h i g h l i g h t s• Information propagation on OSNs is studied considering super-spreading phenomenon. • A SAIR model is proposed to characterize the information propagation with Weibo data.• Super-spreaders in information propagation on OSNs are identified and characterized. • The sensitivity of parameters depicting super-spreading phenomenon is analyzed. a b s t r a c t As the microblogging services are becoming more prosperous in everyday life for users on Online Social Networks (OSNs), it is more favorable for hot topics and breaking news to gain more attraction very soon than ever before, which are so-called ''super-spreading events''. In the information diffusion process of these super-spreading events, messages are passed on from one user to another and numerous individuals are influenced by a relatively small portion of users, a.k.a. super-spreaders. Acquiring an awareness of super-spreading phenomena and an understanding of patterns of wide-ranged information propagations benefits several social media data mining tasks, such as hot topic detection, predictions of information propagation, harmful information monitoring and intervention. Taking into account that super-spreading in both information diffusion and spread of a contagious disease are analogous, in this study, we build a parameterized model, the SAIR model, based on well-known epidemic models to characterize super-spreading phenomenon in tweet information propagation accompanied with super-spreaders. For the purpose of modeling information diffusion, empirical observations on a real-world Weibo dataset are statistically carried out. Both the steady-state analysis on the equilibrium and the validation on real-world Weibo dataset of the proposed model are conducted. The case study that validates the proposed model shows that the SAIR model is much more promising than the conventional SIR model in characterizing a super-spreading event of information propagation. In addition, numerical simulations are carried out and discussed to discover how sensitively the parameters affect the information propagation process.

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In this paper, the existence of antiperiodic solutions for fourth-order impulsive differential equation is obtained by variational approaches and results on the auxiliary system. It is interesting that there is no growth restraint on nonlinear terms and impulsive terms. Besides, any minimizing sequence is bounded in a closed convex set of a space composed of Lipschitzian functions with the appearance of antiperiodic boundary value conditions.

In this paper, we study the multiple solutions for some second-order p-Laplace differential equations with three-point boundary conditions and instantaneous and noninstantaneous impulses. By applying the variational method and critical point theory the multiple solutions are obtained in a Sobolev space. Compared with other local boundary value problems, the three-point boundary value problem is less studied by variational method due to its variational structure. Finally, two examples are given to illustrate the results of multiplicity.

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