Related papers: Critical fluctuations in spatial complex networks

If the behavior of a system with many degrees of freedom can be captured by a small number of collective variables, then plausibly there is an underlying mean-field theory. We show that simple versions of this idea fail to describe the…

This article studies the dynamics of the mean-field approximation of continuous random networks. These networks are stochastic integrodifferential equations driven by Gaussian noise. The kernels in the integral operators are realizations of…

In this work, we study the percolation transition and large deviation properties of generalized canonical network ensembles. This new type of random networks might have a very rich complex structure, including high heterogeneous degree…

Motivated by the empirical analysis of the air transportation system, we define a network model that includes geographical attributes along with topological and weight (traffic) properties. The introduction of geographical attributes is…

As a promising computational paradigm, occurrence of critical states in artificial and biological neural networks has attracted wide-spread attention. An often-made explicit or implicit assumption is that one single critical state is…

We consider a model for random hypergraphs with identifiability, an analogue of connectedness. This model has a phase transition in the proportion of identifiable vertices when the underlying random graph becomes critical. The phase…

Networked dynamical systems, i.e., systems of dynamical units coupled via nontrivial interaction topologies, constitute models of broad classes of complex systems, ranging from gene regulatory and metabolic circuits in our cells to…

The structure of real-world networks is usually difficult to characterize owing to the variation of topological scales, the nondyadic complex interactions, and the fluctuations in the network. We aim to address these problems by introducing…

We demonstrate that the susceptible-infected-susceptible (SIS) model on complex networks can have an inactive Griffiths phase characterized by a slow relaxation dynamics. It contrasts with the mean field theoretical prediction that the SIS…

We review the main tools which allow for the statistical characterization of weighted networks. We then present two case studies, the airline connection network and the scientific collaboration network, which are representative of critical…

In a series of two papers, we investigate the large deviations and asymptotic behavior of stochastic models of brain neural networks with random interaction coefficients. In this first paper, we take into account the spatial structure of…

A system defined by two coupled Ising models, with a bimodal random field acting in one of them, is investigated. The interactions among variables of each Ising system are infinite-ranged, a limit where mean field becomes exact. This model…

The study of the Ising model from a percolation perspective has played a significant role in the modern theory of critical phenomena. We consider the celebrated square-lattice Ising model and construct percolation clusters by placing bonds,…

In this article, the joint fluctuations of the extreme eigenvalues and eigenvectors of a large dimensional sample covariance matrix are analyzed when the associated population covariance matrix is a finite-rank perturbation of the identity…

We present a method to obtain the average and the typical value of the number of critical points of the empirical risk landscape for generalized linear estimation problems and variants. This represents a substantial extension of previous…

In social networks, bursts of activity often result from the imitative behavior between interacting agents. The Ising model, along with its variants in the social sciences, serves as a foundational framework to explain these phenomena…

Understanding the relationship between the heterogeneous structure of complex networks and cooperative phenomena occurring on them remains a key problem in network science. Mean-field theories of spin models on networks constitute a…

The distribution of fracture network is crucial to characterize the behaviors of flow field and solute transport, especially for enhanced geothermal systems, as fractures provide preferential flow paths. However, estimating the parameters…

We propose and analyze a model for phase transitions in an inhomogeneous fluid membrane, that couples local composition with curvature nonlinearly. For asymmetric membranes, our model shows generic non-Ising behavior and the ensuing phase…

Mean-field models of glasses that present a random first order transition exhibit highly non-trivial fluctuations. Building on previous studies that focused on the critical scaling regime, we here obtain a fully quantitative framework for…