose a modification of the clustering coefficient given by the frac
tion of cycles with size four in bipartite networks. Then we compare the two definitions in a special graph, and the results show that the modification one is better to character the network. Next we define a edge-clustering coefficient of bipartite networks to detect the community structure in original bipartite networks.
