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Abstract:

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.

Registro:

Documento: Artículo
Título:Sign Conditions for Injectivity of Generalized Polynomial Maps with Applications to Chemical Reaction Networks and Real Algebraic Geometry
Autor:Müller, S.; Feliu, E.; Regensburger, G.; Conradi, C.; Shiu, A.; Dickenstein, A.
Filiación:Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstraße 69, Linz, 4040, Austria
Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, Copenhagen, 2100, Denmark
Max-Planck-Institut Dynamik komplexer technischer Systeme, Sandtorstr. 1, Magdeburg, 39106, Germany
Department of Mathematics, Texas A&M University, Mailstop 3368, College Station, TX 77843-3368, United States
Dto. de Matemática, FCEN, Universidad de Buenos Aires, and IMAS (UBA-CONICET), Ciudad Universitaria, Pab. I, Buenos Aires, C1428EGA, Argentina
Palabras clave: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
Año:2016
Volumen:16
Número:1
Página de inicio:69
Página de fin:97
DOI: http://dx.doi.org/10.1007/s10208-014-9239-3
Título revista:Foundations of Computational Mathematics
Título revista abreviado:Found. Comput. Math.
ISSN:16153375
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_16153375_v16_n1_p69_Muller

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Citas:

---------- APA ----------
Müller, S., Feliu, E., Regensburger, G., Conradi, C., Shiu, A. & Dickenstein, A. (2016) . Sign Conditions for Injectivity of Generalized Polynomial Maps with Applications to Chemical Reaction Networks and Real Algebraic Geometry. Foundations of Computational Mathematics, 16(1), 69-97.
http://dx.doi.org/10.1007/s10208-014-9239-3
---------- CHICAGO ----------
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" . Foundations of Computational Mathematics 16, no. 1 (2016) : 69-97.
http://dx.doi.org/10.1007/s10208-014-9239-3
---------- MLA ----------
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" . Foundations of Computational Mathematics, vol. 16, no. 1, 2016, pp. 69-97.
http://dx.doi.org/10.1007/s10208-014-9239-3
---------- VANCOUVER ----------
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. Found. Comput. Math. 2016;16(1):69-97.
http://dx.doi.org/10.1007/s10208-014-9239-3