#laplacian — Public Fediverse posts

Modell257: Debajyoti Choudhuri wrote an introductional paper about the Fractional Laplacian that has applications to diffusion problems, probability theory, as well as image processing. Learn about harmonics that sound like music but are actually composed out of functions that solve the Laplace equation without a source term.

https://modellansatz.de/fractional-laplacian

#Mathematics #Laplacian #FunctionalAnalytics #Fourier #FractionalDerivatives #SobolevSpaces #PDEs

Modell257: Debajyoti Choudhuri wrote an introductional paper about the Fractional Laplacian that has applications to diffusion problems, probability theory, as well as image processing. Learn about harmonics that sound like music but are actually composed out of functions that solve the Laplace equation without a source term.

https://modellansatz.de/fractional-laplacian

#Mathematics #Laplacian #FunctionalAnalytics #Fourier #FractionalDerivatives #SobolevSpaces #PDEs

LookingGlass: Generative Anamorphoses via Laplacian Pyramid Warping

https://studios.disneyresearch.com/2025/06/09/lookingglass-generative-anamorphoses-via-laplacian-pyramid-warping/

#HackerNews #LookingGlass #Generative #Anamorphoses #Laplacian #Pyramid #Warping #DisneyResearch

LookingGlass: Generative Anamorphoses via Laplacian Pyramid Warping

https://studios.disneyresearch.com/2025/06/09/lookingglass-generative-anamorphoses-via-laplacian-pyramid-warping/

#HackerNews #LookingGlass #Generative #Anamorphoses #Laplacian #Pyramid #Warping #DisneyResearch

Randomly thought about this topic tonight. One scary #math symbol that comes up in many places is the #Laplacian, that weird triangle Δ! What even is that? While you can do some smart math things to get an intuition for what it means, you can also try to make some simpler calculations! Turns out, it can be seen as a measure of how much a value at a point differs from its surroundings! Always liked this approach to show it to people, since imho you don't need too much background knowledge!

Randomly thought about this topic tonight. One scary #math symbol that comes up in many places is the #Laplacian, that weird triangle Δ! What even is that? While you can do some smart math things to get an intuition for what it means, you can also try to make some simpler calculations! Turns out, it can be seen as a measure of how much a value at a point differs from its surroundings! Always liked this approach to show it to people, since imho you don't need too much background knowledge!

'Radial Basis Approximation of Tensor Fields on Manifolds: From Operator Estimation to Manifold Learning', by John Harlim, Shixiao Willing Jiang, John Wilson Peoples.

http://jmlr.org/papers/v24/22-1193.html

#laplacians #laplacian #manifold

'Radial Basis Approximation of Tensor Fields on Manifolds: From Operator Estimation to Manifold Learning', by John Harlim, Shixiao Willing Jiang, John Wilson Peoples.

http://jmlr.org/papers/v24/22-1193.html

#laplacians #laplacian #manifold

'Large sample spectral analysis of graph-based multi-manifold clustering', by Nicolas Garcia Trillos, Pengfei He, Chenghui Li.

http://jmlr.org/papers/v24/21-1254.html

#laplacians #manifolds #laplacian

'Large sample spectral analysis of graph-based multi-manifold clustering', by Nicolas Garcia Trillos, Pengfei He, Chenghui Li.

http://jmlr.org/papers/v24/21-1254.html

#laplacians #manifolds #laplacian

'Implicit Bias of Gradient Descent for Mean Squared Error Regression with Two-Layer Wide Neural Networks', by Hui Jin, Guido Montufar.

http://jmlr.org/papers/v24/21-0832.html

#gradient #curvature #laplacian

'Implicit Bias of Gradient Descent for Mean Squared Error Regression with Two-Layer Wide Neural Networks', by Hui Jin, Guido Montufar.

http://jmlr.org/papers/v24/21-0832.html

#gradient #curvature #laplacian

#AMDlabnotes presents two brand new blog posts covering #GPU kernel optimization tips and tricks! 🔥

Firstly, we present a post about understanding and controlling register pressure:
https://gpuopen.com/learn/amd-lab-notes/amd-lab-notes-register-pressure-readme/?utm_source=mastodon&utm_medium=social&utm_campaign=amdlabnotes

And secondly, we present the third part of the Finite Difference Method #Laplacian series.

This blog covers even more optimizations to maximize performance on #AMD GPUs:
https://gpuopen.com/learn/amd-lab-notes/amd-lab-notes-finite-difference-docs-laplacian_part3/?utm_source=mastodon&utm_medium=social&utm_campaign=amdlabnotes

#AMDlabnotes presents two brand new blog posts covering #GPU kernel optimization tips and tricks! 🔥

Firstly, we present a post about understanding and controlling register pressure:
https://gpuopen.com/learn/amd-lab-notes/amd-lab-notes-register-pressure-readme/?utm_source=mastodon&utm_medium=social&utm_campaign=amdlabnotes

And secondly, we present the third part of the Finite Difference Method #Laplacian series.

This blog covers even more optimizations to maximize performance on #AMD GPUs:
https://gpuopen.com/learn/amd-lab-notes/amd-lab-notes-finite-difference-docs-laplacian_part3/?utm_source=mastodon&utm_medium=social&utm_campaign=amdlabnotes

#arxivfeed

"Large sample spectral analysis of graph-based multi-manifold clustering'
https://arxiv.org/abs/2107.13610

#data #MMC #manifolds #clustering #graph #laplacian #statistics

Why does anyone like the notation \(\Delta\) for the #Laplacian? I always thought that \(\nabla^2\) was so much more suggestive and lends itself so nicely to the equation \(\nabla^2u = \nabla \cdot (\nabla u)\).

Is it because the Laplacian is so fundamental that it gets annoying to have to always do the superscript 2?