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This paper deals with an application of regression analysis to the regulation of the blood-sugar under diabetes mellitus. Section 2 gives a description of Gram-Schmidt orthogonalization, while Section 3 discusses the difference between Gauss-Markov estimation and Least Squares Estimation. Section 4 is devoted to the statistical analysis of the blood-sugar during the night. The response change of blood-sugar is explained by three variables: time, food and physical activity ("Bewegung"). At the beginning...
This work aims at introducing modelling, theoretical and numerical studies related to a new downscaling technique applied to computational fluid dynamics.
Our method consists in building a local model, forced by large scale information computed thanks to a classical numerical weather predictor.
The local model, compatible with the Navier-Stokes equations, is used
for the small scale computation (downscaling) of the considered
fluid. It is
inspired by Pope's works on turbulence, and consists in...
Biology and medicine are not the only fields that present problems unsolvable through a linear models approach. One way to overcome this obstacle is to use nonlinear methods, even though these are not as thoroughly explored. Another possibility is to linearize and transform the originally nonlinear task to make it accessible to linear methods. In this aricle I investigate an easy and quick criterion to verify suitability of linearization of nonlinear problems via Taylor series expansion so that...
Dans cet article, on donne l'expression numérique du protocole additif de référence sur le croisement pondéré de deux facteurs, pour d'une part un protocole multinumérique, d'autre part un tableau de contingence ternaire. On donne un algorithme de calcul et on montre que, pour un tableau de contingence ternaire, la mesure additive de référence s'obtient à partir de l'analyse des correspondances d'un tableau marginal binaire en mettant en éléments supplémentaires les deux autres tableaux marginaux...
The aim of this paper is to take an in-depth look at the long time behaviour of some continuous time markovian dynamical systems and at its numerical analysis. We first propose a short overview of the main ergodicity properties of time continuous homogeneous Markov processes (stability, positive recurrence). The basic tool is a Lyapunov function. Then, we investigate if these properties still hold for the time discretization of these processes, either with constant or decreasing step (ODE method...
The aim of this paper is to take an in-depth look at the long
time behaviour of some continuous time Markovian dynamical systems and at its
numerical analysis. We first propose a short overview of the main
ergodicity properties
of time continuous homogeneous Markov processes (stability, positive
recurrence). The basic
tool is a Lyapunov function. Then, we investigate if these
properties still hold for
the time discretization of these processes, either with constant or
decreasing step (ODE...
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