No abstract

The Stable Marriage Problem is to find a one-to-one matching for two equally sized sets of agents. Due to its widespread applications in the real world, especially the unique importance to the centralized match maker, a very large number of questions have been extensively studied in this field. This article considers a generalized form of stable marriage problem, where different numbers of men and women need to be matched pairwise and the emergence of single is inevitable. Theoretical analysis and numerical simulations confirm that even small deviations from equal number of two sides can have a large impact on matching solution of Gale-Shapley Algorithm. These results provide insights to many of the real-world applications when matching two sides with unequal number.

The incidence of colorectal cancer (colorectal cancer, CRC) in China has increased in recent years, and its mortality rate has become one of the highest among all cancers. CRC also increasingly affects people’s health and quality of life, and the workloads of medical doctors have further increased due to the lack of sufficient medical resources in China. The goal of this study was to construct an automated expert system using a deep learning technique to predict the probability of early stage CRC based on the patient’s case report and the patient’s attributes. Compared with previous prediction methods, which are either based on sophisticated examinations or have high computational complexity, this method is shown to provide valuable information such as suggesting potentially important early signs to assist in early diagnosis, early treatment and prevention of CRC, hence helping medical doctors reduce the workloads of endoscopies and other treatments.