CPP

Abstract

Mathematical concepts will be discussed that are shared by certain approaches for modelling cardiac waves of electrical activity potential with those that are used in the modelling of other types of waves and also with the methods of imaging science using template matching. The main concept to be discussed is the derivation of optimal path dynamics obtained by applying reduction by symmetry to Hamilton's principle for evolution on the tangent space of smooth invertible maps possessing smooth inverses (diffeomorphisms). This concept is shared by cardiac waves, fluid dynamics, shape dynamics, shallow water waves, imaging science and solitons. Several applications will also be discussed.