Year: 2021
Type: article
Abstract: In this paper we consider the classical problem of computing linear extensions of a given poset which is well known to be a difficult problem. However, in our setting the elements of the poset are multivariate polynomials, and only a small “admissible” subset of these linear extensions, determined implicitly by the evaluation map, are of interest. This seemingly novel problem arises in the study of global dynamics of gene regulatory networks in which case the poset is a Boolean lattice. We provide an algorithm for solving this problem using linear programming for arbitrary partial orders of linear polynomials. This algorithm exploits this additional algebraic structure inherited from the polynomials to efficiently compute the admissible linear extensions. The biologically relevant problem involves multilinear polynomials, and we provide a construction for embedding it into an instance of the linear problem.
DOI: 10.1137/20m1343208
Authors: Shane Kepley, Konstantin Mischaikow, Lun Zhang
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: G2515541506, Collaborative Research: Revealing the Geometry of Spatio-temporal Chaos with Computational Topology: Theory, Numerics and Experiment, Tripods+X:Res: Collaborative Research: Identification of Gene Regulatory Network Function from Data, Collaborative Research: Computational and Data-Enabled Science and Engineering: Characterizing Dynamics of Particle-based Systems, G4713059963, G5270150132, G668241585, HDR TRIPODS: Data Science Principles of the Human-Machine Convergence, Needle in a haystack: effective search for dynamics across the space of networks
OpenAlex ID: W3175812291