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Gabriel Peyré
CNRS researcher at the DMA, École Normale Supérieure. One tweet a day on computational mathematics.
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Gabriel Peyré 4h
Oldies but goldies: S. Farsiu, M.D. Robinson, M. Elad, P. Milanfar, Fast and robust multiframe super resolution, 2004. Introduced L1-type robust fidelity terms for video super-resolution.
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Gabriel Peyré Sep 2
We are starting a new seminar "DHAI - When Digital Humanities Meet Artificial Intelligence". First speaker is Alexei Efros (Berkeley), sept. 17th, 2019, 18h-20h, "Finding Visual Patterns in Large Image Collections"
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Gabriel Peyré Sep 13
The Brachistochrone problem was solved by Bernoulli and is the birth of calculus of variations.
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Ian Goodfellow Sep 12
Hey I keep getting sent your invitations to present at some wonderful conferences - maybe one day I should accept and just rock up and give them the latest in norovirus biology or field sequencing of viruses- think they'd notice?
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Gabriel Peyré Sep 12
Oldies but Goldies: David Donoho, Iain Johnstone, Ideal spatial adaptation by wavelet shrinkage, 1995. Introduces the soft thresholding to solve denoising by leveraging the sparsity of the data in some dictionary (e.g. wavelets).
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Gabriel Peyré Sep 11
Moreau’s decomposition generalizes the orthogonal decomposition from linear spaces to convex functions. It can also be generalized beyond Euclidean spaces using Bregman divergences in place of Euclidean distances.
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Eric Arnebäck Sep 11
when shading geometry, normals are interpolated from the vertex normals. this allows even low-res meshes to look smooth. made a short visualization of this:
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Gabriel Peyré Sep 10
Oldies but Goldies: L. Lovasz and B. Szegedy. Limits of dense graph sequences, 2006. Graphons are both continuous limits of dense discrete graphs and models to sample random dense graphs. The natural topology is the cut-metric.
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Gabriel Peyré Sep 10
Replying to @bekemax
It is the orthogonal projector on the set of orthogonal matrices btw.
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Gabriel Peyré Sep 10
Replying to @bekemax
It is not really Moore Penrose, it is rather simply putting the singular values of M to 1. Moore Penrose would invert them. Here from M=U*diag(s)*V the optimal rotation is U*V.
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Gabriel Peyré Sep 9
In the static regime, the electric / magnetic fields generated by point sources is the superposition of radial monopoles / dipoles.
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Gabriel Peyré Sep 9
Replying to @kgourg @alfcnz
That was my initial reasoning but I should have used a simpler red/blue colormap. Next time...
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Gabriel Peyré Sep 8
Optimal Transport meets Focaccia!
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Gabriel Peyré Sep 8
Oldies but goldies: A. Nadas, Least squares and maximum likelihood estimation of rigid motion. Kabsch-Nadas formula solves orthogonal least square problem (aka orthogonal procrustes). At the heart of the iterative closest point method for registration.
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Gabriel Peyré Sep 7
Heat diffusion vs. wave equation on a surface.
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Gabriel Peyré Sep 6
Oldies but Goldies: Richard Karp, Reducibility Among Combinatorial Problems, 1972. Proved 21 problems to be NP-complete, among which the TSP.
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Gabriel Peyré Sep 5
Matrix decompositions come in many flavors!
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Gabriel Peyré Sep 5
This is a great reference!! Thx! Are you aware of applications of this method? [side note: the proof of the main theorem "it has a limit and its derivative goes to zero" seems a bit fast, a function could have a limit without his derivative going to zero, no?]
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Gabriel Peyré Sep 5
Replying to @docmilanfar
So true :) I love this algorithm so much! I am desesperatly looking for a descente picture of Richard Dennis Sinkhorn.
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Gabriel Peyré Sep 5
Replying to @jsdenain
I hope it is clear by now that convex cones is a strongly recurring theme in my tweets...
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