Related papers: Lattice Theory in Multi-Agent Systems
Action-dependent field theories are systems where the Lagrangian or Hamiltonian depends on new variables that encode the action. They model a larger class of field theories, including non-conservative behavior, while maintaining a…
Spatial constraint systems (scs) are semantic structures for reasoning about spatial and epistemic information in concurrent systems. We develop the theory of scs to reason about the distributed information of potentially infinite groups.…
Autonomous systems typically leverage layered control architectures with a combination of discrete and continuous models operating at different timescales. As a result, layered systems form a new class of hybrid systems composed of systems…
A unified classification and analysis is presented of two dimensional Dirac operators of QCD-like theories in the continuum as well as in a naive lattice discretization. Thereby we consider the quenched theory in the strong coupling limit.…
We study a decentralized variant of stochastic approximation, a data-driven approach for finding the root of an operator under noisy measurements. A network of agents, each with its own operator and data observations, cooperatively find the…
We introduce the notions of multi-suprema and multi-infima for vector spaces equipped with a collection of wedges, generalizing the notions of suprema and infima in ordered vector spaces. Multi-lattices are vector spaces closed under…
Different from most existing distributed localization approaches in static networks where the agents in a network are static, this paper addresses the distributed localization problem in dynamic networks where the positions of the agents…
The transfer matrix in lattice field theory connects the covariant and the initial data frameworks; in spin foam models, it can be written as a composition of elementary cellular amplitudes/propagators. We present a framework for discrete…
Control of multi-agent systems via game theory is investigated. Assume a system level object is given, the utility functions for individual agents are designed to convert a multi-agent system into a potential game. First, for fixed…
In this paper, a discrete-time multi-agent system is presented which is formulated in terms of the delta operator. The proposed multi-agent system can unify discrete-time and continuous-time multi-agent systems. In a multi-agent network, in…
A topos theoretic generalisation of the category of sets allows for modelling spaces which vary according to time intervals. Persistent homology, or more generally, persistence is a central tool in topological data analysis, which examines…
A multi-agent model for individuals endowed with strategies and subject to diffusive effects is proposed. The microscopic state of each agent is described by a spatial position and a probability measure, interpreted as a mixed strategy,…
We study a simple but compelling model of $n$ interacting agents via time-dependent, unidirectional communication. The model finds wide application in a variety of fields including synchronization, swarming and distributed decision making.…
We provide a visual and intuitive introduction to effectively calculating in 2-groups along with explicit examples coming from non-abelian 1- and 2-form gauge theory. In particular, we utilize string diagrams, tools similar to tensor…
A lattice gauge theory with an action polynomial in independent field variables is considered. The link variables are described by unconstrained complex matrices instead of unitary ones. A mechanism which permits to switch off in the…
Complex-valued Laplacians have been shown to be powerful tools in the study of distributed coordination of multi-agent systems in the plane including formation shape control problems and set surrounding control problems. In this paper, we…
We study the variational solution of generic interacting fermionic lattice systems using fermionic Gaussian states and show that the process of "gaussification", leading to a nonlinear closed equation of motion for the covariance matrix, is…
We address the synchronization problem in open multi-agent systems (OMAS) containing both cooperative and antagonistic interactions. In these systems, agents can join or leave the network over time, and the interaction structure may evolve…
The intrinsic connection between lattice theory and topology is fairly well established, For instance, the collection of open subsets of a topological subspace always forms a distributive lattice. Persistent homology has been one of the…
We consider the lattice of all the weak factorization systems on a given finite lattice. We prove that it is semidistributive, trim and congruence uniform. We deduce a graph theoretical approach to the problem of enumerating transfer…