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This paper is concerned with general spatially explicit versions of three stochastic models for the dynamics of money that have been introduced and studied numerically by statistical physicists: the uniform reshuffling model, the immediate…
We prove that for a set of communicating agents to compute the average of their initial positions (average consensus problem), the optimal topology of communication is given by a de Bruijn's graph. Consensus is then reached in a finitely…
We study statistical problems, such as planted clique, its variants, and sparse principal component analysis in the context of average-case communication complexity. Our motivation is to understand the statistical-computational trade-offs…
We include complex connectivity structures and heterogeneity in models of multilayer networks or multilayer hypergraphs growing by preferential attachment. We consider the most generic connectivity structure, where the probability of…
Traditional graph representations are insufficient for modelling real-world phenomena involving multi-entity interactions, such as collaborative projects or protein complexes, necessitating the use of hypergraphs. While hypergraphs preserve…
Interacting particle systems are known for their ability to generate large-scale self-organized structures from simple local interaction rules between each agent and its neighbors. In addition to studying their emergent behavior, a main…
This paper investigates mean field games and control on sparse networks. In the case of large expander graphs, the limit topologies are analyzed using the graphexon framework, which characterizes both dense network limits and sparse…
Social network extensions of Heider's balance theory have not always been consistent. Structural balance theory primarily focuses on graph partitioning, thereby assuming, homogeneity in balance-driven behavior of nodes. We present a general…
Large language models (LLMs) have recently shown strong potential in modeling relational structures. However, existing approaches remain fundamentally graph-centric: they focus on processing pairwise graph structures into tokens that LLMs…
We consider a class of optimal control problems that arise in connection with optimal advertising under uncertainty. Two main features appear in the model: a delay in the control variable driving the state dynamics; a mean-field term both…
Recent interest in the external validity of prediction models (i.e., the problem of different train and test distributions, known as dataset shift) has produced many methods for finding predictive distributions that are invariant to dataset…
In many real-world scenarios, experts must convey complex information with limited message capacity. This paper explores how the availability of messages influences an expert's persuasive ability. We develop a geometric representation of…
We study strategic games on weighted directed graphs, in which the payoff of a player is defined as the sum of the weights on the edges from players who chose the same strategy, augmented by a fixed non-negative integer bonus for picking a…
We introduce a simple time-triggered protocol to achieve communication-efficient non-Bayesian learning over a network. Specifically, we consider a scenario where a group of agents interact over a graph with the aim of discerning the true…
We develop a theory of combinatorial games that is appropriate for describing positions in Hex and other monotone set coloring games. We consider two natural conditions on such games: a game is monotone if all moves available to both…
We introduce and analyse a three-body consensus model (3CM) for non-linear consensus dynamics on hypergraphs. Our model incorporates reinforcing group effects, which can cause shifts in the average state of the system even in if the…
Hypergraphs that can depict interactions beyond pairwise edges have emerged as an appropriate representation for modeling polyadic relations in complex systems. With the recent surge of interest in researching hypergraphs, the centrality…
In the original (1961) Gilbert model of random geometric graphs, nodes are placed according to a Poisson point process, and links formed between those within a fixed range. Motivated by wireless ad-hoc networks "soft" or "probabilistic"…
Maker-Breaker games are played on a hypergraph $(X,\mathcal{F})$, where $\mathcal{F} \subseteq 2^X$ denotes the family of winning sets. Both players alternately claim a predefined amount of edges (called bias) from the board $X$, and Maker…
Contagion processes relying on the exposure to multiple sources are prevalent in social systems, and are effectively represented by hypergraphs. In this Letter, we derive a mean-field model that goes beyond node- and pair-based…