Tootfinder

Undecidability of Translational Tiling of the Plane with Orthogonally Convex Polyominoes
Chao Yang, Zhujun Zhang
https://arxiv.org/abs/2506.12726 https://

Undecidability of Translational Tiling of the Plane with Orthogonally Convex Polyominoes
The first undecidability result on the tiling is the undecidability of translational tiling of the plane with Wang tiles, where there is an additional color matching requirement. Later, researchers obtained several undecidability results on translational tiling problems where the tilings are subject to the geometric shapes of the tiles only. However, all these results are proved by constructing tiles with extremely concave shapes. It is natural to ask: can we obtain undecidability results of tr…

Two Tiling is Undecidable
Jack Stade
https://arxiv.org/abs/2506.11628 https://arxiv.org/pdf/2506.11628…

Two Tiling is Undecidable
We show that the following problem is undecidable: given two polygonal prototiles, determine whether the plane can be tiled with rotated and translated copies of them. This improves a result of Demaine and Langerman [SoCG 2025], who showed undecidability for three tiles. Along the way, we show that tiling with one prototile is undecidable if there can be edge-to-edge matching rules. This is the first result to show undecidability for monotiling with only local matching constraints.

WTF.....
"Extremely disturbing and unethical’: new rules allow VA doctors to refuse to treat Democrats, unmarried veterans"
https://www.theguardian.com/us-news/2025/jun/16/va-doctors-refuse-treat-patients

Trump "honors" the military.
Trump executive order ‘extremely disturbing and unethical’: new rules allow VA doctors to refuse to treat Democrats, unmarried veterans
https://www.theguardian.com/us-news/2025/jun/16/va-doctors-refuse-treat-patients…

‘Extremely disturbing and unethical’: new rules allow VA doctors to refuse to treat Democrats, unmarried veterans | Trump administration | The Guardian https://www.theguardian.com/us-news/2025/jun/16/va-doctors-refuse-treat-patients

Topology-Aware Virtualization over Inter-Core Connected Neural Processing Units
Dahu Feng, Erhu Feng, Dong Du, Pinjie Xu, Yubin Xia, Haibo Chen, Rong Zhao
https://arxiv.org/abs/2506.11446

Topology-Aware Virtualization over Inter-Core Connected Neural Processing Units
With the rapid development of artificial intelligence (AI) applications, an emerging class of AI accelerators, termed Inter-core Connected Neural Processing Units (NPU), has been adopted in both cloud and edge computing environments, like Graphcore IPU, Tenstorrent, etc. Despite their innovative design, these NPUs often demand substantial hardware resources, leading to suboptimal resource utilization due to the imbalance of hardware requirements across various tasks. To address this issue, prio…

🇺🇦 Auf radioeins läuft...
Kevin Morby:
🎵 I Have Been To The Mountain
#NowPlaying #KevinMorby
https://kevinmorby.bandcamp.com/track/i-have-been-to-the-mountain
https://open.spotify.com/track/2umTklGNx0IiiTFFVNZNlC

🇺🇦 #NowPlaying on KEXP's #VarietyMix
Funkadelic:
🎵 Undisco Kidd (Theo Parrish re‐edit)
#Funkadelic
https://rickreinhartmusic.bandcamp.com/track/funkadelic-undisco-kidd
https://open.spotify.com/track/5PSyO7I9OvgQytETfQqeQY

Yesterday Trump told us that his plan was to remove 21m people from the United States,
or 6% of our current population and at least 5% of our total current workforce.
“All of them have to go home.”
A few points about this insane post:
Best estimates are that the total undocumented population in the US is between 12m and 15m.
The figure that Trump and his regime keeps using
- 21m came in under Biden
- is made up and false.
Here’s the latest Pe…

Trump's Escalating Migrant Terror Campaign Is Unpopular, Out Of Control, Inhumane And Doing Enormous Harm To The Country
Leon Krauze, long time Los Angeles Univision anchor, joins us Live at 12:15pm ET today

'Extremely disturbing and unethical': new rules allow VA doctors to refuse to treat Democrats, unmarried veterans (Aaron Glantz/The Guardian)
https://www.theguardian.com/us-news/2025/jun/16/va-doctors-refuse-treat-patients
http://www.memeorandum.com/250616/p29#a250616p29