Related papers: Consensus and Voting on Large Graphs: An Applicati…
This paper is concerned with the probability of consensus in a multivariate, spatially explicit version of the Hegselmann-Krause model for the dynamics of opinions. Individuals are located on the vertices of a finite connected graph…
We study noise sensitivity of the consensus opinion of the voter model on finite graphs, with respect to noise affecting the initial opinions and noise affecting the dynamics. We prove that the final opinion is stable with respect to small…
This paper studies consensus problems for multi-agent systems defined on directed graphs where the consensus dynamics involves nonlinear and discontinuous functions. Sufficient conditions, involving the nonlinear functions and the topology…
Majority-vote model is a much-studied model for social opinion dynamics of two competing opinions. With the recent appreciation that our social network comprises a variety of different layers forming a multiplex network, a natural question…
We focus on an epidemiological model (the archetypical SIR system) defined on graphs and study the asymptotic behavior of the solutions as the number of vertices in the graph diverges. By relying on the theory of so called graphons we…
A paradigm that was successfully applied in the study of both pure and algorithmic problems in graph theory can be colloquially summarized as stating that "any graph is close to being the disjoint union of expanders". Our goal in this paper…
Switching between finitely many continuous-time autonomous steepest descent dynamics for convex functions is considered. Convergence of complete solutions to common minimizers of the convex functions, if such minimizers exist, is shown. The…
In the voter model, vertices of a graph (interpreted as voters) adopt one out of two opinions (0 and 1), and update their opinions at random times by copying the opinion of a neighbor chosen uniformly at random. This process is dual to a…
We describe a generalization of the voter model on complex networks that encompasses different sources of degree-related heterogeneity and that is amenable to direct analytical solution by applying the standard methods of heterogeneous…
We introduce a statistical mechanics formalism for the study of constrained graph evolution as a Markovian stochastic process, in analogy with that available for spin systems, deriving its basic properties and highlighting the role of the…
We study a simple random process in which vertices of a connected graph reach consensus through pairwise interactions. We compute outcome probabilities, which do not depend on the graph structure, and consider the expected time until a…
The notions of noise sensitivity and stability were recently extended for the voter model. In this model, the vertices of a graph have opinions that are updated by uniformly selecting edges. We further extend stability results to different…
We find evidence for a continuum limit of a particular causal set dynamics which depends on only a single ``coupling constant'' $p$ and is easy to simulate on a computer. The model in question is a stochastic process that can also be…
We present a general theoretical analysis of structured prediction with a series of new results. We give new data-dependent margin guarantees for structured prediction for a very wide family of loss functions and a general family of…
In this work, we propose a global model selection criterion to estimate the graph of conditional dependencies of a random vector based on a finite sample. By global criterion, we mean optimizing a function over the entire set of possible…
Consensus protocols play an important role in the study of distributed algorithms. In this paper, we study the effect of bias on two popular consensus protocols, namely, the {\em voter rule} and the {\em 2-choices rule} with binary…
In this paper we make use of graphon theory to study opinion dynamics on large undirected networks. The opinion dynamics models that we take into consideration allow for negative interactions between the individuals, i.e. competing entities…
Majority voting is one of the few black-box interventions that can improve a fixed stochastic predictor: repeated access can be cheaper than changing a high-capability model. Classical fixed-competence theory makes this intervention look…
This paper introduces some tools from graph theory and distributed consensus algorithms to construct an optimal, yet robust, hierarchical information sharing structure for large-scale decision making and control problems. The proposed…
Building upon the theory of graph limits and the Aldous-Hoover representation and inspired by Panchenko's work on asymptotic Gibbs measures (Annals of Probability 2013), we construct continuous embeddings of discrete probability…