Concept

Isometry

Related publications (22)

Energy Bounds For A Fourth-Order Equation In Low Dimensions Related To Wave Maps

For compact, isometrically embedded Riemannian manifolds N -> R-L, we introduce a fourth-order version of the wave maps equation. By energy estimates, we prove an a priori estimate for smooth local solutions in the energy subcritical dimension n = 1, 2. Th ...

AMER MATHEMATICAL SOC2022

Tits Buildings And K-Stability

Giulio Codogni

A polarized variety is K-stable if, for any test configuration, the Donaldson-Futaki invariant is positive. In this paper, inspired by classical geometric invariant theory, we describe the space of test configurations as a limit of a direct system of Tits ...

CAMBRIDGE UNIV PRESS2019

Data-driven Measurement Designs for Magnetic Resonance Imaging

Baran Gözcü

Despite being a powerful medical imaging technique which does not emit any ionizing radiation, magnetic resonance imaging (MRI) always had the major problem of long scanning times that can take up to an hour depending on the application. It also requires u ...

EPFL2019

A theoretical study of COmpRessed SolvING for advection-diffusion-reaction problems

Fabio Nobile, Simone Brugiapaglia

We present a theoretical analysis of the CORSING (COmpRessed SolvING) method for the numerical approximation of partial differential equations based on compressed sensing. In particular, we show that the best s-term approximation of the weak solution of a ...

2018

The Myers-Steenrod Theorem For Finsler Manifolds Of Low Regularity

Marc Troyanov

We prove a version of Myers-Steenrod's theorem for Finsler manifolds under the minimal regularity hypothesis. In particular we show that an isometry between C-k,C-alpha-smooth (or partially smooth) Finsler metrics, with k + alpha > 0, k is an element of N ...

Amer Mathematical Soc2017

Patching And Weak Approximation In Isometry Groups

Eva Bayer Fluckiger

Let R be a semilocal principal ideal domain. Two algebraic objects over R in which scalar extension makes sense (e.g. quadratic spaces) are said to be of the same genus if they become isomorphic after extending scalars to all completions of R and its fract ...

Amer Mathematical Soc2017

Graph-based Isometry Invariant Representation Learning

Pascal Frossard, Renata Khasanova

Learning transformation invariant representations of visual data is an important problem in computer vision. Deep convolutional networks have demonstrated remarkable results for image and video classification tasks. However, they have achieved only limited ...

2017

A Fourier dimensionality reduction model for big data interferometric imaging

Jean-Philippe Thiran, Yves Wiaux, Rafael Eduardo Carrillo Rangel, Vijay Kartik

Data dimensionality reduction in radio interferometry can provide savings of computational resources for image reconstruction through reduced memory footprints and lighter computations per iteration, which is important for the scalability of imaging method ...

Oxford Univ Press2017

Approximation algorithms for geometric dispersion

Alfonso Bolívar Cevallos Manzano

The most basic form of the max-sum dispersion problem (MSD) is as follows: given n points in R^q and an integer k, select a set of k points such that the sum of the pairwise distances within the set is maximal. This is a prominent diversity problem, with w ...

EPFL2016

Dynamics of particles with anisotropic mass depending on time and position

Tudor Ratiu

Representations of solutions of equations describing the diffusion and quantum dynamics of particles in a Riemannian manifold are discussed under the assumption that the mass of particles is anisotropic and depends on both time and position. These equation ...

Springer Verlag2015

Isometries of quadratic spaces

Eva Bayer Fluckiger

Let k be a global field of characteristic not 2, and let f is an element of k[X] be an irreducible polynomial. We show that a non-degenerate quadratic space has an isometry with minimal polynomial f if and only if such an isometry exists over all the compl ...

European Mathematical Soc2015

Right-Protected Data Publishing with Provable Distance-Based Mining

Michail Vlachos, Nikolaos Freris

Protection of one's intellectual property is a topic with important technological and legal facets. We provide mechanisms for establishing the ownership of a dataset consisting of multiple objects. The algorithms also preserve important properties of the d ...

Ieee Computer Soc2014

Metric Learning with Rank and Sparsity Constraints

Volkan Cevher, Baran Gözcü, Bubacarr Bah

Choosing a distance preserving measure or metric is fun- damental to many signal processing algorithms, such as k- means, nearest neighbor searches, hashing, and compressive sensing. In virtually all these applications, the efficiency of the signal process ...

Ieee2014

The rigid limit of N=2 supergravity

Paul Smyth

In this paper we elucidate the rigid limit of N = 2 supergravity coupled to vector and hypermultiplets. In particular we show how the respective scalar field spaces reduce to their global counterparts. In the hypermultiplet sector we focus on the relation ...

Iop Publishing Ltd2013

Fixed points and amenability in non-positive curvature

Nicolas Monod

Consider a proper cocompact CAT(0) space X. We give a complete algebraic characterisation of amenable groups of isometries of X. For amenable discrete subgroups, an even narrower description is derived, implying Q-linearity in the torsion-free case. We est ...

Springer2013

Finite Element Method on Riemann Surfaces and Applications to the Laplacian Spectrum

Marc Maintrot

The objective of this PhD thesis is the approximate computation of the solutions of the Spectral Problem associated with the Laplace operator on a compact Riemann surface without boundaries. A Riemann surface can be seen as a gluing of portions of the Hype ...

EPFL2012

A Game Theoretic Approach to Expander-based Compressive Sensing

Volkan Cevher, Sina Jafarpour

We consider the following expander-based compressive sensing (e-CS) problem: Given Φ ∈ ℝM×N (M

IEEE2011

Online performance guarantees for sparse recovery

Volkan Cevher

A K*-sparse vector x* ∈ RN produces measurements via linear dimensionality reduction as u = Φx* +n, where Φ ∈ RM×N (M

2011

Compressive sensing meets game theory

Volkan Cevher, Sina Jafarpour

We introduce the Multiplicative Update Selector and Estimator (MUSE) algorithm for sparse approximation in under-determined linear regression problems. Given ƒ = Φα* + μ, the MUSE provably and efficiently finds a k-sparse vector α̂ such that ∥Φα̂ − ƒ∥∞ ≤ ∥ ...

IEEE2011

Isometry groups of non-positively curved spaces: Discrete subgroups

Nicolas Monod

We study lattices in non-positively curved metric spaces. Borel density is established in that setting as well as a form of Mostow rigidity. A converse to the flat torus theorem is provided. Geometric arithmeticity results are obtained after a detour throu ...

2009