• compute expanded Lie point symmetries of this manifold;
• use, when possible, these symmetries in order to
  • perform classical Lie reduction (represent this object by a smaller dimensional one associated to fibers given by the symmetries),
  • ``reduce'' the number of parameter of parametric (ordinary) differential/algebraic systems (this operation is a generalization of dimentional analysis, lumping technics, etc; it is just applying classical Lie reduction to parameters considered as constant state variables),
  • ---considering these symmetries as obstruction to a observability/identifiability property---remove this obstruction by a reduction,
  • rewrite an ordinary differential system in a singular perturbated form,
  • etc.

This code works with Maple >9

(Download).

Contributors:

• Alexandre Sedoglavic
• Aslı Ürgüplü

Bibliographic references:

• Lemaire, F., Sedoglavic, A. et Ürgüplü, A. Moving Frame Based Strategies for Reduction of Ordinary Differential/Recurrence Systems using their Expanded Lie Point Symmetries. Internal report. Janvier 2008.     [pdf]  [abstract]  [BibTeX]
• Sedoglavic, A. Reduction of Algebraic Parametric Systems by Rectification of their Affine Expanded Lie Symmetries. Proceedings of Algebraic Biology 2007 – Second International Conference (RISC, Castle of Hagenberg, Austria, July 2–4 2007), H. Anai, K. Horimoto, and T. Kutsia, Eds., vol. 4545 of Lecture Notes in Computer Science, Springer, pp. 277–291.    [pdf]  [abstract]  [BibTeX]
• Hubert, É. et Sedoglavic, A. Polynomial Time Nondimensionalisation of Ordinary Differential Equations via their Lie Point Symmetries. Research report. February 2006.    [pdf]  [abstract]  [BibTeX]

What's new:

• Tue Jun 12 2007: First release

This code works (at least) with Maple 6,7,8,9,10

(Download).

Contributor:

• Alexandre Sedoglavic

Bibliographic reference (citing this package):

• Sedoglavic, A. A probabilistic algorithm to test local algebraic observability in polynomial time. Proceedings of the 2001 International Symposium on Symbolic and Algebraic Computation (London, Canada, July 22–25 2001), B. Mourrain, Ed., ACM press, pp. 309–316.    [pdf]  [abstract]  [BibTeX]

What's new:

• Thu Mar 29 2007: Correction of a bug in observabilitySymmetries (thank's to Martin Fransson).
• Tue Jul 11 2006:
  • Correction of a bug (thank's to Milena Anguelova).
  • Add the procedure observabilitySymmetries that computes simple symmetries (i.e. pure translation and scaling) of model letting its inputs and outputs invariants. Hence, 90 per cent of probabilistic answers (non identifiability) could be now proved.

What's next (if I ever find some times to do it):

• Extend ObservabilitySymmetries in order to compute the 10 per cent remaining symmetries that are not handled now.
• Clean the code, make it faster and usable.
• Implement this algorithm in an open source computer algebra system (mathemagix?)

Some works citing/using this code:

• Structural identifiability of a model for the acetic acid fermentation process, Jiménez-Hornero, J.E. and Santos-Dueñas, I.M. and García-García, I., Mathematical Biosciences, In press, 2008.
• Comparison of two types of population pharmacokinetic model structures of paclitaxel, Martin Fransson and Henrik Gréen. European Journal of Pharmaceutical Sciences 33, 2, 2008.
• Towards individualized drug dosage: general methods and case studies Martin Fransson, Licenciate thesis, Linköping University, Sweden, October, 2007.
• A simple mathematical model of adaptation to high osmolarity in yeast, Gennemark Peter, Nordlander Bodil, Hohmann Stefan and Wedelin Dag. Silico Biology 6, 0018 (2006).
• Modeling of metabolic insulin signaling in adipocytes, Ulfhielm, Erik. Undergraduate thesis, Linköping University, Sweden, Febuary, 2006.
• From In Vitro Biochemistry to In Vivo Understanding of the Glycolytic Oscillations in Saccharomyces Cerevisiae, Cedersund, G., DanØ S., SØrensen P.G. and Jirstrand, M. Proceedings of the conference on Modeling and Simulation in Biology, Medecine and Biomedical Engineering. 2005
• Nonlinear observability and identifiability: General theory and a case study of a kinetic model for S. Cerevisiae, Anguelova, Milena. Licenciate thesis, Chalmers University of Technology and Göteborg University, Sweden, April, 2004.
• Structural identifiability analysis of some highly structured families of statespace models using differential algebra, Gabriella Margaria, Eva Riccomagno, and Lisa J. White. Journal of Mathematical Biology, 49, 5 (November 2004), 433--454.
• Aminoglycoside Nephrotoxicity: Modeling, Simulation and Control. Rougier, F., Claude, D., Maurin, M., Sedoglavic, A., Ducher, M., Corvaisier, S., Jelliffe, R., et Maire, P. Antimicrobial Agents and Chemotherapy, 47, 3 (March 2003), 1010--1016.