Diffusion of Information on Networked Lattices by Gossip

TL;DR

This paper introduces a novel asynchronous Laplacian for networked lattices, enabling data fusion and consensus across heterogeneous structures with proven convergence to stable distributions.

Contribution

It presents a new generalized Laplacian and gossip algorithm for lattice-valued data, extending traditional graph methods to complex, heterogeneous networks.

Findings

The gossip algorithm converges asymptotically to harmonic lattice distributions.

The method applies to lattice consensus, Kripke semantics, and threat detection.

The approach generalizes classical graph Laplacians to lattice-valued data.

Abstract

We study time-dependent dynamics on a network of order lattices, where structure-preserving lattice maps are used to fuse lattice-valued data over vertices and edges. The principal contribution is a novel asynchronous Laplacian, generalizing the usual graph Laplacian, adapted to a network of heterogeneous lattices. The resulting gossip algorithm is shown to converge asymptotically to stable "harmonic" distributions of lattice data. This general theorem is applicable to several general problems, including lattice-valued consensus, Kripke semantics, and threat detection, all using asynchronous local update rules.