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Identifiability and estimation of pharmacokinetic parameters for the ligands of the macrophage mannose receptor

Nathalie Verdiere, Lilianne Denis-Vidal, Ghislaine Joly-Blanchard, Dominique Domurado (2005)

International Journal of Applied Mathematics and Computer Science

The aim of this paper is numerical estimation of pharmacokinetic parameters of the ligands of the macrophage mannose receptor, without knowing it a priori the values of these parameters. However, it first requires a model identifiability analysis, which is done by applying an algorithm implemented in a symbolic computation language. It is shown that this step can lead to a direct numerical estimation algorithm. In this way, a first estimate is computed from noisy simulated observations without it...

Identification of a quasilinear parabolic equation from final data

Luis a. Fernández, Cecilia Pola (2001)

International Journal of Applied Mathematics and Computer Science

We study the identification of the nonlinearities A,(→)b and c appearing in the quasilinear parabolic equation y_t − div(A(y)∇y + (→)b(y)) + c(y) = u inΩ × (0,T), assuming that the solution of an associated boundary value problem is known at the terminal time, y(x,T), over a (probably small) subset of Ω, for each source term u. Our work can be divided into two parts. Firstly, the uniqueness of A,(→)b and c is proved under appropriate assumptions. Secondly, we consider a finite-dimensional optimization...

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