Tootfinder

Il est rare de trouver un auteur capable de restituer, en littérature, le sentiment que procure la photographie de rue. Il capture les rues, les bâtiments, les rencontres comme des archives persistantes qui se dévoilent devant nos yeux. Pourtant, il existe un auteur...
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This https://arxiv.org/abs/2003.11202 has been replaced.
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Set System Blowups
We prove that given a constant $k \ge 2$ and a large set system $\mathcal{F}$ of sets of size at most $w$, a typical $k$-tuple of sets $(S_1, \cdots, S_k)$ from $\mathcal{F}$ can be ``blown up" in the following sense: for each $1 \le i \le k$, we can find a large subfamily $\mathcal{F}_i$ containing $S_i$ so that for $i \neq j$, if $T_i \in \mathcal{F}_i$ and $T_j \in \mathcal{F}_j$ , then $T_i \cap T_j=S_i \cap S_j$. We also show that the answer to the multicolor version of the sunflower conje…

Multiple rational normal forms in Lie theory
Dmitriy Voloshyn
https://arxiv.org/abs/2506.01530 https://arxiv.org/pdf/2506.01530

Multiple rational normal forms in Lie theory
We study the decomposition of a generic element $g \in G$ of a connected reductive complex algebraic group $G$ in the form $g = N(g) B(g) \bar{u} N(g)^{-1}$ where $N: G \dashrightarrow \mathcal{N}_-$ and $B : G \dashrightarrow \mathcal{B}_+$ are rational maps onto a unipotent subgroup $\mathcal{N}_-$ and a Borel subgroup $\mathcal{B}_+$ opposite to $\mathcal{N}_-$, and $\bar{u}$ is a representative of a Weyl group element $u$. We introduce a class of rational Weyl group elements that give rise …

Beyond the LUMIR challenge: The pathway to foundational registration models
Junyu Chen, Shuwen Wei, Joel Honkamaa, Pekka Marttinen, Hang Zhang, Min Liu, Yichao Zhou, Zuopeng Tan, Zhuoyuan Wang, Yi Wang, Hongchao Zhou, Shunbo Hu, Yi Zhang, Qian Tao, Lukas F\"orner, Thomas Wendler, Bailiang Jian, Benedikt Wiestler, Tim Hable, Jin Kim, Dan Ruan, Frederic Madesta, Thilo Sentker, Wiebke Heyer, Lianrui Zuo, Yuwei Dai, Jing Wu, Jerry L. Prince, Harrison Bai, Yong Du, Yihao Liu, Alessa He…

Beyond the LUMIR challenge: The pathway to foundational registration models
Medical image challenges have played a transformative role in advancing the field, catalyzing algorithmic innovation and establishing new performance standards across diverse clinical applications. Image registration, a foundational task in neuroimaging pipelines, has similarly benefited from the Learn2Reg initiative. Building on this foundation, we introduce the Large-scale Unsupervised Brain MRI Image Registration (LUMIR) challenge, a next-generation benchmark designed to assess and advance u…

ClinBench-HPB: A Clinical Benchmark for Evaluating LLMs in Hepato-Pancreato-Biliary Diseases
Yuchong Li, Xiaojun Zeng, Chihua Fang, Jian Yang, Lei Zhang
https://arxiv.org/abs/2506.00095

ClinBench-HPB: A Clinical Benchmark for Evaluating LLMs in Hepato-Pancreato-Biliary Diseases
Hepato-pancreato-biliary (HPB) disorders represent a global public health challenge due to their high morbidity and mortality. Although large language models (LLMs) have shown promising performance in general medical question-answering tasks, the current evaluation benchmarks are mostly derived from standardized examinations or manually designed questions, lacking HPB coverage and clinical cases. To address these issues, we systematically eatablish an HPB disease evaluation benchmark comprising…

Sampling Bayesian probabilities given only sampled priors
Gary Bernstein, William Assignies Doumerg, Michael A. Troxel, Alex Alarcon, Alexandra Amon, Giulia Giannini, Boyan Yin, Sahar Allam, Felipe Andrade-Oliveira, David Brooks, Aurelio Carnero Rosell, Jorge Carretero, Luiz da Costa, Maria Elidaiana da Silva Pereira, Juan De Vicente, Spencer Everett, Josh Frieman, Juan Garcia-Bellido, Daniel Gruen, Samuel Hinton, Devon L. Hollowood, Klaus Honscheid, David James, Sujeong Lee, Jennifer …

