Asynchronous Diffusion of Data on Networked Lattices

04/01/2022

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by   Robert Ghrist, et al.

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We study time-dependent dynamics on a network of algebraic 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. This resulting asynchronous diffusion dynamics are 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.