Markoff numbers, principal ideals and continued fraction expansions by Button, J

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. …”

2-BAND CONTINUED FRACTION CLUSTER APPROXIMATION FOR DISORDERED ALLOYS by Leung, W, Sherrington, D

An effective criterion for periodicity of $ \ell$-adic continued fractions by Capuano, L, Veneziano, F, Zannier, U

“…The theory of continued fractions has been generalized to $ \ell $-adic numbers by several authors and presents many differences with respect to the real case. …”

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. …”

On the Complexity of Computing Probabilistic Bisimilarity by Chen, D, van Breugel, F, Worrell, J

“…We also show that the discounted pseudometric is rational and can be computed exactly in polynomial time using the network simplex algorithm and the continued fraction algorithm. In the undiscounted case we show that the pseudometric is again rational and can be computed exactly in polynomial time using the ellipsoid algorithm. …”

Localization in quasiperiodic chains: a theory based on convergence of local propagators by Duthie, A, Roy, S, Logan, DE

“…Self-consistent theories at high orders are in fact shown to be conceptually connected to the theory based on continued fractions, and in practice converge to the same result. …”

Higher-rank Bohr sets and multiplicative diophantine approximation by Chow, S, Technau, N

“…Hitherto, this was only known on the plane, as previous approaches relied heavily on the theory of continued fractions. Using reduced successive minima in lieu of continued fractions, we develop the structural theory of Bohr sets of arbitrary rank, in the context of diophantine approximation. …”

Buoyancy-Driven Continuous SPLITT Fractionation: A New Technique for Separation of Microspheres by Storey, J, Douglas, P, Ligrani, P, Morten, K

“…A new method of Continuous Fractionation using a SPLITT cell is conceived, developed, and tested, and is demonstrated to be useful for separation of collections of particles with different sizes and densities. …”