相关论文: Transient dynamics for sequence processing neural …

Many real networks are complex and have power-law vertex degree distribution, short diameter, and high clustering. We analyze the network model based on thresholding of the summed vertex weights, which belongs to the class of networks…

We model the evolution of the Internet at the Autonomous System level as a process of competition for users and adaptation of bandwidth capability. We find the exponent of the degree distribution as a simple function of the growth rates of…

Much attention has been devoted recently to the generalization puzzle in deep learning: large, deep networks can generalize well, but existing theories bounding generalization error are exceedingly loose, and thus cannot explain this…

Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…

We consider random networks whose dynamics is described by a rate equation, with transition rates $w_{nm}$ that form a symmetric matrix. The long time evolution of the system is characterized by a diffusion coefficient $D$. In one dimension…

Inspired by scientific collaboration networks, especially our empirical analysis of the network of econophysicists, an evolutionary model for weighted networks is proposed. Both degree-driven and weight-driven models are considered.…

We introduce a minimalistic model based on dynamic node deletion and node duplication with heterodimerisation. The model is intended to capture the essential features of the evolution of protein interaction networks. We derive an exact…

In this paper, we abstract a kind of stochastic processes from evolving processes of growing networks, this process is called growing network Markov chains. Thus the existence and the formulas of degree distribution are transformed to the…

Complex network theory crucially depends on the assumptions made about the degree distribution, while fitting degree distributions to network data is challenging, in particular for scale-free networks with power-law degrees. We present a…

We demonstrate that conventional artificial deep neural networks operating near the phase boundary of the signal propagation dynamics, also known as the edge of chaos, exhibit universal scaling laws of absorbing phase transitions in…

We investigate a growing network model that combines preferential and uniform attachment with two distinct mechanisms of edge deletion. In addition to the usual uniform probability edge deletion, we introduce a novel node-based rule in…

We define a class of growing networks in which new nodes are given a spatial position and are connected to existing nodes with a probability mechanism favoring short distances and high degrees. The competition of preferential attachment and…

We include complex connectivity structures and heterogeneity in models of multilayer networks or multilayer hypergraphs growing by preferential attachment. We consider the most generic connectivity structure, where the probability of…

This paper is a review dealing with the study of large size random recurrent neural networks. The connection weights are selected according to a probability law and it is possible to predict the network dynamics at a macroscopic scale using…

Metabolic networks are known to be scale free but the evolutionary origin of this structural property is not clearly understood. One way of studying the dynamical process is to compare the metabolic networks of species that have arisen at…

We study the synchronization transition in scale-free networks that display power-law asymptotic behaviors in their degree distributions. The critical coupling strength and the order-parameter critical exponent derived by the mean field…

We present a generic threshold model for the co-evolution of the structure of a network and the state of its nodes. We focus on regular directed networks and derive equations for the evolution of the system toward its absorbing state. It is…

Many real-world scale-free networks, such as neural networks and online communication networks, consist of a fixed number of nodes but exhibit dynamic edge fluctuations. However, traditional models frequently overlook scenarios where the…

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…

We present a general model for the growth of weighted networks in which the structural growth is coupled with the edges' weight dynamical evolution. The model is based on a simple weight-driven dynamics and a weights' reinforcement…