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In this paper we propose the Middle-Axis-Rotation (MAR) parametrization of human limbs that addresses the ill-conditioned cases of analytical Inverse Kinematics (IK) algorithms. The MAR parametrization is singularity-free in the reach space of the human li ...
In this report, we use a variety of tools from differential geometry to propose a nonlinear extension of the principal components analysis (PCA) into manifolds setting. This extension, that we shall call principal geodesics analysis (PGA), attempts to find ...
The matrix completion problem consists of finding or approximating a low-rank matrix based on a few samples of this matrix. We propose a new algorithm for matrix completion that minimizes the least-square distance on the sampling set over the Riemannian ma ...
This paper focuses on urban environmental system identification. Wind-flow modeling is a challenging task because of simplifications of complex processes as well as geometry simplifications. Even a more detailed model may not be accurate because of uncerta ...
Institute of Electrical and Electronics Engineers ( IEEE )2013
This work addresses the signatures of catchment geomorphology on base flow recession curves. The study links the time-varying geometry of a river network with a classic parametrization of recession events in the case of 27 catchments located in Switzerland ...
Under mild assumptions, we remove all traces of the axiom of choice from the construction of the maximal globally hyperbolic Cauchy development in general relativity. The construction relies on the notion of direct union manifolds, which we review. The con ...
In this paper we review and we extend the reduced basis approximation and a posteriori error estimation for steady Stokes flows in affinely parametrized geometries, focusing on the role played by the Brezzi's and Babuska's stability constants. The crucial ...
Antarctic megadunes are characterized by significant spatial differences in accumulation rate, with higher accumulation on the windward side and near-zero accumulation on the lee side. This leads to spatial differences in physical properties of snow and su ...
In this paper we obtain parametrizations of the moduli space of principal bundles over a compact Riemann surface using spaces of Hecke modifications in several cases. We begin with a discussion of Hecke modifications for principal bundles and give construc ...
In this paper, the differential geometry of the novel hierarchical Tucker format for tensors is derived. The set HT,k of tensors with fixed tree T and hierarchical rank k is shown to be a smooth quotient manifold, namely the set of orbits of a Lie group ac ...