暂无分享,去创建一个
[1] Éric Schost,et al. Properness Defects of Projections and Computation of at Least One Point in Each Connected Component of a Real Algebraic Set , 2004, Discret. Comput. Geom..
[2] Badal Joshi,et al. A survey of methods for deciding whether a reaction network is multistationary , 2014, 1412.5257.
[3] Alicia Dickenstein,et al. Sign Conditions for Injectivity of Generalized Polynomial Maps with Applications to Chemical Reaction Networks and Real Algebraic Geometry , 2013, Found. Comput. Math..
[4] Seth Sullivant,et al. Algebraic and Geometric Methods in Statistics: The algebraic complexity of maximum likelihood estimation for bivariate missing data , 2009 .
[5] Caroline Uhler,et al. Geometry of maximum likelihood estimation in Gaussian graphical models , 2010, 1012.2643.
[6] George E. Collins,et al. Quantifier elimination for real closed fields by cylindrical algebraic decomposition , 1975 .
[7] Jean-Charles Faugère,et al. Efficient Computation of Zero-Dimensional Gröbner Bases by Change of Ordering , 1993, J. Symb. Comput..
[8] D. Grigor'ev. Complexity of deciding Tarski algebra , 1988 .
[9] H. Hong. An improvement of the projection operator in cylindrical algebraic decomposition , 1990, ISSAC '90.
[10] Donal O'Shea,et al. Ideals, varieties, and algorithms - an introduction to computational algebraic geometry and commutative algebra (2. ed.) , 1997, Undergraduate texts in mathematics.
[11] Kenneth W. Regan,et al. Hilbert’s Proof of His Irreducibility Theorem , 2016, Am. Math. Mon..
[12] Jose Israel Rodriguez,et al. Data-Discriminants of Likelihood Equations , 2015, ISSAC.
[13] Elisenda Feliu,et al. Identifying parameter regions for multistationarity , 2016, PLoS Comput. Biol..
[14] Jacques Demongeot,et al. High-dimensional Switches and the Modeling of Cellular Differentiation 2.2 Mathematical Models , 2022 .
[15] Christopher W. Brown. Simple CAD Construction and its Applications , 2001, J. Symb. Comput..
[16] James Renegar. On the computational complexity and geome-try of the first-order theory of the reals , 1992 .
[17] Zbigniew Jelonek,et al. Testing sets for properness of polynomial mappings , 1999 .
[18] O. Cinquin,et al. Generalized, Switch-Like Competitive Heterodimerization Networks , 2007, Bulletin of mathematical biology.
[19] Dennis S. Arnon,et al. A Cluster-Based Cylindrical Algebraic Decomposition Algorithm , 1985, J. Symb. Comput..
[20] Marc Giusti,et al. A Gröbner Free Alternative for Polynomial System Solving , 2001, J. Complex..
[21] Christopher W. Brown. Fast simplifications for Tarski formulas based on monomial inequalities , 2012, J. Symb. Comput..
[22] Donald St. P. Richards,et al. Counting and locating the solutions of polynomial systems of maximum likelihood equations, I , 2006, J. Symb. Comput..
[23] Mohab Safey El Din,et al. Variant quantifier elimination , 2012, J. Symb. Comput..
[24] Christopher W. Brown. QEPCAD B: a program for computing with semi-algebraic sets using CADs , 2003, SIGS.
[25] J. Renegar,et al. On the Computational Complexity and Geometry of the First-Order Theory of the Reals, Part I , 1989 .
[26] Christopher W. Brown. Constructing a single open cell in a cylindrical algebraic decomposition , 2013, ISSAC '13.
[27] I. M. Gelʹfand,et al. Discriminants, Resultants, and Multidimensional Determinants , 1994 .
[28] Hoon Hong,et al. Simple solution formula construction in cylindrical algebraic decomposition based quantifier elimination , 1992, ISSAC '92.
[29] Bruno Buchberger,et al. Bruno Buchberger's PhD thesis 1965: An algorithm for finding the basis elements of the residue class ring of a zero dimensional polynomial ideal , 2006, J. Symb. Comput..
[30] Éric Schost,et al. Polar varieties and computation of one point in each connected component of a smooth real algebraic set , 2003, ISSAC '03.
[31] B. Sturmfels. SOLVING SYSTEMS OF POLYNOMIAL EQUATIONS , 2002 .
[32] Bernd Sturmfels,et al. The maximum likelihood degree , 2004, math/0406533.
