Using persistent homology to reveal hidden covariates in systems governed by the kinetic Ising model

We propose a method, based on persistent homology, to uncover topological properties of a priori unknown covariates in a system governed by the kinetic Ising model with time-varying external fields. As its starting point the method takes observations of the system under study, a list of suspected or...

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Bibliographic Details
Published inPhysical review. E Vol. 97; no. 3-1; p. 032313
Main Authors Spreemann, Gard, Dunn, Benjamin, Botnan, Magnus Bakke, Baas, Nils A
Format Journal Article
LanguageEnglish
Published United States 01.03.2018
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Summary:We propose a method, based on persistent homology, to uncover topological properties of a priori unknown covariates in a system governed by the kinetic Ising model with time-varying external fields. As its starting point the method takes observations of the system under study, a list of suspected or known covariates, and observations of those covariates. We infer away the contributions of the suspected or known covariates, after which persistent homology reveals topological information about unknown remaining covariates. Our motivating example system is the activity of neurons tuned to the covariates physical position and head direction, but the method is far more general.
ISSN:2470-0053
DOI:10.1103/PhysRevE.97.032313