Publication

Fourier interpolation on the real line

Publications associées (31)

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Rectified-linear-unit (ReLU) neural networks, which play a prominent role in deep learning, generate continuous and piecewise-linear (CPWL) functions. While they provide a powerful parametric representation, the mapping between the parameter and function s ...

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The present invention concerns an energy dispersion calibration method for calibrating an electron spectrometer of an electron spectrometer system including at least one electron emission source, electron optics and the electron spectrometer. The method co ...

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A Statistical Framework to Investigate the Optimality of Signal-Reconstruction Methods

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We present a statistical framework to benchmark the performance of reconstruction algorithms for linear inverse problems, in particular, neural-network-based methods that require large quantities of training data. We generate synthetic signals as realizati ...

2023

Debates on the dorsomedial prefrontal/dorsal anterior cingulate cortex: insights for future research

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The dorsomedial prefrontal cortex/dorsal anterior cingulate cortex (dmPFC/dACC) is a brain area subject to many theories and debates over its function(s). Even its precise anatomical borders are subject to much controversy. In the past decades, the dmPFC/d ...

Oxford Univ Press2023

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This data set provides a computer-assisted proof for the kernel inequalities needed to prove universal optimality in the paper "Universal optimality of the E_8 and Leech lattices and interpolation formulas" (by Cohn, Kumar, Miller, Radchenko, and Viazovska ...

EPFL Infoscience2023

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

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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

Preserving the positivity of the deformation gradient determinant in intergrid interpolation by combining RBFs and SVD: Application to cardiac electromechanics

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The accurate, robust and efficient transfer of the deformation gradient tensor between meshes of different resolution is crucial in cardiac electromechanics simulations. This paper presents a novel method that combines rescaled localized Radial Basis Funct ...

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Benign Overfitting in Deep Neural Networks under Lazy Training

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This paper focuses on over-parameterized deep neural networks (DNNs) with ReLU activation functions and proves that when the data distribution is well-separated, DNNs can achieve Bayesoptimal test error for classification while obtaining (nearly) zero-trai ...

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Detailed chemical abundances of very metal-poor (VMP; [Fe/H] < -2) stars are important for better understanding the first stars, early star formation, and chemical enrichment of galaxies. Big on-going and coming high-resolution spectroscopic surveys provid ...

OXFORD UNIV PRESS2023

Fully solvable finite simplex lattices with open boundaries in arbitrary dimensions

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Finite simplex lattice models are used in different branches of science, e.g., in condensed-matter physics, when studying frustrated magnetic systems and non-Hermitian localization phenomena; or in chemistry, when describing experiments with mixtures. An n ...

Amer Physical Soc2023