Algebraic network reconstruction of discrete dynamical systems
Quantitative Methods
2022-12-07 v1 Algebraic Geometry
Molecular Networks
Abstract
We present a computational algebra solution to reverse engineering the network structure of discrete dynamical systems from data. We use monomial ideals to determine dependencies between variables that encode constraints on the possible wiring diagrams underlying the process generating the discrete-time, continuous-space data. Our work assumes that each variable is either monotone increasing or decreasing. We prove that with enough data, even in the presence of small noise, our method can reconstruct the correct unique wiring diagram.
Cite
@article{arxiv.2212.02601,
title = {Algebraic network reconstruction of discrete dynamical systems},
author = {Heather A. Harrington and Mike Stillman and Alan Veliz-Cuba},
journal= {arXiv preprint arXiv:2212.02601},
year = {2022}
}
Comments
19 pages, 5 figures