|[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):281-292, 2011. [ bib ]|
|[BLLM11]||François Boulier, Marc Lefranc, François Lemaire, and Pierre-Emmanuel Morant. Model Reduction of Chemical Reaction Systems using Elimination. Mathematics in Computer Science, 5:289-301, 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(2-3):185-201, 2010. [ bib ]|
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.
François Boulier, François Lemaire, and Marc Moreno Maza.
Computing differential characteristic sets by change of ordering.
Journal of Symbolic Computation, 45(1):124-149, 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.
François Boulier, François Lemaire, Alexandre Sedoglavic, and
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 |
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.
Pierre-Emmanuel Morant, Quentin Thommen, François Lemaire,
Constant Vandermoëre, Benjamin Parent, and Marc Lefranc.
Oscillations in the expression of a self-repressed gene induced by
a slow transcriptional dynamics.
Physical Review Letters, 102(6):068104, 2009.
Accepted for publication in Physical Review Letters.
[ bib |
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.
An orderly linear PDE system with analytic initial conditions with a
non analytic solution.
Journal of Symbolic Computation, 35(5):487-498, 2003.
Special Issue on Computer Algebra and Computer Analysis.
[ bib ]
We give a linear PDE system, with analytic initial conditions given w.r.t an orderly ranking, the solution of which is not analytic (moreover the solution is not Gevrey for any order). This examples proves that the analyticity Riquier theorem (generalization of the Cauchy-Kovalevskaya theorem) does not generalize to PDE systems endowed with orderly rankings.
|[BLRR13]||François Boulier, François Lemaire, Georg Regensburger, and Markus Rosenkranz. On the integration of differential fractions. In Proceedings of ISSAC'13, 2013. To appear. [ bib ]|
|[BKL+12]||Kirill Batmanov, Céline Kuttler, François Lemaire, Cédric Lhoussaine, and Cristian Versari. Symmetry-based model reduction for approximate stochastic analysis. In CMSB, pages 49-68, 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 semi-algebraic 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 38-51, 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 61-72, Kassel, Germany, 2011. http://hal.archives-ouvertes.fr/hal-00599440. [ 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 73-87, Kassel, Germany, 2011. http://hal.archives-ouvertes.fr/hal-00603290. [ 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 149-166, 2010. [ bib ]|
Samuel Vidal, Michel Petitot, François Boulier, François Lemaire,
and Céline Kuttler.
Models of stochastic gene expression and weyl algebra.
In Proceedings of ANB2010, pages 76-97, 2010.
[ bib |
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.
François Lemaire and Aslı Ürgüplü.
Mabsys: Modeling and analysis of biological systems.
In Proceedings of ANB2010, pages 57-72, 2010.
[ bib |
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.
François Lemaire and Aslı Ürgüplü.
A method for semi-rectifying 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 semi-rectify 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.
François Boulier, Changbo Chen, François Lemaire, and Marc Moreno
Real root isolation of regular chains.
In Asian Symposium on Computer Mathematics, pages 15-29, 2009.
[ bib |
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.
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
22-39. Springer Verlag Berlin Heidelberg, 2008.
[ bib |
Among all the modeling approaches dedicated to cellular biology, differential algebra is particularly related to the well-established 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 quasi-steady 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 207-214. ACM Press, 2008. [ bib ]|
|[BLLM08a]||François Boulier, Marc Lefranc, François Lemaire, and Pierre-Emmanuel Morant. Applying a rigorous quasi-steady 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 56-65. Springer Verlag Berlin Heidelberg, 2008. [ bib | http ]|
|[BLLM08b]||François Boulier, Marc Lefranc, François Lemaire, and Pierre-Emmanuel Morant. Applying a rigorous quasi-steady state approximation method for proving the absence of oscillations in models of genetic circuits. In Proceedings of Journées Ouvertes Biologie Informatique Mathématiques, pages 77-82, 2008. [ bib | .pdf ]|
|[BLL+07]||François Boulier, Marc Lefranc, François Lemaire, Pierre-Emmanuel Morant, and Aslı Ürgüplü. On proving the absence of oscillations in models of genetic circuits. In K. Horimoto H. Anai and T. Kutsia, editors, Proceedings of Algebraic Biology 2007, volume 4545 of LNCS, pages 66-80. Springer Verlag Berlin Heidelberg, 2007. [ bib | http ]|
|[MVP+07]||Pierre-Emmanuel Morant, Constant Vandermoere, Benjamin Parent, François Lemaire, Florence Corellou, Christian Schwartz, François-Yves Bouget, and Marc Lefranc. Oscillateurs génétiques simples. Applications à l'horloge circadienne d'une algue unicellulaire. In proceedings of the Rencontre du non linéaire, Paris, 2007. [ bib | http ]|
Changbo Chen, François Lemaire, Marc Moreno Maza, Wei Pan, and Yuzhen Xie.
