Social influences, the phenomena that one individual's actions can induce similar behaviors among his/her friends via their social ties, have been observed prevailingly in socially networked systems. While most existing work focuses on studying general, macro-level influence (e.g., diffusion); equally important is to understand social influence at microscopic scales (i.e., at the granularity of single individuals, actions, and time-stamps), which may benefit a range of applications. We propose μSI, a microscopic social-influence model wherein: individuals' actions are modeled as temporary interactions between social network (formed by individuals) and object network (formed by targets of actions); one individual's actions influence his/her friends in a dynamic, network-wisemanner (i.e., dependent on both social and object networks). We develop for μSI a suite of novel inference tools that enable to answer questions of the form: How may an occurred interaction trigger another? More importantly, when and where may a new interaction be observed? We carefully address the computational challenges for inferencing over such semantically rich models by dynamically identifying sub-domains of interest and varying the precision of solutions over different subdomains. We demonstrate the breadth and generality of μSI using two seemingly disparate applications. In the context of social tagging service, we show how it can help improve the accuracy and freshness of resource recommendation; in the context of mobile phone call service, we show how it can help improve the efficiency of paging operation. Copyright © 2012 by the Society for Industrial and Applied Mathematics.