Tootfinder

Upper block triangular form for the Laplace-Beltrami operator on the special orthogonal group acquired through a flag of trace polynomials spaces
Petre Birtea, Ioan Casu, Dan Comanescu
https://arxiv.org/abs/2509.08391

Upper block triangular form for the Laplace-Beltrami operator on the special orthogonal group acquired through a flag of trace polynomials spaces
The Laplacian of a general trace polynomial function defined on the special orthogonal group $SO(N)$ is explicitly computed. An invariant flag of spaces generated by trace polynomials is constructed. The matrix of the Laplace-Beltrami operator on $SO(N)$ for this flag of vector spaces takes an upper block triangular form. As a consequence of this construction, the eigenvalues and eigenfunctions of the Laplace-Beltrami operator on $SO(N)$ can be computed in an iterative manner. For the particula…

Construction of Kochen-Specker Sets from Mutually Unbiased Bases
Mirko Navara, Karl Svozil
https://arxiv.org/abs/2509.08636 https://arxiv.org/pdf/2509.0863…

Construction of Kochen-Specker Sets from Mutually Unbiased Bases
We present a systematic, constructive analysis of Kochen-Specker contextuality, emphasizing the foundational importance of complete orthogonal bases (contexts). First, in three dimensions, we generate a complete inventory of 165 rays and 130 bases from mutually unbiased bases. This unified framework reveals that several known constructions are equivalent manifestations of a minimal 69-ray, 50-context Kochen--Specker nucleus and uncovers a striking 40-4-4 generative asymmetry among the mutual un…

Volumes of moduli spaces of directed ribbon graphs and Cut-and-Join operators
Simon Barazer
https://arxiv.org/abs/2507.07308 https://…

Volumes of moduli spaces of directed ribbon graphs and Cut-and-Join operators
In this paper, we investigate the algebraic structure underlying the acyclic decomposition. This decomposition applies to directed metric ribbon graphs and enables the recursive computation of the volumes of their moduli spaces. Building on this, we define integral operators with these volumes and show that they satisfy a Cut-and-Join type equation. Furthermore, we demonstrate that a suitable specialization of these operators gives rise to a generating series for \textit{dessins d'enfants}.

Ideals generated by corner-interval minors
Marie Amalore Nambi
https://arxiv.org/abs/2506.09618 https://arxiv.org/pdf/2506.09618

Ideals generated by corner-interval minors
In this article, we study binomial ideals generated by an arbitrary collection of corner-interval $2$-minors of a generic matrix. We determine the minimal prime ideals of such ideals and characterize their radicality in the special case of corner minors. Moreover, we discuss connectivity properties of contingency tables in algebraic statistics. We compute the Hilbert-Poincaré polynomial of the ideal generated by the set of all corner-interval minors and we derive the formula for the regularity…

Patterns of Patterns III
Joseph Corneli, Charles J. Danoff, Raymond S. Puzio, Sridevi Ayloo, Serge Belich, Mary Tedeschi
https://arxiv.org/abs/2506.09696 h…

Patterns of Patterns III
Building on earlier installments, this paper re-examines the PLACARD pattern. We report on a series of workshops where PLACARD was used to scaffold collaborative reflection, speculative inquiry, and stimulate design pattern generation. These accounts are enriched by a comparison case: virtual workshops carried out with simple AI-based chatbots. We discuss limitations and lessons learned from both the human and multi-agent settings. We conclude by outlining a future development strategy at the i…

AGI is “not a super useful term”? But IIRC, as defined by OpenAI, they’ll hit AGI when they generate $100 billion in profit. So, how’s that coming along? Not so great, huh?
https://www.cnbc.com/2025/08/11/sam-altman-says-agi-is-a-pointless-term-expe…

If you get an invite to this generative art software engineering call, note that if you submit something and it gets accepted, as far as I can tell it would cost you $3000 in open access fees... unless you want it to languish behind a paywall (you'd then only be allowed to share an unedited draft, and even then would have to advertise the paywall on it). They don't seem to want to make this clear in their call.

LL3M: Large Language 3D Modelers
Sining Lu, Guan Chen, Nam Anh Dinh, Itai Lang, Ari Holtzman, Rana Hanocka
https://arxiv.org/abs/2508.08228 https://arxiv.o…

LL3M: Large Language 3D Modelers
We present LL3M, a multi-agent system that leverages pretrained large language models (LLMs) to generate 3D assets by writing interpretable Python code in Blender. We break away from the typical generative approach that learns from a collection of 3D data. Instead, we reformulate shape generation as a code-writing task, enabling greater modularity, editability, and integration with artist workflows. Given a text prompt, LL3M coordinates a team of specialized LLM agents to plan, retrieve, write,…

Generation of realistic cardiac ultrasound sequences with ground truth motion and speckle decorrelation
Thierry Judge, Nicolas Duchateau, Khuram Faraz, Pierre-Marc Jodoin, Olivier Bernard
https://arxiv.org/abs/2509.05261

Generation of realistic cardiac ultrasound sequences with ground truth motion and speckle decorrelation
Simulated ultrasound image sequences are key for training and validating machine learning algorithms for left ventricular strain estimation. Several simulation pipelines have been proposed to generate sequences with corresponding ground truth motion, but they suffer from limited realism as they do not consider speckle decorrelation. In this work, we address this limitation by proposing an improved simulation framework that explicitly accounts for speckle decorrelation. Our method builds on an e…

Black-White Cell Capacity in $k$-ary Words and Permutations
Sela Fried
https://arxiv.org/abs/2509.07533 https://arxiv.org/pdf/2509.07533

Black-White Cell Capacity in $k$-ary Words and Permutations
We introduce a new bargraph statistic that we call black-white cell capacity. It is obtained by coloring the cells of the bargraph in a chessboard style and recording the numbers of black and white cells contained in the bargraph. We study two word families under this statistic: $k$-ary words and permutations. We obtain the corresponding generating function, in the $k$-ary words case, and a closed-form formula for each $n$, in the permutations case. Of special interest are words containing an e…