Tootfinder

RationalVLA: A Rational Vision-Language-Action Model with Dual System
Wenxuan Song, Jiayi Chen, Wenxue Li, Xu He, Han Zhao, Pengxiang Ding Shiyan Su, Feilong Tang, Xuelian Cheng, Donglin Wang, Zongyuan Ge, Xinhu Zheng, Zhe Liu, Hesheng Wang, Yunhui Liu, Haoang Li
https://arxiv.org/abs/2506.10826

RationalVLA: A Rational Vision-Language-Action Model with Dual System
A fundamental requirement for real-world robotic deployment is the ability to understand and respond to natural language instructions. Existing language-conditioned manipulation tasks typically assume that instructions are perfectly aligned with the environment. This assumption limits robustness and generalization in realistic scenarios where instructions may be ambiguous, irrelevant, or infeasible. To address this problem, we introduce RAtional MAnipulation (RAMA), a new benchmark that challen…

Initial ideal of a general rational or elliptic curve on quadrics
Francesca Cioffi, Davide Franco, Giovanna Ilardi
https://arxiv.org/abs/2506.12428 https:/…

Initial ideal of a general rational or elliptic curve on quadrics
Over an algebraically closed field of characteristic zero, we prove that the generic initial ideal with respect to the degree reverse lexicographic term order of a general rational or elliptic curve on quadrics is almost revlex. Following constructive arguments, our proof combines features of a pencil of quadrics, interpolation methods and the notion of double generic initial ideal.

On isomorphisms of semi-free Hamiltonian $S^1$-manifolds and fixed point data
Liat Kessler, Nikolas Wardenski
https://arxiv.org/abs/2505.14000 https://

On isomorphisms of semi-free Hamiltonian $S^1$-manifolds and fixed point data
Following Gonzales, we answer the question of whether the isomorphism type of a semi-free Hamiltonian $S^1$-manifold of dimension six is determined by certain data on the critical levels. We first give counter examples showing that Gonzales' assumptions are not sufficient for a positive answer. Then we prove that it is enough to further assume that the reduced spaces of dimension four are symplectic rational surfaces and the interior fixed surfaces are restricted to at most one level. The addit…

@… well, there are two separate problems here right? One is a scenario in which the textarea is readonly-esque and you want to report the value with line numbers outside of editing. The other is reporting line numbers while a user is editing? I’m not even sure what the latter might look like? e.g. “Your cursor is on line 4, which has the following code:”?

This https://arxiv.org/abs/2505.12887 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

RetinaLogos: Fine-Grained Synthesis of High-Resolution Retinal Images Through Captions
The scarcity of high-quality, labelled retinal imaging data, which presents a significant challenge in the development of machine learning models for ophthalmology, hinders progress in the field. To synthesise Colour Fundus Photographs (CFPs), existing methods primarily relying on predefined disease labels face significant limitations. However, current methods remain limited, thus failing to generate images for broader categories with diverse and fine-grained anatomical structures. To overcome …

This https://arxiv.org/abs/1908.03249 has been replaced.
link: https://scholar.google.com/scholar?q=a

Pairwise Rational Points on a Parabola
This paper presents a solution to the following open problem in Number Theory and Geometry: How many points can you find on the (half) parabola $y=x^2$, $x>0$, so that the distance between any pair of them is rational? This problem sounds like a geometry problem, but it is likely to require techniques in number theory. That's because, to determine if the distance between (a,b) and (s,t) is rational, you need to test whether $(a-s)^2$ + $(b-t)^2$ is the square of a rational number...and such que…

This https://arxiv.org/abs/2504.21059 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A remark on the number of automorphisms of some algebraic structures
In these notes we look at the following question. Given a category $\mathcal C$ of algebraic structure (e.g. the category of groups, monoids, partial groups, ...) and a rational $r\in \mathbb Q$, does there exists an element $x\in \mathcal C$ such that the size of its automorphism group $\text{Aut}_{\mathcal C} (x)$ divided by the size of $x$ (whatever that would means) is equal to $r$\,? To our knowledge, this question was introduced by Tărnăuceanu in the category of groups. Here, we answer …

Propylenidene: A New Carbon Two-dimensional Material Featuring Tilted Dirac Cones
Jose A. S. Laranjeira, K. A. L. Lima, Nicolas F. Martins, Luis A. Cabral, L. A. Ribeiro Junior, Julio R. Sambrano
https://arxiv.org/abs/2506.03494

Propylenidene: A New Carbon Two-dimensional Material Featuring Tilted Dirac Cones
Two-dimensional (2D) carbon allotropes have drawn significant interest owing to their impressive physical and chemical characteristics. Following graphene's isolation, a wide range of 2D carbon materials has been suggested, each with distinct electronic, mechanical, and optical traits. Rational design and synthesis of new 2D carbon structures hinge on experimentally reported precursors. Here, we present a 2D carbon allotrope, propylenidene (PPD), originating from the highly strained bicycloprop…