[BLPMM18] 
François Boulier, François Lemaire, Adrien Poteaux, and Marc
Moreno Maza.
An Equivalence Theorem For Regular Differential Chains.
Journal of Symbolic Computation, pages 127, 2018.
[ bib 
http 
.pdf ]
Keywords: resultants ; characteristic set ; regular chain ; differential algebra ; resultant ; regularity 
[BLL^{+}16] 
François Boulier, Joseph Lallemand, François Lemaire, Georg
Regensburger, and Markus Rosenkranz.
Additive Normal Forms and Integration of Differential Fractions.
Journal of Symbolic Computation, 2016.
[ bib 
http ]
Keywords: Differential algebra ; differential fraction ; integration 
[BLRH15]  François Boulier, François Lemaire, Valery G. Romanovski, and M. Han. Qualitative Investigation of a Gene Model Using Computer Algebra Algorithms. Programming and Computer Software, 41(2):105111, 2015. [ bib  http ] 
[NHL^{+}11]  M. Nakatsui, K. Horimoto, F. Lemaire, A. Ürgüplü, A. Sedoglavic, and F. Boulier. Brute force meets bruno force in parameter optimisation: introduction of novel constraints for parameter accuracy improvement by symbolic computation. IET Systems Biology, 5(5):281292, 2011. [ bib ] 
[BLLM11]  François Boulier, Marc Lefranc, François Lemaire, and PierreEmmanuel Morant. Model Reduction of Chemical Reaction Systems using Elimination. Mathematics in Computer Science, 5:289301, 2011. Presented at the international conference MACIS 2007, submitted to Mathematics in Computer Science, Special Issue on Polynomial System Solving in July 2008. [ bib  http ] 
[BL10]  François Boulier and François Lemaire. A normal form algorithm for regular differential chains. Mathematics in Computer Science, 4(23):185201, 2010. [ bib ] 
[LMPX10] 
François Lemaire, Marc Moreno Maza, Wei Pan, and Yuzhen Xie.
When does (t) equal sat(t)?
Journal of Symbolic Computation, 2010.
Special Issue for ISSAC 2008.
[ bib ]
Given a regular chain T, we aim at finding an efficient way for computing a system of generators of Sat(T), the saturated ideal of T. A natural idea is to test whether the equality <T>=Sat(T) holds, that is, whether T generates its saturated ideal. By generalizing the notion of primitivity from univariate polynomials to regular chains, we establish a necessary and sufficient condition, together with a Gröbner basis free algorithm, for testing this equality. Our experimental results illustrate the efficiency of this approach in practice.

[BLM10] 
François Boulier, François Lemaire, and Marc Moreno Maza.
Computing differential characteristic sets by change of ordering.
Journal of Symbolic Computation, 45(1):124149, 2010.
[ bib ]
We describe an algorithm for converting a characteristic set of a prime differential ideal from one ranking into another. This algorithm was implemented in many different languages and has been applied within various software and projects. It permitted to solve formerly unsolved problems.

[BLSÜ09] 
François Boulier, François Lemaire, Alexandre Sedoglavic, and
Aslı Ürgüplü.
Towards an automated reduction method for polynomial ode models of
biochemical reaction systems.
Mathematics in Computer Science, 2009.
Special Issue on Symbolic Computation in Biology.
[ bib 
http ]
This paper presents the first version of an algorithmic scheme dedicated to the model reduction problem, in the context of polynomial ODE models derived from generalized chemical reaction systems. This scheme, which relies on computer algebra, is implemented within a new MAPLE package. It is applied over an example. The qualitative analysis of the reduced model is afterwards completely carried out, proving the practical relevance of our methods.

[MTL^{+}09] 
PierreEmmanuel Morant, Quentin Thommen, François Lemaire,
Constant Vandermoëre, Benjamin Parent, and Marc Lefranc.
Oscillations in the expression of a selfrepressed gene induced by
a slow transcriptional dynamics.
Physical Review Letters, 102(6):068104, 2009.
Accepted for publication in Physical Review Letters.
[ bib 
http ]
We revisit the dynamics of a gene repressed by its own protein in the case where the transcription rate does not adapt instantaneously to protein concentration but is a dynamical variable. We derive analytical criteria for the appearance of sustained oscillations and find that they require degradation mechanisms much less nonlinear than for infinitely fast regulation. Deterministic predictions are also compared with stochastic simulations of this minimal genetic oscillator.

