Tootfinder

The "other" day job - what matters
#CreativeLife #BeBetter
https://muz4now.com/2025/the…

The "other" day job - what matters
Stan Stewart - @muz4now

On matrices commuting with their Frobenius
Fabian Gundlach, B\'eranger Seguin
https://arxiv.org/abs/2506.08695 https://arxiv.org/…

On matrices commuting with their Frobenius
The Frobenius of a matrix $M$ with coefficients in $\bar{\mathbb F}_p$ is the matrix $σ(M)$ obtained by raising each coefficient to the $p$-th power. We consider the question of counting matrices with coefficients in $\mathbb F_q$ which commute with their Frobenius, asymptotically when $q$ is a large power of $p$. We give answers for matrices of size $2$, for diagonalizable matrices, and for matrices whose eigenspaces are defined over $\mathbb F_p$. Moreover, we explain what is needed to solve…

The CN matrix of a pure braid projection
Yuko Ozawa, Ayaka Shimizu, Yoshiro Yaguchi
https://arxiv.org/abs/2506.08659 https://arxiv.or…

The CN matrix of a pure braid projection
The CN matrix of an $n$-braid projection $B$ is an $n \times n$ matrix such that each $(i,j)$ entry indicates the number of crossings between $i^{th}$ and $j^{th}$ strands of $B$. In this paper, patterns of an $n \times n$ matrix to be a CN matrix are discussed and the CN matrix of a pure 6-braid projection is characterized. As an application, the OU matrix of a pure 6-braid diagram and the crossing matrix of a positive pure 6-braid are also characterized.

It matters. I care. (Molly White/Citation Needed)
https://www.citationneeded.news/it-matters-i-care/
http://www.memeorandum.com/250611/p150#a250611p150

Efficient Prediction of SO(3)-Equivariant Hamiltonian Matrices via SO(2) Local Frames
Haiyang Yu, Yuchao Lin, Xuan Zhang, Xiaofeng Qian, Shuiwang Ji
https://arxiv.org/abs/2506.09398

Efficient Prediction of SO(3)-Equivariant Hamiltonian Matrices via SO(2) Local Frames
We consider the task of predicting Hamiltonian matrices to accelerate electronic structure calculations, which plays an important role in physics, chemistry, and materials science. Motivated by the inherent relationship between the off-diagonal blocks of the Hamiltonian matrix and the SO(2) local frame, we propose a novel and efficient network, called QHNetV2, that achieves global SO(3) equivariance without the costly SO(3) Clebsch-Gordan tensor products. This is achieved by introducing a set o…

Vacuum Homogeneous and Nonhomogeneous Metrics with Conventional and Quantized Metric Tensor: Singular or Nonsingular Solution
A. Tawfik (Egyptian Ctr. Theor. Phys., Cairo,Future U. in Egypt), S. G. Elgendi (Islamic U. in Madinah), M. Hanafy (Benha U.)
https://arxiv.org/abs/2506.08254

Vacuum Homogeneous and Nonhomogeneous Metrics with Conventional and Quantized Metric Tensor: Singular or Nonsingular Solution
To investigate whether the Universe underwent a singularity or maintained a nonsingular state, we carry out analytical and numerical analyses of the evolution of the Raychaudhuri equations in vacuum, alongside homogeneous and nonhomogeneous cosmic backgrounds. The results obtained from the Schwarzschild, Friedmann--Lemaitre--Robertson--Walker (FLRW), and Einstein--Gilbert--Straus (EGS) metrics are systematically compared. Analyzing the results from both, conventional and quantized metric tensor…

Bravo for CA suing Trump, but please take note: the law will not save us. It matters, this lawsuit matters, but it will not save us.
https://mastodon.social/@lawfare/114660080006061244

🇺🇦 Auf radioeins läuft...
Mother's Cake:
🎵 Love Your Smell
#NowPlaying #MothersCake
https://motherscake.bandcamp.com/track/love-your-smell-2
https://open.spotify.com/track/29T0PK2Mnlerq2IsHWk5IE

Refining ensemble $N$-representability of one-body density matrices from partial information
Julia Liebert, Anna O. Schouten, Irma Avdic, Christian Schilling, David A. Mazziotti
https://arxiv.org/abs/2506.09960

Refining ensemble $N$-representability of one-body density matrices from partial information
The $N$-representability problem places fundamental constraints on reduced density matrices (RDMs) that originate from physical many-fermion quantum states. Motivated by recent developments in functional theories, we introduce a hierarchy of ensemble one-body $N$-representability problems that incorporate partial knowledge of the one-body reduced density matrices (1RDMs) within an ensemble of $N$-fermion states with fixed weights $w_i$. Specifically, we propose a systematic relaxation that redu…

A Metrics-Oriented Architectural Model to Characterize Complexity on Machine Learning-Enabled Systems
Renato Cordeiro Ferreira (University of S\~ao Paulo, Jheronimus Academy of Data Science, Technical University of Eindhoven, Tilburg University)
https://arxiv.org/abs/2506.08153

A Metrics-Oriented Architectural Model to Characterize Complexity on Machine Learning-Enabled Systems
How can the complexity of ML-enabled systems be managed effectively? The goal of this research is to investigate how complexity affects ML-Enabled Systems (MLES). To address this question, this research aims to introduce a metrics-based architectural model to characterize the complexity of MLES. The goal is to support architectural decisions, providing a guideline for the inception and growth of these systems. This paper showcases the first step for creating the metrics-based architectural mode…