Domain-Informed Spline Interpolation

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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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

This study compares three imputation methods applied to the field observations of hydraulic head in subsurface hydrology. Hydrogeological studies that analyze the timeseries of groundwater elevations often face issues with missing data that may mislead bot ...

Region extraction is a very common task in both Computer Science and Engineering with several applications in object recognition and motion analysis, among others. Most of the literature focuses on regions delimited by straight lines, often in the special ...

Reduced-order models are indispensable for multi-query or real-time problems. However, there are still many challenges to constructing efficient ROMs for time-dependent parametrized problems. Using a linear reduced space is inefficient for time-dependent n ...

Fourier transforms are an often necessary component in many computational tasks, and can be computed efficiently through the fast Fourier transform (FFT) algorithm. However, many applications involve an underlying continuous signal, and a more natural choi ...

Fetal brain diffusion magnetic resonance images (MRI) are often acquired with a lower through-plane than in-plane resolution. This anisotropy is often overcome by classical upsampling methods such as linear or cubic interpolation. In this work, we employ a ...

We obtain new Fourier interpolation and uniqueness results in all dimensions, extending methods and results by the first author and M. Sousa [11] and the second author [12]. We show that the only Schwartz function which, together with its Fourier transform ...

MRI is a non-invasive medical imaging modality that is sensitive to patient motion, which constitutes a major limitation in most clinical applications. Solutions may arise from the reduction of acquisition times or from motion-correction techniques, either ...

The goal of this thesis is to study continuous-domain inverse problems for the reconstruction of sparse signals and to develop efficient algorithms to solve such problems computationally. The task is to recover a signal of interest as a continuous function ...

We show that isogeometric Galerkin discretizations of eigenvalue problems related to the Laplace operator subject to any standard type of homogeneous boundary conditions have no outliers in certain optimal spline subspaces. Roughly speaking, these optimal ...

Let K be a totally real number field of degree n >= 2. The inverse different of K gives rise to a lattice in Rn. We prove that the space of Schwartz Fourier eigenfunctions on R-n which vanish on the "component-wise square root" of this lattice, is infinite ...

The underlying geometrical structure of the latent space in deep generative models is in most cases not Euclidean, which may lead to biases when comparing interpolation capabilities of two models. Smoothness and plausibility of linear interpolations in lat ...

In every dimension d >= 2, we give an explicit formula that expresses the values of any Schwartz function on R-d only in terms of its restrictions, and the restrictions of its Fourier transform, to all origin-centered spheres whose radius is the square roo ...

Many engineering fields rely on frequency-domain dynamical systems for the mathematical modeling of physical (electrical/mechanical/etc.) structures. With the growing need for more accurate and reliable results, the computational burden incurred by frequen ...

Domain-Informed Spline Interpolation

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Interpolation and Quantifiers in Ortholattices

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

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

Stable Nonconvex-Nonconcave Training via Linear Interpolation

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

Benign Overfitting in Deep Neural Networks under Lazy Training

Comparison of Three Imputation Methods for Groundwater Level Timeseries

Region Extraction in Mesh Intersection

Non-intrusive data-driven reduced-order modeling for time-dependent parametrized problems

pyFFS: A Python Library for Fast Fourier Series Computation and Interpolation with GPU Acceleration

Through-Plane Super-Resolution With Autoencoders in Diffusion Magnetic Resonance Imaging of the Developing Human Brain

Perturbed Fourier uniqueness and interpolation results in higher dimensions

Choreography Controlled (ChoCo) brain MRI artifact generation for labeled motion-corrupted datasets

Variational Methods For Continuous-Domain Inverse Problems: the Quest for the Sparsest Solution

Application of optimal spline subspaces for the removal of spurious outliers in isogeometric discretizations

Fourier non-uniqueness sets from totally real number fields

On Linear Interpolation in the Latent Space of Deep Generative Models

Fourier Interpolation From Spheres

Model order reduction based on functional rational approximants for parametric PDEs with meromorphic structure