Tootfinder

Refining Yoneda Lemma under Finiteness Constrains and Applications
Antonio Ceres, Cristina Costoya, Antonio Viruel
https://arxiv.org/abs/2506.01501 https:/…

Refining Yoneda Lemma under Finiteness Constrains and Applications
Classical Yoneda Lemma asserts that the isomorphism type of an object $a$ in a category $C$ is determined by the natural type of the set-valued functor $Hom_C(a,-)$. Here we show that if finiteness hypothesis are assumed to hold in $C$, then the isomorphism type of an object $a$ in $C$ is determined by the integer-valued function $|Hom_C(a,-)|$ on objects in $C$. We present applications of this result to the isomorphism problem in Group, Graph, and Ring Theory.

PIMBS: Efficient Body Schema Learning for Musculoskeletal Humanoids with Physics-Informed Neural Networks
Kento Kawaharazuka, Takahiro Hattori, Keita Yoneda, Kei Okada
https://arxiv.org/abs/2506.20343

PIMBS: Efficient Body Schema Learning for Musculoskeletal Humanoids with Physics-Informed Neural Networks
Musculoskeletal humanoids are robots that closely mimic the human musculoskeletal system, offering various advantages such as variable stiffness control, redundancy, and flexibility. However, their body structure is complex, and muscle paths often significantly deviate from geometric models. To address this, numerous studies have been conducted to learn body schema, particularly the relationships among joint angles, muscle tension, and muscle length. These studies typically rely solely on data …

Dividing Conflicting Items Fairly
Ayumi Igarashi, Pasin Manurangsi, Hirotaka Yoneda
https://arxiv.org/abs/2506.14149 https://arxiv.or…

Dividing Conflicting Items Fairly
We study the allocation of indivisible goods under conflicting constraints, represented by a graph. In this framework, vertices correspond to goods and edges correspond to conflicts between a pair of goods. Each agent is allocated an independent set in the graph. In a recent work of Kumar et al. (2024), it was shown that a maximal EF1 allocation exists for interval graphs and two agents with monotone valuations. We significantly extend this result by establishing that a maximal EF1 allocation e…