Efficient computations of irredundant triangular decompositions with
the regularchains library.
In Yong Shi, G. Dick van Albada, Jack Dongarra, and Peter M. A.
Sloot, editors, ICCS '07: Proceedings of the 7th international
conference on Computational Science, Part II, volume 4488 of Lecture
Notes in Computer Science, pages 268-271. Springer-Verlag, 2007.
[ bib |
We present new functionalities that we have added to the RegularChains library in Maple to efficiently compute irredundant triangular decompositions. We report on the implementation of different strategies. Our experiments show that, for difficult input systems, the computing time for removing redundant components can be reduced to a small portion of the total time needed for solving these systems.
|[CGL+07]||Changbo Chen, Oleg Golubitsky, François Lemaire, Marc Moreno Maza, and Wei Pan. Comprehensive triangular decomposition. In Computer Algebra in Scientific Computing, volume 4770 of Lecture Notes in Computer Science, pages 73-101. Springer, 2007. [ bib | .pdf ]|
|[BLM06]||François Boulier, François Lemaire, and Marc Moreno Maza. Well known theorems on triangular systems and the D5 principle. In Proceedings of Transgressive Computing 2006, pages 79-91, Granada, Spain, 2006. [ bib | http ]|
François Lemaire, Marc Moreno Maza, and Yuzhen Xie.
Making a sophisticated symbolic solver available to different
communities of users.
In Asian Technology Conference in Mathematics'06, Hong Kong,
[ bib ]
Triangular decompositions have become one of the major tools for solving systems of non-linear algebraic or differential equations symbolically. These decompositions display more geometrical information than other symbolic descriptions of polynomial systems. However, their specifications and the algorithms computing them are quite sophisticated. Their implementation in mathematical software, their accessibility, and ease of use for non-expert users are challenges that we discuss in this paper. We discuss our solutions and illustrate them with the implementation of an algorithm for triangular decompositions, called Triade, in three computer algebra systems: AXIOM, ALDOR, and MAPLE, targeting different communities of users. We believe that these implementations of the same sophisticated mathematical algorithm for different communities of experts, advanced users, and non-experts is a unique experience in the area of symbolic computations which could benefit other algorithms in this field.
François Lemaire, Marc Moreno Maza, and Yuzhen Xie.
The RegularChains library in MAPLE 10.
In Ilias S. Kotsireas, editor, The MAPLE conference, pages
355-368, Waterloo, Canada, 2005.
[ bib ]
The RegularChains library provide facilities for symbolic computations with systems of polynomial equations. In particular, it allows to compute modulo a set of algebraic relations. Automatic case discussion (and recombination) handles zero-divisors and parameters. This permits triangular decomposition of polynomial equations
|[BDVHL04]||François Boulier, Lilianne Denis-Vidal, Thibaut Henin, and François Lemaire. LÉPISME. In proceedings of the ICPSS conference, 2004. Submitted to the Journal of Symbolic Computation. [ bib | http ]|
Joe Bonasia, François Lemaire, Greg Reid, and Lihong Zhi.
Determination of approximate symmetries of differential equations.
In David Gomez-Ullate, editor, CRM proceedings and Lectures
Notes, volume 39, pages 233-249. American Mathematical Society, 2004.
