Related papers: Message passing and cyclicity transition
Message passing techniques on networks encompasses a family of related methods that can be employed to ascertain many important properties of a network. It is widely considered to be the state of the art formulation for networked systems…
Multiplex networks describe a large variety of complex systems including infrastructures, transportation networks and biological systems. Most of these networks feature a significant link overlap. It is therefore of particular importance to…
Networks and network computations have become a primary mathematical tool for analyzing the structure of many kinds of complex systems, ranging from the Internet and transportation networks to biochemical interactions and social networks. A…
It is well known that tree-based theories can describe the properties of undirected clustered networks with extremely accurate results [S. Melnik, \textit{et al}. Phys. Rev. E 83, 036112 (2011)]. It is reasonable to suggest that a motif…
Hypergraph networks are closer to real life because they can reflect higher-order interactions, so researchers have begun using them to build models for real-world networks. The mean-field approach is the current tool for studying the…
Percolation in complex networks is viewed as both: a process that mimics network degradation and a tool that reveals peculiarities of the underlying network structure. During the course of percolation, networks undergo non-trivial…
The interaction among spreading processes on a complex network is a nontrivial phenomenon of great importance. It has recently been realized that cooperative effects among infective diseases can give rise to qualitative changes in the…
Belief propagation is a widely used message passing method for the solution of probabilistic models on networks such as epidemic models, spin models, and Bayesian graphical models, but it suffers from the serious shortcoming that it works…
Percolation is a model for random damage to a network. It is one of the simplest models that displays a phase transition: when the network is severely damaged, it falls apart in many small connected components, while if the damage is light,…
In this paper we offer a solution to a long-standing problem in the study of networks. Message passing is a fundamental technique for calculations on networks and graphs. The first versions of the method appeared in the 1930s and over the…
Belief Propagation (BP) is an efficient message-passing algorithm widely used for inference in graphical models and for solving various problems in statistical physics. However, BP often yields inaccurate estimates of order parameters and…
During the past two decades, percolation has long served as a basic paradigm for network resilience, community formation and so on in complex systems. While the percolation transition is known as one of the most robust continuous…
The Message-Passing Approach (MPA) is the state-of-the-art technique to obtain quasi-analytical predictions for percolation on real complex networks. Besides being intuitive and straightforward, it has the advantage of being mathematically…
Recently increasing attention has been addressed to the fluctuations observed in percolation defined in single and multiplex networks. These fluctuations are extremely important to characterize the robustness of real finite networks but…
Graphical models use the intuitive and well-studied methods of graph theory to implicitly represent dependencies between variables in large systems. They can model the global behaviour of a complex system by specifying only local factors.…
Probabilistic graphical models are a powerful concept for modeling high-dimensional distributions. Besides modeling distributions, probabilistic graphical models also provide an elegant framework for performing statistical inference;…
Motivation: In the last few years a growing interest in biology has been shifting towards the problem of optimal information extraction from the huge amount of data generated via large scale and high-throughput techniques. One of the most…
For a setting in which a large number of asymmetrically informed agents are randomly matched into groups over time, exchanging their information with each other when matched, we provide an explicit solution for the dynamics of the…
The stochastic addition of either vertices or connections in a network leads to the observation of the percolation transition, a structural change with the appearance of a connected component encompassing a finite fraction of the system.…
We present new message passing algorithms for performing inference with graphical models. Our methods are designed for the most difficult inference problems where loopy belief propagation and other heuristics fail to converge. Belief…