Related papers: Stochastic Minority on Graphs
Characterization of real-world complex systems increasingly involves the study of their topological structure using graph theory. Among global network properties, small-world property, consisting in existence of relatively short paths…
In this work and the supporting Parts II [2] and III [3], we provide a rather detailed analysis of the stability and performance of asynchronous strategies for solving distributed optimization and adaptation problems over networks. We…
Population structure can have a significant effect on evolution. For some systems with sufficient symmetry, analytic results can be derived within the mathematical framework of evolutionary graph theory which relate to the outcome of the…
In this paper, we study the effect of (a)synchronism on the dynamics of elementary cellular automata. Within the framework of our study, we choose five distinct update schemes, selected from the family of periodic update modes: parallel,…
We study the minority-opinion dynamics over a fully-connected network of $n$ nodes with binary opinions. Upon activation, a node receives a sample of opinions from a limited number of neighbors chosen uniformly at random. Each activated…
In majority dynamics, agents located at the vertices of an undirected simple graph update their binary opinions synchronously by adopting those of the majority of their neighbors. On infinite unimodular transitive graphs (e.g., Cayley…
It is well-known that the fundamental diagram in a realistic traffic system is featured by capacity drop. From a mesoscopic approach, we demonstrate that such a phenomenon is linked to the unique properties of stochastic noise, which, when…
Replacing conventional power sources by renewable sources in current power grids drastically alters their structure and functionality. The resulting grid will be far more decentralized with an distinctly different topology. Here we analyze…
Power grids are undergoing major changes from a few large producers to smart grids build upon renewable energies. Mathematical models for power grid dynamics have to be adapted to capture, when dynamic nodes can achieve synchronization to a…
Majority dynamics on a graph $G$ is a deterministic process such that every vertex updates its $\pm 1$-assignment according to the majority assignment on its neighbor simultaneously at each step. Benjamini, Chan, O'Donnel, Tamuz and Tan…
Randomly evolving systems composed by elements which interact among each other have always been of great interest in several scientific fields. This work deals with the synchronization phenomenon, that could be roughly defined as the…
We analyze networked heterogeneous nonlinear systems, with diffusive coupling and interconnected over a generic static directed graph. Due to the network's hetereogeneity, complete synchronization is impossible, in general, but an emergent…
Complexity of dynamical networks can arise not only from the complexity of the topological structure but also from the time evolution of the topology. In this paper, we study the synchronous motion of coupled maps in time-varying complex…
We study discrete dynamical systems through the topological concepts of limit set, which consists of all points that can be reached arbitrarily late, and asymptotic set, which consists of all adhering values of orbits. In particular, we…
We establish and generalise several bounds for various random walk quantities including the mixing time and the maximum hitting time. Unlike previous analyses, our derivations are based on rather intuitive notions of local expansion…
We study synchronization and consensus in a group of dynamical systems coupled via multiple directed networks. We show that even though the coupling in a single network may not be sufficient to synchronize the systems, combination of…
We study the dynamics of the Stochastic Sandpile Model on finite graphs, with two main results. First, we describe a procedure to exactly sample from the stationary distribution of the model in all connected finite graphs, extending a…
We consider 3-Majority, a probabilistic consensus dynamics on a complete graph with $n$ vertices, each vertex starting with one of $k$ initial opinions. At each discrete time step, a vertex $u$ is chosen uniformly at random. The selected…
The evolution of many stochastic systems is accurately described by random walks on graphs. We here explore the close connection between local steady-state fluctuations of random walks and the global structure of the underlying graph.…
Modularity is a very widely used measure of the level of clustering or community structure in networks. Here we consider a recent generalisation of the definition of modularity to temporal graphs, whose edge-sets change over discrete…