Publications related to Dynamics of particles with anisotropic mass depending on time and position

Nonlinear Finite Elements in Dynamics

This report focuses on the implementation of the finite element method for nonlinear dynamical problems arising in solid mechanics. The theory of continuum mechanics is extensively covered in the literature and it is assumed the reader is already familiar ...

2020

Semi-discrete optimal transport: a solution procedure for the unsquared Euclidean distance case

Valentin Hartmann

We consider the problem of finding an optimal transport plan between an absolutely continuous measure and a finitely supported measure of the same total mass when the transport cost is the unsquared Euclidean distance. We may think of this problem as close ...

SPRINGER HEIDELBERG2020

Geodesic flows on real forms of complex semi-simple Lie groups of rigid body type

Tudor Ratiu

The geodesic flows are studied on real forms of complex semi-simple Lie groups with respect to a left-invariant (pseudo-)Riemannian metric of rigid body type. The Williamson types of the isolated relative equilibria on generic adjoint orbits are determined ...

SPRINGER INTERNATIONAL PUBLISHING AG2020

How ageing shapes body and space representations: A comparison study between healthy young and older adults

Olaf Blanke, Andrea Serino, Michela Bassolino, Matteo Franza, Giuliana Sorrentino, Charlène Zuber

To efficiently interact with the external world, the brain needs to represent the size of the involved body parts - body representations (BR) - and the space around the body in which the interactions with the environment take place - peripersonal space rep ...

2020

Escaping from saddle points on Riemannian manifolds

Nicolas Henri Bernard Flammarion, Yue Sun

We consider minimizing a nonconvex, smooth function f on a Riemannian manifold 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 points on the manif ...

2019

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

Nicolas Henri Bernard Flammarion

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

A General Theory of Equivariant CNNs on Homogeneous Spaces

Mario Geiger

We present a general theory of Group equivariant Convolutional Neural Networks (G-CNNs) on homogeneous spaces such as Euclidean space and the sphere. Feature maps in these networks represent fields on a homogeneous base space, and layers are equivariant ma ...

NEURAL INFORMATION PROCESSING SYSTEMS (NIPS)2019

Boundedness and Decay of Solutions for Some Fractional Magnetic Schrodinger Equations in R-N

We prove that nontrivial weak solutions of a class of fractional magnetic Schrodinger equations in RN are bounded and vanish at infinity. ...

2018

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

Geometric deep learning: going beyond Euclidean data

Pierre Vandergheynst, Michael Bronstein

Many signal processing problems involve data whose underlying structure is non-Euclidean, but may be modeled as a manifold or (combinatorial) graph. For instance, in social networks, the characteristics of users can be modeled as signals on the vertices of ...

2017

Dynamics of particles with anisotropic mass depending on time and position

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Nonlinear Finite Elements in Dynamics

Semi-discrete optimal transport: a solution procedure for the unsquared Euclidean distance case

Geodesic flows on real forms of complex semi-simple Lie groups of rigid body type

How ageing shapes body and space representations: A comparison study between healthy young and older adults

Escaping from saddle points on Riemannian manifolds

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

A General Theory of Equivariant CNNs on Homogeneous Spaces

Boundedness and Decay of Solutions for Some Fractional Magnetic Schrodinger Equations in R-N

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

Geometric deep learning: going beyond Euclidean data

Nonlinear Finite Elements in Dynamics

Geodesic flows on real forms of complex semi-simple Lie groups of rigid body type

How ageing shapes body and space representations: A comparison study between healthy young and older adults

Semi-discrete optimal transport: a solution procedure for the unsquared Euclidean distance case

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

Escaping from saddle points on Riemannian manifolds

A General Theory of Equivariant CNNs on Homogeneous Spaces

Boundedness and Decay of Solutions for Some Fractional Magnetic Schrodinger Equations in R-N

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

Geometric deep learning: going beyond Euclidean data