Tootfinder

Google says Gemini 2.5 Flash Image, aka Nano Banana, is now generally available and supports more aspect ratios, priced at $0.039/image and $30/1M output tokens (Google Developers Blog)
https://developers.googleblog.com/en/gemini-2…

Gemini 2.5 Flash Image now ready for production with new aspect ratios- Google Developers Blog
Our state-of-the-art image generation and editing model which has captured the imagination of the wo...

"Mag er mich überhaupt?"
#catcontent

🌴 Scientists identify potential climate solutions in 'grassy trees'
#trees

Scientists identify potential climate solutions in 'grassy trees'
Bamboo, palm, and banana trees look and act like trees, but are actually closer to grasses in how they grow because—unlike trees—their stems do not grow wider over time. However, due to their towering structure, scientists struggled with how to both classify them and to fully understand their biology—and benefits.

Trump offers Qatar, which gave him a fancy plane, a NATO-like security guarantee (Steve Benen/MSNBC)
https://www.msnbc.com/rachel-maddow-show/maddowblog/trump-offers-qatar-gave-fancy-plane-nato-security-guarantee-rcna235175
http://www.memeorandum.com/251002/p116#a251002p116

On cuts of small chromatic number in sparse graphs
Guillaume Aubian, Marthe Bonamy, Romain Bourneuf, Oscar Fontaine, Lucas Picasarri-Arrieta
https://arxiv.org/abs/2510.01791 htt…

On cuts of small chromatic number in sparse graphs
For a given integer $k$, let $\ell_k$ denote the supremum $\ell$ such that every sufficiently large graph $G$ with average degree less than $2\ell$ admits a separator $X \subseteq V(G)$ for which $χ(G[X]) < k$. Motivated by the values of $\ell_1$, $\ell_2$ and $\ell_3$, a natural conjecture suggests that $\ell_k = k$ for all $k$. We prove that this conjecture fails dramatically: asymptotically, the trivial lower bound $\ell_k \geq \tfrac{k}{2}$ is tight. More precisely, we prove that for every…

VGDM: Vision-Guided Diffusion Model for Brain Tumor Detection and Segmentation
Arman Behnam
https://arxiv.org/abs/2510.02086 https://arxiv.org/pdf/2510.020…

VGDM: Vision-Guided Diffusion Model for Brain Tumor Detection and Segmentation
Accurate detection and segmentation of brain tumors from magnetic resonance imaging (MRI) are essential for diagnosis, treatment planning, and clinical monitoring. While convolutional architectures such as U-Net have long been the backbone of medical image segmentation, their limited capacity to capture long-range dependencies constrains performance on complex tumor structures. Recent advances in diffusion models have demonstrated strong potential for generating high-fidelity medical images and…

A ceramic mug by Hell Wench https://bsky.app/profile/bmann.ca/post/3m4houjzte62j

Boris (@bmann.ca)
A ceramic mug by Hell Wench

Why the acting CDC director's background does not inspire confidence (Steve Benen/MSNBC)
https://www.msnbc.com/rachel-maddow-show/maddowblog/acting-cdc-directors-background-not-inspire-confidence-rcna228822
http://www.memeorandum.com/250903/p98#a250903p98

Clique number of xor-powers of Kneser graphs
Zolt\'an F\"uredi, Andr\'as Imolay, \'Ad\'am Schweitzer
https://arxiv.org/abs/2510.01509 https://

Clique number of xor-powers of Kneser graphs
Let $f_\ell(n, k)$ denote the clique number of the xor-product of $\ell$ isomorphic Kneser graphs KG(n,k). Alon and Lubetzky investigated the case of complete graphs as a coding theory problem and showed $f_\ell(n,1)\leq \ell n +1$. Imolay, Kocsis, and Schweitzer proved that $f_2(n,k)\leq n/k +c(k)$. Here, the order of magnitude of $c(k)$ is determined to be $Θ\left( k \binom{2k}{k} \right)$. By explicit constructions and by an algebraic proof, it is shown that $\ell n- 2\ell-1 \leq f_\ell(n…

Monochromatic components with many edges in random graphs
Hannah Fox, Sammy Luo
https://arxiv.org/abs/2509.01766 https://arxiv.org/pdf/2509.01766

Monochromatic components with many edges in random graphs
In an $r$-coloring of edges of the complete graph on $n$ vertices, how many edges are there in the largest monochromatic connected component? A construction of Gyárfás shows that for infinitely many values of $r$, there exist colorings where all monochromatic components have at most $\left(\frac{1}{r^2-r}+o(1)\right)\binom{n}{2}$ edges. Conlon, Luo, and Tyomkyn conjectured that components with at least this many edges are attainable for all $r \ge 3$. Conlon, Luo, and Tyomkyn proved this conj…