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Concept

Curvature of Riemannian manifolds

Publications associées (26)

Anomalous and Chern topological waves in hyperbolic networks

Romain Christophe Rémy Fleury, Haoye Qin, Zhe Zhang, Aleksi Antoine Bossart, Zhechen Zhang

Hyperbolic lattices are a new type of synthetic materials based on regular tessellations in non-Euclidean spaces with constant negative curvature. While so far, there has been several theoretical investigations of hyperbolic topological media, experimental ...

Nature Research2024

A structured prediction approach for robot imitation learning

Aude Billard, Iason Batzianoulis

We propose a structured prediction approach for robot imitation learning from demonstrations. Among various tools for robot imitation learning, supervised learning has been observed to have a prominent role. Structured prediction is a form of supervised le ...

Sage Publications Ltd2023

Indentation and stability of woven domes

Pedro Miguel Nunes Pereira de Almeida Reis, Tian Chen, Samuel Jean Bernard Poincloux, Tomohiko Sano, Célestin Vallat

Discrete domes are doubly curved structures comprising a network of beam-like elements. We study the mechanics of discrete domes made of ribbons woven in a pentagonal triaxial pattern. Experiments and finite element simulations are performed to characteriz ...

ELSEVIER2023

In-situ atomic level observation of the strain response of graphene lattice

Klaus Kern, Jz -Yuan Juo

Strain is inevitable in two-dimensional (2D) materials, regardless of whether the film is suspended or supported. However, the direct measurement of strain response at the atomic scale is challenging due to the difficulties of maintaining both flexibility ...

Nature Portfolio2023

A geometric optimal control approach for imitation and generalization of manipulation skills

Sylvain Calinon, Amirreza Razmjoo Fard

Daily manipulation tasks are characterized by regular features associated with the task structure, which can be described by multiple geometric primitives related to actions and object shapes. Only using Cartesian coordinate systems cannot fully represent ...

Elsevier2023

RMAML: Riemannian meta-learning with orthogonality constraints

Soumava Kumar Roy

Meta-learning is the core capability that enables intelligent systems to rapidly generalize their prior ex-perience to learn new tasks. In general, the optimization-based methods formalize the meta-learning as a bi-level optimization problem, that is a nes ...

ELSEVIER SCI LTD2023

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

Tangent functional connectomes uncover more unique phenotypic traits

Mingkui Wang, Enrico Amico

Functional connectomes (FCs) containing pairwise estimations of functional couplings between pairs of brain regions are commonly represented by correlation matrices. As symmetric positive definite matrices, FCs can be transformed via tangent space projecti ...

CELL PRESS2023

Piecewise Affine Curvature model: a reduced-order model for soft robot-environment interaction beyond PCC

Josephine Anna Eleanor Hughes, Francesco Stella, Qinghua Guan

Soft robot are celebrated for their propensity to enable compliant and complex robot-environment interactions. Soft robotic manipulators, or slender continuum structure robots have the potential to exploit these interactions to enable new exploration and m ...

IEEE2023

An Accelerated First-Order Method for Non-convex Optimization on Manifolds

Nicolas Boumal, Christopher Arnold Criscitiello

We describe the first gradient methods on Riemannian manifolds to achieve accelerated rates in the non-convex case. Under Lipschitz assumptions on the Riemannian gradient and Hessian of the cost function, these methods find approximate first-order critical ...

SPRINGER2022

Continuation Methods For Riemannian Optimization

Daniel Kressner, Axel Elie Joseph Séguin

Numerical continuation in the context of optimization can be used to mitigate convergence issues due to a poor initial guess. In this work, we extend this idea to Riemannian optimization problems, that is, the minimization of a target function on a Riemann ...

SIAM PUBLICATIONS2022

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

How Lagrangian States Evolve Into Random Waves

Alejandro Rivera

In this paper, we consider a compact connected manifold (X, g) of negative curvature, and a family of semi-classical Lagrangian states f(h)(x) = a(x)e(i phi(x)/h) on X. For a wide family of phases phi, we show that f(h), when evolved by the semi-classical ...

ECOLE POLYTECHNIQUE2022

Computational Design of Weingarten Surfaces

Mark Pauly, Davide Pellis

In this paper we study Weingarten surfaces and explore their potential for fabrication-aware design in freeform architecture. Weingarten surfaces are characterized by a functional relation between their principal curvatures that implicitly defines approxim ...

2021

Instability of a thin viscous film flowing under an inclined substrate: steady patterns

François Gallaire, Gioele Mariano Nicolò Balestra, Pier Giuseppe Ledda, Gaëtan Pierre Clément Lerisson

The flow of a thin film coating the underside of an inclined substrate is studied. We measure experimentally spatial growth rates and compare them to the linear stability analysis of a flat film modelled by the lubrication equation. When forced by a statio ...

Cambridge University Press2020

Adaptive Gradient Descent without Descent

We present a strikingly simple proof that two rules are sufficient to automate gradient descent: 1) don’t increase the stepsize too fast and 2) don’t overstep the local curvature. No need for functional values, no line search, no information about the func ...

2020

Towards a geometry independent traction-separation and angle relation due to large scale bridging in DCB configuration

John Botsis, Georgios Pappas

Traction-separation relations due to large scale bridging in composites are very important in modeling their fracture response. Several works demonstrated that such relations are dependent upon the specimen's stiffness and loading conditions. Experimental ...

ELSEVIER SCI LTD2020

Nonlinear buckling behavior of a complete spherical shell under uniform external pressure and homogenous natural curvature

Matteo Pezzulla

In this work, we consider the stability of a spherical shell under combined loading from a uniform external pressure and a homogenous natural curvature. Nonmechanical stimuli, such as one that tends to modify the rest curvature of an elastic body, are prev ...

AMER PHYSICAL SOC2020

Full field dependence of primary aberrations in perturbed double-plane symmetric systems with a circular pupil

Toralf Scharf, Alessandro Grosso

This paper deals with the theory of primary aberrations for perturbed double-plane symmetric optical systems consisting of a combination of tilted and decentered surfaces and a circular pupil. First, the analytical expressions describing the full field beh ...

OPTICAL SOC AMER2020

Robot skills learning with Riemannian manifolds: Leveraging geometry-awareness in robot learning, optimization and control

Noémie Laure Gwendoline Jaquier

Humans exhibit outstanding learning and adaptation capabilities while performing various types of manipulation tasks. When learning new skills, humans are able to extract important information by observing examples of a task and efficiently refine a priori ...

EPFL2020