[33] Christopher W. Brown. Improved Projection for Cylindrical Algebraic Decomposition , 2001, J. Symb. Comput..
[34] Elizabeth Gross,et al. Maximum likelihood degree of variance component models , 2011, 1111.3308.
[35] Jonathan D. Hauenstein. Maximum Likelihood for Matrices with Rank Constraints , 2014 .
[36] Marie-Françoise Roy,et al. On the combinatorial and algebraic complexity of quantifier elimination , 1996, JACM.
[37] Jose Israel Rodriguez,et al. A probabilistic algorithm for computing data-discriminants of likelihood equations , 2015, J. Symb. Comput..
[38] Botong Wang,et al. The signed Euler characteristic of very affine varieties , 2014, 1403.4371.
[39] Bican Xia,et al. Special algorithm for stability analysis of multistable biological regulatory systems , 2013, J. Symb. Comput..
[40] James Renegar,et al. On the Computational Complexity and Geometry of the First-Order Theory of the Reals, Part I: Introduction. Preliminaries. The Geometry of Semi-Algebraic Sets. The Decision Problem for the Existential Theory of the Reals , 1992, J. Symb. Comput..
[41] Gheorghe Craciun,et al. Homotopy methods for counting reaction network equilibria. , 2007, Mathematical biosciences.
[42] Changbo Chen,et al. Triangular decomposition of semi-algebraic systems , 2013, J. Symb. Comput..
[43] Fabrice Rouillier,et al. Workspace and Joint Space Analysis of the 3-RPS Parallel Robot , 2014 .
[44] J. E. Morais,et al. Straight--Line Programs in Geometric Elimination Theory , 1996, alg-geom/9609005.
[45] Scott McCallum,et al. On projection in CAD-based quantifier elimination with equational constraint , 1999, ISSAC '99.
[46] June Huh,et al. The maximum likelihood degree of a very affine variety , 2012, Compositio Mathematica.
[47] Seth Sullivant,et al. Lectures on Algebraic Statistics , 2008 .
[48] Fabrice Rouillier,et al. Solving parametric polynomial systems , 2004, J. Symb. Comput..
[49] Jose Israel Rodriguez,et al. Maximum likelihood for dual varieties , 2014, SNC.
[50] Bican Xia,et al. A complete algorithm for automated discovering of a class of inequality-type theorems , 2001, Science in China Series F Information Sciences.
[51] Alicia Dickenstein,et al. Multistationarity in Structured Reaction Networks , 2018, Bulletin of mathematical biology.
[52] Jose Israel Rodriguez,et al. Maximum likelihood geometry in the presence of data zeros , 2013, ISSAC.
[53] J. Demongeot,et al. Positive and negative feedback: striking a balance between necessary antagonists. , 2002, Journal of theoretical biology.
[54] S. Basu,et al. Algorithms in real algebraic geometry , 2003 .
[55] S. Basu,et al. COMPUTING ROADMAPS OF SEMI-ALGEBRAIC SETS ON A VARIETY , 1999 .
[56] Bernd Sturmfels,et al. Solving the Likelihood Equations , 2005, Found. Comput. Math..
[57] Martin Feinberg,et al. Multiple Equilibria in Complex Chemical Reaction Networks: I. the Injectivity Property * , 2006 .
[58] Maria Grazia Marinari,et al. The shape of the Shape Lemma , 1994, ISSAC '94.
[59] Masahiro Shiota,et al. Nash triviality in families of Nash manifolds , 1992 .
[60] Scott McCallum,et al. An Improved Projection Operation for Cylindrical Algebraic Decomposition of Three-Dimensional Space , 1988, J. Symb. Comput..
[61] Sébastien Briot,et al. Solution regions in the parameter space of a 3-RRR decoupled robot for a prescribed workspace , 2012, ARK.
[62] G. Sacks. A DECISION METHOD FOR ELEMENTARY ALGEBRA AND GEOMETRY , 2003 .
[63] J. Faugère. A new efficient algorithm for computing Gröbner bases (F4) , 1999 .
[64] George E. Collins,et al. Partial Cylindrical Algebraic Decomposition for Quantifier Elimination , 1991, J. Symb. Comput..
[65] Jose Israel Rodriguez,et al. The maximum likelihood degree of toric varieties , 2017, J. Symb. Comput..
[66] Dietrich Flockerzi,et al. Multistationarity in Sequential Distributed Multisite Phosphorylation Networks , 2013, Bulletin of Mathematical Biology.