Cubic spline interpolation on Euclidean space is a standard topic in numerical analysis, with
countless applications in science and technology. In several emerging fields, for example …

The quantum Hamiltonians in non inertial frames, while proper to describe the time
evolution, might give a false information about the radiation of physical systems. The formal …

Left Lie reduction is a technique used in the study of curves in bi-invariant Lie groups [32,
33, 40]. Although the manifold SPD (n) of all n× n symmetric positive-definite matrices is not …

The approaches to Classical and Quantum Mechanics are quite different in many aspects,
the most striking one being the linear structure which is present in the Hilbert space H and …

This article presents a novel resolution to the problem of spline interpolation versus least-
squares fitting on smooth Riemannian manifolds utilizing the method of gradient flows of …

We study a trajectory-planning problem whose solution path evolves by means of a Lie
group action and passes near a designated set of target positions at particular times. This is …

The problem of recovering continuous time signals from a set of discrete measurements is ill-
posed in a classical sense (non-uniqueness of solution). Our approach introduces …

We study quantum dynamics of the adiabatic search algorithm with the equivalent two-level
system. Its adiabatic and non-adiabatic evolution is studied and visualized as trajectories of …

This thesis is centred around higher-order invariant variational problems defined on Lie
groups. We are mainly motivated by applications in computational anatomy and quantum …

Quantum splines are curves in a Hilbert space or, equivalently, in the corresponding Hilbert
projective space, which generalize the notion of Riemannian cubic splines to the quantum …