Publications related to A Gauss-Bonnet Theorem for Asymptotically Conical Manifolds and Manifolds with Conical Singularities

Improved Bounds for Discretization of Langevin Diffusions: Near-Optimal Rates without Convexity

We consider minimizing a nonconvex, smooth function

f

on a Riemannian manifold

\mathcal{M}

. We show that a perturbed version of Riemannian gradient descent algorithm converges to a second-order stationary point (and hence is able to escape saddle point ...

2019

Configuration Spaces Of Products

Kathryn Hess Bellwald

We show that the configuration spaces of a product of parallelizable manifolds may be recovered from those of the factors as the Boardman-Vogt tensor product of right modules over the operads of little cubes of the appropriate dimension. We also discuss an ...

2019

A central limit theorem for integrals of random waves

Marius Christopher Lemm, Matthew De Courcy-Ireland

We derive a central limit theorem for the mean-square of random waves in the high-frequency limit over shrinking sets. Our proof applies to any compact Riemannian manifold of arbitrary dimension, thanks to the universality of the local Weyl law. The key te ...

2019

Detecting Anisotropic Inclusions Through EIT

Jan Cristina

We study the evolution equation where is the Dirichlet-Neumann operator of a decreasing family of Riemannian manifolds with boundary . We derive a lower bound for the solution of such an equation, and apply it to a quantitative density estimate for the res ...

Springer2017

Improving hand and wrist activity detection using tactile sensors and tensor regression methods on Riemannian manifolds

Sylvain Calinon, Noémie Laure Gwendoline Jaquier

Simultaneous and proportional control of a prosthetic hand and wrist is still a controversial issue, although giant steps have lately been made in this direction. In this paper, we study the application of a novel machine learning method to the problem, wi ...

2017

An Approach for Imitation Learning on Riemannian Manifolds

Sylvain Calinon

In imitation learning, multivariate Gaussians are widely used to encode robot behaviors. Such approaches do not provide the ability to properly represent end-effector orientation, as the distance metric in the space of orientations is not Euclidean. In thi ...

2017

Stochastic Composite Least-Squares Regression with Convergence Rate O(1/n)

Nicolas Henri Bernard Flammarion

We consider the minimization of a function deﬁned on a Riemannian manifold M accessible only through unbiased estimates of its gradients. We develop a geometric framework to transform a sequence of slowly converging iterates generated from stochastic gradi ...

2017

The tropical momentum map: a classification of toric log symplectic manifolds

Tudor Ratiu

We give a generalization of toric symplectic geometry to Poisson manifolds which are symplectic away from a collection of hypersurfaces forming a normal crossing configuration. We introduce the tropical momentum map, which takes values in a generalization ...

Springer Verlag2017

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

Bi-Jacobi Fields And Riemannian Cubics For Left-Invariant SO(3)

Tudor Ratiu

Bi-Jacobi fields are generalized Jacobi fields, and are used to efficiently compute approximations to Riemannian cubic splines in a Riemannian manifold M. Calculating bi-Jacobi fields is straightforward when M is a symmetric space such as bi-invariant SO(3 ...

Int Press Boston, Inc2016

A Gauss-Bonnet Theorem for Asymptotically Conical Manifolds and Manifolds with Conical Singularities

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Improved Bounds for Discretization of Langevin Diffusions: Near-Optimal Rates without Convexity

Configuration Spaces Of Products

A central limit theorem for integrals of random waves

Detecting Anisotropic Inclusions Through EIT

Improving hand and wrist activity detection using tactile sensors and tensor regression methods on Riemannian manifolds

An Approach for Imitation Learning on Riemannian Manifolds

Stochastic Composite Least-Squares Regression with Convergence Rate O(1/n)

The tropical momentum map: a classification of toric log symplectic manifolds

The Myers-Steenrod Theorem For Finsler Manifolds Of Low Regularity

Bi-Jacobi Fields And Riemannian Cubics For Left-Invariant SO(3)

Bi-Jacobi Fields And Riemannian Cubics For Left-Invariant SO(3)

Detecting Anisotropic Inclusions Through EIT

Stochastic Composite Least-Squares Regression with Convergence Rate O(1/n)

Improving hand and wrist activity detection using tactile sensors and tensor regression methods on Riemannian manifolds

An Approach for Imitation Learning on Riemannian Manifolds

The Myers-Steenrod Theorem For Finsler Manifolds Of Low Regularity

A central limit theorem for integrals of random waves

Improved Bounds for Discretization of Langevin Diffusions: Near-Optimal Rates without Convexity

The tropical momentum map: a classification of toric log symplectic manifolds

Configuration Spaces Of Products