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Partial trace relations beyond normal matrices
Pablo Costa Rico, Michael M. Wolf
https://arxiv.org/abs/2507.18278 https://arxiv.org/pdf/2507.18278

Partial trace relations beyond normal matrices
We investigate the relationship between partial traces and their dilations for general complex matrices, focusing on two main aspects: the existence of (joint) dilations and norm inequalities relating partial traces and their dilations. Throughout our analysis, we pay particular attention to rank constraints. We find that every pair of matrices of equal size and trace admits dilations of any rank larger than one. We generalize Audenaert's subadditivity inequality to encompass general matrices, …

Exact Matrix Seriation through Mathematical Optimization: Stress and Effectiveness-Based Models
V\'ictor Blanco, Alfredo Mar\'in, Justo Puerto
https://arxiv.org/abs/2506.19821

Exact Matrix Seriation through Mathematical Optimization: Stress and Effectiveness-Based Models
Matrix seriation, the problem of permuting the rows and columns of a matrix to uncover latent structure, is a fundamental technique in data science, particularly in the visualization and analysis of relational data. Applications span clustering, anomaly detection, and beyond. In this work, we present a unified framework grounded in mathematical optimization to address matrix seriation from a rigorous, model-based perspective. Our approach leverages combinatorial and mixed-integer optimization t…

🇺🇦 #NowPlaying on KEXP's #MiddayShow
Mother’s Finest:
🎵 Can’t Fight the Feeling
#MothersFinest
https://open.spotify.com/track/5W0YJ6p8W2ssMBb5hWsYML

I brimmed the tank on the #motorcycle tonight after an evening ride. Now that the pickup truck isn't in my life, I get to go back to the only gasoline that I buy being for this thing.

🇺🇦 #NowPlaying on BBCRadio3's #RoundMidnight
Chick Corea:
🎵 Matrix from Now He Sings, Now He Sobs (feat. Roy Haynes)
#ChickCorea
https://open.spotify.com/track/13VdXFe27FOq9CW2CJaxID
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Bayesian Variable Selection in Multivariate Regression Under Collinearity in the Design Matrix
Joyee Ghosh, Xun Li
https://arxiv.org/abs/2507.17975 https://

Bayesian Variable Selection in Multivariate Regression Under Collinearity in the Design Matrix
We consider the problem of variable selection in Bayesian multivariate linear regression models, involving multiple response and predictor variables, under multivariate normal errors. In the absence of a known covariance structure, specifying a model with a non-diagonal covariance matrix is appealing. Modeling dependency in the random errors through a non-diagonal covariance matrix is generally expected to lead to improved estimation of the regression coefficients. In this article, we highlight…

NASA’s NICER (Neutron star Interior Composition Explorer), an X-ray telescope on the International Space Station, has paused observations due to a problem with one of the motors that drives its ability to track cosmic objects: #NICER team paused operations June 17 when performance degradation in the motor began affecting science observations. Engineers are investigating the cause and potential solutions.

Amazing #video of an #earthquake where large areas were moved for several meters(!) within 1.3 seconds: https://youtu.be/77ubC4bcgRM

A High-Dimensional Statistical Theory for Convex and Nonconvex Matrix Sensing
Joshua Agterberg, Ren\'e Vidal
https://arxiv.org/abs/2506.20659 https://

A High-Dimensional Statistical Theory for Convex and Nonconvex Matrix Sensing
The problem of matrix sensing, or trace regression, is a problem wherein one wishes to estimate a low-rank matrix from linear measurements perturbed with noise. A number of existing works have studied both convex and nonconvex approaches to this problem, establishing minimax error rates when the number of measurements is sufficiently large relative to the rank and dimension of the low-rank matrix, though a precise comparison of these procedures still remains unexplored. In this work we provide …

Arme minister Sophie. Geen enkele maatregel die je zelf hebt genomen doet iets goeds voor het klimaat. Nog één maattegel had je achter de hand en dan wordt die tegengegouden door de ontkenners in de kamer, ook door je eigen partij, je EIGEN PARTIJ, die altijd zo lief voor je is geweest...
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