Post-Perseids Sunrise At Raisting Earth Station (2026)
(Pictures from between 5-6AM this morning... I still need to process the meteor shower images from the hour before, but not holding my breath...)
#LandscapePhotography #RadioTelescope
Cowboys Players Took Matters Into Their Own Hands to Start Week 6 https://heavy.com/sports/nfl/dallas-cowboys/players-took-matters-into-own-hands/
I submit that a moving melodic bassline is a most underrated musical device. And this band, the Lucksmiths, are the antidote. Consider https://thelucksmiths.bandcamp.com/track/motorscooter (and everything else in their catalogue)...
Spectral phase transitions in Gaussian multi-index models
Florent Krzakala, Pierre Mergny, Vanessa Piccolo
https://arxiv.org/abs/2608.12183 https://arxiv.org/pdf/2608.12183 https://arxiv.org/html/2608.12183
arXiv:2608.12183v1 Announce Type: new
Abstract: Recovering a low-dimensional latent subspace from nonlinear observations of Gaussian covariates in high dimensions is a fundamental problem in feature learning. Here, we consider Gaussian multi-index models in which the covariates $\boldsymbol{x}_i \stackrel{\mathrm{i.i.d.}}{\sim} \mathcal{N}(0,\boldsymbol{I}_d)$ and the responses $\boldsymbol{y}_i$ depend on $\boldsymbol{x}_i$ only through its projection onto an unknown $r$-dimensional subspace. Earlier work based on approximate message passing (AMP) identified a sharp threshold for weak recovery [Troiani et al., 2025], raising the question of whether it can be attained, without side information, by a spectral method. We answer this affirmatively and develop a general random matrix theory for matrix-valued spectral estimators of the form \[\boldsymbol{D}_n=\frac{1}{n}\sum_{i=1}^n\boldsymbol{T}(\boldsymbol{y}_i)\otimes\boldsymbol{x}_i\boldsymbol{x}_i^\top,\] where $\boldsymbol{T}$ is an arbitrary bounded symmetric matrix-valued preprocessing map of fixed dimension. As $n,d \to \infty$ with $n/d\to\alpha$, we prove that the empirical spectral measure of $\boldsymbol{D}_n$ converges almost surely to a deterministic compactly supported distribution characterized by a matrix-valued self-consistent equation. We then establish a spectral phase transition for the largest eigenvalue: below threshold it sticks to the bulk edge, while above threshold an outlier emerges. We characterize the outlier location through a finite-dimensional deterministic equation and show that the associated spectral estimator achieves weak recovery of the latent subspace. Finally, we prove that the AMP-derived preprocessing of [Defilippis et al., 2025] is optimal among all bounded matrix-valued preprocessing maps of any fixed dimension. Its transition coincides with the AMP weak-recovery threshold, proving the general spectral conjecture of [Defilippis et al., 2025].
toXiv_bot_toot
🇺🇦 #NowPlaying on KEXP's #VarietyMix
Mad Iris:
🎵 Employee of the Month
#MadIris
https://madiris.bandcamp.com/track/employee-of-the-month
https://open.spotify.com/track/70fGIBLg6XvOlD62ADKQyT
I couldn't decide what to do today and where to go. I got up too late for a longer hike due to the heat. In the end I just got on my bike and followed the road and pushed myself for some training effect.
It was a really enjoyable ride except for the last 10km where the heat got really annoying.
Is this a #silentsunday contribution? I think so... No talking, less thinking, j…
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🎞️ LUCKY SHD 100 (6x6)
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Wise
Daphy Michel,
who suffered from severe mental illness,
was found more than 20 miles away from her home in Charleroi,
wearing summer clothes in freezing weather.
In June, Michel’s death was ruled a homicide.
An attorney for the family said they are planning to file a lawsuit.
Michel’s death isn’t recorded on ICE’s website. “ICE had NOTHING to do with this woman’s death,” DHS declared on social media.
ICE reporting also doesn’t account for people who die…