39 citations · 312 across the 32 of their papers we have counts for
33 papers
A short proof of Isserlis' theorem
Hans Z. Munthe-Kaas, Olivier Verdier, Gilles Vilmart
We show that Isserlis' theorem follows as a corollary to the invariant tensor theorem for isotropic tensors.
The aromatic bicomplex for the description of divergence-free aromatic forms and volume-preserving integrators
Adrien Laurent, Robert I. McLachlan, Hans Z. Munthe-Kaas +1
Aromatic B-series were introduced as an extension of standard Butcher-series for the study of volume-preserving integrators. It was proven with their help that the only volume-pres…
Ablation Path Saliency
Justus Sagemüller, Olivier Verdier
Various types of saliency methods have been proposed for explaining black-box classification. In image applications, this means highlighting the part of the image that is most rele…
Linear inverse problems with nonnegativity constraints: singularity of optimisers
Camille Pouchol, Olivier Verdier
We look at continuum solutions in optimisation problems associated to linear inverse problems with non-negativity constraint . We focus on the case where the noi…
ML-EM algorithm with known continuous movement model
Camille Pouchol, Olivier Verdier
In Positron Emission Tomography, movement leads to blurry reconstructions when not accounted for. Whether known a priori or estimated jointly to reconstruction, motion models are i…
The ML-EM algorithm in continuum: sparse measure solutions
Camille Pouchol, Olivier Verdier
Linear inverse problems with Poisson noise and non-negative unknown are ubiquitous in applications, for instance in Positron Emission Tomography (PET) in medical…
Spatiotemporal PET reconstruction using ML-EM with learned diffeomorphic deformation
Ozan Öktem, Camille Pouchol, Olivier Verdier
Patient movement in emission tomography deteriorates reconstruction quality because of motion blur. Gating the data improves the situation somewhat: each gate contains a movement p…
Invariant connections, Lie algebra actions, and foundations of numerical integration on manifolds
Hans Z. Munthe-Kaas, Ari Stern, Olivier Verdier
Motivated by numerical integration on manifolds, we relate the algebraic properties of invariant connections to their geometric properties. Using this perspective, we generalize so…
Task adapted reconstruction for inverse problems
Jonas Adler, Sebastian Lunz, Olivier Verdier +2
The paper considers the problem of performing a task defined on a model parameter that is only observed indirectly through noisy data in an ill-posed inverse problem. A key aspect…
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…
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…
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…
Numerical Study of Nonlinear Dispersive Wave Models with SpecTraVVave
Henrik Kalisch, Daulet Moldabayev, Olivier Verdier
In nonlinear dispersive evolution equations, the competing effects of nonlinearity and dispersion make a number of interesting phenomena possible. In the current work, the focus is…
Full affine equivariance and weak natural transformations in numerical analysis - the case of B-Series
Olivier Verdier
Many algorithms in numerical analysis are affine equivariant: they are immune to changes of affine coordinates. This is because those algorithms are defined using affine invariant…
Extension of Matrix Pencil Reduction to Abelian Categories
Olivier Verdier
Matrix pencils, or pairs of matrices, are used in a variety of applications. By the Kronecker decomposition Theorem, they admit a normal form. This normal form consists of four par…
Symmetry reduction for central force problems
Robert I McLachlan, Klas Modin, Olivier Verdier
We given an elementary illustration of symmetry reduction for central force problems, drawing phase portraits of the reduced dynamics as the intersection of Casimir and energy leve…
Butcher series: A story of rooted trees and numerical methods for evolution equations
Robert I McLachlan, Klas Modin, Hans Munthe-Kaas +1
Butcher series appear when Runge-Kutta methods for ordinary differential equations are expanded in power series of the step size parameter. Each term in a Butcher series consists o…
Geometry of discrete-time spin systems
Robert I. McLachlan, Klas Modin, Olivier Verdier
Classical Hamiltonian spin systems are continuous dynamical systems on the symplectic phase space . In this paper we investigate the underlying geometry of a time discreti…
A classification of volume preserving generating forms in R^3
Olivier Verdier, Huiyan Xue, Antonella Zanna
In earlier work, Lomeli and Meiss used a generalization of the symplectic approach to study volume preserving generating differential forms. In particular, for the c…
Multi-symplectic discretisation of wave map equations
David Cohen, Olivier Verdier
We present a new multi-symplectic formulation of constrained Hamiltonian partial differential equations, and we study the associated local conservation laws. A multi-symplectic dis…
B-series methods are exactly the affine equivariant methods
Robert I. McLachlan, Klas Modin, Hans Munthe-Kaas +1
Butcher series, also called B-series, are a type of expansion, fundamental in the analysis of numerical integration. Numerical methods that can be expanded in B-series are defined…
Integrators on homogeneous spaces: Isotropy choice and connections
Hans Munthe-Kaas, Olivier Verdier
We consider numerical integrators of ODEs on homogeneous spaces (spheres, affine spaces, hyperbolic spaces). Homogeneous spaces are equipped with a built-in symmetry. A numerical i…
Symplectic integrators for spin systems
Robert I. McLachlan, Klas Modin, Olivier Verdier
We present a symplectic integrator, based on the canonical midpoint rule, for classical spin systems in which each spin is a unit vector in . Unlike splitting methods…
A minimal-variable symplectic integrator on spheres
Robert I. McLachlan, Klas Modin, Olivier Verdier
We construct a symplectic, globally defined, minimal-coordinate, equivariant integrator on products of 2-spheres. Examples of corresponding Hamiltonian systems, called spin systems…