Tootfinder

UOPSL: Unpaired OCT Predilection Sites Learning for Fundus Image Diagnosis Augmentation
Zhihao Zhao, Yinzheng Zhao, Junjie Yang, Xiangtong Yao, Quanmin Liang, Daniel Zapp, Kai Huang, Nassir Navab, M. Ali Nasseri
https://arxiv.org/abs/2509.08624

UOPSL: Unpaired OCT Predilection Sites Learning for Fundus Image Diagnosis Augmentation
Significant advancements in AI-driven multimodal medical image diagnosis have led to substantial improvements in ophthalmic disease identification in recent years. However, acquiring paired multimodal ophthalmic images remains prohibitively expensive. While fundus photography is simple and cost-effective, the limited availability of OCT data and inherent modality imbalance hinder further progress. Conventional approaches that rely solely on fundus or textual features often fail to capture fine-…

Ciekawostka: jak w Portalu Pasażera #PLK wyszukacie połączenia Zgorzelec – Wrocław Główny na sobotę rano, to zaproponuje wam przesiadkę w Węglińcu. Z elementem: "Postój tylko dla wysiadających, brak możliwości rozpoczęcia podróży na tym przystanku osobowym."
#PKP

Rational functions that share finite values with their first derivative
Andreas Sauer, Andreas Schweizer
https://arxiv.org/abs/2509.08517 https://arxiv.org…

Rational functions that share finite values with their first derivative
We treat shared value problems for rational functions $R(z)$ and their derivative $R'(z)$ in the plane and on the sphere. We also consider shared values for the pair $R(w)$ and $\partial_{z} R = λw \cdot R'(w)$ on ${\mathbb C} \setminus \{ 0 \}$ and $\widehat{\mathbb C}$, again with rational functions $R$. In ${\mathbb C} \setminus \{ 0 \}$ this is related to shared values of meromorphic functions $f : {\mathbb C} \to \widehat{\mathbb C}$ and $f'$ through $f(z)=R(w)$ with $w=\exp(λz)$, while …

Expressive Power of Deep Networks on Manifolds: Simultaneous Approximation
Hanfei Zhou, Lei Shi
https://arxiv.org/abs/2509.09362 https://arxiv.org/pdf/2509…

Expressive Power of Deep Networks on Manifolds: Simultaneous Approximation
A key challenge in scientific machine learning is solving partial differential equations (PDEs) on complex domains, where the curved geometry complicates the approximation of functions and their derivatives required by differential operators. This paper establishes the first simultaneous approximation theory for deep neural networks on manifolds. We prove that a constant-depth $\mathrm{ReLU}^{k-1}$ network with bounded weights--a property that plays a crucial role in controlling generalization …

Fragmented Spin Liquid and Shadow Pinch Points in Dipole-Octupole Pyrochlore Spin Systems
Daniel Lozano-G\'omez, Han Yan
https://arxiv.org/abs/2509.09205 https://

Fragmented Spin Liquid and Shadow Pinch Points in Dipole-Octupole Pyrochlore Spin Systems
We study the classical dipole-octupole pyrochlore spin systems in an external magnetic field along the $[111]$ direction. We identify an intermediate fragmented spin liquid phase that precedes full spin saturation, characterized by the coexistence of three phenomena: U(1) spin liquid on the Kagome planes, spontaneous $\mathbb{Z}_2$ symmetry breaking, and partial spin polarization from explicit symmetry breaking. We show that even without dipolar interactions, the dipolar components can form a s…

An update on the existence of integer Heffter arrays
Fiorenza Morini, Marco Antonio Pellegrini
https://arxiv.org/abs/2510.08302 https://arxiv.org/pdf/2510.…

An update on the existence of integer Heffter arrays
An integer Heffter array $H(m,n;s;k)$ is an $m\times n$ partially filled array whose entries are the elements of a subset $Ω\subset \mathbb{Z}$ such that $\{Ω,-Ω\}$ is a partition of the set $\{1,2,\ldots,2nk\}$ and such that the following conditions are satisfied: each row contains $s$ filled cells, each column contains $k$ filled cells, the elements in every row and column add up to $0$. It was conjectured by Dan Archdeacon that an integer $\H(m,n;s;k)$ exists if and only if $ms=nk$, $3\le…

How to Teach Large Multimodal Models New Skills
Zhen Zhu, Yiming Gong, Yao Xiao, Yaoyao Liu, Derek Hoiem
https://arxiv.org/abs/2510.08564 https://arxiv.org…

How to Teach Large Multimodal Models New Skills
How can we teach large multimodal models (LMMs) new skills without erasing prior abilities? We study sequential fine-tuning on five target skills while monitoring general ability on eight held-out benchmarks across three model families. We observe that apparent "forgetting" on held-out tasks after narrow fine-tuning can partly recover at later stages. We trace this behavior to a measurable shift in the output token distribution, manifested through a simple counting-bias probe that co-varies wit…

OmniMap: A General Mapping Framework Integrating Optics, Geometry, and Semantics
Yinan Deng, Yufeng Yue, Jianyu Dou, Jingyu Zhao, Jiahui Wang, Yujie Tang, Yi Yang, Mengyin Fu
https://arxiv.org/abs/2509.07500

OmniMap: A General Mapping Framework Integrating Optics, Geometry, and Semantics
Robotic systems demand accurate and comprehensive 3D environment perception, requiring simultaneous capture of photo-realistic appearance (optical), precise layout shape (geometric), and open-vocabulary scene understanding (semantic). Existing methods typically achieve only partial fulfillment of these requirements while exhibiting optical blurring, geometric irregularities, and semantic ambiguities. To address these challenges, we propose OmniMap. Overall, OmniMap represents the first online m…

Permutation-Invariant Spectral Learning via Dyson Diffusion
Tassilo Schwarz, Cai Dieball, Constantin Kogler, Kevin Lam, Renaud Lambiotte, Arnaud Doucet, Alja\v{z} Godec, George Deligiannidis
https://arxiv.org/abs/2510.08535

Permutation-Invariant Spectral Learning via Dyson Diffusion
Diffusion models are central to generative modeling and have been adapted to graphs by diffusing adjacency matrix representations. The challenge of having up to $n!$ such representations for graphs with $n$ nodes is only partially mitigated by using permutation-equivariant learning architectures. Despite their computational efficiency, existing graph diffusion models struggle to distinguish certain graph families, unless graph data are augmented with ad hoc features. This shortcoming stems from…

Quasilinear problems with critical Sobolev exponent for the Grushin p-Laplace operator
Somnath Gandal, Annunziata Loiudice, Jagmohan Tyagi
https://arxiv.org/abs/2509.06138 https…

Quasilinear problems with critical Sobolev exponent for the Grushin p-Laplace operator
We study the following class of quasilinear degenerate elliptic equations with critical nonlinearity \begin{align*} \begin{cases}-Δ_{γ,p} u= λ|u|^{q-2}u+|u|^{p_γ^{*}-2}u & \text{ in } Ω\subset \mathbb{R}^N, \\ u=0 & \text{ on } \partial Ω, \end{cases} \end{align*} where $Δ_{γ, p}v:=\sum_{i=1}^N X_i(|\nabla_γu|^{p-2}X_i u)$ is the Grushin $p$-Laplace operator, $z:=(x, y) \in \mathbb{R}^N$, $N=m+n,$ $m,n \geq 1,$, where $\nabla_γ=(X_1, \ldots, X_N)$ is th…