Tootfinder

Combined Public Service Announcement and Today I Learned: if you have `CLICOLOR=1` on macOS, if you do an `ls` of a directory which is inside iCloud Drive, evicted files (i.e., those that cannot be immediately used, but need to be downloaded first from iCloud) show with a grey background… see below:
First, both files are in iCloud, but not locally available. They have a dotted cloud icons in the iCloud Status field of the Finder window, and a greyed background in the output of the `ls` …

With the advent of ELIZA, Joseph Weizenbaum's first psychotherapist chatbot, NLP took another major step with pattern-based substitution algorithms based on simple regular expressions.
Weizenbaum, Joseph (1966). ELIZA—a computer program for the study of natural language communication between man and machine. Com. of the ACM. 9: 36–45.

On Berger's Isoperimetric Problem
Fan Kang
https://arxiv.org/abs/2506.05775 https://arxiv.org/pdf/2506.05775

On Berger's Isoperimetric Problem
Berger's isoperimetric problem asks if the flat equilateral torus is $λ_1$-maximal. In 1996, Nadirashvili first gave a positive answer. In this paper, we use El Soufi-Ilias-Ros's method and Bryant's result (arXiv:1507.01485) to give a new proof.

Max/Min Puzzles in Geometry IV
James M Parks
https://arxiv.org/abs/2505.03744 https://arxiv.org/pdf/2505.03744

Max/Min Puzzles in Geometry IV
In the previous paper, Max/Min Puzzles in Geometry III, we searched for the smallest area triangle which contained a regular unit polygon (Square, Pentagon, Hexagon). In this paper we will work in 3-dimensions, and search for the smallest regular Tetrahedron which contains a regular unit polyhedron (Cube, Octahedron, Icosahedron, Dodecahedron).

🇺🇦 #NowPlaying on KEXP's #VarietyMix
The Go! Team:
🎵 Ladyflash
#TheGoTeam
https://thegoteam.bandcamp.com/track/ladyflash-monster-rally-remix
https://open.spotify.com/track/6pVTFOItC56aBNhMVjoGje

Propose or Vote: A simple Democratic Procedure
Hans Gersbach
https://arxiv.org/abs/2506.05998 https://arxiv.org/pdf/2506.05998…

Propose or Vote: A simple Democratic Procedure
This paper introduces a simple democratic procedure. In a first stage, all members of a polity decide whether to apply for proposal-making or later vote on proposals made in the second stage. This procedure is called Propose or Vote (PoV). With appropriate default points and majority voting over two randomly selected proposals, the PoV procedure can implement the Condorcet winner with only one round of voting if a Condorcet winner exists. We explore ways to establish uniqueness, alternative vot…

An 8TB corpus of copyright-free text for training AI models. Comes with two 7B models trained as proof-of-concept.
https://github.com/r-three/common-pile/blob/main/paper.pdf
I'm glad somebody has finally done this. The "we need to break copyrig…

First-eigenvalue maximization and inflation of maps
Shin Nayatani
https://arxiv.org/abs/2506.05681 https://arxiv.org/pdf/2506.05681…

First-eigenvalue maximization and inflation of maps
Given a compact manifold equipped with a volume element and a Riemannian metric, we formulate and study a dual pair of optimization problems: one concerning smooth maps from the manifold into the Hilbert space $l^2$ and the other concerning the smallest positive eigenvalue of the Bakry-Emery Laplacian. We present examples of manifolds for which these problems can be solved explicitly. We also prove a Nadirashvili-type theorem.

An improved upper bound for the second eigenvalue on tori
Fan Kang
https://arxiv.org/abs/2506.05846 https://arxiv.org/pdf/2506.05846

An improved upper bound for the second eigenvalue on tori
In this paper, we consider the problem of maximizing the second non-zero eigenvalue $λ_2(T,g)$ of the Laplace-Beltrami operator on a torus $(T,g)$, among all unit-area metrics in a fixed conformal class. Based on work by Karpukhin-Stern and Eddaoudi-Girouard, we give an explicit upper bound for $λ_2(T,g)$ in a fixed conformal class of the torus. Our bound improves previous estimates based on conformal area and shows that, in the majority of conformal classes, the second eigenvalue is strictly…

A Concurrent Generalized Kropina Change
A. Soleiman, Ebtsam H. Taha
https://arxiv.org/abs/2506.06000 https://arxiv.org/pdf/2506.06000…

A Concurrent Generalized Kropina Change
This paper investigates a generalized Kropina metric featuring a specific $π$-form. Start with a Finsler manifold $(M,F)$ admits a concurrent $π$-vector field $\overlineφ$, then, examine the $ϕ$-concurrent generalized Kropina change defined by $\widehat{F}=\frac{F^{m+1}}{Φ^{m}}$, where $Φ$ represents the corresponding $1$-form. We investigate the fundamental geometric objects associated with $\widehat{F}$ in an intrinsic manner after adopting this modification and present an example of a …