[ bib ]
There has been considerable progress in the theory and computer implementation of symbolic computation algorithms to automatically determine and exploit exact symmetries of exact differential equations. Such programs usually apply a finite number of exact differentiations and eliminations to the overdetermined linearized equations for the unknown symmetries (the symmetry defining equations), to complete them to certain involutive or standard forms. The symmetry properties can be determined from these involutive forms.
|[Lem02]||François Lemaire. Les classements les plus généraux assurant l'analycité des systèmes orthonomes pour des conditions initiales analytiques. In Victor G. Ganzha, Ernst W. Mayr, and Evgenii V. Vorozhtsov, editors, proceedings of Computer Algebra in Scientific computation 2002, pages 207-219, Yalta, Ukraine, 2002. Institüt für Informatik, Technische Universität München. [ bib ]|
|[BLM01]||François Boulier, François Lemaire, and Marc Moreno Maza. PARDI! In ISSAC'01: Proceedings of the 2001 international symposium on Symbolic and algebraic computation, pages 38-47, New York, NY, USA, 2001. ACM Press. [ bib | http ]|
|[BL00]||François Boulier and François Lemaire. Computing canonical representatives of regular differential ideals. In ISSAC'00: Proceedings of the 2000 International Symposium on Symbolic and algebraic computation, pages 38-47, New York, NY, USA, 2000. ACM Press. [ bib | http ]|
|[Lem13]||François Lemaire. Computer algebra applied to chemical reaction systems, 2013. Invited at the Dagstuhl Seminar 12462. [ bib | DOI | http ]|
Solving a chemical reaction system by a pde.
Presented at FELIM, Limoges, march 2012.
[ bib ]
|[Lem11]||François Lemaire. Application of differential algebra to the quasi-steady 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 quasi-steady 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 quasi-steady 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 - Rhône-Alpes, France. [ bib ]|
François Lemaire, Alexandre Sedoglavic, and Aslı
Moving Frame Based Strategies for Reduction of Ordinary
Differential/Recurrence Systems using their Expanded Lie Point
[ bib |
When an ordinary differential/recurrence system presents a m-parameters 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 avoid-for differential systems-the 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.
|[BL07]||François Boulier and François Lemaire. A computer scientist point of view on Hilbert's differential theorem of zeros. Submitted to Applicable Algebra in Engineering, Communication and Computing, 2007. [ bib | http ]|
|[LRZ06]||François Lemaire, Greg Reid, and Yang Zhang. Non-commutative Riquier theory in moving frames of differential operators. Submitted to the Journal of Computation and Mathematics, 2006. [ bib ]|
|[BLM07]||François Boulier, François Lemaire, and Marc Moreno Maza. Computing differential characteristic sets by change of ordering. Technical report, Université Lille I, 2007. Submitted to the Journal of Symbolic Computation. [ bib | http ]|
|[BLM01b]||François Boulier, François Lemaire, and Marc Moreno Maza. Well known theorems on triangular systems. Technical report, Université Lille I, 59655, Villeneuve d'Ascq, France, November 2001. Ref. LIFL 2001-09. [ bib ]|
|[BLM01a]||François Boulier, François Lemaire, and Marc Moreno Maza. PARDI ! Technical report, Université Lille I, LIFL, 59655, Villeneuve d'Ascq, France, 2001. Ref. LIFL 2001-01, short version presented at ISSAC 2001. [ bib ]|
|[Lem01]||François Lemaire. An orderly linear PDE system with analytic initial conditions with a non analytic solution. Technical Report LIFL 2001-10, Université Lille I, LIFL, 59655 Villeneuve d'Ascq France, 2001. (to appear in the JSC Special Issue on Computer Algebra and Computer Analysis). [ bib ]|
Contribution à l'algorithmique en algèbre
PhD thesis, Université Lille I, 59655, Villeneuve d'Ascq, France,
[ bib |
This thesis is dedicated to the study of nonlinear partial differential equations systems. The chosen approach is differential algebra. Given a system of differential equations, we seek information about its solutions. To do so, we first compute particular systems (called differential regular chains) such that the union of their solutions coincide with the solutions of the initial system. This thesis mainly presents new results in symbolic computation. Chapter 2 clarifies the link between regular chains and differential regular chains. Two new algorithms (given in chapters 4 and 5) improve existing algorithms computing these differential regular chains. These algorithms involve purely algebraic techniques which help reduce expression swell and help avoid unnecessary computations. Previously intractable problems have been solved using these techniques. An algorithm computing the normal form of a differential polynomial modulo a differential regular chain is described in chapter 2. The last results deal with analysis. The solutions we consider are formal power series. Chapter 3 gives sufficient conditions for a solution to be analytic. The same chapter presents a counter-example to a conjecture dealing with the analyticity of formal solutions.
Mis à jour le 3 October 2016 à 10:14:36.