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In this paper, we give three theoretical and practical contributions for solving polynomial ODE or PDE systems. The first one is practical: an algorithm which improves the purely algebraic part of Rosenfeld—Gröbner (the polynomial ODE or PDE systems simplifier which is the core of the Maple 5.5 diffalg package). It is a variant of lextriangular(More)
BACKGROUND Hydroxyethylstarch used for volume restoration in brain-dead kidney donors has been associated with impaired kidney function in the transplant recipients. We undertook a multicentre randomised study to assess the frequency of acute renal failure (ARF) in patients with severe sepsis or septic shock treated with hydroxyethylstarch or gelatin. (More)
We introduce the concept of comprehensive triangular decomposition (CTD) for a parametric polynomial system F with coefficients in a field. In broad words, this is a finite partition of the the parameter space into regions, so that within each region the " geometry " (number of irreducible components together with their dimensions and degrees) of the(More)
We evaluated whether a knowledge-based system (KBS) connected to a ventilator in pressure support mode could correctly predict the ability of patients to tolerate total withdrawal from ventilatory support. The KBS was designed to continuously adapt ventilatory assistance to the needs of the patient, to manage a strategy of gradually decreasing ventilatory(More)
In this paper, we apply a rigorous quasi-steady state approximation method on a family of models describing a gene regulated by a polymer of its own protein. We study the absence of oscillations for this family of models and prove that Poincaré-Andronov-Hopf bifurcations arise if and only if the number of polymerizations is greater than 8. A result(More)
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,(More)
The procedure for weaning a patient with respiratory insufficiency from mechanical ventilation may be complex and requires expertise obtained by long clinical practice. We designed a knowledge-based system for the management of patients receiving respiratory support and implemented a weaning procedure. The system is intended for patients whose spontaneous(More)