Related papers: Renormalization flows in complex networks
The discovery of small world and scale free properties of many real world networks has revolutionized the way we study, analyze, model and process networks. An important way to analyze these complex networks is to visualize them using graph…
As the deep neural networks are being applied to complex tasks, the size of the networks and architecture increases and their topology becomes more complicated too. At the same time, training becomes slow and at some instances inefficient.…
The era of data deluge has sparked the interest in graph-based learning methods in a number of disciplines such as sociology, biology, neuroscience, or engineering. In this paper, we introduce a graph recurrent neural network (GRNN) for…
We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant…
Physicists study a wide variety of phenomena creating new interdisciplinary research fields by applying theories and methods originally developed in physics in order to solve problems in economics, social science, biology, medicine,…
Understanding the structure and dynamics of biological networks is one of the important challenges in system biology. In addition, increasing amount of experimental data in biological networks necessitate the use of efficient methods to…
Multiplex networks are collections of networks with identical nodes but distinct layers of edges. They are genuine representations for a large variety of real systems whose elements interact in multiple fashions or flavors. However,…
Despite huge successes on a wide range of tasks, neural networks are known to sometimes struggle to generalise to unseen data. Many approaches have been proposed over the years to promote the generalisation ability of neural networks,…
Renormalization is a powerful technique in statistical physics to extract the large-scale behavior of interacting many-body models. These notes aim to give an introduction to perturbative methods that operate on the level of the stochastic…
Network sampling is integral to the analysis of social, information, and biological networks. Since many real-world networks are massive in size, continuously evolving, and/or distributed in nature, the network structure is often sampled in…
A network is a typical expressive form of representing complex systems in terms of vertices and links, in which the pattern of interactions amongst components of the network is intricate. The network can be static that does not change over…
The robustness of complex networks was one of the first phenomena studied after the inception of network science. However, many contemporary presentations of this theory do not go beyond the original papers. Here we revisit this topic with…
Many dynamical processes of complex systems can be understood as the dynamics of a group of nodes interacting on a given network structure. However, finding such interaction structure and node dynamics from time series of node behaviours is…
The results of the renormalization group are commonly advertised as the existence of power law singularities near critical points. The classic predictions are often violated and logarithmic and exponential corrections are treated on a…
The network structure (or topology) of a dynamical network is often unavailable or uncertain. Hence, we consider the problem of network reconstruction. Network reconstruction aims at inferring the topology of a dynamical network using…
We explain how to use diffusion models to learn inverse renormalization group flows of statistical and quantum field theories. Diffusion models are a class of machine learning models which have been used to generate samples from complex…
The success of new scientific areas can be assessed by their potential for contributing to new theoretical approaches and in applications to real-world problems. Complex networks have fared extremely well in both of these aspects, with…
We propose a renormalization group treatment of stochastically growing networks. As an example, we study percolation on growing scale-free networks in the framework of a real-space renormalization group approach. As a result, we find that…
This chapter aims at reviewing complex networks models and methods that were either developed for or applied to socioeconomic issues, and pertinent to the theme of New Economic Geography. After an introduction to the foundations of the…
The behavior of complex systems is determined not only by the topological organization of their interconnections but also by the dynamical processes taking place among their constituents. A faithful modeling of the dynamics is essential…