Beyond Interpolation: Optimal Reconstruction by Quasi-Interpolation

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When two objects slide against each other, wear and friction occur at their interface. The accumulation of wear forms what is commonly referred to as a ``third-body''. Understanding third-body evolution has significant applications in industry, where contr ...

Statistical (machine-learning, ML) models are more and more often used in computational chemistry as a substitute to more expensive ab initio and parametrizable methods. While the ML algorithms are capable of learning physical laws implicitly from data, ad ...

We introduce an algorithm to reconstruct a mesh from discrete samples of a shape's Signed Distance Function (SDF). A simple geometric reinterpretation of the SDF lets us formulate the problem through a point cloud, from which a surface can be extracted wit ...

Functional data are typically modeled as sample paths of smooth stochastic processes in order to mitigate the fact that they are often observed discretely and noisily, occasionally irregularly and sparsely. The smoothness assumption is imposed to allow for ...

A space-time adaptive algorithm is presented to solve the incompressible Navier-Stokes equations. Time discretization is performed with the BDF2 method while continuous, piecewise linear anisotropic finite elements are used for the space discretization. Th ...

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 ...

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 ...

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 ...

Integrating functions on discrete domains into neural networks is key to developing their capability to reason about discrete objects. But, discrete domains are (I) not naturally amenable to gradient-based optimization, and (II) incompatible with deep lear ...

We prove that every Schwartz function in Euclidean space can be completely recovered given only its restrictions and the restrictions of its Fourier transform to all origin-centered spheres whose radii are square roots of integers. In particular, the only ...

We consider the problem of learning implicit neural representations (INRs) for signals on non-Euclidean domains. In the Euclidean case, INRs are trained on a discrete sampling of a signal over a regular lattice. Here, we assume that the continuous signal e ...

Here we discuss "hidden variables", which are typically introduced during an experiment as a consequence of the application of two independent variables together to create a stimulus. With increased sophistication in modern chemical biology tools and relat ...

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 study experiment design for unique identification of the causal graph of a system where the graph may contain cycles. The presence of cycles in the structure introduces major challenges for experiment design as, unlike acyclic graphs, learning the skele ...

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 ...

In recent work, methods from the theory of modular forms were used to obtain Fourier uniqueness results in several key dimensions (d = 1, 8, 24), in which a function could be uniquely reconstructed from the values of it and its Fourier transform on a discr ...

The aim of this thesis is to implement, analyze and improve the selected low noise clock generation and distribution techniques for ADC implementations. The thesis is divided into two parts. The first part focuses on the sampling phase generation and distr ...

Sampling has always been at the heart of signal processing providing a bridge between the analogue world and discrete representations of it, as our ability to process data in continuous space is quite limited. Furthermore, sampling plays a key part in unde ...

The analysis of the effect of sub-sampling phase detector (SSPD) timing nonidealities on Type-I sub-sampling phase-locked loop (SSPLL) is presented. The nonidealities considered are the delay between the complementary sampling clocks and the propagation de ...

Beyond Interpolation: Optimal Reconstruction by Quasi-Interpolation

Chattez avec Graph Search

Modeling friction and wear using an adaptive discrete-continuum coupling

Encoding quantum-chemical knowledge into machine-learning models of complex molecular properties

Reach For the Arcs: Reconstructing Surfaces from SDFs via Tangent Points

Functional data analysis with rough sample paths?

An adaptive space-time algorithm for the incompressible Navier-Stokes equations

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

Perturbed Fourier uniqueness and interpolation results in higher dimensions

Fourier non-uniqueness sets from totally real number fields

Neural Set Function Extensions: Learning with Discrete Functions in High Dimensions

Fourier uniqueness and interpolation in Euclidean space

Generalised Implicit Neural Representations

Hiding in Plain Sight: The Issue of Hidden Variables

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

A Unified Experiment Design Approach for Cyclic and Acyclic Causal Models

Fourier Interpolation From Spheres

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

Fourier uniqueness in even dimensions

Low Noise Clock Generation: Modeling, Analysis and Implementation

Uncertain Sampling with Certain Priors

Discrete Time Analysis of Phase Detector Timing Nonidealities in Type-I Sub-Sampling PLL