Publications related to Polynomial interpolation

Interpolation and Quantifiers in Ortholattices

Viktor Kuncak, Simon Guilloud, Sankalp Gambhir

We study quantifiers and interpolation properties in orthologic, a non-distributive weakening of classical logic that is sound for formula validity with respect to classical logic, yet has a quadratic-time decision procedure. We present a sequent-based pro ...

Cham2024

Interpolation and Quantifiers in Ortholattices

Viktor Kuncak, Simon Guilloud, Sankalp Gambhir

We study quantifiers and interpolation properties in ortho- logic, a non-distributive weakening of classical logic that is sound for formula validity with respect to classical logic, yet has a quadratic-time decision procedure. We present a sequent-based p ...

2024

Unlabeled Principal Component Analysis and Matrix Completion

Yunzhen Yao, Liangzu Peng

We introduce robust principal component analysis from a data matrix in which the entries of its columns have been corrupted by permutations, termed Unlabeled Principal Component Analysis (UPCA). Using algebraic geometry, we establish that UPCA is a well-de ...

Microtome Publ2024

Performance and accuracy of cross‐section tracking methods for hydromorphological habitat assessment in wadable rivers with sparse canopy conditions

Giovanni De Cesare, Paolo Perona, Robin Schroff

This article investigates the performance and accuracy of continuous Real-Time Kinematic (RTK) Global Navigation Satellite System (GNSS) position tracking for hydromorphological surveys, based on a comprehensive river restoration monitoring campaign. The a ...

2024

TIC-TAC: A Framework for Improved Covariance Estimation in Deep Heteroscedastic Regression

Mathieu Salzmann, Alexandre Massoud Alahi, Megh Hiren Shukla

Deep heteroscedastic regression involves jointly optimizing the mean and covariance of the predicted distribution using the negative log-likelihood. However, recent works show that this may result in sub-optimal convergence due to the challenges associated ...

2024

Computer-assisted proof of kernel inequalities

Maryna Viazovska, Abhinav Kumar

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

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

Alfio Quarteroni, Francesco Regazzoni

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 ...

Lausanne2023

Stable Nonconvex-Nonconcave Training via Linear Interpolation

Volkan Cevher, Thomas Michaelsen Pethick, Wanyun Xie

This paper presents a theoretical analysis of linear interpolation as a principled method for stabilizing (large-scale) neural network training. We argue that instabilities in the optimization process are often caused by the nonmonotonicity of the loss lan ...

2023

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Polynomial interpolation

Interpolation and Quantifiers in Ortholattices

Interpolation and Quantifiers in Ortholattices

Unlabeled Principal Component Analysis and Matrix Completion

Performance and accuracy of cross‐section tracking methods for hydromorphological habitat assessment in wadable rivers with sparse canopy conditions

TIC-TAC: A Framework for Improved Covariance Estimation in Deep Heteroscedastic Regression

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

Computer-assisted proof of kernel inequalities

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

Stable Nonconvex-Nonconcave Training via Linear Interpolation

Analysis of accretion disc structure and stability using open code for vertical structure

Graph Chatbot

Chat with Graph Search

TIC-TAC: A Framework for Improved Covariance Estimation in Deep Heteroscedastic Regression

Performance and accuracy of cross‐section tracking methods for hydromorphological habitat assessment in wadable rivers with sparse canopy conditions

Unlabeled Principal Component Analysis and Matrix Completion

Interpolation and Quantifiers in Ortholattices

Interpolation and Quantifiers in Ortholattices

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

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

Analysis of accretion disc structure and stability using open code for vertical structure

Computer-assisted proof of kernel inequalities

Stable Nonconvex-Nonconcave Training via Linear Interpolation