Multipolynomial resultant algorithms
Journal of Symbolic Computation
Algorithmic algebra
REDLOG: computer algebra meets computer logic
ACM SIGSAM Bulletin
Nonlinear control system design by quantifier elimination
Journal of Symbolic Computation - Special issue: applications of quantifier elimination
Simulation and optimization by quantifier elimination
Journal of Symbolic Computation - Special issue: applications of quantifier elimination
MARS: a MAPLE/MATLAB/C resultant-based solver
ISSAC '98 Proceedings of the 1998 international symposium on Symbolic and algebraic computation
Mathematical physiology
Algebraic Geometry and Computer Vision: Polynomial Systems, Real andComplex Roots
Journal of Mathematical Imaging and Vision
Computer algebra in the life sciences
ACM SIGSAM Bulletin
Series of Abstractions for Hybrid Automata
HSCC '02 Proceedings of the 5th International Workshop on Hybrid Systems: Computation and Control
Algorithmic algebraic model checking: hybrid automata and systems biology
Algorithmic algebraic model checking: hybrid automata and systems biology
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)
Algorithmic Algebraic Model Checking III: Approximate Methods
Electronic Notes in Theoretical Computer Science (ENTCS)
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part III
ATVA'05 Proceedings of the Third international conference on Automated Technology for Verification and Analysis
Algorithmic algebraic model checking i: challenges from systems biology
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
Taylor approximation for hybrid systems
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Hi-index | 0.00 |
A series of papers, all under the title of Algorithmic Algebraic Model Checking (AAMC), has sought to combine techniques from algorithmic algebra, model checking and dynamical systems to examine how a biochemical hybrid dynamical system can be made amenable to temporal analysis, even when the initial conditions and unknown parameters may only be treated as symbolic variables. This paper examines how to specialize this framework to metabolic control analysis (MCA) involving many reactions operating at many dissimilar time-scales. In the earlier AAMC papers, it has been shown that the dynamics of various biochemical semi-algebraic hybrid automata could be unraveled using powerful techniques from computational real algebraic geometry. More specifically, the resulting algebraic model checking techniques were found to be suitable for biochemical networks modeled using general mass action (GMA) based ODEs. This paper scrutinizes how the special properties of metabolic networks-a subclass of the biochemical networks previously handled-can be exploited to gain improvement in computational efficiency. The paper introduces a general framework for performing symbolic temporal reasoning over metabolic network hybrid automata that handles both GMA-based equilibrium estimation and flux balance analysis (FBA).While algebraic polynomial equations over Q[x1, ..., xn] can be symbolically solved using Gröbner bases or Wu-Ritt characteristic sets, the FBA-based estimation can be performed symbolically by rephrasing the algebraic optimization problem as a quantifier elimination problem. Effectively, an approximate hybrid automaton that simulates the metabolic network is derived, and is thus amenable to manipulation by the algebraic model checking techniques previously described in the AAMC papers.