[BLR^{+}17] 
François Boulier, François Lemaire, Markus Rosenkranz, Rosane
Ushirobira, and Nathalie Verdière.
On Symbolic Approaches to IntegroDifferential Equations.
In Niculescu SilviuIulian and Ditzinger Thomas, editors,
Algebraic and Symbolic Computation Methods in Dynamical Systems, Advances
in Delays and Dynamics. Springer, 2017.
[ bib 
http 
.pdf ]
Keywords: integrodifferential ; computer algebra ; elimination theory ; parameter estimation 
[BLP^{+}17] 
François Boulier, François Lemaire, Adrien Poteaux, Alban Quadrat,
Nathalie Verdière, Nathalie Corson, Valentina Lanza, Hélène
Castel, Pierrick Gandolfo, Vincent Compère, and Emmanuel Gérardin.
Identifiability, IntegroDifferential Equations and Neurobiology.
Talk Afternotes.
In Journées Annuelles du GT BIOSS, Montpellier, France,
March 2017.
[ bib 
http ]
Keywords: integrodifferential equations ; computer algebra ; identifiability ; neurobiology ; modeling 
[LT16] 
François Lemaire and Alexandre Temperville.
Computing Sparse Representations of Systems of Rational Fractions.
In Computer Algebra in Scientific Computing, pages 349 
366, Bucharest, Romania, September 2016.
[ bib 
DOI 
http 
.pdf ]
Keywords: parametric systems ; simplification of rational fractions ; sparse basis of vector spaces 
[BL15]  François Boulier and François Lemaire. Finding First Integrals Using Normal Forms Modulo Differential Regular Chains. In Computer Algebra in Scientific Computing 2015, Computer Algebra in Scientific Computing, pages 101118, Aachen, Germany, September 2015. Springer. [ bib  http ] 
[LT14] 
François Lemaire and Alexandre Temperville.
On Defining and Computing “Good” Conservation Laws.
In Computational Methods in Systems Biology, Proceedings of
CMSB 2014, pages 1  19, Manchester, United Kingdom, November 2014.
[ bib 
DOI 
http 
.pdf ]
Keywords: conservation analysis ; sparse conservation laws ; biological models ; sparse null space ; greedy algorithm 
[BKL^{+}14]  François Boulier, Anja Korporal, François Lemaire, Wilfrid Perruquetti, Adrien Poteaux, and Rosane Ushirobira. An Algorithm for Converting Nonlinear Differential Equations to Integral Equations with an Application to Parameter Estimation from Noisy Data. In Computer Algebra in Scientific Computing, pages 28  43, Warsaw, Poland, September 2014. [ bib  http  .pdf ] 
[BLRR13]  François Boulier, François Lemaire, Georg Regensburger, and Markus Rosenkranz. On the integration of differential fractions. In ISSAC'13, pages 18, Boston, United States, 2013. [ bib  http ] 
[BL13]  François Boulier and François Lemaire. On the Integration of Differential Fractions. In Differential Algebra and Related Topics V, Villeneuve d'Ascq, France, 2013. [ bib  http ] 
[BKL^{+}12]  Kirill Batmanov, Céline Kuttler, François Lemaire, Cédric Lhoussaine, and Cristian Versari. Symmetrybased model reduction for approximate stochastic analysis. In CMSB, pages 4968, 2012. [ bib ] 
[Lem11]  François Lemaire. The freemabsys project and the mabsys library. In Presented at the MAGIX@LIX Conference, École Polytechnique, 2011. [ bib  .pdf ] 
[CDL^{+}11]  Changbo Chen, James H. Davenport, François Lemaire, Marc Moreno Maza, Nalina Phisanbut, Bican Xia, Rong Xiao, and Yuzhen Xie. Solving semialgebraic systems with the regularchains library in maple. In Stefan Raschau, editor, Proceedings of the Fourth International Conference on Mathematical Aspects of Computer Science and Information Sciences (MACIS2011), pages 3851, 2011. [ bib ] 
[BLS11]  François Boulier, François Lemaire, and Alexandre Sedoglavic. On the Regularity Property of Differential Polynomials Modulo Regular Differential Chains. In Proceedings of Computer Algebra in Scientific Computing, LNCS 6885, pages 6172, Kassel, Germany, 2011. http://hal.archivesouvertes.fr/hal00599440. [ bib ] 
[BLPS11]  François Boulier, François Lemaire, Michel Petitot, and Alexandre Sedoglavic. Chemical Reaction Systems, Computer Algebra and Systems Biology. In Vladimir Gerdt et al., editor, Proceedings of Computer Algebra in Scientific Computing, LNCS 6885, pages 7387, Kassel, Germany, 2011. http://hal.archivesouvertes.fr/hal00603290. [ bib ] 
[NSL^{+}10]  Masahiko Nakatsui, Alexandre Sedoglavic, François Lemaire, François Boulier, Asli Ürgüplü, and Katsuhisa Horimoto. A general procedure for accurate parameter estimation in dynamic systems using new estimation errors. In ANB, pages 149166, 2010. [ bib ] 
[VPB^{+}10] 
Samuel Vidal, Michel Petitot, François Boulier, François Lemaire,
and Céline Kuttler.
Models of stochastic gene expression and weyl algebra.
In Proceedings of ANB2010, pages 7697, 2010.
[ bib 
.pdf ]
This paper presents a symbolic algorithm for computing the ODE systems which describe the evolution of the moments associated to a chemical reaction system, considered from a stochastic point of view. The algorithm, which is formulated in the Weyl algebra, seems more efficient than the corresponding method, based on partial derivatives. In particular, an efficient method for handling conservation laws is presented. The output of the algorithm can be used for a further investigation of the system behaviour, by numerical methods. Relevant examples are carried out.

