Tales told by coloured tangles

Tangle machines are a topologically inspired diagrammatic formalism to describe information flow in networks. This paper begins with an expository account of tangle machines motivated by the problem of describing `covariance intersection' fusion of Gaussian estimators in networks. It then gives two examples in which tangle machines tell stories of adiabatic quantum computations, and discusses learning tangle machines from data.Comment: 29 pages, 28 figures. Revised to be more self-containe