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The goal of this thesis is the development and the analysis of numerical methods for problems where the unknown is a curve on a smooth manifold. In particular, the thesis is structured around the three following problems: homotopy continuation, curve inter ...
In algorithms for solving optimization problems constrained to a smooth manifold, retractions are a well-established tool to ensure that the iterates stay on the manifold. More recently, it has been demonstrated that retractions are a useful concept for ot ...
Every newly created object goes through several initialization states: starting from a state where all fields are uninitialized until all of them are assigned. Any operation on the object during its initialization process, which usually happens in the cons ...
We prove equidistribution at shrinking scales for the monochromatic ensemble on a compact Riemannian manifold of any dimension. This ensemble on an arbitrary manifold takes a slowly growing spectral window in order to synthesize a random function. With hig ...
This article presents an overview of robot learning and adaptive control applications that can benefit from a joint use of Riemannian geometry and probabilistic representations. The roles of Riemannian manifolds, geodesics and parallel transport in robotic ...
Every newly created object goes through several initialization states: starting from a state where all fields are uninitialized until all of them are assigned. Any operation on the object during its initialization process, which usually happens in the cons ...
We investigate the impact of more realistic room simulation for training far-field keyword spotting systems without fine-tuning on in-domain data. To this end, we study the impact of incorporating the following factors in the room impulse response (RIR) ge ...
The inception of object-oriented programming introduces a category of bugs related to object construction: initialization errors. Every newly created object goes through several initialization states: starting from a state where all fields are uninitialize ...
The purpose of this thesis is to provide an intrinsic proof of a Gauss-Bonnet-Chern formula for complete Riemannian manifolds with finitely many conical singularities and asymptotically conical ends. A geometric invariant is associated to the link of both ...
In this paper, we provide a simple pedagogical proof of the existence of covariant renormalizations in Euclidean perturbative quantum field theory on closed Riemannian manifolds, following the Epstein–Glaser philosophy. We rely on a local method that allow ...
