ADVERTISEMENT ALLOCATION AND TRUST MECHANISMS DESIGN IN SOCIAL NETWORKS

Social network sites (SNS), such as Facebook, Google+ and Twitter, have attracted hundreds of millions of users daily since their appearance. Within SNS, users connect to each other, express their identity, disseminate information and form cooperation by interacting with their connected peers. The increasing popularity and ubiquity of SNS usage and the invaluable user behaviors and connections give birth to many applications and business models. We look into several important problems within the social network ecosystem. The first one is the SNS advertisement allocation problem. The other two are related to trust mechanisms design in social network setting, including local trust inference and global trust evaluation. In SNS advertising, we study the problem of advertisement allocation from the ad platform's angle, and discuss its differences with the advertising model in the search engine setting. By leveraging the connection between social networks and hyperbolic geometry, we propose to solve the problem via approximation using hyperbolic embedding and convex optimization. A hyperbolic embedding method, \hcm, is designed for the SNS ad allocation problem, and several components are introduced to realize the optimization formulation. We show the advantages of our new approach in solving the problem compared to the baseline integer programming (IP) formulation. In studying the problem of trust mechanisms in social networks, we consider the existence of distrust (i.e. negative trust) relationships, and differentiate between the concept of local trust and global trust in social network setting. In the problem of local trust inference, we propose a 2-D trust model. Based on the model, we develop a semiring-based trust inference framework. In global trust evaluation, we consider a general setting with conflicting opinions, and propose a consensus-based approach to solve the complex problem in signed trust networks.

Phase transitions in gene networks evolved under different selection rules

Mathematical models of gene regulation are a powerful tool for understanding the complex features of genetic control. While various modeling efforts have been successful at explaining gene expression dynamics, much less is known about how evolution shapes the structure of these networks. An important feature of gene regulatory networks is their stability in response to environmental perturbations. Regulatory systems are thought to have evolved to exist near the transition between stability and instability, in order to have the required stability to environmental fluctuations while also being able to achieve a wide variety of functions (corresponding to different dynamical patterns). We study a simplified model of gene network evolution in which links are added via different selection rules. These growth models are inspired by recent work on `explosive' percolation which shows that when network links are added through competitive rather than random processes, the connectivity phase transition can be significantly delayed, and when it is reached, it appears to be first order (discontinuous, e.g., going from no failure at all to large expected failure) instead of second order (continuous, e.g., going from no failure at all to very small expected failure). We find that by modifying the traditional framework for networks grown via competitive link addition to capture how gene networks evolve to avoid damage propagation, we also see significant delays in the transition that depend on the selection rules, but the transitions always appear continuous rather than `explosive'.