Parameter identification for an abstract Cauchy problem by quasilinearization
Abstract : A parameter identification problem is considered in the context of a linear abstract Cauchy problem with a parameter-dependent evolution operator. Conditions are investigated under which the gradient of the state with respect to a parameter possesses smoothness properties which lead to local convergence of an estimation algorithm based on quasilinearization. Numerical results are presented concerning estimation of unknown parameters in delay-differential equations. (JHD)
Sensitivity analysis and parameter estimation for a model of Chlamydia Trachomatis infection
In this paper we consider a parameter estimation problem for delay differential equations that are typical in the bioscience. The problem is motivated by a model of the dynamics of the intracellular development cycle of Chlamydia Trachomatis and can be formulated as a inverse problem for a system of delay equations. We derive the continuous sensitivity equations and show that the corresponding initial value problem is well-posed. The sensitivity equations are used to compute gradients in the optimization loop for the parameter estimation problem. Numerical examples are given to illustrate the key ideas and we close with a note about the use of continuous sensitivity equations in the design of experiments.
DIFFERENTIAL CALCULUS OF SEVERAL VARIABLES WITH MATHEMATICA OR MAPLE
The use of Computer Algebra Systems (CAS) in Mathematical Laboratories at Engineering Schools is increasing. Therefore, it has become necessary to undertake a new educational approach in the teaching of many mathematical topics. Obviously it is not possible to give the same lectures as in the 1950,s. The CAS allows us to experiment and teach in “a different way”. The students' mathematical knowledge at the beginning of their studies in the University is completely different. Moreover we have fewer credits assigned to Mathematical topics in engineering curriculum. The objective of he authors, professors of different Spanish Universities, is to try to demonstrate a new way to use the CAS, concretely Maple and Mathematica, as a support in the teaching of Differential Calculus of Several Variables. They take advantage of the computer's graphical capacities to sketch the graphs of surfaces defined in explicit, parametric or implicit form. They survey the general topics: limits, partial derivatives, differentiability, chain rule, implicit functions and extreme values. For each topic, they give a few basic instructions of the CAS used; afterwards they give several examples, in increasing order of difficulty, and finally the students must solve exercises and try to establish a general procedure for a quite general problem. In this paper we have included several examples used in this survey.