Tootfinder

No-dimensional Tverberg-type problems
Alexander Polyanskii
https://arxiv.org/abs/2506.13451 https://arxiv.org/pdf/2506.13451

No-dimensional Tverberg-type problems
Recently, Adiprasito et al. have initiated the study of the so-called no-dimensional Tverberg problem. This problem can be informally stated as follows: Given $n\geq k$, partition an $n$-point set in Euclidean space into $k$ parts such that their convex hulls intersect a ball of relatively small radius. In this survey, we aim to present the recent progress towards solving the no-dimensional Tverberg problem and new open questions arising in its context. Also, we discuss the colorful variation…

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Corner-Sharing PS$_4$-BS$_4$ Modes Facilitate Fast Ion Conduction in Lithium Thioborophosphate Iodide Glassy Solid Electrolytes
Yun An
https://arxiv.org/abs/2507.08215

Corner-Sharing PS$_4$-BS$_4$ Modes Facilitate Fast Ion Conduction in Lithium Thioborophosphate Iodide Glassy Solid Electrolytes
Glassy solid electrolytes (GSEs), with their amorphous nature and the absence of grain boundaries, make them highly attractive for applications in all-solid-state lithium batteries (ASSLBs), a leading candidate for next-generation energy storage technologies. A recently developed lithium thioborophosphate iodide GSE, composed of 30Li$_2$S-25B$_2$S$_3$-45LiI-5P$_2$S$_5$ (LBPSI), has demonstrated excellent room-temperature ionic conductivity and low activation energy. Despite this exciting findin…

Digital Minimalism: Using One Device for Everything
https://theprivacydad.com/digital-minimalism-using-a-single-device-for-everything/
Using a smartphone for everything is technically a form of digital minimalism, but its constant physical …

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Internet exploitation and abuse of children is a unique category of online crime and therefore cannot be used lightly by any side in debates around regulation of online privacy tools.
https://theprivacydad.com/privacy-tools-vs-online-child-exploitat…