Abstract. In this paper, we propose a model of kinetics of antigens and antibodies based upon experiments conducted by Husby et al. on immune response against orally administrated ovalbumin. A differential algebraic system of equations is derived from the proposed model. We investigated the characteristics of the system and consequently desired numerical methods. In addition, the model parameters are estimated using experimental data, which are the concentrations of ovalbumins in the blood. The kinetics are also simulated with the estimated parameters. Throughout our work, the possible contributions of computational scientific approaches to the analysis of the mechanism of allergies are illustrated.

Abstract. In this paper, we deal with optimization problems on the Grassmann manifold, which is regarded as a quotient manifold of the Stiefel manifold by the orthogonal group. We develop Newton’s method for minimization of a general objective function. In particular, Newton’s equation is derived as a linear system of equations on a horizontal space. We also propose an efficient method for solving the linear system without explicitly using the representation matrix of the Hessian of the objective function based on the Krylov subspace method.