Related papers: Coarse-graining Directed Networks with Ergodic Set…

This chapter discusses the interplay between structure and dynamics in complex networks. Given a particular network with an endowed dynamics, our goal is to find partitions aligned with the dynamical process acting on top of the network. We…

Algorithms and dynamics over networks often involve randomization, and randomization may result in oscillating dynamics which fail to converge in a deterministic sense. In this paper, we observe this undesired feature in three applications,…

We explore a systematic approach to studying the dynamics of evolving networks at a coarse-grained, system level. We emphasize the importance of finding good observables (network properties) in terms of which coarse grained models can be…

We study expanding circle maps interacting in a heterogeneous random network. Heterogeneity means that some nodes in the network are massively connected, while the remaining nodes are only poorly connected. We provide a probabilistic…

We study the diffusive transport of Markovian random walks on arbitrary networks with stochastic resetting to multiple nodes. We deduce analytical expressions for the stationary occupation probability and for the mean and global first…

We study the evolution of a random weighted network with complex nonlinear dynamics at each node, whose activity may cease as a result of interactions with other nodes. Starting from a knowledge of the micro-level behaviour at each node, we…

The characterization of the "most connected" nodes in static or slowly evolving complex networks has helped in understanding and predicting the behavior of social, biological, and technological networked systems, including their robustness…

Finding accurate reduced descriptions for large, complex, dynamically evolving networks is a crucial enabler to their simulation, analysis, and, ultimately, design. Here we propose and illustrate a systematic and powerful approach to…

Can evolving networks be inferred and modeled without directly observing their nodes and edges? In many applications, the edges of a dynamic network might not be observed, but one can observe the dynamics of stochastic cascading processes…

The concept of weak ergodicity breaking is defined and studied in the context of deterministic dynamics. We show that weak ergodicity breaking describes a weakly chaotic dynamical system: a nonlinear map which generates subdiffusion…

Our ability to uncover complex network structure and dynamics from data is fundamental to understanding and controlling collective dynamics in complex systems. Despite recent progress in this area, reconstructing networks with stochastic…

Dynamical systems often exhibit the emergence of long-lived coherent sets, which are regions in state space that keep their geometric integrity to a high extent and thus play an important role in transport. In this article, we provide a…

While routinely used in other areas of dynamics, image sets are ill-defined objects in general non-invertible measurable dynamics. We propose a way of consistently working with image sets of null-preserving (and hence, in particular, of…

The design of deep neural networks remains somewhat of an art rather than precise science. By tentatively adopting ergodic theory considerations on top of viewing the network as the time evolution of a dynamical system, with each layer…

Networks with a prescribed power-law scaling in the spectrum of the graph Laplacian can be generated by evolutionary optimization. The Laplacian spectrum encodes the dynamical behavior of many important processes. Here, the networks are…

We provide a framework for studying randomly coloured point sets in a locally compact, second-countable space on which a metrisable unimodular group acts continuously and properly. We first construct and describe an appropriate dynamical…

Motivated by microscopic traffic modeling, we analyze dynamical systems which have a piecewise linear concave dynamics not necessarily monotonic. We introduce a deterministic Petri net extension where edges may have negative weights. The…

Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…

Here we present the entropic dynamics formalism for networks. That is, a framework for the dynamics of graphs meant to represent a network derived from the principle of maximum entropy and the rate of transition is obtained taking into…

This study addresses the challenge of predicting network dynamics, such as forecasting disease spread in social networks or estimating species populations in predator-prey networks. Accurate predictions in large networks are difficult due…