Search Engine Drives the Evolution of Social Networks

The search engine is tightly coupled with social networks and is primarily designed for users to acquire interested information. Specifically, the search engine assists the information dissemination for social networks, i.e., enabling users to access interested contents with keywords-searching and promoting the process of contents-transferring from the source users directly to potential interested users. Accompanying such processes, the social network evolves as new links emerge between users with common interests. However, there is no clear understanding of such a "chicken-and-egg" problem, namely, new links encourage more social interactions, and vice versa. In this paper, we aim to quantitatively characterize the social network evolution phenomenon driven by a search engine. First, we propose a search network model for social network evolution. Second, we adopt two performance metrics, namely, degree distribution and network diameter. Theoretically, we prove that the degree distribution follows an intensified power-law, and the network diameter shrinks. Third, we quantitatively show that the search engine accelerates the rumor propagation in social networks. Finally, based on four real-world data sets (i.e., CDBLP, Facebook, Weibo Tweets, P2P), we verify our theoretical findings. Furthermore, we find that the search engine dramatically increases the speed of rumor propagation.Comment: 9 pages, 11 figure

U(1)U(1) gauge vector field on a codimension-2 brane

In this paper, we obtain a gauge invariant effective action for a bulk massless $U(1)$ gauge vector field on a brane with codimension two by using a general Kaluza-Klein (KK) decomposition for the field. It suggests that there exist two types of scalar KK modes to keep the gauge invariance of the action for the massive vector KK modes. Both the vector and scalar KK modes can be massive. The masses of the vector KK modes $m^{(n)}$ contain two parts, $m_{1}^{(n)}$ and $m_{2}^{(n)}$, due to the existence of the two extra dimensions. The masses of the two types of scalar KK modes $m_{\phi}^{(n)}$ and $m_{\varphi}^{(n)}$ are related to the vector ones, i.e., $m_{\phi}^{(n)}=m_{1}^{(n)}$ and $m_{\varphi}^{(n)}=m_{2}^{(n)}$. Moreover, we derive two Schr\"{o}dinger-like equations for the vector KK modes, for which the effective potentials are just the functions of the warp factor.Comment: 15 pages,no figures, accepted by JHE