Histone methylation in pancreatic cancer and its clinical implications.

Pancreatic cancer (PC) is an aggressive human cancer. Appropriate methods for the diagnosis and treatment of PC have not been found at the genetic level, thus making epigenetics a promising research path in studies of PC. Histone methylation is one of the most complicated types of epigenetic modifications and has proved crucial in the development of PC. Histone methylation is a reversible process regulated by readers, writers, and erasers. Some writers and erasers can be recognized as potential biomarkers and candidate therapeutic targets in PC because of their unusual expression in PC cells compared with normal pancreatic cells. Based on the impact that writers have on the development of PC, some inhibitors of writers have been developed. However, few inhibitors of erasers have been developed and put to clinical use. Meanwhile, there is not enough research on the reader domains. Therefore, the study of erasers and readers is still a promising area. This review focuses on the regulatory mechanism of histone methylation, and the diagnosis and chemotherapy of PC based on it. The future of epigenetic modification in PC research is also discussed.

Doubly Nonnegative and Semidefinite Relaxations for the Densest k-Subgraph Problem.

The densest k-subgraph (DkS) maximization problem is to find a set of k vertices with maximum total weight of edges in the subgraph induced by this set. This problem is in general NP-hard. In this paper, two relaxation methods for solving the DkS problem are presented. One is doubly nonnegative relaxation, and the other is semidefinite relaxation with tighter relaxation compare with the relaxation of standard semidefinite. The two relaxation problems are equivalent under the suitable conditions. Moreover, the corresponding approximation ratios' results are given for these relaxation problems. Finally, some numerical examples are tested to show the comparison of these relaxation problems, and the numerical results show that the doubly nonnegative relaxation is more promising than the semidefinite relaxation for solving some DkS problems.