Weak identifiability for differential algebraic systems
Tài liệu tham khảo
Anstett-Collin, 2020, A priori identifiability: an overview on definitions and approaches, Annu. Rev. Control, 50, 139, 10.1016/j.arcontrol.2020.10.006
Bearup, 2013, The input-output relationship approach to structural identifiability analysis, Comput. Methods Programs Biomed., 109, 171, 10.1016/j.cmpb.2012.10.012
Bellu, 2007, DAISY: a new software tool to test global identifiability of biological and physiological systems, Comput. Methods Programs Biomed., 88, 52, 10.1016/j.cmpb.2007.07.002
Brouwer, 2017, A systematic approach to determining the identifiability of multistage carcinogenesis models, Risk Anal., 37, 1375, 10.1111/risa.12684
Craciun, 2008, Identifiability of chemical reaction networks, J. Math. Chem., 44, 244, 10.1007/s10910-007-9307-x
D'Alfonso, 2011, A geometric index reduction method for implicit systems of differential algebraic equations, J. Symb. Comput., 46, 1114, 10.1016/j.jsc.2011.05.012
D'Alfonso, 2006, On the complexity of the resolvent representation of some prime differential ideals, J. Complex., 22, 396, 10.1016/j.jco.2005.10.002
Giusti, 1993, La détermination des points isolés et de la dimension d'une variété algébrique peut se faire en temps polynomial, vol. XXXIV, 216
Giusti, 1998, Straight-line programs in geometric elimination theory, J. Pure Appl. Algebra, 124, 101, 10.1016/S0022-4049(96)00099-0
Giusti, 2001, A Gröbner free alternative for polynomial systems solving, J. Complex., 17, 154, 10.1006/jcom.2000.0571
Harris, 1995, Algebraic Geometry. A First Course, vol. 133
Heintz, 1982, Testing polynomials which are easy to compute, vol. 30, 237
Hodge, 1953
Hong, 2020, Global identifiability of differential models, Commun. Pure Appl. Math., 73, 1831, 10.1002/cpa.21921
Jeronimo, 2019, Identifiability from a few species for a class of biochemical reaction networks, Bull. Math. Biol., 81, 2133, 10.1007/s11538-019-00594-0
Karlsson, 2012, An efficient method for structural identifiability analysis of large dynamical systems, IFAC Proc. Vol., 45, 941, 10.3182/20120711-3-BE-2027.00381
Krick, 1996, A computational method for Diophantine approximation, Prog. Math., 143, 193
Lecerf, 2003, Computing the equidimensional decomposition of an algebraic closed set by means of lifting fibers, J. Complex., 19, 564, 10.1016/S0885-064X(03)00031-1
Ljung, 1994, On global identifiability for arbitrary model parametrizations, Automatica, 30, 265, 10.1016/0005-1098(94)90029-9
Meshkat, 2009, An algorithm for finding globally identifiable parameter combinations of nonlinear ODE models using Gröbner bases, Math. Biosci., 222, 61, 10.1016/j.mbs.2009.08.010
Meshkat, 2018, Algebraic tools for the analysis of state space models, vol. 77, 171
Ollivier, 1990
Ovchinnikov, 2021, Computing all identifiable functions of parameters for ODE models, Syst. Control Lett., 157, 10.1016/j.sysconle.2021.105030
Ovchinnikov, 2022, Multi-experiment parameter identifiability of ODEs and model theory, SIAM J. Appl. Algebra Geom., 6, 339, 10.1137/21M1389845
Ovchinnikov, 2023, Input-output equations and identifiability of linear ODE models, IEEE Trans. Autom. Control, 68, 812, 10.1109/TAC.2022.3145571
Ovchinnikov
Pardo, 2022, A promenade through correct test sequences I: degree of constructible sets, Bézout's Inequality and density, J. Complex., 68, 10.1016/j.jco.2021.101588
Pohjanpalo, 1978, System identifiability based on the power series expansion of the solution, Math. Biosci., 41, 21, 10.1016/0025-5564(78)90063-9
Puddu, 1998, An effective algorithm for quantifier elimination over algebraically closed fields using straight line programs, J. Pure Appl. Algebra, 129, 173, 10.1016/S0022-4049(97)00068-6
Ritt, 1950
Saccomani, 2003, Parameter identifiability of nonlinear systems: the role of initial conditions, Automatica, 39, 619, 10.1016/S0005-1098(02)00302-3
Schwartz, 1980, Fast probabilistic algorithms for verification of polynomial identities, J. ACM, 27, 701, 10.1145/322217.322225
Sedoglavic, 2002, A probabilistic algorithm to test local algebraic observability in polynomial time, J. Symb. Comput., 33, 735, 10.1006/jsco.2002.0532
Sweedler, 1993, Using Groebner bases to determine the algebraic and transcendental nature of field extensions: return of the killer tag variables, vol. 673, 66
Zippel, 1979, Probabilistic algorithms for sparse polynomials, vol. 72, 216