The Dynamics of Public Opinion in Complex Networks

This paper studies the problem of public opinion formation and concentrates on the interplays among three factors: individual attributes, environmental influences and information flow. We present a simple model to analyze the dynamics of four types of networks. Our simulations suggest that regular communities establish not only local consensus, but also global diversity in public opinions. However, when small world networks, random networks, or scale-free networks model social relationships, the results are sensitive to the elasticity coefficient of environmental influences and the average connectivity of the type of network. For example, a community with a higher average connectivity has a higher probability of consensus. Yet, it is misleading to predict results merely based on the characteristic path length of networks. In the process of changing environmental influences and average connectivity, sensitive areas are discovered in the system. By sensitive areas we mean that interior randomness emerges and we cannot predict unequivocally how many opinions will remain upon reaching equilibrium. We also investigate the role of authoritative individuals in information control. While enhancing average connectivity facilitates the diffusion of the authoritative opinion, it makes individuals subject to disturbance from non-authorities as well. Thus, a moderate average connectivity may be preferable because then the public will most likely form an opinion that is parallel with the authoritative one. In a community with a scale-free structure, the influence of authoritative individuals keeps constant with the change of the average connectivity. Provided that the influence of individuals is proportional to the number of their acquaintances, the smallest percentage of authorities is required for a controlled consensus in a scale free network. This study shows that the dynamics of public opinion varies from community to community due to the different degree of impressionability of people and the distinct social network structure of the community.Public Opinion, Complex Network, Consensus, Agent-Based Model

Feature selection with interactions in logistic regression models using multivariate synergies for a GWAS application

Abstract Background Genotype-phenotype association has been one of the long-standing problems in bioinformatics. Identifying both the marginal and epistatic effects among genetic markers, such as Single Nucleotide Polymorphisms (SNPs), has been extensively integrated in Genome-Wide Association Studies (GWAS) to help derive “causal” genetic risk factors and their interactions, which play critical roles in life and disease systems. Identifying “synergistic” interactions with respect to the outcome of interest can help accurate phenotypic prediction and understand the underlying mechanism of system behavior. Many statistical measures for estimating synergistic interactions have been proposed in the literature for such a purpose. However, except for empirical performance, there is still no theoretical analysis on the power and limitation of these synergistic interaction measures. Results In this paper, it is shown that the existing information-theoretic multivariate synergy depends on a small subset of the interaction parameters in the model, sometimes on only one interaction parameter. In addition, an adjusted version of multivariate synergy is proposed as a new measure to estimate the interactive effects, with experiments conducted over both simulated data sets and a real-world GWAS data set to show the effectiveness. Conclusions We provide rigorous theoretical analysis and empirical evidence on why the information-theoretic multivariate synergy helps with identifying genetic risk factors via synergistic interactions. We further establish the rigorous sample complexity analysis on detecting interactive effects, confirmed by both simulated and real-world data sets.https://deepblue.lib.umich.edu/bitstream/2027.42/142802/1/12864_2018_Article_4552.pd