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

Physical Review. E
Gard SpreemannNils A Baas

Abstract

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.

References

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Citations

Aug 15, 2019·Network Neuroscience·Jean-Baptiste BardinKathryn Hess
Aug 20, 2021·Current Opinion in Neurobiology·Cole HurwitzMatthias H Hennig
Jan 14, 2022·Nature·Richard J GardnerEdvard I Moser

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