Sign Conditions for Injectivity of Generalized Polynomial Maps with Applications to Chemical Reaction Networks and Real Algebraic Geometry

We give necessary and sufficient conditions in terms of sign vectors for the injectivity of families of polynomial maps with arbitrary real exponents defined on the positive orthant. Our work relates and extends existing injectivity conditions expressed in terms of Jacobian matrices and determinants...

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Autores principales: Müller, S., Feliu, E., Regensburger, G., Conradi, C., Shiu, A., Dickenstein, A.
Formato: JOUR
Materias:
Descartes’ rule of signs
Oriented matroid
Power-law kinetics
Restricted injectivity
Sign vector
Algebra
Chemical reactions
Geometry
Jacobian matrices
Reaction kinetics
Descartes
Injectivity
Sign vectors
Polynomials
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_16153375_v16_n1_p69_Muller
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_16153375_v16_n1_p69_Muller2023-10-03T16:28:14Z Sign Conditions for Injectivity of Generalized Polynomial Maps with Applications to Chemical Reaction Networks and Real Algebraic Geometry Müller, S. Feliu, E. Regensburger, G. Conradi, C. Shiu, A. Dickenstein, A. Descartes’ rule of signs Oriented matroid Power-law kinetics Restricted injectivity Sign vector Algebra Chemical reactions Geometry Jacobian matrices Reaction kinetics Descartes Injectivity Oriented matroid Power-law kinetics Sign vectors Polynomials We give necessary and sufficient conditions in terms of sign vectors for the injectivity of families of polynomial maps with arbitrary real exponents defined on the positive orthant. Our work relates and extends existing injectivity conditions expressed in terms of Jacobian matrices and determinants. In the context of chemical reaction networks with power-law kinetics, our results can be used to preclude as well as to guarantee multiple positive steady states. In the context of real algebraic geometry, our work recognizes a prior result of Craciun, Garcia-Puente, and Sottile, together with work of two of the authors, as the first partial multivariate generalization of the classical Descartes’ rule, which bounds the number of positive real roots of a univariate real polynomial in terms of the number of sign variations of its coefficients. © 2015, SFoCM. Fil:Dickenstein, A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_16153375_v16_n1_p69_Muller
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Descartes’ rule of signs
Oriented matroid
Power-law kinetics
Restricted injectivity
Sign vector
Algebra
Chemical reactions
Geometry
Jacobian matrices
Reaction kinetics
Descartes
Injectivity
Oriented matroid
Power-law kinetics
Sign vectors
Polynomials
spellingShingle Descartes’ rule of signs
Oriented matroid
Power-law kinetics
Restricted injectivity
Sign vector
Algebra
Chemical reactions
Geometry
Jacobian matrices
Reaction kinetics
Descartes
Injectivity
Oriented matroid
Power-law kinetics
Sign vectors
Polynomials
Müller, S.
Feliu, E.
Regensburger, G.
Conradi, C.
Shiu, A.
Dickenstein, A.
Sign Conditions for Injectivity of Generalized Polynomial Maps with Applications to Chemical Reaction Networks and Real Algebraic Geometry
topic_facet Descartes’ rule of signs
Oriented matroid
Power-law kinetics
Restricted injectivity
Sign vector
Algebra
Chemical reactions
Geometry
Jacobian matrices
Reaction kinetics
Descartes
Injectivity
Oriented matroid
Power-law kinetics
Sign vectors
Polynomials
description We give necessary and sufficient conditions in terms of sign vectors for the injectivity of families of polynomial maps with arbitrary real exponents defined on the positive orthant. Our work relates and extends existing injectivity conditions expressed in terms of Jacobian matrices and determinants. In the context of chemical reaction networks with power-law kinetics, our results can be used to preclude as well as to guarantee multiple positive steady states. In the context of real algebraic geometry, our work recognizes a prior result of Craciun, Garcia-Puente, and Sottile, together with work of two of the authors, as the first partial multivariate generalization of the classical Descartes’ rule, which bounds the number of positive real roots of a univariate real polynomial in terms of the number of sign variations of its coefficients. © 2015, SFoCM.
format JOUR
author Müller, S.
Feliu, E.
Regensburger, G.
Conradi, C.
Shiu, A.
Dickenstein, A.
author_facet Müller, S.
Feliu, E.
Regensburger, G.
Conradi, C.
Shiu, A.
Dickenstein, A.
author_sort Müller, S.
title Sign Conditions for Injectivity of Generalized Polynomial Maps with Applications to Chemical Reaction Networks and Real Algebraic Geometry
title_short Sign Conditions for Injectivity of Generalized Polynomial Maps with Applications to Chemical Reaction Networks and Real Algebraic Geometry
title_full Sign Conditions for Injectivity of Generalized Polynomial Maps with Applications to Chemical Reaction Networks and Real Algebraic Geometry
title_fullStr Sign Conditions for Injectivity of Generalized Polynomial Maps with Applications to Chemical Reaction Networks and Real Algebraic Geometry
title_full_unstemmed Sign Conditions for Injectivity of Generalized Polynomial Maps with Applications to Chemical Reaction Networks and Real Algebraic Geometry
title_sort sign conditions for injectivity of generalized polynomial maps with applications to chemical reaction networks and real algebraic geometry
url http://hdl.handle.net/20.500.12110/paper_16153375_v16_n1_p69_Muller
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AT regensburgerg signconditionsforinjectivityofgeneralizedpolynomialmapswithapplicationstochemicalreactionnetworksandrealalgebraicgeometry
AT conradic signconditionsforinjectivityofgeneralizedpolynomialmapswithapplicationstochemicalreactionnetworksandrealalgebraicgeometry
AT shiua signconditionsforinjectivityofgeneralizedpolynomialmapswithapplicationstochemicalreactionnetworksandrealalgebraicgeometry
AT dickensteina signconditionsforinjectivityofgeneralizedpolynomialmapswithapplicationstochemicalreactionnetworksandrealalgebraicgeometry
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