Package: topologyR 0.4.0

topologyR: Topological Connectivity Analysis for Numeric Data

Builds topologies on the vertex set of a graph from the closed neighbourhoods of its vertices, a closed-neighbourhood variant of the construction of Nada, El Atik and Atef (2018) <doi:10.1002/mma.4726>, and computes their connected components exactly through the specialization preorder, without enumerating the topology. For time series it builds the horizontal and natural visibility graphs (Luque et al., 2009, <doi:10.1103/PhysRevE.80.046103>; Lacasa et al., 2008, <doi:10.1073/pnas.0709247105>) at equally or unequally spaced instants, deciding the natural criterion exactly under IEEE 754 double arithmetic, and from their directed versions the forward and backward topologies, a bitopological space in the sense of Kelly (1963) <doi:10.1112/plms/s3-13.1.71>, together with the Alexandrov topology of reachability. Reading a series backwards, with its instants reflected, exchanges the two topologies, so the difference of their numbers of components changes sign.

Authors:José Mauricio Gómez Julián [aut, cre]