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We're used to hearing pianos in public spaces - London Bridge Station has a minimalist organ!

Rankin-Selberg integrals for $\mathrm{GSpin}$ groups with application to the global Gan-Gross-Prasad conjecture
Pan Yan
https://arxiv.org/abs/2508.09066 https://

Rankin-Selberg integrals for $\mathrm{GSpin}$ groups with application to the global Gan-Gross-Prasad conjecture
We construct Rankin-Selberg integrals using Bessel models for a product of tensor product partial $L$-functions \begin{equation*} L^S(s,π\timesτ_1) L^S(s,π\timesτ_2)\cdots L^S(s,π\timesτ_r) \end{equation*} where $π$ is an irreducible cuspidal automorphic representation of a quasi-split $\mathrm{GSpin}$ group, and $τ_1, \cdots, τ_r$ are irreducible unitary cuspidal automorphic representations of $\mathrm{GL}_{k_1}, \cdots, \mathrm{GL}_{k_r}$ respectively. As an application, we prove one…

Am 11. Juni waren wir auf der #UkraineDemo in München! 🇺🇦🇪🇺🏴‍☠️
Bilder, beim nächsten mal hoffentlich mehr und bessere: https://x.com/AlexKohler1/status/1943698709016965616

KI-Update kompakt: Datenschutz, CatAttack, Meta-Emitter, Peer-Review
Das "KI-Update" liefert werktäglich eine Zusammenfassung der wichtigsten KI-Entwicklungen.
https://www.

What Breaks Knowledge Graph based RAG? Empirical Insights into Reasoning under Incomplete Knowledge
Dongzhuoran Zhou, Yuqicheng Zhu, Xiaxia Wang, Hongkuan Zhou, Yuan He, Jiaoyan Chen, Evgeny Kharlamov, Steffen Staab
https://arxiv.org/abs/2508.08344

What Breaks Knowledge Graph based RAG? Empirical Insights into Reasoning under Incomplete Knowledge
Knowledge Graph-based Retrieval-Augmented Generation (KG-RAG) is an increasingly explored approach for combining the reasoning capabilities of large language models with the structured evidence of knowledge graphs. However, current evaluation practices fall short: existing benchmarks often include questions that can be directly answered using existing triples in KG, making it unclear whether models perform reasoning or simply retrieve answers directly. Moreover, inconsistent evaluation metrics …

Klear-CodeTest: Scalable Test Case Generation for Code Reinforcement Learning
Jia Fu, Xinyu Yang, Hongzhi Zhang, Yahui Liu, Jingyuan Zhang, Qi Wang, Fuzheng Zhang, Guorui Zhou
https://arxiv.org/abs/2508.05710

Klear-CodeTest: Scalable Test Case Generation for Code Reinforcement Learning
Precise, correct feedback is crucial for effectively training large language models (LLMs) in code reinforcement learning. However, synthesizing high-quality test cases remains a profoundly challenging and unsolved problem. In this work, we present Klear-CodeTest, a comprehensive test case synthesis framework featuring rigorous verification to ensure quality and reliability of test cases. Our approach achieves broad coverage of programming problems via a novel Generator-Validation (G-V) framewo…

Relative timestamps are dumb. This is a particularly dumb example, but there's literally no way to improve it while keeping it a relative timestamp.

Mutually equi-biased bases
Seyed Javad Akhtarshenas, Saman Karimi, Mahdi Salehi
https://arxiv.org/abs/2508.08969 https://arxiv.org/pdf/2508.08969

Mutually equi-biased bases
In the framework of mutually unbiased bases (MUBs), a measurement in one basis gives \emph{no information} about the outcomes of measurements in another basis. Here, we relax the no-information condition by allowing the $d$ outcomes to be predicted according to a predefined probability distribution $q=(q_0,\cdots,q_{d-1})$. The notion of mutual unbiasedness, however, is preserved by requiring that the extracted information is the same for any preparation and any measurement; regardless of which…

Optimal convergence rates in multiscale elliptic homogenization
Weisheng Niu, Yao Xu, Jinping Zhuge
https://arxiv.org/abs/2509.09410 https://arxiv.org/pdf/…

Optimal convergence rates in multiscale elliptic homogenization
This paper is devoted to the quantitative homogenization of multiscale elliptic operator $-\nabla\cdot A_\varepsilon \nabla$, where $A_\varepsilon(x) = A(x/\varepsilon_1, x/\varepsilon_2,\cdots, x/\varepsilon_n)$, $\varepsilon = (\varepsilon_1, \varepsilon_2,\cdots, \varepsilon_n) \in (0,1]^n$ and $\varepsilon_i > \varepsilon_{i+1}$. We assume that $A(y_1,y_2,\cdots, y_n)$ is 1-periodic in each $y_i \in \mathbb{R}^d$ and real analytic. Classically, the method of reiterated homogenization has be…

The Diophantine Frobenius Problem revisited
Yuchen Ding, Weijia Wang, Hao Zhang
https://arxiv.org/abs/2509.08599 https://arxiv.org/pdf/2509.08599

The Diophantine Frobenius Problem revisited
Let $k\ge 2$ and $a_1, a_2, \cdots, a_k$ be positive integers with \[ \gcd(a_1, a_2, \cdots, a_k)=1. \] It is proved that there exists a positive integer $G_{a_1, a_2, \cdots, a_k}$ such that every integer $n$ strictly greater than it can be represented as the form \[ n=a_1x_1+a_2x_2+\cdots+a_kx_k, \quad (x_1, x_2, \cdots, x_k\in\mathbb{Z}_{\ge 0},~\gcd(x_1, x_2, \cdots, x_k)=1). \] We then investigate the size of $G_{a_1, a_2}$ explicitly. Our result strengthens the primality requirement of $x…