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Geometric Learning: Leveraging differential geometry for learning and control

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Anomalous and Chern topological waves in hyperbolic networks

Romain Christophe Rémy Fleury, Haoye Qin, 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 ...

2024

Hybrid Quadratic Programming - Pullback Bundle Dynamical Systems Control

Aude Billard, Bernardo Fichera

Dynamical System (DS)-based closed-loop control is a simple and effective way to generate reactive motion policies that well generalize to the robotic workspace, while retaining stability guarantees. Lately the formalism has been expanded in order to handl ...

SPRINGER INTERNATIONAL PUBLISHING AG2023

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The task of discovering equivalent entities in knowledge graphs (KGs), so-called KG entity alignment, has drawn much attention to overcome the incompleteness problem of KGs. The majority of existing techniques learns the pointwise representations of entiti ...

London2023

Dynamic Modeling of an Origami Prismatic Joint

Jamie Paik, Mustafa Mete, Jian-Lin Huang

Dynamic modeling of folding joints is critical for predicting dynamic behavior, optimizing design parameters, and developing control strategies for origami robots and machines. Although kinematics of the folded joints exists, little research describes thei ...

IEEE2023

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We investigate the effect of defect geometry in dictating the sensitivity of the critical buckling conditions of spherical shells under external pressure loading. Specifically, we perform a comparative study between shells containing dimpled (inward) versu ...

ASME2023

Relative, local and global dimension in complex networks

Alexis Arnaudon

Dimension is a fundamental property of objects and the space in which they are embedded. Yet ideal notions of dimension, as in Euclidean spaces, do not always translate to physical spaces, which can be constrained by boundaries and distorted by inhomogenei ...

NATURE PORTFOLIO2022

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

UCLID-Net: Single View Reconstruction in Object Space

Pascal Fua, Benoît Alain René Guillard, Edoardo Remelli

Most state-of-the-art deep geometric learning single-view reconstruction approaches rely on encoder-decoder architectures that output either shape parametrizations or implicit representations. However, these representations rarely preserve the Euclidean st ...

2020

The compass in the eye: The "geometric mechanics" of Viviani at the bedside of the Brunelleschi dome

Simon François Dumas Primbault

During the 17th century, being an engineer at the Medici Court was a discipline at the intersection of mathematics, and the pictorial and mechanical arts. Born out of the heritage of Alberti, Vinci, and Vasari, the Accademia del disegno - founded on the th ...

ARMAND COLIN2020

Better Guarantees for k-Means and Euclidean k-Median by Primal-Dual Algorithms

Ola Nils Anders Svensson, Ashkan Norouzi Fard, Justin Dean Ward

Clustering is a classic topic in optimization with k-means being one of the most fundamental such problems. In the absence of any restrictions on the input, the best-known algorithm for k-means in Euclidean space with a provable guarantee is a simple local ...

SIAM PUBLICATIONS2020