Tootfinder

Supreme Court turns away RNC challenge to Pennsylvania ballot ruling
https://thehill.com/regulation/court-battles/5338008-supreme-court-rnc-pennsylvania-challenge/

Supreme Court turns away RNC challenge to Pennsylvania ballot ruling (Zach Schonfeld/The Hill)
https://thehill.com/regulation/court-battles/5338008-supreme-court-rnc-pennsylvania-challenge/
http://www.memeorandum.com/250606/p143#a250606p143

The Hesse pencil of plane curves and osculating conics
Ewelina Nawara
https://arxiv.org/abs/2506.04662 https://arxiv.org/pdf/2506.046…

The Hesse pencil of plane curves and osculating conics
In this paper, we revisit the classical problem of determining osculating conics and sextactic points for a given algebraic curve. Our focus is on a particular family of plane cubic curves known as the Hesse pencil. By employing classical tools from projective differential geometry, we derive explicit coordinates for these special points. The resulting formulas not only clarify previous approaches but also lead to the construction of new families of free and nearly free curves, extending recent…

Determinants of Random Unitary Pencils
Michael T. Jury, George Roman
https://arxiv.org/abs/2506.04400 https://arxiv.org/pdf/2506.0440…

Determinants of Random Unitary Pencils
We investigate determinants of random unitary pencils (with scalar or matrix coefficients), which generalize the characteristic polynomial of a single unitary matrix. In particular we examine moments of such determinants, obtained by integrating against the Haar measure on the unitary group. We obtain an exact formula in the case of scalar coefficients, and conjecture an asymptotic formula in the general case, and prove a special case of the conjecture.

"wehe du pinkelst ins Becken!"

🇺🇦 #NowPlaying on #BBC6Music's #NickGrimshaw
pencil:
🎵 Honest Song
#pencil
https://open.spotify.com/track/1jOHyaoZuxjJuHvkaf3AAK
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Diffusion Transformer-based Universal Dose Denoising for Pencil Beam Scanning Proton Therapy
Yuzhen Ding, Jason Holmes, Hongying Feng, Martin Bues, Lisa A. McGee, Jean-Claude M. Rwigema, Nathan Y. Yu, Terence S. Sio, Sameer R. Keole, William W. Wong, Steven E. Schild, Jonathan B. Ashman, Sujay A. Vora, Daniel J. Ma, Samir H. Patel, Wei Liu
https://…

Diffusion Transformer-based Universal Dose Denoising for Pencil Beam Scanning Proton Therapy
Purpose: Intensity-modulated proton therapy (IMPT) offers precise tumor coverage while sparing organs at risk (OARs) in head and neck (H&N) cancer. However, its sensitivity to anatomical changes requires frequent adaptation through online adaptive radiation therapy (oART), which depends on fast, accurate dose calculation via Monte Carlo (MC) simulations. Reducing particle count accelerates MC but degrades accuracy. To address this, denoising low-statistics MC dose maps is proposed to enable fas…

Modelling shadows in scattered light observations as signals from companions in protoplanetary discs
Deniz Akansoy, Helen C. Petrou, Giulia Ballabio, Anna B. T. Penzlin
https://arxiv.org/abs/2506.04415

Modelling shadows in scattered light observations as signals from companions in protoplanetary discs
Over the past decade, SPHERE scattered light observations of protoplanetary discs have revealed previously unseen features with unprecedented resolution. One such feature are radial streaks of reduced brightness that are commonly interpreted as shadows. A possible cause for these shadows is an embedded companion within the disc. In this work, we use 3D radiative transfer simulations with RADMC-3D to investigate the shadowing effects of embedded companions across a range of orbital distances (5-…

@… is so brilliant.
https://socel.net/@catandgirl/114189949826454819
took me like three tries to get the punchline here

Cat and Girl (@catandgirl@socel.net)
Attached: 1 image Scenes from a future.

This https://arxiv.org/abs/2502.12010 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Hyperplane arrangements and the Gauss map of a pencil
We show that the coefficients of the characteristic polynomial of a central hyperplane arrangement $\mathcal A$, coincide with the multidegrees of the Gauss map of a pencil of hypersurfaces naturally associated to $\mathcal A$. As a consequence, we obtain a proof of the Heron-Rota-Welsh conjecture for matroids representable over a field of characteristic zero.