We discuss methods for a priori selection of parameters to be estimated in inverse problem formulations (such as Maximum Likelihood, Ordinary and Generalized Least Squares) for dynamical systems with numerous state variables and an even larger number of parameters. We illustrate the ideas with an in-host model for HIV dynamics which has been successfully validated with clinical data and used fo...

Following the work of Enright [3] there has been interest in studying second derivative methods for solving stiff ordinary differential equations. Successful implementations of second derivative methods have been reported by Enright [3], Sacks-Davis [9], [10] and Addison[l]. Wallace and Gupta [13] have suggested a polynomial formulation of the usual first-derivative multistep methods. Recently ...

Traditional medicines are effective but the standardization of Ayurvedic formulations is essential in order to assess the quality of drugs, based on the concentration of their active principles. Department of AYUSH has given preliminary guidelines for standardizing these conventional formulations, for uniformity of batches in production of Ayurvedic formulation and it is necessary to develop me...

In this work we investigate the advantages of multiscale methods in Petrov-Galerkin (PG) formulation in a general framework. The framework is subject to a localized orthogonal decomposition of a high dimensional solution space into a low dimensional multiscale space and a high dimensional remainder space with negligible fine scale information. As a model problem we consider the Poisson problem....

This paper develops a robust and distributed decision-making procedure for mathematically modelin 9 and computationally supporting simultaneous decision-making by members of an engineering team. The procedure (1) treats variations in the design posed by other members of the design team as conceptual noise; (2) incorporates such noise factors into conceptually robust decision-making; (3) provide...

In Burrage and Burrage (1996) it was shown that by introducing a very general formulation for stochastic Runge-Kutta methods, the previous strong order barrier of order one could be broken without having to use higher derivative terms. In particular, methods of strong order 1.5 were developed in which a Stratonovich integral of order one and one of order two were present in the formulation. In ...