Typical optimal design methods for inverse or parameter estimation problems are designed to choose optimal sampling distributions through minimization of a specific cost function related to the resulting error in parameter estimates. It is hoped that the inverse problem will produce parameter estimates with increased accuracy using data collected according… (More)
We consider the problem of estimating a modeling parameter using a weighted least squares criterion (,) = ∑ =1 1 () 2 (() − (,)) 2 for given data by introducing an abstract framework involving generalized measurement procedures characterized by probability measures. We take an optimal design perspective, the general premise (illustrated via examples) being… (More)
The purpose of this paper is to introduce a new spline approximation scheme for retarded functional differential equations. The special feature of this approximation scheme is that it preserves the product space structure of retarded systems and approximates the adjoint semigroup in a strong sense. These facts guarantee the convergence of the solution… (More)
For an infinite-dimensional linear quadratic control problem in Hilbert space, approximation of the solution of the algebraic Riccati operator equation in the strong operator topology is considered under conditions weaker than uniform exponential stability of the approximating systems. As an application, strong convergence of the approximating Riccati… (More)
We present formulations of the Trotter-Kato theorem for approximation of linear C 0-semigroups which provide very useful framework when convergence of numerical approximations to solutions of PDEs are studied. Applicability of our results is demonstrated using a first order hyperbolic equation , a wave equation and Stokes' equation as illustrative examples.
The goal of this report is to discuss educational approaches for bridging the different perspectives of the physiological and mathematical disciplines. These approaches can enhance the learning experience for physiology, medical, and mathematics students and simultaneously act to stimulate mathematical/physiological/clinical interdisciplinary research.… (More)
This article examines the functional and clinical impact of time delays that arise in human physiological systems, especially control systems. An overview of the mathematical and physiological contexts for considering time delays will be illustrated, from the system level to cell level, by examining models that incorporate time delays. This examination will… (More)