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

[1]  Günter M. Ziegler,et al.  Oriented Matroids , 2017, Handbook of Discrete and Computational Geometry, 2nd Ed..

[2]  Alicia Dickenstein,et al.  Descartes' Rule of Signs for Polynomial Systems supported on Circuits , 2016, ArXiv.

[3]  Georg Regensburger,et al.  Generalized Mass-Action Systems and Positive Solutions of Polynomial Equations with Real and Symbolic Exponents , 2014, CASC.

[4]  Murad Banaji,et al.  Some Results on Injectivity and Multistationarity in Chemical Reaction Networks , 2013, SIAM J. Appl. Dyn. Syst..

[5]  M. Banaji,et al.  Some remarks on injectivity of chemical reaction networks , 2013 .

[6]  Elisenda Feliu,et al.  A computational method to preclude multistationarity in networks of interacting species , 2013, Bioinform..

[7]  Dietrich Flockerzi,et al.  Multistationarity in Sequential Distributed Multisite Phosphorylation Networks , 2013, Bulletin of Mathematical Biology.

[8]  Thorsten Theobald,et al.  Polyhedral and Algebraic Methods in Computational Geometry , 2013, Universitext.

[9]  Elisenda Feliu,et al.  Preclusion of switch behavior in networks with mass-action kinetics , 2012, Appl. Math. Comput..

[10]  Georg Regensburger,et al.  Generalized Mass Action Systems: Complex Balancing Equilibria and Sign Vectors of the Stoichiometric and Kinetic-Order Subspaces , 2012, SIAM J. Appl. Math..

[11]  Gilles Gnacadja,et al.  A Jacobian criterion for the simultaneous injectivity on positive variables of linearly parameterized polynomial maps , 2012 .

[12]  Dietrich Flockerzi,et al.  Multistationarity in mass action networks with applications to ERK activation , 2012, Journal of mathematical biology.

[13]  Ernst Althaus,et al.  Certifying feasibility and objective value of linear programs , 2012, Oper. Res. Lett..

[14]  H. Koeppl,et al.  Global injectivity and multiple equilibria in uni- and bi-molecular reaction networks , 2012 .

[15]  Martin Feinberg,et al.  Concordant chemical reaction networks and the Species-Reaction Graph. , 2012, Mathematical biosciences.

[16]  Elisenda Feliu,et al.  Power-Law Kinetics and Determinant Criteria for the Preclusion of Multistationarity in Networks of Interacting Species , 2012, SIAM J. Appl. Dyn. Syst..

[17]  Elisenda Feliu,et al.  Preclusion of switch behavior in reaction networks with mass-action kinetics , 2011, 1109.5149.

[18]  Martin Feinberg,et al.  Concordant chemical reaction networks. , 2011, Mathematical biosciences.

[19]  Frank Sottile,et al.  Injectivity of 2D Toric Bézier Patches , 2011, 2011 12th International Conference on Computer-Aided Design and Computer Graphics.

[20]  Badal Joshi,et al.  Simplifying the Jacobian Criterion for Precluding Multistationarity in Chemical Reaction Networks , 2011, SIAM J. Appl. Math..

[21]  Anne Shiu,et al.  Chemical Reaction Systems with Toric Steady States , 2011, Bulletin of Mathematical Biology.

[22]  Felix Kubler,et al.  Tackling Multiplicity of Equilibria with Gröbner Bases , 2010, Oper. Res..

[23]  Dietrich Flockerzi,et al.  Switching in Mass Action Networks Based on Linear Inequalities , 2010, SIAM J. Appl. Dyn. Syst..

[24]  Vitaly Katsnelson,et al.  Sign patterns for chemical reaction networks , 2009, 0904.2960.

[25]  Murad Banaji,et al.  Graph-theoretic approaches to injectivity and multiple equilibria in systems of interacting elements , 2009, 0903.1190.

[26]  Murad Banaji,et al.  Graph-theoretic criteria for injectivity and unique equilibria in general chemical reaction systems , 2008, Adv. Appl. Math..

[27]  Gheorghe Craciun,et al.  Multigraph Conditions for Multistability, Oscillations and Pattern Formation in Biochemical Reaction Networks , 2008, Proceedings of the IEEE.

[28]  Frank Sottile,et al.  Some Geometrical Aspects of Control Points for Toric Patches , 2008, MMCS.

[29]  J. William Helton,et al.  Determinant Expansions of Signed Matrices and of Certain Jacobians , 2008, SIAM J. Matrix Anal. Appl..

[30]  Gheorghe Craciun,et al.  Homotopy methods for counting reaction network equilibria. , 2007, Mathematical biosciences.

[31]  William J. Cook,et al.  Exact solutions to linear programming problems , 2007, Oper. Res. Lett..

[32]  Murad Banaji,et al.  P Matrix Properties, Injectivity, and Stability in Chemical Reaction Systems , 2007, SIAM J. Appl. Math..

[33]  Stephen P. Boyd,et al.  A tutorial on geometric programming , 2007, Optimization and Engineering.

[34]  Frank Sottile,et al.  Real Solutions to Equations from Geometry , 2006, University lecture series.

