On global identifiability for arbitrary model parametrizations
Automatica (Journal of IFAC)
Representation for the radical of a finitely generated differential ideal
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
Singular perturbation methods in control: analysis and design
Singular perturbation methods in control: analysis and design
A probabilistic algorithm to test local algebraic observability in polynomial time
Journal of Symbolic Computation - Computer algebra: Selected papers from ISSAC 2001
Elimination Practice: Software Tools and Applications
Elimination Practice: Software Tools and Applications
AB '08 Proceedings of the 3rd international conference on Algebraic Biology
Computing differential characteristic sets by change of ordering
Journal of Symbolic Computation
On proving the absence of oscillations in models of genetic circuits
AB'07 Proceedings of the 2nd international conference on Algebraic biology
A general procedure for accurate parameter estimation in dynamic systems using new estimation errors
ANB'10 Proceedings of the 4th international conference on Algebraic and Numeric Biology
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Among all the modeling approaches dedicated to cellular biology, differential algebra is particularly related to the well-established one based on nonlinear differential equations. In this paper, it is shown that differential algebra makes one of the model reduction methods both simple and algorithmic: the quasi-steady state approximation theory, in the particular setting of generalized chemical reactions systems. This recent breakthrough may suggest some evolution of modeling techniques based on nonlinear differential equations, by incorporating the reduction hypotheses in the models. Potential improvements of parameters fitting methods are discussed too.