[LÜ10a] 
François Lemaire and Aslı Ürgüplü.
Mabsys: Modeling and analysis of biological systems.
In Proceedings of ANB2010, pages 5772, 2010.
[ bib 
.pdf ]
We present the MABSys package which gathers, as much as possible, some functions to carry out the modeling of biochemical reaction networks, their qualitative analysis and the exact simplification of systems of ordinary differential equations. Then we discuss Tyson's negative feedback oscillator model and the parameters values for which this system oscillates.

[LÜ10b] 
François Lemaire and Aslı Ürgüplü.
A method for semirectifying algebraic and differential systems using
scaling type lie point symmetries with linear algebra.
In ACM Press, editor, Proceedings of the International Symposium
on Symbolic and algebraic computation, 2010.
[ bib ]
We present two new algorithms based on Lie symmetries that respectively allow to semirectify algebraic systems and reduce the number of parameters on which the steady points of a differential system depend. These algorithms facilitate the qualitative analysis of algebraic and differential systems. They are designed with a strong view towards applications, such as modeling in biology. Their implementation, already available in our MABSys package, is of polynomial time complexity in the input size.

[BCLM09] 
François Boulier, Changbo Chen, François Lemaire, and Marc Moreno
Maza.
Real root isolation of regular chains.
In Asian Symposium on Computer Mathematics, pages 1529, 2009.
[ bib 
.pdf ]
We present an algorithm RealRootIsolate for isolating the real roots of a system of multivariate polynomials given by a zerodimensional squarefree regular chain. The output of the algorithm is guaranteed in the sense that all real roots are obtained and are described by boxes of arbitrary precision. Real roots are encoded with a hybrid representation, combining a symbolic object, namely a regular chain, and a numerical approximation given by intervals. Our isolation algorithm is a generalization, for regular chains, of the algorithm proposed by Collins and Akritas. We have implemented RealRootIsolate as a command of the module SemiAlgebraicSetTools of the RegularChains library in Maple. Benchmarks are reported.

