Related papers: A Novel Analytical Method for Evolutionary Graph T…
The study of time-varying (dynamic) networks (graphs) is of fundamental importance for computer network analytics. Several methods have been proposed to detect the effect of significant structural changes in a time series of graphs. The…
Population structure and spatial heterogeneity are integral components of evolutionary dynamics, in general, and of evolution of cooperation, in particular. Structure can promote the emergence of cooperation in some populations and suppress…
Dynamic graphs provide a flexible data abstraction for modelling many sorts of real-world systems, such as transport, trade, and social networks. Graph neural networks (GNNs) are powerful tools allowing for different kinds of prediction and…
Graph combinatorial optimization problems are widely applicable and notoriously difficult to compute; for example, consider the traveling salesman or facility location problems. In this paper, we explore the feasibility of using…
Statistical inference for exponential-family models of random graphs with dependent edges is challenging. We stress the importance of additional structure and show that additional structure facilitates statistical inference. A simple…
The rate of biological evolution depends on the fixation probability and on the fixation time of new mutants. Intensive research has focused on identifying population structures that augment the fixation probability of advantageous mutants.…
Outstanding achievements of graph neural networks for spatiotemporal time series analysis show that relational constraints introduce an effective inductive bias into neural forecasting architectures. Often, however, the relational…
We reconsider the deterministic haploid mutation-selection equation with two types. This is an ordinary differential equation that describes the type distribution (forward in time) in a population of infinite size. This paper establishes…
We use the combination of ideas and results from the theory of graph limits and nonlinear evolution equations to provide a rigorous mathematical justification for taking continuum limit for certain nonlocally coupled networks and to extend…
Evolutionary game theory is a framework to formalize the evolution of collectives ("populations") of competing agents that are playing a game and, after every round, update their strategies to maximize individual payoffs. There are two…
Evolutionary graph theory is the study of evolutionary dynamics in structured populations. A well-known problem in evolutionary graph theory is that the spread of mutation (measured by fixation probability) is impacted by the graph type…
We study large fluctuations in evolutionary games belonging to the coordination and anti-coordination classes. The dynamics of these games, modeling cooperation dilemmas, is characterized by a coexistence fixed point separating two…
Deep generative models for graphs have exhibited promising performance in ever-increasing domains such as design of molecules (i.e, graph of atoms) and structure prediction of proteins (i.e., graph of amino acids). Existing work typically…
Many complex systems are composed of interacting parts, and the underlying laws are usually simple and universal. While graph neural networks provide a useful relational inductive bias for modeling such systems, generalization to new system…
We generalize the scattering transform to graphs and consequently construct a convolutional neural network on graphs. We show that under certain conditions, any feature generated by such a network is approximately invariant to permutations…
Graphical Gaussian models have proven to be useful tools for exploring network structures based on multivariate data. Applications to studies of gene expression have generated substantial interest in these models, and resulting recent…
We discuss a model for evolutionary game dynamics in a growing, network-structured population. In our model, new players can either make connections to random preexisting players or preferentially attach to those that have been successful…
Evolutionary algorithms based on modeling the statistical dependencies (interactions) between the variables have been proposed to solve a wide range of complex problems. These algorithms learn and sample probabilistic graphical models able…
A new mathematical model for evolutionary games on graphs is proposed to extend the classical replicator equation to finite populations of players organized on a network with generic topology. Classical results from game theory,…
Fixation probabilities are essential for characterizing stochastic evolutionary dynamics, but analytical results remain limited mainly to systems with two competing types. We develop a perturbative framework to compute fixation…