A new method for solving algebraic systems of positive dimension
Discrete Applied Mathematics - Special volume on applied algebra, algebraic algorithms, and error-correcting codes
Partial Cylindrical Algebraic Decomposition for quantifier elimination
Journal of Symbolic Computation
A generalized Euclidean algorithm for computing triangular representations of algebraic varieties
Journal of Symbolic Computation
An elimination method for polynomial systems
Journal of Symbolic Computation
Recent advances on determining the number of real roots of parametric polynomials
Journal of Symbolic Computation - Special issue on polynomial elimination—algorithms and applications
Computing triangular systems and regular systems
Journal of Symbolic Computation
An algorithm for isolating the real solutions of semi-algebraic systems
Journal of Symbolic Computation
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Real solving for positive dimensional systems
Journal of Symbolic Computation
Elimination Practice: Software Tools and Applications
Elimination Practice: Software Tools and Applications
Real solution isolation using interval arithmetic
Computers & Mathematics with Applications
Program Verification by Using DISCOVERER
Verified Software: Theories, Tools, Experiments
Algebraic Analysis of Bifurcation and Limit Cycles for Biological Systems
AB '08 Proceedings of the 3rd international conference on Algebraic Biology
The Smallest Multistationary Mass-Preserving Chemical Reaction Network
AB '08 Proceedings of the 3rd international conference on Algebraic Biology
On proving the absence of oscillations in models of genetic circuits
AB'07 Proceedings of the 2nd international conference on Algebraic biology
AB'07 Proceedings of the 2nd international conference on Algebraic biology
Algebraic analysis on asymptotic stability of continuous dynamical systems
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Semi-algebraic description of the equilibria of dynamical systems
CASC'11 Proceedings of the 13th international conference on Computer algebra in scientific computing
Discovering polynomial Lyapunov functions for continuous dynamical systems
Journal of Symbolic Computation
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This paper presents a new and general approach for analyzing the stability of a large class of biological networks, modeled as autonomous systems of differential equations, using real solving and solution classification. The proposed approach, based on the classical technique of linearization from the qualitative theory of ordinary differential equations yet with exact symbolic computation, is applied to analyzing the local stability of the Cdc2-cyclin B/Wee1 system and the Mos/MEK/p42 MAPK cascade, two well-known models for cell and protein signaling that have been studied extensively in the literature. We provide rigorous proofs and generalizations for some of the previous results established experimentally and report our new findings.