Publications related to Biodegradable Implantable Microsystems

From low-rank retractions to dynamical low-rank approximation and back

Daniel Kressner, Axel Elie Joseph Séguin, Gianluca Ceruti

In algorithms for solving optimization problems constrained to a smooth manifold, retractions are a well-established tool to ensure that the iterates stay on the manifold. More recently, it has been demonstrated that retractions are a useful concept for ot ...

Springer2024

Retraction-based numerical methods for continuation, interpolation and time integration on manifolds

Axel Elie Joseph Séguin

The goal of this thesis is the development and the analysis of numerical methods for problems where the unknown is a curve on a smooth manifold. In particular, the thesis is structured around the three following problems: homotopy continuation, curve inter ...

EPFL2023

Finding stationary points on bounded-rank matrices: a geometric hurdle and a smooth remedy

Nicolas Boumal

We consider the problem of provably finding a stationary point of a smooth function to be minimized on the variety of bounded-rank matrices. This turns out to be unexpectedly delicate. We trace the difficulty back to a geometric obstacle: On a nonsmooth se ...

SPRINGER HEIDELBERG2022

Shrinking Scale Equidistribution for Monochromatic Random Waves on Compact Manifolds

Matthew De Courcy-Ireland

We prove equidistribution at shrinking scales for the monochromatic ensemble on a compact Riemannian manifold of any dimension. This ensemble on an arbitrary manifold takes a slowly growing spectral window in order to synthesize a random function. With hig ...

OXFORD UNIV PRESS2021

Gaussians on Riemannian Manifolds for Robot Learning and Adaptive Control

Sylvain Calinon

This article presents an overview of robot learning and adaptive control applications that can benefit from a joint use of Riemannian geometry and probabilistic representations. The roles of Riemannian manifolds, geodesics and parallel transport in robotic ...

2020

Mechanoresponsive Micro- and Nanoparticles

Harm-Anton Klok, Friederike Katharina Metze

Mechanical stimuli are ubiquitous in the human body. In contrast to biochemical stimuli such as pH, redox, hypoxia or enzymes as well as exogenous stimuli such as magnetic fields, temperature or ultrasound, endogenous biomechanical stimuli have only receiv ...

2019

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

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

Adrien Giuliano Marcone

The purpose of this thesis is to provide an intrinsic proof of a Gauss-Bonnet-Chern formula for complete Riemannian manifolds with finitely many conical singularities and asymptotically conical ends. A geometric invariant is associated to the link of both ...

EPFL2019

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

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

Biodegradable Implantable Microsystems

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From low-rank retractions to dynamical low-rank approximation and back

Retraction-based numerical methods for continuation, interpolation and time integration on manifolds

Finding stationary points on bounded-rank matrices: a geometric hurdle and a smooth remedy

Shrinking Scale Equidistribution for Monochromatic Random Waves on Compact Manifolds

Gaussians on Riemannian Manifolds for Robot Learning and Adaptive Control

Mechanoresponsive Micro- and Nanoparticles

Escaping from saddle points on Riemannian manifolds

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

Detecting Anisotropic Inclusions Through EIT

Retraction-based numerical methods for continuation, interpolation and time integration on manifolds

Gaussians on Riemannian Manifolds for Robot Learning and Adaptive Control

Escaping from saddle points on Riemannian manifolds

Detecting Anisotropic Inclusions Through EIT

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

From low-rank retractions to dynamical low-rank approximation and back

Shrinking Scale Equidistribution for Monochromatic Random Waves on Compact Manifolds

Mechanoresponsive Micro- and Nanoparticles

Finding stationary points on bounded-rank matrices: a geometric hurdle and a smooth remedy

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