Target set selection in social networks with tiered influence and activation thresholds

Thanks to the mass adoption of internet and mobile devices, users of the social media can seamlessly and spontaneously connect with their friends, followers and followees. Consequently, social media networks have gradually become the major venue for broadcasting and relaying information, and is casting great influences on the people in many aspects of their daily lives. Thus locating those influential users in social media has become crucially important for the successes of many viral marketing, cyber security, politics, and safety-related applications. In this study, we address the problem through solving the tiered influence and activation thresholds target set selection problem, which is to find the seed nodes that can influence the most users within a limited time frame. Both the minimum influential seeds and maximum influence within budget problems are considered in this study. Besides, this study proposes several models exploiting different requirements on seed nodes selection, such as maximum activation, early activation and dynamic threshold. These time-indexed integer program models suffer from the computational difficulties due to the large numbers of binary variables to model influence actions at each time epoch. To address this challenge, this paper designs and leverages several efficient algorithms, i.e., Graph Partition, Nodes Selection, Greedy algorithm, recursive threshold back algorithm and two-stage approach in time, especially for large-scale networks. Computational results show that it is beneficial to apply either the breadth first search or depth first search greedy algorithms for the large instances. In addition, algorithms based on node selection methods perform better in the long-tailed networks.

Influence maximization in social media networks concerning dynamic user behaviors via reinforcement learning

This study examines the influence maximization (IM) problem via information cascades within random graphs, the topology of which dynamically changes due to the uncertainty of user behavior. This study leverages the discrete choice model (DCM) to calculate the probabilities of the existence of the directed arc between any two nodes. In this IM problem, the DCM provides a good description and prediction of user behavior in terms of following or not following a neighboring user. To find the maximal influence at the end of a finite-time horizon, this study models the IM problem by using multistage stochastic programming, which can help a decision-maker to select the optimal seed nodes by which to broadcast messages efficiently. Since computational complexity grows exponentially with network size and time horizon, the original model is not solvable within a reasonable time. This study then uses two different approaches by which to approximate the optimal decision: myopic two-stage stochastic programming and reinforcement learning via the Markov decision process. Computational experiments show that the reinforcement learning method outperforms the myopic two-stage stochastic programming method.

Influence network design via multi-level optimization considering boundedly rational user behaviours in social media networks

Social media networks have been playing an increasingly more important role for both socialization and information diffusion. Political campaign can gain more supporters by attracting more mass attention and influencing them directly, while commercial campaigns can increase their companies’ profits by expanding social media connection with new users. To build the optimal network structure to influence the whole, this paper studies mathematical models to simulate the users’ behaviours interacting with others in the information provider’s network. The behaviours of concerns include information re-posting and following/unfollowing other users. Linear threshold propagation model is used to determine the re-posting actions, Boundedly Rational User Equilibrium (BRUE) models are used to determine the following or unfollowing actions. Hence, the topology of the network changes and depends on the information provider’s plan to post various kinds of information. A three-level optimization model is proposed to maximize total number of connections, the goal of the top level. The second level simulates user behaviours under BRUE. The third level maximizes the each user’s utility defined in the second level. This paper solves this problem using exact algorithms for a small-scale synthetic network. For a large-scale problem, this paper uses heuristic algorithms based on large neighbourhood search. This paper also discusses possible reasons why the BRUE model may be a more accurate simulation of users’ actions compared to game theory. Comparisons from the BRUE model to game theoretical model show that the BRUE model performs significantly better than game theoretical model.

Network-based indices of individual and collective advising impacts in mathematics

Advising and mentoring Ph.D. students is an increasingly important aspect of the academic profession. We define and interpret a family of metrics (collectively referred to as “a-indices”) that can potentially be applied to “ranking academic advisors” using the academic genealogical records of scientists, with the emphasis on taking into account not only the number of students advised by an individual, but also subsequent academic advising records of those students. We also define and calculate the extensions of the proposed indices that account for student co-advising (referred to as “adjusted a-indices”). In addition, we extend some of the proposed metrics to ranking universities and countries with respect to their “collective” advising impacts, as well as track the evolution of these metrics over the past several decades. To illustrate the proposed metrics, we consider the social network of over 200,000 mathematicians (as of July 2018) constructed using the Mathematics Genealogy Project data.