Social influence on selection behaviour: distinguishing local- and global-driven preferential attachment

Social influence drives human selection behaviours when numerous objects competing for limited attentions, which leads to the 'rich get richer' dynamics where popular objects tend to get more attentions. However, evidences have been found that, both the global information of the whole system and the local information among one's friends have significant influence over the one's selection. Consequently, a key question raises that, it is the local information or the global information more determinative for one's selection? Here we compare the local-based influence and global-based influence. We show that, the selection behaviour is mainly driven by the local popularity of the objects while the global popularity plays a supplementary role driving the behaviour only when there is little local information for the user to refer to. Thereby, we propose a network model to describe the mechanism of user-object interaction evolution with social influence, where the users perform either local-driven or global-driven preferential attachments to the objects, i.e., the probability of an objects to be selected by a target user is proportional to either its local popularity or global popularity. The simulation suggests that, about 75% of the attachments should be driven by the local popularity to reproduce the empirical observations. It means that, at least in the studied context where users chose businesses on Yelp, there is a probability of 75% for a user to make a selection according to the local popularity. The proposed model and the numerical findings may shed some light on the study of social influence and evolving social systems

Dynamical classification of analytic one-frequency quasi-periodic SO(3,R)\mathrm{SO}(3,\mathbb{R})-cocycles

We establish a close connection between acceleration and dynamical degree for one-frequency quasi-periodic compact cocycles, by showing that two vectors derived separately from each coincide. Based on this, we provide a dynamical classification of one-frequency quasi-periodic $\mathrm{SO}(3,\mathbb{R})$-cocycles