Tootfinder

"The last hit song of Belgian singer Stromae, called “Santé”, is a tribute to all those workers behind the scenes in our modern world; the ones growing or catching the food we eat; the ones transporting us; the ones building and cleaning our facilities; those who more often than not, we simply do not see.
How long until Stromae releases an update to this song including software workers among those groups? Not very long."

Divide Et Impera
Divide and Conquer is a common technique for algorithm design: quicksort, discrete Fourier transforms, and even MapReduce are common examples of such a technique. It consists in breaking down a problem into smaller parts, so as to solve the whole of the problem. It is also a common technique in politics, known and applied since before the times of the Roman Empire. It consists in breaking down society into smaller parts, so as to rule the whole of society.

A Submillisecond Fourier and Wavelet-based Model to Extract Variable Candidates from the #NEOWISE Single-exposure Database: https://iopscience.iop.org/article/10.3847/1538-3881/ad7fe6 -> xeet about the very young author: https://x.com/MAstronomers/status/2004334592908505508 -> reaction by the new NASA Administrator: https://x.com/rookisaacman/status/2004772750494499104

Regularized Random Fourier Features and Finite Element Reconstruction for Operator Learning in Sobolev Space
Xinyue Yu, Hayden Schaeffer
https://arxiv.org/abs/2512.17884 https://arxiv.org/pdf/2512.17884 https://arxiv.org/html/2512.17884
arXiv:2512.17884v1 Announce Type: new
Abstract: Operator learning is a data-driven approximation of mappings between infinite-dimensional function spaces, such as the solution operators of partial differential equations. Kernel-based operator learning can offer accurate, theoretically justified approximations that require less training than standard methods. However, they can become computationally prohibitive for large training sets and can be sensitive to noise. We propose a regularized random Fourier feature (RRFF) approach, coupled with a finite element reconstruction map (RRFF-FEM), for learning operators from noisy data. The method uses random features drawn from multivariate Student's $t$ distributions, together with frequency-weighted Tikhonov regularization that suppresses high-frequency noise. We establish high-probability bounds on the extreme singular values of the associated random feature matrix and show that when the number of features $N$ scales like $m \log m$ with the number of training samples $m$, the system is well-conditioned, which yields estimation and generalization guarantees. Detailed numerical experiments on benchmark PDE problems, including advection, Burgers', Darcy flow, Helmholtz, Navier-Stokes, and structural mechanics, demonstrate that RRFF and RRFF-FEM are robust to noise and achieve improved performance with reduced training time compared to the unregularized random feature model, while maintaining competitive accuracy relative to kernel and neural operator tests.
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