Mean-field theory for scale-free random networks

Random networks with complex topology are common in Nature, describing systems as diverse as the world wide web or social and business networks. Recently, it has been demonstrated that most large networks for which topological information is available display scale-free features. Here we study the scaling properties of the recently introduced scale-free model, that can account for the observed power-law distribution of the connectivities. We develop a mean-field method to predict the growth dynamics of the individual vertices, and use this to calculate analytically the connectivity distribution and the scaling exponents. The mean-field method can be used to address the properties of two variants of the scale-free model, that do not display power-law scaling.Comment: 19 pages, 6 figure

Non-Coding RNAs Improve the Predictive Power of Network Medicine

Network Medicine has improved the mechanistic understanding of disease, offering quantitative insights into disease mechanisms, comorbidities, and novel diagnostic tools and therapeutic treatments. Yet, most network-based approaches rely on a comprehensive map of protein-protein interactions, ignoring interactions mediated by non-coding RNAs (ncRNAs). Here, we systematically combine experimentally confirmed binding interactions mediated by ncRNA with protein-protein interactions, constructing the first comprehensive network of all physical interactions in the human cell. We find that the inclusion of ncRNA, expands the number of genes in the interactome by 46% and the number of interactions by 107%, significantly enhancing our ability to identify disease modules. Indeed, we find that 132 diseases, lacked a statistically significant disease module in the protein-based interactome, but have a statistically significant disease module after inclusion of ncRNA-mediated interactions, making these diseases accessible to the tools of network medicine. We show that the inclusion of ncRNAs helps unveil disease-disease relationships that were not detectable before and expands our ability to predict comorbidity patterns between diseases. Taken together, we find that including non-coding interactions improves both the breath and the predictive accuracy of network medicine.Comment: Paper and S

Modeling and Predicting Popularity Dynamics via Reinforced Poisson Processes

An ability to predict the popularity dynamics of individual items within a complex evolving system has important implications in an array of areas. Here we propose a generative probabilistic framework using a reinforced Poisson process to model explicitly the process through which individual items gain their popularity. This model distinguishes itself from existing models via its capability of modeling the arrival process of popularity and its remarkable power at predicting the popularity of individual items. It possesses the flexibility of applying Bayesian treatment to further improve the predictive power using a conjugate prior. Extensive experiments on a longitudinal citation dataset demonstrate that this model consistently outperforms existing popularity prediction methods.Comment: 8 pages, 5 figure; 3 table