Related papers: Networks with many structural scales: a Renormaliz…

While scale-invariant modeling has substantially boosted the performance of visual recognition tasks, it remains largely under-explored in deep networks based image restoration. Naively applying those scale-invariant techniques (e.g.…

We demonstrate, both analytically and numerically, that learning dynamics of neural networks is generically attracted towards a self-organized critical state. The effect can be modeled with quartic interactions between non-trainable…

Structure entails function and thus a structural description of the brain will help to understand its function and may provide insights into many properties of brain systems, from their robustness and recovery from damage, to their dynamics…

We introduce a family of scale-invariant entropy statistics derived from logarithmically aggregated distance distributions of point processes, with prime numbers serving as a motivating example. The construction associates to each finite…

The structure of complex networks in previous research has been widely described as scale-free networks generated by the preferential attachment model. However, the preferential attachment model does not take into account the detailed…

Many complex systems in nature and society can be described in terms of networks capturing the intricate web of connections among the units they are made of. A key question is how to interpret the global organization of such networks as the…

Through the distinction between ``real'' and ``virtual'' links between the nodes of a graph, we develop a set of simple rules leading to scale-free networks with a tunable degree distribution exponent. Albeit sharing some similarities with…

We consider distributed consensus in networks where the agents have integrator dynamics of order two or higher ($n\ge 2$). We assume all feedback to be localized in the sense that each agent has a bounded number of neighbors and consider a…

We study the notion of approximate entropy within the framework of network theory. Approximate entropy is an uncertainty measure originally proposed in the context of dynamical systems and time series. We firstly define a purely structural…

Scale-free (SF) networks and small world networks have been found to occur in very diverse contexts. It is this striking universality which makes one look for widely applicable mechanisms which lead to the formation of such networks. In…

Spatial phenomena are subject to scale effects, but there are rarely studies addressing such effects on spatially embedded contact networks. There are two types of structure in these networks, network structure and spatial structure. The…

Real-life networks often encounter vertex dysfunctions, which are usually followed by recoveries after appropriate maintenances. In this paper we present our research on a model of scale-free networks whose vertices are regularly removed…

Interconnected networks describe the dynamics of important systems in a wide range such as biological systems and electrical power grids. Some important features of these systems were successfully studied and understood through simplified…

The origin of scale-free degree distributions in the context of networks is addressed through an analogous non-network model in which the node degree corresponds to the number of balls in a box and the rewiring of links to balls moving…

We propose a simple model that aims at describing, in a stylized manner, how local breakdowns due unbalances or congestion propagate in real dynamical networks. The model converges to a self-organized critical stationary state in which the…

Based on a rigorous extension of classical statistical mechanics to networks, we study a specific microscopic network Hamiltonian. The form of this Hamiltonian is derived from the assumption that individual nodes increase/decrease their…

This article presents a theory for constructing hierarchical networks in such a way that the networks are guaranteed to be provably scale covariant. We first present a general sufficiency argument for obtaining scale covariance, which holds…

Most Graph Neural Networks (GNNs) operate at the first-order scale, even though multi-scale representations are known to be crucial in domains such as image classification. In this work, we investigate whether GNNs can similarly benefit…

Many real-world complex systems such as social, biological, information as well as technological systems results of a decentralized and unplanned evolution which leads to a common structuration. Irrespective of their origin, these so-called…

Materials, at their essence, are networks defined by homogeneity: uniform bonds, fixed thicknesses, and discrete length scales. Mechanical metamaterials, while representing structurally more diverse microstructures, remain defined by the…