Tootfinder

Minimal Pair-Based Evaluation of Code-Switching
Igor Sterner, Simone Teufel
https://arxiv.org/abs/2506.01840 https://arxiv.org/pdf/25…

Minimal Pair-Based Evaluation of Code-Switching
There is a lack of an evaluation methodology that estimates the extent to which large language models (LLMs) use code-switching (CS) in the same way as bilinguals. Existing methods do not have wide language coverage, fail to account for the diverse range of CS phenomena, or do not scale. We propose an intervention based on minimal pairs of CS. Each minimal pair contains one naturally occurring CS sentence and one minimally manipulated variant. We collect up to 1,000 such pairs each for 11 langu…

A Minimal Substitution Basis for the Kalmar Elementary Functions
Mihai Prunescu, Lorenzo Sauras-Altuzarra, Joseph M. Shunia
https://arxiv.org/abs/2505.23787

A Minimal Substitution Basis for the Kalmar Elementary Functions
We show that the class of Kalmar elementary functions can be inductively generated from the addition, the integer remainder and the base-two exponentiation, hence improving previous results by Marchenkov and Mazzanti. In addition, we further prove that the substitution basis defined by these three operations is minimal.

This https://arxiv.org/abs/2504.15962 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csRO_…

Blimp-based Crime Scene Analysis
Crime is a critical problem -- which often takes place behind closed doors, posing additional difficulties for investigators. To bring hidden truths to light, evidence at indoor crime scenes must be documented before any contamination or degradation occurs. Here, we address this challenge from the perspective of artificial intelligence (AI), computer vision, and robotics: Specifically, we explore the use of a blimp as a "floating camera" to drift over and record evidence with minimal disturbanc…

A Computational Search for Minimal Obstruction Graphs for the Lov\'{a}sz--Schrijver SDP Hierarchy
Yu Hin Au, Levent Tun\c{c}el
https://arxiv.org/abs/2505.24735

A Computational Search for Minimal Obstruction Graphs for the Lovász--Schrijver SDP Hierarchy
We study the lift-and-project relaxations of the stable set polytope of graphs generated by $\text{LS}_+$, the SDP lift-and-project operator devised by Lovász and Schrijver. In particular, we focus on searching for $\ell$-minimal graphs, which are graphs on $3\ell$ vertices whose stable set polytope has rank $\ell$ with respect to $\text{LS}_+$. These are the graphs which are the most challenging for the $\text{LS}_+$ operator according to one of the main complexity measures (smallest graphs w…

Finite groups with the minimal generating set exchange property
Andrea Lucchini, Patricia Medina Capilla
https://arxiv.org/abs/2506.01638 https://

Finite groups with the minimal generating set exchange property
Let $d(G)$ be the smallest cardinality of a generating set of a finite group $G.$ We give a complete classification of the finite groups with the property that, whenever $ \langle x_1, \dots, x_{d(G)} \rangle = \langle y_1, \dots, y_{d(G)} \rangle = G$, for any $1 \leq i \leq d(G)$ there exists $1 \leq j \leq d(G)$ such that $\langle x_1, \dots, x_{i-1}, y_j, x_{i+1}, \dots, x_{d(G)} \rangle = G.$ We also prove that for every finite group $G$ and every maximal subgroup $M$ of $G$, there exists …

Finitely Summable $K$-homology, the Index Pairing, and Cantor Minimal Systems
Levi Lorenzo
https://arxiv.org/abs/2505.24135 https://a…

Finitely Summable $K$-homology, the Index Pairing, and Cantor Minimal Systems
We study index pairings for crossed-product $C^*$-algebras arising from minimal actions on the Cantor set. We utilize Putnam's orbit-breaking AF-subalgebras and embeddings to show we can compute any index pairing for Cantor minimal system crossed products using Connes' trace formulas. In the case of odometers, we show that the associated algebras have uniformly finitely summable $K$-homology.

This https://arxiv.org/abs/2409.07408 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Hilbert schemes for crepant partial resolutions
For $n\geq 1$, we construct the Hilbert scheme of $n$ points on any crepant partial resolution of a Kleinian singularity as a Nakajima quiver variety for an explicit GIT stability parameter. This generalises and unifies existing quiver variety constructions of the Hilbert scheme of points on the minimal resolution of a Kleinian singularity, and on the Kleinian singularity itself.

The Hasse principle for homogeneous polynomials with random coefficients over thin sets II
Daniel Flores, Kiseok Yeon
https://arxiv.org/abs/2506.01291 http…

The Hasse principle for homogeneous polynomials with random coefficients over thin sets II
Let $d$ and $n$ be natural numbers. Let $ν_{d,n}: \mathbb{R}^n\rightarrow \mathbb{R}^{N}$ denote the Veronese embedding with $N=N_{n,d}:=\binom{n+d-1}{d}$, defined by listing all the monomials of degree $d$ in $n$ variables using the lexicographical ordering. Let $\langle \boldsymbol{a}, ν_{d,n}(\boldsymbol{x})\rangle\in \mathbb{Z}[\boldsymbol{x}]$ be a homogeneous polynomial in $n$ variables of degree $d$ with integer coefficients $\boldsymbol{a}$, where $\langle\cdot,\cdot\rangle$ denotes t…

This https://arxiv.org/abs/2406.14930 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

An independence of the MIN principle from the PHP principle
The minimization principle $\textsf{MIN}(\triangleleft)$ studied in bounded arithmetic says that a strict linear ordering $\triangleleft$ on any finite interval $[0,\dots,n)$ has the minimal element. We shall prove that bounded arithmetic theory $\textsf{T}^1_2(\triangleleft)$ augmented by instances of the pigeonhole principle for all $Δ^b_1(\triangleleft)$ formulas does not prove $\textsf{MIN}(\triangleleft)$.

Identifiability through special linear measurements
Fulvio Gesmundo, Alexandros Grosdos, Andr\'e Uschmajew
https://arxiv.org/abs/2505.24328 https://

Identifiability through special linear measurements
We show that one can always identify a point on an algebraic variety $X$ uniquely with $\dim X +1$ generic linear measurements taken themselves from a variety under minimal assumptions. As illustrated by several examples the result is sharp, that is, $\dim X$ measurements are in general not enough for unique identifiability.