[35]  G. Craciun,et al.  Multiple Equilibria in Complex Chemical Reaction Networks: II. The Species-Reaction Graph , 2006, SIAM J. Appl. Math..

[36]  Jörg Rambau,et al.  TOPCOM: Triangulations of Point Configurations and Oriented Matroids , 2002 .

[37]  Komei Fukuda,et al.  Cocircuit Graphs and Efficient Orientation Reconstruction in Oriented Matroids , 2001, Eur. J. Comb..

[38]  Martin Feinberg,et al.  Multiple steady states for chemical reaction networks of deficiency one , 1995 .

[39]  M. Feinberg.  The existence and uniqueness of steady states for a class of chemical reaction networks , 1995 .

[40]  G. Ziegler.  Lectures on Polytopes , 1994 .

[41]  I. M. Gelʹfand,et al.  Discriminants, Resultants, and Multidimensional Determinants , 1994 .

[42]  P. Kaye.  Infectious diseases of humans: Dynamics and control , 1993 .

[43]  Bernd Sturmfels.  Oriented Matroids , 1993 .

[44]  H. P. Williams.  THEORY OF LINEAR AND INTEGER PROGRAMMING (Wiley-Interscience Series in Discrete Mathematics and Optimization) , 1989 .

[45]  E. Voit,et al.  Recasting nonlinear differential equations as S-systems: a canonical nonlinear form , 1987 .

[46]  A. Schrijver.  Theory of linear and integer programming , 1986, Wiley-Interscience series in discrete mathematics and optimization.

[47]  P. Waage,et al.  Studies concerning affinity , 1986 .

[48]  I. W. Sandberg,et al.  Existence and Uniqueness of Solutions for the Equations of Nonlinear DC Networks , 1972 .

[49]  P. Wallis,et al.  A Source Book in Mathematics, 1200-1800 , 1971, The Mathematical Gazette.

[50]  M. Savageau.  Biochemical systems analysis. II. The steady-state solutions for an n-pool system using a power-law approximation. , 1969, Journal of theoretical biology.

[51]  D. Gale,et al.  The Jacobian matrix and global univalence of mappings , 1965 .

[52]  G. Hardy.  A Source Book in Mathematics , 1930, Nature.

[53]  David Eugene Smith,et al.  A source book in mathematics , 1930 .

[54]  M. Uhr.  STRUCTURAL ANALYSIS OF INFERENCE PROBLEMS ARISING IN SYSTEMS BIOLOGY , 2012 .

[55]  Jörg Raisch,et al.  Multistationarity in the activation of a MAPK: parametrizing the relevant region in parameter space. , 2008, Mathematical biosciences.

[56]  採編典藏組.  Society for Industrial and Applied Mathematics(SIAM) , 2008 .

[57]  Martin Feinberg,et al.  Multiple Equilibria in Complex Chemical Reaction Networks: I. the Injectivity Property * , 2006 .

[58]  Andrew J. Sommese,et al.  The numerical solution of systems of polynomials - arising in engineering and science , 2005 .

[59]  M. Feinberg,et al.  Multiple Equilibria in Complex Chemical Reaction Networks: Ii. the Species-reaction Graph * , 2005 .

[60]  M. Feinberg,et al.  Multiple Equilibria in Complex Chemical Reaction Networks: I. The Injectivity Property , 2005, SIAM J. Appl. Math..

[61]  J. Bauer,et al.  Chemical reaction network theory for in-silico biologists , 2003 .

[62]  S. Basu,et al.  Algorithms in real algebraic geometry , 2003 .

[63]  Gert Vegter,et al.  In handbook of discrete and computational geometry , 1997 .

[64]  SETH CHAIKENDefinition,et al.  Oriented Matroid Pairs, Theory and an Electric Application , 1996 .

[65]  Richard A. Brualdi,et al.  Matrices of sign-solvable linear systems: Master bibliography , 1995 .

[66]  M. Feinberg.  Chemical reaction network structure and the stability of complex isothermal reactors—II. Multiple steady states for networks of deficiency one , 1988 .

[67]  M. Feinberg.  Chemical reaction network structure and the stability of complex isothermal reactors—I. The deficiency zero and deficiency one theorems , 1987 .

[68]  F. Horn.  Necessary and sufficient conditions for complex balancing in chemical kinetics , 1972 .

[69]  M. Feinberg.  Complex balancing in general kinetic systems , 1972 .

[70]  R. Jackson,et al.  General mass action kinetics , 1972 .

[71]  M. W. Birch.  Maximum Likelihood in Three-Way Contingency Tables , 1963 .

[72]  M. Feinberg,et al.  Multiple Equilibria in Complex Chemical Reaction Networks: Extensions to Entrapped Species Models , 2022 .

[73]  Martin Feinberg,et al.  Multiple Equilibria in Complex Chemical Reaction Networks: Semiopen Mass Action Systems * , 2022 .

[74]  Daniel E. Steffy,et al.  Konrad-zuse-zentrum F ¨ Ur Informationstechnik Berlin Improving the Accuracy of Linear Programming Solvers with Iterative Refinement Improving the Accuracy of Linear Programming Solvers with Iterative Refinement * , 2022 .