[BL08] 
François Boulier and François Lemaire.
Differential algebra and system modeling in cellular biology.
In M. Rosenkranz K. Horimoto, G. Regensburger and T. Kutsia, editors,
Proceedings of Algebraic Biology 2008, volume 5147 of LNCS, pages
2239. Springer Verlag Berlin Heidelberg, 2008.
Tutorial.
[ bib 
http ]
Among all the modeling approaches dedicated to cellular biology, differential algebra is particularly related to the wellestablished one based on nonlinear differential equations. In this paper, it is shown that differential algebra makes both simple and algorithmic one of the model reduction methods, the quasisteady 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.

[LMPX08]  François Lemaire, Marc Moreno Maza, Wei Pan, and Yuzhen Xie. When does (t) equal sat(t)? In Proceedings of the International Symposium on Symbolic and algebraic computation, pages 207214. ACM Press, 2008. [ bib ] 
[BLLM08a]  François Boulier, Marc Lefranc, François Lemaire, and PierreEmmanuel Morant. Applying a rigorous quasisteady state approximation method for proving the absence of oscillations in models of genetic circuits. In M. Rosenkranz K. Horimoto, G. Regensburger and T. Kutsia, editors, Proceedings of Algebraic Biology 2008, volume 5147 of LNCS, pages 5665. Springer Verlag Berlin Heidelberg, 2008. [ bib  http ] 
[BLLM08b]  François Boulier, Marc Lefranc, François Lemaire, and PierreEmmanuel Morant. Applying a rigorous quasisteady state approximation method for proving the absence of oscillations in models of genetic circuits. In Proceedings of Journées Ouvertes Biologie Informatique Mathématiques, pages 7782, 2008. [ bib  .pdf ] 
[Lem13]  François Lemaire. Computer algebra applied to chemical reaction systems, 2013. Invited at the Dagstuhl Seminar 12462. [ bib  DOI  http ] 
[Lem12] 
Fran}ois Lemaire.
Solving a chemical reaction system by a pde.
Presented at FELIM, Limoges, march 2012.
undef.
[ bib ]
No abstract

[Lem11]  François Lemaire. Application of differential algebra to the quasisteady state approximation in biology and physics, February 2011. Invited talk in the Experimentelle und konstruktive Algebra Graduiertenkolleg, RWTH Aachen University, Germany. [ bib  http ] 
[Lem10]  François Lemaire. Application of differential algebra to the quasisteady state approximation in biology and physics, October 2010. Invited talk at the Dart IV conference, Beijing, China. [ bib ] 
[Lem09b]  François Lemaire. Differential elimination and application to biology, November 2009. Invited talk in the Seminar at the CRBC, AIST, Tokyo, Japan. [ bib ] 
[Lem09a]  François Lemaire. Applying a rigorous quasisteady state approximation method for proving the absence of oscillations in models of genetic circuits, January 2009. Invited talk in the Seminar at at INRIA Grenoble  RhôneAlpes, France. [ bib ] 
[BCC^{+}18]  François Boulier, Hélène Castel, Nathalie Corson, Valentina Lanza, François Lemaire, Adrien Poteaux, Alban Quadrat, and Nathalie Verdière. SymbolicNumeric Methods for Nonlinear IntegroDifferential Modeling. working paper or preprint, April 2018. [ bib  http  .pdf ] 
[LSÜ08] 
François Lemaire, Alexandre Sedoglavic, and Aslı
Ürgüplü.
Moving Frame Based Strategies for Reduction of Ordinary
Differential/Recurrence Systems using their Expanded Lie Point
Symmetries.
01 2008.
[ bib 
http ]
When an ordinary differential/recurrence system presents a mparameters solvable group of symmetries, Lie group theory states that its number of variables could be reduce by m. This reduction process is classically done by rewriting original problem in an invariant coordinates set for these symmetries. We show how to use computational strategies using non explicit (infinitesimal) data representation in the reduction process and thus, how to avoidfor differential systemsthe explicit expansive computation of these invariants. Thus, these strategies lead to efficient algorithms that were used in the maple implementation. Keywords: Lie point symmetry. Reduction process. Computer Algebra. 
Mis à jour le 18 April 2018 à 16:38:57.