THE H-PRINCIPLE - NEW IDEAS, ALGORITHMS AND METHODS IN APPLIED-MATHEMATICS AND STATISTICS

The H-principle, or the Heisenberg principle of mathematical modelling, is a new principle of carrying out mathematical analysis of data. It has its conceptual basis in the philosophical discussions of the 1920s concerning description of physical systems. It is a mathematical formulation of concepts given in the Heisenberg uncertainty relation. The main idea is to include the model uncertainties in the modelling procedure. The principle suggests that the modelling is carried out in steps, such that at each step we determine the improvement and the associated precison. The improvement and the associated precision are then balanced in a way prescribed by the Heisenberg uncertainty principle. This principle thus prescribes how the modelling procedure should be carried out. We have applied this to different fields of science. It has then generated new ideas, algorithms and methods. Here we shall present some results arrived at, when this principle was applied to some important areas of science. The algorithms are illustrated by chemometric examples.