Tootfinder

Quadratic relations for ninth variations of Schur functions and application to Schur multiple zeta functions
Wataru Takeda, Yoshinori Yamasaki
https://arxiv.org/abs/2508.03150 h…

Quadratic relations for ninth variations of Schur functions and application to Schur multiple zeta functions
Macdonald's ninth variation of Schur functions is a broad generalization of the classical Schur function and its variants, defined via the Jacobi-Trudi determinant formula. In this paper, we establish various algebraic relations for $S^{(r)}_{λ/μ}(X)$, a class of the ninth variation introduced by Nakagawa, Noumi, Shirakawa, and Yamada, by combining the Jacobi-Trudi formula with determinant formulas such as the Desnanot-Jacobi adjoint matrix theorem and the Plücker relations, which generalize…

🇺🇦 #NowPlaying on KEXP's #VarietyMix
Chaz Bundick Meets The Mattson 2:
🎵 Star Stuff
#ChazBundickMeetsTheMattson2
https://chazbundickmeetsthemattson2.bandcamp.com/album/star-stuff

This https://arxiv.org/abs/2402.15158 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

General infinitesimal variations of Hodge structure of ample curves in surfaces
Given a smooth projective complex curve inside a smooth projective surface, one can ask how its Hodge structure varies when the curve moves inside the surface. In this paper we develop a general theory to study the infinitesimal version of this question in the case of ample curves. We can then apply the machinery to show that the infinitesimal variation of Hodge structure of a general deformation of an ample curve in $\mathbb{P}^1\times\mathbb{P}^1$ is an isomorphism.

CardiffNLP at CLEARS-2025: Prompting Large Language Models for Plain Language and Easy-to-Read Text Rewriting
Mutaz Ayesh, Nicol\'as Guti\'errez-Rol\'on, Fernando Alva-Manchego
https://arxiv.org/abs/2508.03240

CardiffNLP at CLEARS-2025: Prompting Large Language Models for Plain Language and Easy-to-Read Text Rewriting
This paper details the CardiffNLP team's contribution to the CLEARS shared task on Spanish text adaptation, hosted by IberLEF 2025. The shared task contained two subtasks and the team submitted to both. Our team took an LLM-prompting approach with different prompt variations. While we initially experimented with LLaMA-3.2, we adopted Gemma-3 for our final submission, and landed third place in Subtask 1 and second place in Subtask 2. We detail our numerous prompt variations, examples, and experi…

On the Wasserstein Geodesic Principal Component Analysis of probability measures
Nina Vesseron, Elsa Cazelles, Alice Le Brigant, Thierry Klein
https://arxiv.org/abs/2506.04480

On the Wasserstein Geodesic Principal Component Analysis of probability measures
This paper focuses on Geodesic Principal Component Analysis (GPCA) on a collection of probability distributions using the Otto-Wasserstein geometry. The goal is to identify geodesic curves in the space of probability measures that best capture the modes of variation of the underlying dataset. We first address the case of a collection of Gaussian distributions, and show how to lift the computations in the space of invertible linear maps. For the more general setting of absolutely continuous prob…

This https://arxiv.org/abs/2506.04091 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Mapped Exponent and Asymptotic Critical Exponent of Words
We study how much injective morphisms can increase the repetitiveness of a given word. This question has a few possible variations depending on the meaning of ``repetitiveness''. We concentrate on fractional exponents of finite words and asymptotic critical exponents of infinite words. We characterize finite words that, when mapped by injective morphisms, can have arbitrarily high fractional exponent. For infinite words, alongside other results, we show that the asymptotic critical exponent gro…

Revisiting Active Learning under (Human) Label Variation
Cornelia Gruber, Helen Alber, Bernd Bischl, G\"oran Kauermann, Barbara Plank, Matthias A{\ss}enmacher
https://arxiv.org/abs/2507.02593

Revisiting Active Learning under (Human) Label Variation
Access to high-quality labeled data remains a limiting factor in applied supervised learning. While label variation (LV), i.e., differing labels for the same instance, is common, especially in natural language processing, annotation frameworks often still rest on the assumption of a single ground truth. This overlooks human label variation (HLV), the occurrence of plausible differences in annotations, as an informative signal. Similarly, active learning (AL), a popular approach to optimizing th…

🇺🇦 #NowPlaying on KEXP's #VarietyMix
WITCH:
🎵 Tiponde Madzi
#WITCH
https://w-i-t-c-h.bandcamp.com/track/tiponde-madzi
https://open.spotify.com/track/4ujCBh72JoubgvD8dAKm5x

Slow graph bootstrap percolation III: Chain constructions
David Fabian, Patrick Morris, Tibor Szab\'o
https://arxiv.org/abs/2508.03835 https://arxiv.or…

Slow graph bootstrap percolation III: Chain constructions
For graphs $H$, we study the extremal function $M_H(n)$ which is the maximum running time (until stabilisation) of an $H$-bootstrap percolation process on $n$ vertices. Building on previous work in the clique case $H=K_k$, we develop a general framework of chain constructions. We demonstrate the flexibility of this framework by applying several variations of the method to give lower bounds on $M_H(n)$ for a wide variety of different graphs $H$ including dense graphs, random graphs and complete …

🇺🇦 #NowPlaying on KEXP's #VarietyMix
Death Cab for Cutie:
🎵 Soul Meets Body
#DeathCabforCutie
https://souzalex.bandcamp.com/track/death-cab-for-cutie-soul-meets-body-souza-remix
https://open.spotify.com/track/6Wuv7MrhesuDsuGv8vcrOd