Publications associées à All in Good Time: Long-lasting Postdictive Effects Discrete Perception

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

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 ...

Academic Press Inc Elsevier Science2023

Functional data analysis with rough sample paths?

Victor Panaretos, Neda Mohammadi Jouzdani

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 ...

TAYLOR & FRANCIS LTD2024

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

Andreas Loukas, Nikolaos Karalias

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 ...

2022

Fourier uniqueness and interpolation in Euclidean space

Martin Peter Stoller

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 ...

EPFL2022

Gradient-Based Learning of Discrete Structured Measurement Operators for Signal Recovery

Jonathan Paul Sauder

Countless signal processing applications include the reconstruction of signals from few indirect linear measurements. The design of effective measurement operators is typically constrained by the underlying hardware and physics, posing a challenging and of ...

2022

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

Martin Vetterli, Paul Hurley, Sepand Kashani, Matthieu Martin Jean-André Simeoni, Eric Bezzam

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 ...

SIAM2022

Fourier non-uniqueness sets from totally real number fields

Martin Peter Stoller

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 ...

EUROPEAN MATHEMATICAL SOC-EMS2022

A Continuized View on Nesterov Acceleration

Nicolas Henri Bernard Flammarion, Raphaël Jean Berthier

We introduce the "continuized" Nesterov acceleration, a close variant of Nesterov acceleration whose variables are indexed by a continuous time parameter. The two variables continuously mix following a linear ordinary differential equation and take gradien ...

2021

Optimal Policies for Age and Distortion in a Discrete-Time Model

Emre Telatar, Reka Inovan, Yunus Inan

We propose a simple model to study the tradeoff between timeliness and distortion, where different pieces of data have a different cost of not being sent. We pose the question of finding the optimal tradeoff as a policy design problem amenable to dynamic p ...

IEEE2021

Fourier uniqueness in even dimensions

Maryna Viazovska

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 ...

National Academy of Sciences2021

Uncertain Sampling with Certain Priors

Golnooshsadat Elhami

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 ...

EPFL2021

Numerical Methods for First and Second Order Fully Nonlinear Partial Differential Equations

Dimitrios Gourzoulidis

This thesis focuses on the numerical analysis of partial differential equations (PDEs) with an emphasis on first and second-order fully nonlinear PDEs. The main goal is the design of numerical methods to solve a variety of equations such as orthogonal maps ...

EPFL2021

Low Noise Clock Generation: Modeling, Analysis and Implementation

Duygu Kostak

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 ...

EPFL2021

Discrete Time Analysis of Phase Detector Linear Range Extension in Sub-Sampling PLL

Yusuf Leblebici, Duygu Kostak

The discrete time analysis of the phase detector linear range extension in the first and the second order sub sampling phase-locked loop (SSPLL) is presented. The aim is to understand how much the stability and the pull-in range are affected by the linear ...

IEEE2020

Functional Inverse Problems on Spheres: Theory, Algorithms and Applications

Matthieu Martin Jean-André Simeoni

Many scientific inquiries in natural sciences involve approximating a spherical field -namely a scalar quantity defined over a continuum of directions- from generalised samples of the latter (e.g. directional samples, local averages, etc). Such an approxim ...

EPFL2020

An adaptive algorithm for the transport equation with time dependent velocity

Marco Picasso, Samuel Dubuis

An a posteriori error estimate is derived for the approximation of the transport equation with a time dependent transport velocity. Continuous, piecewise linear, anisotropic finite elements are used for space discretization, the Crank-Nicolson scheme schem ...

2020

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

Yusuf Leblebici, Duygu Kostak

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 ...

IEEE2020

Detection Under One-Bit Messaging Over Adaptive Networks

Ali H. Sayed

This paper studies the operation of multi-agent networks engaged in binary decision tasks, and derives performance expressions and performance operating curves under challenging conditions with some revealing insights. One of the main challenges in the ana ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2019

A Universal Sampling Method for Reconstructing Signals with Simple Fourier Transforms

Mikhail Kapralov, Amir Zandieh

Reconstructing continuous signals based on a small number of discrete samples is a fundamental problem across science and engineering. We are often interested in signals with "simple" Fourier structure - e.g., those involving frequencies within a bounded r ...

ASSOC COMPUTING MACHINERY2019

Neural BTF Compression and Interpolation

Wenzel Alban Jakob

The Bidirectional Texture Function (BTF) is a data-driven solution to render materials with complex appearance. A typical capture contains tens of thousands of images of a material sample under varying viewing and lighting conditions. While capable of fait ...

WILEY2019