- ExpandedLiePointSymmetry: A maple package that, given a manifold (an algebaic variety defined by an algebraic system, orbits defined by ordinary differential equations, etc.) allows to
(see examples there, If you have any
question, just send an email to Alexandre Sedoglavic).
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,
This code works with Maple >9
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]
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
Polynomial Time Nondimensionalisation of Ordinary Differential
Equations via their Lie Point Symmetries. Research report. February 2006. [pdf] [abstract] [BibTeX]
Tue Jun 12 2007:
A maple package that test
observability/identifiability of ordinary differential systems in
polynomial time. See there
what could be done using this package. If you have any question, just
send an email to Alexandre Sedoglavic.
This code works (at least) with Maple 6,7,8,9,10
Bibliographic reference (citing this package):
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]
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,
A simple mathematical model of adaptation to high
osmolarity in yeast, Gennemark Peter, Nordlander
Bodil, Hohmann Stefan and Wedelin Dag. Silico Biology 6,
of metabolic insulin signaling in adipocytes,
Ulfhielm, Erik. Undergraduate thesis, Linköping
University, Sweden, Febuary, 2006.
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
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.
Last modified: Tue Aug 1 15:46:34 CEST 2006