Z-Score-Based Modularity for Community Detection in Networks.

Identifying community structure in networks is an issue of particular interest in network science. The modularity introduced by Newman and Girvan is the most popular quality function for community detection in networks. In this study, we identify a problem in the concept of modularity and suggest a solution to overcome this problem. Specifically, we obtain a new quality function for community detection. We refer to the function as Z-modularity because it measures the Z-score of a given partition with respect to the fraction of the number of edges within communities. Our theoretical analysis shows that Z-modularity mitigates the resolution limit of the original modularity in certain cases. Computational experiments using both artificial networks and well-known real-world networks demonstrate the validity and reliability of the proposed quality function.

Modifications and structure-activity relationships at the 2-position of 4-sulfonamidopyrimidine derivatives as potent endothelin antagonists.

To improve water solubility and to study structure-activity relationships, we modified the structure of the pyrimidine nucleus of each of a series of potent ET(A) antagonists, 3a and 4a, at the 2-position. In a previous study, each of these antagonists showed an extremely high affinity for the ET(A) receptor in porcine aortic membrane (IC(50) 3a; < 0.001 nM, 4a; 0.0039 nM). Two modification methods, one being the addition of organolithium followed by DDQ oxidation and the other being the nucleophilic substitution of 2-(methylsulfonyl)pyrimidine, were applied individually to synthesize 2-substituted-4-sulfonamidopyrimidine derivatives. The introduction of aryl, heteroaryl, alkyl, amino, alkoxy, or alkylthio groups into the 2-position varied the affinity. Derivatives with hydrophilic groups at the 2-position showed higher water solubility but tended to reduce the affinity for the ET(A) receptor.