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The geometry of algorithms using hierarchical tensors

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Some applications of symmetries in differential geometry and dynamical systems

Oana Mihaela Dragulete

This thesis deals with applications of Lie symmetries in differential geometry and dynamical systems. The first chapter of the thesis studies the singular reduction of symmetries of cosphere bundles, the conservation properties of contact systems and their ...

EPFL2007

Optimal control of geodesics in Riemannian manifolds

Roland Rozsnyo

The aim of this dissertation is to solve numerically the following problem, denoted by P : given a Riemannian manifold and two points a and b belonging to that manifold, find a tangent vector T at a, such that expa(T) = b, assuming that T exists. This prob ...

EPFL2007

Symmetry breaking in mechanical systems

The first part of this thesis studies the problem of symmetry breaking in the context of simple mechanical systems with compact symmetry Lie group G. In this part we shall assume that the principal stratum of the G-action on the configuration space Q of a ...

EPFL2005

Optimal control of geodesics in Riemannian manifolds

Klaus-Dieter Semmler, Roland Rozsnyo

Summary: We present a method based on an optimal control technique for numerical computations of geodesic paths between two fixed points of a Riemannian manifold under the assumption of existence. In this method, the control variable is the tangent vector ...

2004

Stereographic Frames of Wavelets on the Sphere

Pierre Vandergheynst, Laurent Jacques, Iva Bogdanova Vandergheynst

In this technical report the Discrete Wavelet Frames are build on the already existing Spherical Continuous Wavelet Transform. The spherical half-continuous frames are explored, i.e when the position on the sphere is kept continuous variable. Then, the con ...

2004

Tangent Vector Kernels for Invariant Image Classification with SVMs

Samy Bengio, Alexei Pozdnoukhov

This paper presents an application of the general sample-to-object approach to the problem of invariant image classification. The approach results in defining new SVM kernels based on tangent vectors that take into account prior information on known invari ...

2004

Tangent Vector Kernels for Invariant Image Classification with SVMs

Samy Bengio, Alexei Pozdnoukhov

IDIAP2003