The paper “Point cloud continuation: extracting manifolds from observables of a dynamical system“, co-authored by Michael Henderson (IBM New York) and Imran Nasim (IBM England, Surrey), has been accepted for publication in the SIAM Journal of Applied Dynamical Systems (journal link here). In the numerical study of dynamical systems, there are applications where equations or good initial guesses are not available, and a data-driven approach based on a set of observations of the system is useful. These observations take the form of a cloud of points in phase space. The observations lie on a smooth manifold in several important situations like stable invariant manifolds, some attractors, and parts of bifurcation surfaces. The paper of Henderson & Nasim describes an algorithm, based on multiparameter continuation methods, for finding a smooth manifold from a cloud of points that samples the manifold. The finalform preprint is available on Researchgate (link here). The image below shows Figure 9 from the paper.