Publications related to An Approach for Imitation Learning on Riemannian Manifolds

Stability of stationary wave maps from a curved background to a sphere

We study time and space equivariant wave maps from

M \times \mathbb{R} \rightarrow S^2

, where

M

is dieomorphic to a two dimensional sphere and admits an action of

SO(2)

by isometries. We assume that metric on

M

can be written as $dr^2+f^2(r)d\theta ...

2016

Codimension one stability of the catenoid under the vanishing mean curvature flow in Minkowski space

Joachim Krieger, Roland Donninger, Willie Wai Yeung Wong

We study time-like hypersurfaces with vanishing mean curvature in the (3+1) dimensional Minkowski space, which are the hyperbolic counterparts to minimal embeddings of Riemannian manifolds. The catenoid is a stationary solution of the associated Cauchy pro ...

Duke Univ Press2015

Continuum percolation of polydisperse hyperspheres in infinite dimensions

Claudio Grimaldi

We analyze the critical connectivity of systems of penetrable d-dimensional spheres having size distributions in terms of weighed random geometrical graphs, in which vertex coordinates correspond to random positions of the sphere centers, and edges are for ...

Amer Physical Soc2015

Evaluation of control strategies for fixed-wing drones following slow-moving ground agents

Dario Floreano, Jean-Christophe Zufferey, Grégoire Hilaire Marie Heitz, Maja Varga

There are many situations where fixed-wing drones may be required to track ground moving agents, such as humans or cars, which are typically slower than drones. Some control strategies have been proposed and validated in simulations using the average dista ...

Elsevier2015

Principal Flows

Victor Panaretos, Tung Huy Pham, Zhigang Yao

We revisit the problem of extending the notion of principal component analysis (PCA) to multivariate datasets that satisfy nonlinear constraints, therefore lying on Riemannian manifolds. Our aim is to determine curves on the manifold that retain their cano ...

American Statistical Association2014

Gaussian distribution for the divisor function and Hecke eigenvalues in arithmetic progressions

Philippe Michel

We show that, in a restricted range, the divisor function of integers in residue classes modulo a prime follows a Gaussian distribution, and a similar result for Hecke eigenvalues of classical holomorphic cusp forms. Furthermore, we obtain the joint distri ...

European Mathematical Soc2014

Full blow-up range for co-rotaional wave maps to surfaces of revolution

Can Gao

We construct blow-up solutions of the energy critical wave map equation on

\mathbb{R}^{2+1}\to \mathcal N

with polynomial blow-up rate (

t^{-1-\nu}

for blow-up at

t=0

) in the case when

\mathcal N

is a surface of revolution. Here we extend the blow-u ...

2014

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

Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group. II

Martins Bruveris, Martin Bauer

The geodesic distance vanishes on the group of compactly supported diffeomorphisms of a Riemannian manifold of bounded geometry, for the right invariant weak Riemannian metric which is induced by the Sobolev metric of order on the Lie algebra of vector fie ...

Springer Verlag2013

Harmonic Maps on Smooth Metric Measure Spaces and on Riemannian Polyhedra

Zahra Sinaei

This thesis is a study of harmonic maps in two different settings. The first part is concerned with harmonic maps from smooth metric measure spaces to Riemannian manifolds. The second part is study of harmonic maps from Riemannian polyhedra to non-positive ...

EPFL2013

An Approach for Imitation Learning on Riemannian Manifolds

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Stability of stationary wave maps from a curved background to a sphere

Codimension one stability of the catenoid under the vanishing mean curvature flow in Minkowski space

Continuum percolation of polydisperse hyperspheres in infinite dimensions

Evaluation of control strategies for fixed-wing drones following slow-moving ground agents

Principal Flows

Gaussian distribution for the divisor function and Hecke eigenvalues in arithmetic progressions

Full blow-up range for co-rotaional wave maps to surfaces of revolution

Tangent space estimation for smooth embeddings of Riemannian manifolds

Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group. II

Harmonic Maps on Smooth Metric Measure Spaces and on Riemannian Polyhedra

Codimension one stability of the catenoid under the vanishing mean curvature flow in Minkowski space

Principal Flows

Stability of stationary wave maps from a curved background to a sphere

Continuum percolation of polydisperse hyperspheres in infinite dimensions

Gaussian distribution for the divisor function and Hecke eigenvalues in arithmetic progressions

Harmonic Maps on Smooth Metric Measure Spaces and on Riemannian Polyhedra

Tangent space estimation for smooth embeddings of Riemannian manifolds

Evaluation of control strategies for fixed-wing drones following slow-moving ground agents

Full blow-up range for co-rotaional wave maps to surfaces of revolution

Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group. II