Tootfinder

Computing fault-tolerant metric dimension of graphs using their primary subgraphs
S. Prabhu, Sandi Klav\v{z}ar, K. Bharani Dharan, S. Radha
https://arxiv.org/abs/2509.14300 http…

Computing fault-tolerant metric dimension of graphs using their primary subgraphs
The metric dimension of a graph is the cardinality of a minimum resolving set, which is the set of vertices such that the distance representations of every vertex with respect to that set are unique. A fault-tolerant metric basis is a resolving set with a minimum cardinality that continues to resolve the graph even after the removal of any one of its vertices. The fault-tolerant metric dimension is the cardinality of such a fault-tolerant metric basis. In this article, we investigate the fault-…

As usual we watched the "Stoertebekker" stage play at Ralswiek on Rügen Island. The stage setups and wardrobes were as awesome as always. They really try to improve on that every year and come up with clever mechanisms to transform the building for the various acts of the play. The script this year left room for desire ;) Nevertheless a happing worth attending
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Tonight I had a dream involving meeting a (recovered) fefe. Highly unusual, don't recall ever having dreams involving him before. In any case, let's hope for his best recovery and hopefully the dream will become reality at some point #fefe

from my link log —
Rubik's cube perfect scramble.
https://www.solutionslookingforproblems.com/post/the-rubik-s-cube-perfect-scramble
saved 2025-08-02

The Rubik's Cube Perfect Scramble
The ChallengeI was playing with my son’s Rubik’s Cubes and tried to scramble a cube randomly so that no two squares with the same color were side by side. Here’s one way to do it: But I wanted a scramble that looked like a random scramble. No matter how many different moves I made, I couldn’t do it. Every time I separated two squares with the same color, two other squares of the same color would touch somewhere else.Looking for an easy answer, I went to puzzling.stackexchange.com and fo…

Kid1 is preparing to DM his first ever D&D campaign (he'll run it starting in the fall). He's been constantly bouncing ideas off me for the past few weeks. He's come up with what's IMHO a setting that's fun and should work well, both in the prepped parts and on the fly: he's modelling the campaign on Gormenghast. I suspect some of his more bizarre ideas will fall away once play begins. Still, it's been great listening to him dream up a custom version of a part…

Absolutely continuous representing measures of complex sequences
Philipp J. di Dio
https://arxiv.org/abs/2509.11339 https://arxiv.org/pdf/2509.11339…

Absolutely continuous representing measures of complex sequences
In 1989, A. J. Duran [Proc. Amer. Math. Soc. 107 (1989), 731-741] showed, that for every complex sequence $(s_α)_{α\in\mathbb{N}_0^n}$ there exists a Schwartz function $f\in\mathcal{S}(\mathbb{R}^n,\mathbb{C})$ with $\mathrm{supp}\, f\subseteq [0,\infty)^n$ such that $s_α= \int x^α\cdot f(x)~\mathrm{d}x$ for all $α\in\mathbb{N}_0^n$. It has been claimed to be a generalization of the result by T. Sherman [Rend. Circ. Mat. Palermo 13 (1964), 273-278], that every complex sequences is represen…

Kargo: ad prices fell 4.4% on FAST channels and grew 4.5% on VOD from May to June as big-name subscription services compete with FAST channels for ad dollars (The Information)
https://www.theinformation.com/articles/amazon-prime-videos-tv…

Amazon Prime Video Floods TV Ad Market, Stealing Dollars From FAST Channels
Until recently, it seemed video streaming had a channel for every taste. Fans of the 1970s Western drama “Little House on the Prairie,” for instance, could spend time on the channel by the same name watching old episodes. The same is true for the 1980s crime drama “Murder She Wrote” and the ...

XBOF: A Cost-Efficient CXL JBOF with Inter-SSD Compute Resource Sharing
Shushu Yi, Yuda An, Li Peng, Xiurui Pan, Qiao Li, Jieming Yin, Guangyan Zhang, Wenfei Wu, Diyu Zhou, Zhenlin Wang, Xiaolin Wang, Yingwei Luo, Ke Zhou, Jie Zhang
https://arxiv.org/abs/2509.10251

XBOF: A Cost-Efficient CXL JBOF with Inter-SSD Compute Resource Sharing
Enterprise SSDs integrate numerous computing resources (e.g., ARM processor and onboard DRAM) to satisfy the ever-increasing performance requirements of I/O bursts. While these resources substantially elevate the monetary costs of SSDs, the sporadic nature of I/O bursts causes severe SSD resource underutilization in just a bunch of flash (JBOF) level. Tackling this challenge, we propose XBOF, a cost-efficient JBOF design, which only reserves moderate computing resources in SSDs at low monetary …

Bills somehow find a way to stun Ravens: 'I’m in a dream state right now' https://www.nytimes.com/athletic/6609941/2025/09/08/bills-ravens-comeback-joey-bosa/