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Differential geometry: a natural tool for describing symmetry operations

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Symplectic Dynamical Low Rank approximation of wave equations with random parameters

Fabio Nobile, Eleonora Musharbash

In this paper we propose a dynamical low-rank strategy for the approximation of second order wave equations with random parameters. The governing equation is rewritten in Hamiltonian form and the approximate solution is expanded over a set of

2S

dynamica ...

2017

La coupe du roi and other methods to halve objects

Dieter Schwarzenbach

The symmetry theory of halving objects into two identical fragments is developed and illustrated by examples. La coupe du roi is a fascinating way to slice an apple into chiral fragments with the same handedness. It may be applied to any object with point ...

De Gruyter2015

Signal structure: from manifolds to molecules and structured sparsity

Sofia Karygianni

Effective representation methods and proper signal priors are crucial in most signal processing applications. In this thesis we focus on different structured models and we design appropriate schemes that allow the discovery of low dimensional latent struct ...

EPFL2015

An indiscrete Bieberbach theorem: from amenable CAT$(0)$ groups to Tits buildings

Nicolas Monod

Non-positively curved spaces admitting a cocompact isometric action of an amenable group are investigated. A classification is established under the assumption that there is no global fixed point at infinity under the full isometry group. The visual bounda ...

2015

Tangent-based manifold approximation with locally linear models

Pascal Frossard, Sofia Karygianni

In this paper, we consider the problem of manifold approximation with affine subspaces. Our objective is to discover a set of low dimensional affine subspaces that represent manifold data accurately while preserving the manifold's structure. For this purpo ...

Elsevier2014

The geometry of algorithms using hierarchical tensors

André Uschmajew

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 ...

2013

Tangent space estimation for smooth embeddings of Riemannian manifolds

Pascal Frossard, Elif Vural, Hemant Tyagi

Numerous dimensionality reduction problems in data analysis involve the recovery of low-dimensional models or the learning of manifolds underlying sets of data. Many manifold learning methods require the estimation of the tangent space of the manifold at a ...

2013

In this work we do a theoretical analysis of the local sampling conditions for points lying on a quadratic embedding of a Riemannian manifold in a Euclidean space. The embedding is assumed to be quadratic at a reference point

P

. Our analysis is based on ...

2011

We prove that the multiplier algebra of the Drury-Arveson Hardy space H-n(2) on the unit ball in C-n has no corona in its maximal ideal space, thus generalizing the corona theorem of L. Carleson to higher dimensions. This result is obtained as a corollary ...

2011

The role of the tangent bundle for symmetry operations and modulated structures

Gervais Chapuis, Kurt Schenk, Philippe Kocian

An equivalence relation on the tangent bundle of a manifold is defined in order to extend a structure (modulated or not) onto it. This extension affords a representation of a structure in any tangent space and that in another tangent space can easily be de ...

2010

P

. Our analysis is based on ...

2011

Symplectic Dynamical Low Rank approximation of wave equations with random parameters

Fabio Nobile, Eleonora Musharbash

2S

dynamica ...

2017