Mastodawn

Ah, yet another riveting #bedtime story about the thrilling escapades of #wavelets on #graphs 🤓✨. Because nothing screams excitement like spectral graph theory from 2009, now with 100% more arXiv-nerdery! 🔍📚💤
https://arxiv.org/abs/0912.3848 #spectraltheory #arXiv #nerdy #stories #HackerNews #ngated

Wavelets on Graphs via Spectral Graph Theory

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 decomposition of the discrete graph Laplacian $Ł$. Given a wavelet generating kernel $g$ and a scale parameter $t$, we define the scaled wavelet operator $T_g^t = g(tŁ)$. The spectral graph wavelets are then formed by localizing this operator by applying it to an indicator function. Subject to an admissibility condition on $g$, this procedure defines an invertible transform. We explore the localization properties of the wavelets in the limit of fine scales. Additionally, we present a fast Chebyshev polynomial approximation algorithm for computing the transform that avoids the need for diagonalizing $Ł$. We highlight potential applications of the transform through examples of wavelets on graphs corresponding to a variety of different problem domains.

arXiv.org

RTG 2491 Jan 19, 2025

We are happy to announce that we have *9* open positions for

#PhD candidates / Doctoral researchers (all genders welcome)

here at the #RTG for #FourierAnalysis and #SpectralTheory / @migoettingen.

Pay grade 13 TV-L/75%, three years, starting date is 01.10.2025, application deadline is 14.03.2025.

https://www.uni-goettingen.de/en/607635.html

#JobAd #jobs #WeAreHiring #Spektraltheorie #Göttingen #GAUG #MathematischesInstitut #Mathematik #Mathematics

RTG 2491 "Fourier Analysis and Spectral Theory" - Georg-August-University Göttingen

Website of the Georg-August-University Göttingen

Georg-August Universität Göttingen

katch wreck Sep 2, 2023

in many ways, #mathematical #physics is based on the #smoothing properties of the #integral

#integrableSystems #mathematicalPhysics #complexAnalysis #spectralTheory #harmonicAnalysis #functionalAnalysis #mathematicalAnalysis #differentialEquations #ODEs #PDEs #SDEs #DEs #equations #BrownianMotion #LangevinDynamics #dynamics #Langevin #StochasticDifferentialEquations #StochasticProcesses #WienerProcess #OrnsteinUhlenbeck #HarmonicOscillator #WaveEquation #Newton #Newtonian #Maxwell #Einstein

Victoria Stuart 🇨🇦 🏳️‍⚧️Jul 30, 2023

Functions are Vectors
https://thenumb.at/Functions-are-Vectors
Discussion: https://news.ycombinator.com/item?id=36921446

Conceptualizing functions as infinite-dimensional vectors lets us apply linear algebra to vast landscape of new problems, f. image/geometry processing, curve fitting, light transport, machine learning

See also:
https://mastodon.social/@persagen/110798154360357308
Signal processing interpretation of noise-reduction convolutional neural networks

#mathematics #vectors #LinearAlgebra #MachineLearning #SpectralTheory #SignalProcessing #functions

Functions are Vectors

Erwin Schrödinger Institute Jun 20, 2023

Maciej Zworski from
@UCBerkeley
holding a lecture on #EllipticRegularity 🧐

within the framework of the thematic programme #SpectralTheory

Erwin Schrödinger Institute Jun 16, 2023

We kicked off with a new thematic programme on #SpectralTheory 2 weeks ago, but the 1st focus week is happening 🔜.
Are you joining? 😉

As you could expect, you can reach the schedule and more at https://esi.ac.at/events/e425/ and the talks on our YT Channel at https://youtube.com/@ESIVienna/featured

#GeneralRelativity #HawkingRadiation #StationarySpacetimes #HilbertSpaces

@univienna

(Visit Twitter for the video: https://twitter.com/ESIVienna/status/1669714303581028352)

Erwin Schrödinger Institute Apr 12, 2023

Are you keen to read about results in #MathematicalPhysics and Analysis of #PDEs? Take a look at the paper of our previous workshop participant! 🧐

#FunctionalAnalysis #SpectralTheory
@univienna

https://arxiv.org/pdf/2303.04527.pdf

Erwin Schrödinger Institute Dec 15, 2022

Are you into #MathematicalPhysics? 📏 Read the latest paper of our visitor from the workshop #SpectralTheory of differential operators in #quantumtheory. 📗

https://arxiv.org/pdf/2109.04052.pdf

@univienna