Related papers: Heterogeneous pair approximation for voter models …

We use the annealed formulation of complex networks to study the dynamical behavior of disease spreading on both static and adaptive networked systems. This unifying approach relies on the annealed adjacency matrix, representing one network…

We develop novel hierarchical reciprocal graphical models to infer gene networks from heterogeneous data. In the case of data that can be naturally divided into known groups, we propose to connect graphs by introducing a hierarchical prior…

Multistate dynamical processes on networks, where nodes can occupy one of a multitude of discrete states, are gaining widespread use because of their ability to recreate realistic, complex behaviour that cannot be adequately captured by…

The heterogeneity of the influence processes is an important feature of social systems: how we perceive social influence and how we influence other individuals is heavily influenced by our opinion and non-opinion attributes. The latter…

In mathematical models of epidemic diffusion on networks based upon systems of differential equations, it is convenient to use the Heterogeneous Mean Field approximation (HMF) because it allows to write one single equation for all nodes of…

Mean-field variational methods are widely used for approximate posterior inference in many probabilistic models. In a typical application, mean-field methods approximately compute the posterior with a coordinate-ascent optimization…

Since real-world objects and their interactions are often multi-modal and multi-typed, heterogeneous networks have been widely used as a more powerful, realistic, and generic superclass of traditional homogeneous networks (graphs).…

The voter model is a classical interacting particle system modelling how consensus is formed across a network. We analyse the time to consensus for the voter model when the underlying graph is a subcritical scale-free random graph.…

A network embedding is a representation of a large graph in a low-dimensional space, where vertices are modeled as vectors. The objective of a good embedding is to preserve the proximity between vertices in the original graph. This way,…

Much recent research activity has been devoted to empirical study and theoretical models of complex networks (random graphs) with three qualitative features: power-law degree distribution, local clustering of edges, and small diameter. We…

While network science has become an indispensable tool for studying complex systems, the conventional use of pairwise links often shows limitations in describing high-order interactions properly. Hypergraphs, where each edge can connect…

We address the problem of using observational data to estimate peer contagion effects, the influence of treatments applied to individuals in a network on the outcomes of their neighbors. A main challenge to such estimation is that homophily…

In this paper, we develop a graphical modeling framework for the inference of networks across multiple sample groups and data types. In medical studies, this setting arises whenever a set of subjects, which may be heterogeneous due to…

Many complex dynamical systems in the real world, including ecological, climate, financial, and power-grid systems, often show critical transitions, or tipping points, in which the system's dynamics suddenly transit into a qualitatively…

Mean-field analysis is an important tool for understanding dynamics on complex networks. However, surprisingly little attention has been paid to the question of whether mean-field predictions are accurate, and this is particularly true for…

Moment-closure approximations are an important tool in the analysis of the dynamics on both static and adaptive networks. Here, we provide a broad survey over different approximation schemes by applying each of them to the adaptive voter…

We analytically derive mean-field models for all-to-all coupled networks of heterogeneous, adapting, two-dimensional integrate and fire neurons. The class of models we consider includes the Izhikevich, adaptive exponential, and quartic…

We investigate systems of interacting stochastic differential equations with two kinds of heterogeneity: one originating from different weights of the linkages, and one concerning their asymptotic relevance when the system becomes large. To…

We study the family of network models derived by requiring the expected properties of a graph ensemble to match a given set of measurements of a real-world network, while maximizing the entropy of the ensemble. Models of this type play the…

We provide a general framework for analyzing degree correlations between nodes separated by more than one step (i.e., beyond nearest neighbors) in complex networks. One probability and four conditional probabilities are introduced to fully…