Related papers: Lattice Theory in Multi-Agent Systems
Local interaction laws governing multi-agent systems can be difficult to recover from trajectory data, even when the dynamics are observed faithfully. In systems governed by a nonlinear sheaf Laplacian -- a generalization of the graph…
Latent variable models for network data extract a summary of the relational structure underlying an observed network. The simplest possible models subdivide nodes of the network into clusters; the probability of a link between any two nodes…
We explore the relationship between lattice field theory and graph theory, placing special emphasis on the interplay between Dirac and scalar lattice operators and matrices within the realm of spectral graph theory. Beyond delving into…
This paper brings cooperative protocols for multi-agent systems with agents having a finite state-space. Both scalar single-integrator consensus and general LTI systems synchronization are considered. Systems having a finite state-space…
Denning's lattice model provided secure information flow analyses with an intuitive mathematical foundation: the lattice ordering determines permitted flows. We examine how this framework may be extended to support the flow of information…
We discuss how to formulate lattice gauge theories in the Tensor Network language. In this way we obtain both a consistent truncation scheme of the Kogut-Susskind lattice gauge theories and a Tensor Network variational ansatz for gauge…
This paper develops a control-theoretic framework for analyzing agentic systems embedded within feedback control loops, where an AI agent may adapt controller parameters, select among control strategies, invoke external tools, reconfigure…
The processing of signals on simplicial and cellular complexes defined by nodes, edges, and higher-order cells has recently emerged as a principled extension of graph signal processing for signals supported on more general topological…
In this work, we consider a multi-population system where the dynamics of each agent evolve according to a system of stochastic differential equations in a general functional setup, determined by the global state of the system. Each agent…
This paper presented insights into the implementation of transactive multi-agent systems over flow networks where local resources are decentralized. Agents have local resource demand and supply, and are interconnected through a flow network…
We construct and classify topological lattice field theories in three dimensions. After defining a general class of local lattice field theories, we impose invariance under arbitrary topology-preserving deformations of the underlying…
Motivated by the increasing interest in the explicit representation and handling of various "preference" structures arising in modern digital economy, this work introduces a new class of "one-to-many stable-matching" problems where a set of…
The theory of Monotone Comparative Statics (MCS) has traditionally required a lattice structure, excluding certain multidimensional environments such as mixed-strategy games where this property fails. We show that this structure is not…
A higher dimensional lattice space can be decomposed into a number of four-dimensional lattices called as layers. The higher dimensional gauge theory on the lattice can be interpreted as four-dimensional gauge theories on the multi-layer…
The paper addresses the synchronization of multi-agent systems with continuous-time dynamics interacting through a very general class of monotonic continuous signal functions that covers estimation biases, approximation of discrete…
In this article we introduce theory and algorithms for learning discrete representations that take on a lattice that is embedded in an Euclidean space. Lattice representations possess an interesting combination of properties: a) they can be…
This paper investigates multi-agent frequencybased patrolling of intersecting, circle graphs under conditions where graph nodes have non-uniform visitation requirements and agents have limited ability to communicate. The task is modeled as…
This paper presents a trust-based predictive multi-agent consensus protocol that analyses neighbours' anticipation data and makes coordination decisions. Agents in the network share their future predicted data over a finite look-ahead…
A concept of abstract inductive definition on a complete lattice is formulated and studied. As an application, a constructive and predicative version of Tarski's fixed point theorem is obtained.
Complex systems are characterized by multiple spatial and temporal scales. A natural framework to capture their multiscale nature is that of multilayer networks, where different layers represent distinct physical processes that often…