79 citations · 638 across the 61 of their papers we have counts for
6 papers · 1 filter
Geometric Hydrodynamics via Madelung Transform
Boris Khesin, Gerard Misiolek, Klas Modin
We introduce a geometric framework to study Newton's equations on infinite-dimensional configuration spaces of diffeomorphisms and smooth probability densities. It turns out that s…
What makes nonholonomic integrators work?
Klas Modin, Olivier Verdier
A nonholonomic system is a mechanical system with velocity constraints not originating from position constraints; rolling without slipping is the typical example. A nonholonomic in…
Diffeomorphic random sampling using optimal information transport
Martin Bauer, Sarang Joshi, Klas Modin
In this article we explore an algorithm for diffeomorphic random sampling of nonuniform probability distributions on Riemannian manifolds. The algorithm is based on optimal informa…
A Numerical Algorithm for C2-splines on Symmetric Spaces
Geir Bogfjellmo, Klas Modin, Olivier Verdier
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 exam…
On Geodesic Completeness for Riemannian Metrics on Smooth Probability Densities
Martin Bauer, Sarang Joshi, Klas Modin
The geometric approach to optimal transport and information theory has triggered the interpretation of probability densities as an infinite-dimensional Riemannian manifold. The mos…
Currents and finite elements as tools for shape space
James Benn, Stephen Marsland, Robert I McLachlan +2
The nonlinear spaces of shapes (unparameterized immersed curves or submanifolds) are of interest for many applications in image analysis, such as the identification of shapes that…