Continued Fractions and Unique Factorization on Digraphs by Giscard, P, Thwaite, S, Jaksch, D

“…We show that the characteristic series of walks (paths) between any two vertices of any finite digraph or weighted digraph G is given by a universal continued fraction of finite depth involving the simple paths and simple cycles of G. …”

An Exact Formulation of the Time-Ordered Exponential using Path-Sums by Giscard, P, Lui, K, Thwaite, S, Jaksch, D

“…The path-sum formulation gives $\mathsf{OE}[\mathsf{H}]$ as a branched continued fraction of finite depth and breadth. The terms of the path-sum have an elementary interpretation as self-avoiding walks and self-avoiding polygons on a graph. …”

Exact Inference on Gaussian Graphical Models of Arbitrary Topology using Path-Sums by Giscard, P, Choo, Z, Thwaite, S, Jaksch, D

“…The path-sum formulation gives the covariance between each pair of variables as a branched continued fraction of finite depth and breadth. Our method originates from the closed-form resummation of infinite families of terms of the walk-sum representation of the covariance matrix. …”

Exact inference on Gaussian graphical models of arbitrary topology using path-sums by Giscard, P, Choo, Z, Thwaite, S, Jaksch, D

“…The path-sum formulation gives the covariance between each pair of variables as a branched continued fraction of finite depth and breadth. Our method originates from the closed-form resummation of infinite families of terms of the walk-sum representation of the covariance matrix. …”

A graph theoretic approach to matrix functions and quantum dynamics by Giscard, P

“…This yields a universal continued fraction representation for the formal series of all walks on digraphs. …”