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The permutation dimension of the Klein 4-group
Henry Harman
https://arxiv.org/abs/2507.11469 https://arxiv.org/pdf/2507.11469

The permutation dimension of the Klein 4-group
Let $G$ be a finite group and $k$ a field of characteristic $p > 0$. Balmer and Gallauer's recent result on finite $p$-permutation resolutions of $kG$-modules motivates the study of an intriguing new invariant; the $p$-permutation dimension. Following Walsh's success with cyclic groups of prime order, we compute the (global) $p$-permutation dimension of the Klein 4-group in characteristic $p := 2$, along with the dimensions for each of its indecomposable modules.

JOBS> H-Net Job Guide Weekly Report for H-Buddhism: 9 June - 16 June https://networks.h-net.org/group/announcements/20070802/h-net-job-guide-weekly-report-h-buddhism-9-june-16-june

The Raiders' Position Group Feeling Pete Carroll's Impact the Most https://www.si.com/nfl/raiders/las-vegas-patrick-graham-pete-carroll-patrick-mahomes-justin-herbert

Hydroxylated Mg-rich amorphous silicates as catalysts for molecular hydrogen formation in the interstellar medium
V. Mennella, T. Suhasaria, B. Kerkeni, G. Ouerfelli
https://arxiv.org/abs/2506.11596

Hydroxylated Mg-rich amorphous silicates as catalysts for molecular hydrogen formation in the interstellar medium
We present results from an experimental study on the interaction of atomic deuterium with Mg-rich amorphous enstatite and forsterite type silicates. Infrared spectroscopy was used to examine the process. During D atom exposure, deuteroxyl group formation was observed. The cross section for OD group formation, estimated from the OD stretching band intensity with D atom fluence, is 4.2.10^{-18} cm^2 for both silicates. HD (D2) molecules form via D atom abstraction of chemisorbed H(D) atoms from O…

An inverse problem on a metric graph with cycle
Sergei Avdonin, Julian Edward
https://arxiv.org/abs/2508.10121 https://arxiv.org/pdf/2508.10121

An inverse problem on a metric graph with cycle
Consider a quantum graph consisting of a ring with two attached edges, and assume Kirchhoff-Neumann conditions hold at the internal vertices. Associated to this graph is a Schrödinger type operator $L=-Δ+q(x)$ with Dirichlet boundary conditions at the two boundary nodes. Let $\{ ω_n^2, \ φ_n(x)\}$ be the eigenvalues and associated normalized eigenfunctions. Let $v_1$ be a boundary vertex, and $v_2$ the adjacent internal vertex. Assume we know the following data: $\{ ω_n^2,\partial_x φ_n(v…

The maximum number of triangles in $K_{1,s,t}$-free graphs
Asier Calbet, Ritesh Goenka
https://arxiv.org/abs/2508.10611 https://arxiv.org/pdf/2508.10611

The maximum number of triangles in $K_{1,s,t}$-free graphs
We consider the following generalized Turán problem: For $2 \le s \le t$, what is the maximum number of triangles in a $K_{1,s,t}$-free graph on $n$ vertices? The previously best known lower and upper bounds are $Ω(n^2)$ and $o(n^{3-1/s})$, respectively. To the best of our knowledge, all known proofs of the upper bound use the triangle removal lemma. We give a new elementary proof that avoids the use of the triangle removal lemma and improves the upper bound to $O\left(n^{3-1/s}(\log n)^{-1+1…

Sources: Instagram and TikTok are working on versions of their apps customized to run on TV screens, following YouTube's success in attracting a TV audience (The Information)
https://www.theinformation.com/articles/tiktok-instag…

TikTok, Instagram Plot TV Apps Following YouTube’s Success
Rejoice, couch potatoes. TikTok and Instagram, following YouTube’s lead, are working on ways to make it easier for viewers to watch videos from their apps on TV screens. The social media giants see an opportunity to grab some of the ad dollars flowing to the streaming TV market. Meta Platforms’ ...

Three-year Program in Logic and Debate. The Art of Reasoning in the Nālandā Tradition https://networks.h-net.org/group/announcements/20122261/three-year-program-logic-and-debate-art-reasoning-nalanda-tradition…

R2GenKG: Hierarchical Multi-modal Knowledge Graph for LLM-based Radiology Report Generation
Futian Wang, Yuhan Qiao, Xiao Wang, Fuling Wang, Yuxiang Zhang, Dengdi Sun
https://arxiv.org/abs/2508.03426

R2GenKG: Hierarchical Multi-modal Knowledge Graph for LLM-based Radiology Report Generation
X-ray medical report generation is one of the important applications of artificial intelligence in healthcare. With the support of large foundation models, the quality of medical report generation has significantly improved. However, challenges such as hallucination and weak disease diagnostic capability still persist. In this paper, we first construct a large-scale multi-modal medical knowledge graph (termed M3KG) based on the ground truth medical report using the GPT-4o. It contains 2477 enti…

Sources: Instagram and TikTok are working on versions of their apps customized to run on TV screens, following YouTube's success in attracting a TV audience (The Information)
https://www.theinformation.com/articles/tiktok-instag…

TikTok, Instagram Plot TV Apps Following YouTube’s Success
Rejoice, couch potatoes. TikTok and Instagram, following YouTube’s lead, are working on ways to make it easier for viewers to watch videos from their apps on TV screens. The social media giants see an opportunity to grab some of the ad dollars flowing to the streaming TV market. Meta Platforms’ ...