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In recent years, social networks have attracted the interest of researchers from diverse disciplines. Competing types of information, such as positive and negative information about a topic or marketing information for similar products from different companies, often diffuse in social networks simultaneously. However, most previous studies only consider one type of information using the susceptible-infectiousrecovered or susceptible-infectious-susceptible models. In this paper, we propose a competitive diffusion model to describe the diffusion processes of two types of information in social networks, analyze the stability of the diffusion infection-free equilibrium, and study the diffusion processes by numerical simulations. The results show that the information with the larger probabilities of being received and reposted diffuses more broadly and suppresses the competitor. We also find that the initial number of spreader nodes, the degrees of participants, and network structures all affect the scope of information diffusion.

Rating prediction is an important technology in the personalized recommendation field. Prediction results are influenced by many factors, such as time, and their accuracy directly affects the quality of the recommendation. Current time-based collaborative filtering (CF) algorithms have improved the technology of prediction accuracy to a certain extent, but they fail to differentiate the time-sensitivity of different users, which further affects prediction accuracy. To address this issue, we have proposed a rating prediction algorithm based on user time-sensitivity differences. First, we analyzed and modeled the time sensitivities of users, utilized cosine distance and relative entropy to build a judgment function, and then judged the time sensitivities of users based on a voting strategy. Next, we applied the time-sensitivity difference to improve the traditional CF algorithm and optimized the combination of parameters. Finally, we tested our algorithm on standard datasets. The experimental results showed that there are many users who have different sensitivities to time. According to these experimental results, our proposed algorithm has achieved a higher prediction accuracy than other state-of-the-art algorithms.