Tootfinder

Notes on the Invariance of Tautness Under Lie Sphere Transformations
Thomas E. Cecil
https://arxiv.org/abs/2506.08834 https://arxiv.o…

Notes on the Invariance of Tautness Under Lie Sphere Transformations
An embedding $ϕ:V \rightarrow S^n$ of a compact, connected manifold $V$ into the unit sphere $S^n \subset {\bf R}^{n+1}$ is said to be taut, if every nondegenerate spherical distance function $d_p$, $p \in S^n$, is a perfect Morse function on $V$, i.e., it has the minimum number of critical points on $V$ required by the Morse inequalities. In these notes, we give an exposition of the proof of the invariance of tautness under Lie sphere transformations due to Álvarez Paiva. First we extend the…

Leveraging Reference Documents for Zero-Shot Ranking via Large Language Models
Jieran Li, Xiuyuan Hu, Yang Zhao, Shengyao Zhuang, Hao Zhang
https://arxiv.org/abs/2506.11452

Leveraging Reference Documents for Zero-Shot Ranking via Large Language Models
Large Language Models (LLMs) have demonstrated exceptional performance in the task of text ranking for information retrieval. While Pointwise ranking approaches offer computational efficiency by scoring documents independently, they often yield biased relevance estimates due to the lack of inter-document comparisons. In contrast, Pairwise methods improve ranking accuracy by explicitly comparing document pairs, but suffer from substantial computational overhead with quadratic complexity ($O(n^2)…

FlowDrag: 3D-aware Drag-based Image Editing with Mesh-guided Deformation Vector Flow Fields
Gwanhyeong Koo, Sunjae Yoon, Younghwan Lee, Ji Woo Hong, Chang D. Yoo
https://arxiv.org/abs/2507.08285

FlowDrag: 3D-aware Drag-based Image Editing with Mesh-guided Deformation Vector Flow Fields
Drag-based editing allows precise object manipulation through point-based control, offering user convenience. However, current methods often suffer from a geometric inconsistency problem by focusing exclusively on matching user-defined points, neglecting the broader geometry and leading to artifacts or unstable edits. We propose FlowDrag, which leverages geometric information for more accurate and coherent transformations. Our approach constructs a 3D mesh from the image, using an energy functi…