On Defining and Computing “Good” Conservation Laws

Lemaire, François; Temperville, Alexandre

doi:10.1007/978-3-319-12982-2_1

Cited by 2 publications

(4 citation statements)

References 12 publications

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“…Except the CSBmodulo call, the instructions of Algorithm getSparsestFraction are done at most in O(n 3 ). In fact, the complexity of getSparsestFraction is dominated by the one of CSBmodulo, which can be exponential in n in the worst case [8].…”

Section: Complexity Of Getsparsestfractionmentioning

confidence: 99%

“…Following Lemma 1 is a rephrasing of [8,Theorem 1]. It is the key ingredient ensuring the greedy approach chosen in [8], which consists in repeatedly reducing the number of nonzeros of some row of M , until it is not possible anymore.…”

Section: Application To Systems Of Odesmentioning

confidence: 99%

“…The relatively small improvement between (1) and (2) in terms of degrees proves useful while searching for a Hopf Bifurcation. Indeed, the Routh-Hurwitz criterion applied on systems (1) and (2) leads to semi-algebraic systems of the form h 1 , h 2 , h 3 , h 4 = 0, h 5 , h 6 , h 7 > 0, with respective degrees 9, 2, 9, 42, 12, 20, 23 in the case of (1), and smaller degrees 7,2,7,32,8,14,19 in the case of (2).…”

Section: Introductionmentioning

confidence: 99%

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Computing Sparse Representations of Systems of Rational Fractions

Lemaire

Temperville

2016

Computer Algebra in Scientific Computing

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International audienceWe present new algorithms for computing sparse representations of systems of parametric rational fractions by means of change of coordinates. Our algorithms are based on computing sparse matrices encoding the degrees of the parameters occurring in the fractions. Our methods facilitate further qualitative analysis of systems involving rational fractions. Contrary to symmetry based approaches which reduce the number of parameters, our methods only increase the sparsity, and are thus complementary. Previously hand made computations can now be fully automated by our methods

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Section: Complexity Of Getsparsestfractionmentioning

confidence: 99%

Section: Application To Systems Of Odesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Computing Sparse Representations of Systems of Rational Fractions

Lemaire

Temperville

2016

Computer Algebra in Scientific Computing

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“…Exact conservation laws, i.e., first integrals of the full dynamics, were already used for model order reduction. If such quantities exist, the model can be reduced by eliminating a number of variables and equations equal to the number of independent conservation laws [28,31]. In the present work, we introduce the approximate conservation laws that are quantities conserved by the fast dynamics.…”

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confidence: 99%

Reduction of Chemical Reaction Networks with Approximate Conservation Laws

Desoeuvres,

Iosif,

Lüders

et al. 2024

SIAM J. Appl. Dyn. Syst.

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Model reduction of fast-slow chemical reaction networks based on the quasi-steady state approximation fails when the fast subsystem has first integrals. We call these first integrals approximate conservation laws. In order to define fast subsystems and identify approximate conservation laws, we use ideas from tropical geometry. We prove that any approximate conservation law evolves more slowly than all the species involved in it and therefore represents a supplementary slow variable in an extended system. By elimination of some variables of the extended system, we obtain networks without approximate conservation laws, which can be reduced by standard singular perturbation methods. The field of applications of approximate conservation laws covers the quasi-equilibrium approximation, which is well known in biochemistry. We discuss reductions of slow-fast as well as multiple timescale systems. Networks with multiple timescales have hierarchical relaxation. At a given timescale, our multiple timescale reduction method defines three subsystems composed of (i) slaved fast variables satisfying algebraic equations, (ii) slow driving variables satisfying reduced ordinary differential equations, and (iii) quenched much slower variables that are constant. The algebraic equations satisfied by fast variables define chains of nested normally hyperbolic invariant manifolds. In such chains, faster manifolds are of higher dimension and contain the slower manifolds. Our reduction methods are introduced algorithmically for networks with monomial reaction rates and linear, monomial, or polynomial approximate conservation laws. We propose symbolic algorithms to reshape and rescale the networks such that geometric singular perturbation theory can be applied to them, test the applicability of the theory, and finally reduce the networks. As a proof of concept, we apply this method to a model of the TGF-beta signaling pathway.

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On Defining and Computing “Good” Conservation Laws

Cited by 2 publications

References 12 publications

Computing Sparse Representations of Systems of Rational Fractions

Computing Sparse Representations of Systems of Rational Fractions

Reduction of Chemical Reaction Networks with Approximate Conservation Laws

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