Tootfinder

A group-theoretic approach to Shannon capacity of graphs and a limit theorem from lattice packings
Pjotr Buys, Sven Polak, Jeroen Zuiddam
https://arxiv.org/abs/2506.14654

A group-theoretic approach to Shannon capacity of graphs and a limit theorem from lattice packings
We develop a group-theoretic approach to the Shannon capacity problem. Using this approach we extend and recover, in a structured and unified manner, various families of previously known lower bounds on the Shannon capacity. Bohman (2003) proved that, in the limit $p\to\infty$, the Shannon capacity of cycle graphs $Θ(C_p)$ converges to the fractional clique covering number, that is, $\lim_{p \to \infty} p/2 - Θ(C_p) = 0$. We strengthen this result by proving that the same is true for all frac…

Der
International Day for Women in Maritime wurde auch in Douala, Kamerun 🇨🇲 gefeiert.
Im Foyer du Marin traf sich die örtliche WISTA* Gruppe und unsere dortige Mitarbeiterin Ina Bammann ist jetzt Mitglied.
*Women in shipping trade association - für Frauen in maritimen Berufen
Das Foto zeigt die Kameruner WISTA Frauen mit dem Leitungspaar unseres Foyer, Ina und Klaus Bammann

Fünf weitere Jahre - 65 Mio. pro Jahr! Bayern vor Vertragsverlängerung #News #Nachrichten

Dr. GPT Will See You Now, but Should It? Exploring the Benefits and Harms of Large Language Models in Medical Diagnosis using Crowdsourced Clinical Cases
Bonam Mingole, Aditya Majumdar, Firdaus Ahmed Choudhury, Jennifer L. Kraschnewski, Shyam S. Sundar, Amulya Yadav
https://arxiv.org/abs/2506.13805…

Dr. GPT Will See You Now, but Should It? Exploring the Benefits and Harms of Large Language Models in Medical Diagnosis using Crowdsourced Clinical Cases
The proliferation of Large Language Models (LLMs) in high-stakes applications such as medical (self-)diagnosis and preliminary triage raises significant ethical and practical concerns about the effectiveness, appropriateness, and possible harmfulness of the use of these technologies for health-related concerns and queries. Some prior work has considered the effectiveness of LLMs in answering expert-written health queries/prompts, questions from medical examination banks, or queries based on pre…

Galderatxo bat: Nire emazteak gidatzeko baimena atara dau eta kotxe (automatiko) bat erosi dogu. Orain, nire txanda da gidatzeko baimena ateratzeko.
Zentzukoa da martxazko gidatzeko baimena ateratzea ala errazagoa izango zan automatikoa ateratzea jakinda ez dodala inoiz ere gidatuko martxazko kotxe bat? Esan gura dot: gure kotxea automatikoa da.

Strijd om lijsttrekkerschap zorgt binnen NSC voor chaos en verdeeldheid - #nos
https://nos.nl/artikel/2571405-strijd-om-lijsttrekkerscha…

Trump Organization eyes a new Trump-branded wireless service, complete with gold phones (Steve Benen/MSNBC)
https://www.msnbc.com/rachel-maddow-show/maddowblog/trump-mobile-phone-service-t1-rcna213261
http://www.memeorandum.com/250616/p76#a250616p76

Eating the last hot cross buns of the season with bacon and banana. Recommended

Maximally-Informative Retrieval for State Space Model Generation
Evan Becker, Benjamin Bowman, Matthew Trager, Tian Yu Liu, Luca Zancato, Wei Xia, Stefano Soatto
https://arxiv.org/abs/2506.12149

Maximally-Informative Retrieval for State Space Model Generation
Given a query and dataset, the optimal way of answering the query is to make use all the information available. Modern LLMs exhibit impressive ability to memorize training data, but data not deemed important during training is forgotten, and information outside that training set cannot be made use of. Processing an entire dataset at inference time is infeasible due to the bounded nature of model resources (e.g. context size in transformers or states in state space models), meaning we must resor…

Largest dyadic dual VC-dimension of non-piercing families
Xinqi Huang, Yuzhen Qi, Mingyuan Rong, Zixiang Xu
https://arxiv.org/abs/2506.13606 https://

Largest dyadic dual VC-dimension of non-piercing families
The dyadic dual VC-dimension of a set system \( \mathcal{F} \) is the largest integer \( \ell \) such that there exist \( \ell \) sets \( F_1, F_{2}, \dots, F_\ell \in \mathcal{F} \), where every pair \( \{i, j\} \in \binom{[\ell]}{2} \) is witnessed by an element \( a_{i,j} \in F_i \cap F_j \) that does not belong to any other set \( F_k \) with \( k \in [\ell] \setminus \{i, j\} \). In this paper, we determine the largest dyadic dual VC-dimension of a non-piercing family is exactly $4$, provi…