Sampling Bayesian probabilities given only sampled priors
A typical Bayesian inference on the values of some parameters of interest $q$ from some data $D$ involves running a Markov Chain (MC) to sample from the posterior $p(q,n | D) \propto \mathcal{L}(D | q,n) p(q) p(n),$ where $n$ are some nuisance parameters. In many cases, the nuisance parameters are high-dimensional, and their prior $p(n)$ is itself defined only by a set of samples that have been drawn from some other MC. Two problems arise: first, the MC for the posterior will typicall…

Regularity and pointwise convergence for dispersive equations with asymptotically concave phase on Damek-Ricci spaces
Utsav Dewan
https://arxiv.org/abs/2506.00881

Regularity and pointwise convergence for dispersive equations with asymptotically concave phase on Damek-Ricci spaces
We study the Carleson's problem on Damek-Ricci spaces $S$ for dispersive equations: \begin{equation*} \begin{cases} i\frac{\partial u}{\partial t} +Ψ(\sqrt{-\mathcal{L}} )u=0\:,\: (x,t) \in S \times \mathbb{R} \:, \\ u(0,\cdot)=f\:,\: \text{ on } S \:, \end{cases} \end{equation*} where $\mathcal{L}= Δ$, the Laplace-Beltrami operator or $\tildeΔ$, the shifted Laplace-Beltrami operator, so that the corresponding phase function $ψ$ satisfies for some $a \in (0,1)$, the large frequency as…

Statistical Interaction Driven Thermoelectricity and Violation of Wiedemann-Franz Law
Sampurna Karmakar, Amulya Ratnakar, Sourin Das
https://arxiv.org/abs/2506.01930

Statistical Interaction Driven Thermoelectricity and Violation of Wiedemann-Franz Law
Quantum transport anomalies in systems obeying Haldane-Wu fractional exclusion statistics, characterized by the statistical interactions parameter $g$ are investigated. We identify particle-hole symmetry breaking of the Haldane-Wu distribution function via its deviations of the maximum entropy ($\mathcal{S}_{g}^{max}$), evaluated at the chemical potential, from the value ${k_B} \ln 2$ (a value that holds only at the free fermion limit, $g=1$). A duality relation, $g\,\mathcal{S}_{g}^{max}=\math…

Cardinalities of the total number of independent sets
Benedek Kov\'acs, Zolt\'an L\'or\'ant Nagy
https://arxiv.org/abs/2505.24794 https://

Cardinalities of the total number of independent sets
We study the set of numbers the total number of independent sets can admit in $n$-vertex graphs. In this paper, we prove that the cardinality of this set $\mathcal{N}i(n)$ is very close to $2^n$ in the following sense: $\mathcal{N}i(n)/2^n = O(n^{-1/5})$ while for infinitely many $n$, we have $\log_2(\mathcal{N}i(n)/2^n)\ge -2^{(1+o(1)\sqrt{\log_2 n}}$. This set is also precisely the set of possible values of the independence polynomial $I_G(x)$ at $x=1$ for $n$-vertex graphs $G$. As an applica…

TumorGen: Boundary-Aware Tumor-Mask Synthesis with Rectified Flow Matching
Shengyuan Liu, Wenting Chen, Boyun Zheng, Wentao Pan, Xiang Li, Yixuan Yuan
https://arxiv.org/abs/2505.24687

TumorGen: Boundary-Aware Tumor-Mask Synthesis with Rectified Flow Matching
Tumor data synthesis offers a promising solution to the shortage of annotated medical datasets. However, current approaches either limit tumor diversity by using predefined masks or employ computationally expensive two-stage processes with multiple denoising steps, causing computational inefficiency. Additionally, these methods typically rely on binary masks that fail to capture the gradual transitions characteristic of tumor boundaries. We present TumorGen, a novel Boundary-Aware Tumor-Mask Sy…