Concept

Discrete Laplace operator

Related publications (68)

Parametric dictionary learning for graph signals

We propose a parametric dictionary learning algorithm to design structured dictionaries that sparsely represent graph signals. We incorporate the graph structure by forcing the learned dictionaries to be concatenations of subdictionaries that are polynomia ...

2013

On the Sparsity of Wavelet Coefficients for Signals on Graphs

Pierre Vandergheynst, Benjamin Ricaud, David Shuman

A number of new localized, multiscale transforms have recently been introduced to analyze data residing on weighted graphs. In signal processing tasks such as regularization and compression, much of the power of classical wavelets on the real line is deriv ...

Spie-Int Soc Optical Engineering2013

Generalized reduced basis methods and n-width estimates for the approximation of the solution manifold of parametric PDEs

Alfio Quarteroni, Gianluigi Rozza, Andrea Manzoni, Toni Mikael Lassila

The set of solutions of a parameter-dependent linear partial differential equation with smooth coefficients typically forms a compact manifold in a Hilbert space. In this paper we review the generalized reduced basis method as a fast computational tool for ...

Springer2012

Clustering with Multi-Layer Graphs: A Spectral Perspective

Pascal Frossard, Pierre Vandergheynst, Xiaowen Dong

Observational data usually comes with a multimodal nature, which means that it can be naturally represented by a multi-layer graph whose layers share the same set of vertices (users) with different edges (pairwise relationships). In this paper, we address ...

Institute of Electrical and Electronics Engineers2012

Wavelets on graphs via spectral graph theory

Pierre Vandergheynst, Rémi Gribonval

We propose a novel method for constructing wavelet transforms of functions defined on the vertices of an arbitrary finite weighted graph. Our approach is based on defining scaling using the the graph analogue of the Fourier domain, namely the spectral deco ...

Elsevier2011

Trace Identities For Commutators, With Applications To The Distribution Of Eigenvalues

Joachim Stubbe

We prove trace identities for commutators of operators, which are used to derive sum rules and sharp universal bounds for the eigenvalues of periodic Schrodinger operators and Schrodinger operators on immersed manifolds. In particular, we prove bounds on t ...

2011

A lower bound for algebraic connectivity based on the connection-graph-stability method

Martin Hasler, Ali Ajdari Rad, Mahdi Jalili

This paper introduces the connection-graph-stability method and uses it to establish a new lower bound on the algebraic connectivity of graphs (the second smallest eigenvalue of the Laplacian matrix of the graph) that is sharper than the previously publish ...

Elsevier2011

Universal Bounds And Semiclassical Estimates For Eigenvalues Of Abstract Schrodinger Operators

Joachim Stubbe

We prove trace inequalities for a self-adjoint operator on an abstract Hilbert space, which extend those known previously for Laplacians and Schrodinger operators, freeing them from restrictive assumptions on the nature of the spectrum and allowing operato ...

2010

On the spectral estimates for Schrödinger type operators. The case of small local dimension

The behavior of the discrete spectrum of the Schr"odinger operator

-\D - V

, in quite a general setting, up to a large extent is determined by the behavior of the corresponding heat kernel

P(t;x,y)

t\to 0

and

t\to\infty

. If this behavior is powe ...

2010

Isogeometric analysis in electromagnetics: B-splines approximation

Annalisa Buffa, Rafael Vazquez Hernandez

We introduce a new discretization scheme for Maxwell equations in two space dimension. Inspired by the new paradigm of Isogeometric analysis introduced in Hughes et al. (2005) [16], we propose an algorithm based on the use of bivariate B-splines spaces sui ...

2010

Graph Chatbot

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

On the spectral estimates for Schrödinger type operators. The case of small local dimension

The behavior of the discrete spectrum of the Schr"odinger operator

-\D - V

, in quite a general setting, up to a large extent is determined by the behavior of the corresponding heat kernel

P(t;x,y)

t\to 0

and

t\to\infty

. If this behavior is powe ...

2010