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

100%
Verdiere N., Denis-Vidal L., Joly-Blanchard G., Domurado D.
International Journal of Applied Mathematics and Computer Science
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2005
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tom 15
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nr 4
517-526
EN
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 a priori parameter values. Then the resulting parameter estimate is improved by using the classical least-squares method.
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Set-membership identifiability of nonlinear models and related parameter estimation properties

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Jauberthie C., Travé-Massuyès L., Verdière N.
International Journal of Applied Mathematics and Computer Science
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2016
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tom 26
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nr 4
803-813
EN
Identifiability guarantees that the mathematical model of a dynamic system is well defined in the sense that it maps unambiguously its parameters to the output trajectories. This paper casts identifiability in a set-membership (SM) framework and relates recently introduced properties, namely, SM-identifiability, μ-SM-identifiability, and ε-SM-identifiability, to the properties of parameter estimation problems. Soundness and ε-consistency are proposed to characterize these problems and the solution returned by the algorithm used to solve them. This paper also contributes by carefully motivating and comparing SM-identifiability, μ-SM-identifiability and ε-SM-identifiability with related properties found in the literature, and by providing a method based on differential algebra to check these properties.
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Source localization and sensor placement in environmental monitoring

75%
Khapalov A.
International Journal of Applied Mathematics and Computer Science
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2010
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tom 20
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nr 3
445-458
EN
In this paper we discuss two closely related problems arising in environmental monitoring. The first is the source localization problem linked to the question How can one find an unknown "contamination source"? The second is an associated sensor placement problem: Where should we place sensors that are capable of providing the necessary "adequate data" for that? Our approach is based on some concepts and ideas developed in mathematical control theory of partial differential equations.
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