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Concept

Euclidean space

Related publications (28)

A Functional Perspective on Information Measures

Amedeo Roberto Esposito

Since the birth of Information Theory, researchers have defined and exploited various information measures, as well as endowed them with operational meanings. Some were born as a "solution to a problem", like Shannon's Entropy and Mutual Information. Other ...

EPFL2022

PDE-Aware Deep Learning for Inverse Problems in Cardiac Electrophysiology

Alfio Quarteroni, Simone Deparis, Stefano Pagani, Riccardo Tenderini

In this work, we present a PDE-aware deep learning model for the numerical solution to the inverse problem of electrocardiography. The model both leverages data availability and exploits the knowledge of a physically based mathematical model, expressed by ...

2022

Linearization and Identification of Multiple-Attractor Dynamical Systems through Laplacian Eigenmaps

Aude Billard, Bernardo Fichera

Dynamical Systems (DS) are fundamental to the modeling and understanding time evolving phenomena, and have application in physics, biology and control. As determining an analytical description of the dynamics is often difficult, data-driven approaches are ...

Microtome Publishing2022

Fermionic wave functions from neural-network constrained hidden states

Giuseppe Carleo

We introduce a systematically improvable family of variational wave functions for the simulation of strongly correlated fermionic systems. This family consists of Slater determinants in an augmented Hilbert space involving “hidden” additional fermionic deg ...

2022

On Generalizations of Some Distance Based Classifiers for HDLSS Data

Soham Sarkar

In high dimension, low sample size (HDLSS) settings, classifiers based on Euclidean distances like the nearest neighbor classifier and the average distance classifier perform quite poorly if differences between locations of the underlying populations get m ...

Microtome Publishing2022

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

Determining crack kinematics from imaged crack patterns

Katrin Beyer, Bryan German Pantoja Rosero, Amir Rezaie, Ketson Roberto Maximiano Dos Santos

Determining the relationship between the cause of damage and the subsequent structural behavior of infrastructure systems requires an accurate characterization of the propagation of cracks, which represents the evolution of the damage state. When no inform ...

2022

Realizing doubles: a conjugation zoo

Jérôme Scherer

Conjugation spaces are topological spaces equipped with an involution such that their fixed points have the same mod 2 cohomology (as a graded vector space, a ring and even an unstable algebra) but with all degrees divided by two, generalizing the classica ...

CAMBRIDGE UNIV PRESS2021