KAC-RICE FORMULAS AND THE NUMBER OF SOLUTIONS OF PARAMETRIZED SYSTEMS OF POLYNOMIAL EQUATIONS

Research output: Contribution to journal › Journal article › Research › peer-review

Standard

KAC-RICE FORMULAS AND THE NUMBER OF SOLUTIONS OF PARAMETRIZED SYSTEMS OF POLYNOMIAL EQUATIONS. / Feliu, Elisenda; Sadeghimanesh, Amirhosein.

In: Mathematics of Computation, Vol. 91, No. 338, 2022, p. 2739-2769.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Feliu, E & Sadeghimanesh, A 2022, 'KAC-RICE FORMULAS AND THE NUMBER OF SOLUTIONS OF PARAMETRIZED SYSTEMS OF POLYNOMIAL EQUATIONS', Mathematics of Computation, vol. 91, no. 338, pp. 2739-2769. https://doi.org/10.1090/mcom/3760

APA

Feliu, E., & Sadeghimanesh, A. (2022). KAC-RICE FORMULAS AND THE NUMBER OF SOLUTIONS OF PARAMETRIZED SYSTEMS OF POLYNOMIAL EQUATIONS. Mathematics of Computation, 91(338), 2739-2769. https://doi.org/10.1090/mcom/3760

Vancouver

Feliu E, Sadeghimanesh A. KAC-RICE FORMULAS AND THE NUMBER OF SOLUTIONS OF PARAMETRIZED SYSTEMS OF POLYNOMIAL EQUATIONS. Mathematics of Computation. 2022;91(338):2739-2769. https://doi.org/10.1090/mcom/3760

Author

Feliu, Elisenda ; Sadeghimanesh, Amirhosein. / KAC-RICE FORMULAS AND THE NUMBER OF SOLUTIONS OF PARAMETRIZED SYSTEMS OF POLYNOMIAL EQUATIONS. In: Mathematics of Computation. 2022 ; Vol. 91, No. 338. pp. 2739-2769.

Bibtex

@article{1f6fae7e2f1640b4aba1cea1d62fc741,
title = "KAC-RICE FORMULAS AND THE NUMBER OF SOLUTIONS OF PARAMETRIZED SYSTEMS OF POLYNOMIAL EQUATIONS",
abstract = "Kac-Rice formulas express the expected number of elements a fiber of a random field has in terms of a multivariate integral. We consider here parametrized systems of polynomial equations that are linear in enough parameters, and provide a Kac-Rice formula for the expected number of solutions of the system when the parameters follow continuous distributions. Combined with Monte Carlo integration, we apply the formula to partition the parameter region according to the number of solutions or find a region in parameter space where the system has the maximal number of solutions. The motivation stems from the study of steady states of chemical reaction networks and gives new tools for the open problem of identifying the parameter region where the network has at least two positive steady states. We illustrate with numerous examples that our approach successfully handles a larger number of parameters than exact methods",
keywords = "Kac-Rice formula, Monte Carlo integration, multistationarity, parameter region, polynomial system",
author = "Elisenda Feliu and Amirhosein Sadeghimanesh",
note = "Publisher Copyright: {\textcopyright} 2022 American Mathematical Society",
year = "2022",
doi = "10.1090/mcom/3760",
language = "English",
volume = "91",
pages = "2739--2769",
journal = "Mathematics of Computation",
issn = "0025-5718",
publisher = "American Mathematical Society",
number = "338",

}

RIS

TY - JOUR

T1 - KAC-RICE FORMULAS AND THE NUMBER OF SOLUTIONS OF PARAMETRIZED SYSTEMS OF POLYNOMIAL EQUATIONS

AU - Feliu, Elisenda

AU - Sadeghimanesh, Amirhosein

N1 - Publisher Copyright: © 2022 American Mathematical Society

PY - 2022

Y1 - 2022

N2 - Kac-Rice formulas express the expected number of elements a fiber of a random field has in terms of a multivariate integral. We consider here parametrized systems of polynomial equations that are linear in enough parameters, and provide a Kac-Rice formula for the expected number of solutions of the system when the parameters follow continuous distributions. Combined with Monte Carlo integration, we apply the formula to partition the parameter region according to the number of solutions or find a region in parameter space where the system has the maximal number of solutions. The motivation stems from the study of steady states of chemical reaction networks and gives new tools for the open problem of identifying the parameter region where the network has at least two positive steady states. We illustrate with numerous examples that our approach successfully handles a larger number of parameters than exact methods

AB - Kac-Rice formulas express the expected number of elements a fiber of a random field has in terms of a multivariate integral. We consider here parametrized systems of polynomial equations that are linear in enough parameters, and provide a Kac-Rice formula for the expected number of solutions of the system when the parameters follow continuous distributions. Combined with Monte Carlo integration, we apply the formula to partition the parameter region according to the number of solutions or find a region in parameter space where the system has the maximal number of solutions. The motivation stems from the study of steady states of chemical reaction networks and gives new tools for the open problem of identifying the parameter region where the network has at least two positive steady states. We illustrate with numerous examples that our approach successfully handles a larger number of parameters than exact methods

KW - Kac-Rice formula

KW - Monte Carlo integration

KW - multistationarity

KW - parameter region

KW - polynomial system

U2 - 10.1090/mcom/3760

DO - 10.1090/mcom/3760

M3 - Journal article

AN - SCOPUS:85139238286

VL - 91

SP - 2739

EP - 2769

JO - Mathematics of Computation

JF - Mathematics of Computation

SN - 0025-5718

IS - 338

ER -

ID: 342674952