Dimension and degeneracy of solutions of parametric polynomial systems arising from reaction networks

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Dimension and degeneracy of solutions of parametric polynomial systems arising from reaction networks. / Feliu, Elisenda; Henriksson, Oskar; Pascual-Escudero, Beatriz.

arXiv preprint, 2023.

Research output: Working paper › Preprint › Research

Harvard

Feliu, E, Henriksson, O & Pascual-Escudero, B 2023 'Dimension and degeneracy of solutions of parametric polynomial systems arising from reaction networks' arXiv preprint.

APA

Feliu, E., Henriksson, O., & Pascual-Escudero, B. (2023). Dimension and degeneracy of solutions of parametric polynomial systems arising from reaction networks. arXiv preprint.

Vancouver

Feliu E, Henriksson O, Pascual-Escudero B. Dimension and degeneracy of solutions of parametric polynomial systems arising from reaction networks. arXiv preprint. 2023 Apr 5.

Author

Feliu, Elisenda ; Henriksson, Oskar ; Pascual-Escudero, Beatriz. / Dimension and degeneracy of solutions of parametric polynomial systems arising from reaction networks. arXiv preprint, 2023.

Bibtex

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title = "Dimension and degeneracy of solutions of parametric polynomial systems arising from reaction networks",
abstract = "We study the generic dimension of the solution set over C^*, R^* and R_{>0} of parametric polynomial systems that consist of linear combinations of monomials scaled by free parameters. We establish a relation between this dimension, Zariski denseness of the set of parameters for which the system has solutions, and the existence of nondegenerate solutions, which enables fast dimension computations. Systems of this form are used to describe the steady states of reaction networks modeled with mass-action kinetics, and as a corollary of our results, we prove that weakly reversible networks have finitely many steady states for generic reaction rate constants and total concentrations.",
keywords = "math.AG, q-bio.MN, q-bio.QM",
author = "Elisenda Feliu and Oskar Henriksson and Beatriz Pascual-Escudero",
year = "2023",
month = apr,
day = "5",
language = "English",
publisher = "arXiv preprint",
type = "WorkingPaper",
institution = "arXiv preprint",

}

RIS

TY - UNPB

T1 - Dimension and degeneracy of solutions of parametric polynomial systems arising from reaction networks

AU - Feliu, Elisenda

AU - Henriksson, Oskar

AU - Pascual-Escudero, Beatriz

PY - 2023/4/5

Y1 - 2023/4/5

N2 - We study the generic dimension of the solution set over C^*, R^* and R_{>0} of parametric polynomial systems that consist of linear combinations of monomials scaled by free parameters. We establish a relation between this dimension, Zariski denseness of the set of parameters for which the system has solutions, and the existence of nondegenerate solutions, which enables fast dimension computations. Systems of this form are used to describe the steady states of reaction networks modeled with mass-action kinetics, and as a corollary of our results, we prove that weakly reversible networks have finitely many steady states for generic reaction rate constants and total concentrations.

AB - We study the generic dimension of the solution set over C^*, R^* and R_{>0} of parametric polynomial systems that consist of linear combinations of monomials scaled by free parameters. We establish a relation between this dimension, Zariski denseness of the set of parameters for which the system has solutions, and the existence of nondegenerate solutions, which enables fast dimension computations. Systems of this form are used to describe the steady states of reaction networks modeled with mass-action kinetics, and as a corollary of our results, we prove that weakly reversible networks have finitely many steady states for generic reaction rate constants and total concentrations.

KW - math.AG

KW - q-bio.MN

KW - q-bio.QM

M3 - Preprint

BT - Dimension and degeneracy of solutions of parametric polynomial systems arising from reaction networks

PB - arXiv preprint

ER -

ID: 343132299