Related papers: Exploring the adaptive voter model dynamics with a…
We study a model for switching strategies in the Prisoner's Dilemma game on adaptive networks of player pairings that coevolve as players attempt to maximize their return. We use a node-based strategy model wherein each player follows one…
We study the dynamics of opinion formation in a heterogeneous voter model on a complete graph, in which each agent is endowed with an integer fitness parameter $k \ge 0$, in addition to its $+$ or $-$ opinion state. The evolution of the…
We present the partial evolutionary tensor neural networks (pETNNs), a novel framework for solving time-dependent partial differential equations with high accuracy and capable of handling high-dimensional problems. Our architecture…
Finding accurate solutions to partial differential equations (PDEs) is a crucial task in all scientific and engineering disciplines. It has recently been shown that machine learning methods can improve the solution accuracy by correcting…
We investigate a nonlinear version of coevolving voter models, in which node states and network structure update as a coupled stochastic dynamical process. Most prior work on coevolving voter models has focused on linear update rules with…
The symmetric exclusion process and the voter model are two interacting particle systems for which a dual finite particle system allows one to characterize its invariant measures. Adding spontaneous births and deaths to the two processes…
We introduce the incremental voter model (IVM), a discrete-opinion multi-agent system where agents undergo step-wise transitions biased by the opinion of a randomly selected persuader. Our incremental voter model comprises a large…
We propose a new method for spatio-temporal forecasting on arbitrarily distributed points. Assuming that the observed system follows an unknown partial differential equation, we derive a continuous-time model for the dynamics of the data…
Physical systems whose dynamics are governed by partial differential equations (PDEs) find applications in numerous fields, from engineering design to weather forecasting. The process of obtaining the solution from such PDEs may be…
We extract data-driven, intrinsic spatial coordinates from observations of the dynamics of large systems of coupled heterogeneous agents. These coordinates then serve as an emergent space in which to learn predictive models in the form of…
We consider a modification of the adaptive contact process which, interpreted in the context of opinion dynamics, breaks the symmetry of the coevolutionary voter model by assigning to each node type a different strategy to promote…
Social networks have become an inseparable part of human life and processing them in an efficient manner is a top priority in the study of networks. These networks are highly dynamic and they are growing incessantly. Inspired by the concept…
The modern machine learning methods allow one to obtain the data-driven models in various ways. However, the more complex the model is, the harder it is to interpret. In the paper, we describe the algorithm for the mathematical equations…
The analysis of network data has gained considerable interest in recent years. This also includes the analysis of large, high-dimensional networks with hundreds and thousands of nodes. While exponential random graph models serve as…
The Transformer architecture has revolutionized artificial intelligence, yet a principled theoretical understanding of its internal mechanisms remains elusive. This paper introduces a novel analytical framework that reconceptualizes the…
In many complex systems, states and interaction structure coevolve towards a dynamic equilibrium. For the adaptive contact process, we obtain approximate expressions for the degree distributions that characterize the interaction network in…
This study investigates adversarial attacks conducted to distort voter model dynamics in complex networks. Specifically, a simple adversarial attack method is proposed to hold the state of opinions of an individual closer to the target…
Neutral models aspire to explain biodiversity patterns in ecosystems where species difference can be neglected, as it might occur at a specific trophic level, and perfect symmetry is assumed between species. Voter-like models capture the…
In nonlinear voter models the transitions between two states depend in a nonlinear manner on the frequencies of these states in the neighborhood. We investigate the role of these nonlinearities on the global outcome of the dynamics for a…
The accurate numerical solution of partial differential equations is a central task in numerical analysis allowing to model a wide range of natural phenomena by employing specialized solvers depending on the scenario of application. Here,…