Publications associées à Laplacien discret

Outlier-free spline spaces for isogeometric discretizations of biharmonic and polyharmonic eigenvalue problems

We present outlier-free isogeometric Galerkin discretizations of eigenvalue problems related to the biharmonic and the polyharmonic operator in the univariate setting. These are Galerkin discretizations in certain spline subspaces that provide accurate app ...

Elsevier Science Sa2023

Fredholm transformation on Laplacian and rapid stabilization for the heat equation

Shengquan Xiang

We study the rapid stabilization of the heat equation on the 1-dimensional torus using the backstepping method with a Fredholm transformation. This classical framework allows us to present the backstepping method with Fredholm transformations for the Lapla ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2022

SPECTRE: Spectral Conditioning Helps to Overcome the Expressivity Limits of One-shot Graph Generators

Nathanaël Perraudin, Andreas Loukas, Karolis Martinkus

We approach the graph generation problem from a spectral perspective by first generating the dominant parts of the graph Laplacian spectrum and then building a graph matching these eigenvalues and eigenvectors. Spectral conditioning allows for direct model ...

JMLR-JOURNAL MACHINE LEARNING RESEARCH2022

A smooth basis for atomistic machine learning

Michele Ceriotti, Kevin Kazuki Huguenin-Dumittan, Filippo Bigi

Machine learning frameworks based on correlations of interatomic positions begin with a discretized description of the density of other atoms in the neighborhood of each atom in the system. Symmetry considerations support the use of spherical harmonics to ...

AIP Publishing2022

Annihilation Filter Approach For Estimating Graph Dynamics From Diffusion Processes

Pascal Frossard, Arun Venkitaraman

We propose an approach for estimating graph diffusion processes using annihilation filters from a finite set of observations of the diffusion process made at regular intervals. Our approach is based on the key observation that a graph diffusion process can ...

IEEE2022

Multiscale Representation Learning of Graph Data With Node Affinity

Pascal Frossard, Chenglin Li, Xing Gao

Graph neural networks have emerged as a popular and powerful tool for learning hierarchical representation of graph data. In complement to graph convolution operators, graph pooling is crucial for extracting hierarchical representation of data in graph neu ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2021

SiML: Sieved Maximum Likelihood for Array Signal Processing

Paul Hurley, Matthieu Martin Jean-André Simeoni

Stochastic Maximum Likelihood (SML) is a popular direction of arrival (DOA) estimation technique in array signal processing. It is a parametric method that jointly estimates signal and instrument noise by maximum likelihood, achieving excellent statistical ...

2021

A Laplacian approach to stubborn agents and their role in opinion formation on influence networks

Melvyn Sandy Tyloo

Within the framework of a simple model for social influence, the Taylor model, we analytically investigate the role of stubborn agents in the overall opinion dynamics of networked systems. Similar to zealots, stubborn agents are biased towards a certain op ...

2020

The sliding Frank-Wolfe algorithm and its application to super-resolution microscopy

Emmanuel Emilien Louis Soubies, Quentin Alain Denoyelle, Gabriel Peyré

This paper showcases the theoretical and numerical performance of the Sliding Frank-Wolfe, which is a novel optimization algorithm to solve the BLASSO sparse spikes super-resolution problem. The BLASSO is a continuous (i.e. off-the-grid or grid-less) count ...

2020

OrthoNet: Multilayer Network Data Clustering

Pascal Frossard, Mireille El Gheche, Giovanni Chierchia

Network data appears in very diverse applications, like biological, social, or sensor networks. Clustering of network nodes into categories or communities has thus become a very common task in machine learning and data mining. Network data comes with some ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020