Tootfinder

Im using case_when() quite a lot, case_match() is new to me: #rstats

A general vectorised switch() — case_match
This function allows you to vectorise multiple switch() statements. Each case is evaluated sequentially and the first match for each element determines the corresponding value in the output vector. If no cases match, the .default is used. case_match() is an R equivalent of the SQL "simple" CASE WHEN statement. Connection to case_when() While case_when() uses logical expressions on the left-hand side of the formula, case_match() uses values to match against .x with. The following two statement…

🇺🇦 #NowPlaying on KEXP's #MiddayShow
R.E.M.:
🎵 Feeling Gravity’s Pull
#REM
https://thesilencekit.bandcamp.com/track/feeling-gravitys-pull-r-e-m-cover
https://open.spotify.com/track/2n2l2dKnQX4ihHVe0dDUYf

Equivariant CM minimization for extremal manifolds
Gabriel Frey
https://arxiv.org/abs/2506.10679 https://arxiv.org/pdf/2506.10679

Equivariant CM minimization for extremal manifolds
We prove an equivariant version of the CM minimization conjecture for extremal Kähler manifolds. This involves proving that, given an equivariant punctured family of polarized varieties, a relative version of the CM degree is strictly minimized by an extremal filling. This generalizes a result by Hattori for cscK manifolds with discrete automorphism group by allowing automorphisms and extremal metrics. As a main tool, we extend results by Székelyhidi on asymptotic filtration Chow stability …

This https://arxiv.org/abs/2308.01456 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Decomposing a signed graph into rooted circuits
We prove a precise min-max theorem for the following problem. Let $G$ be an Eulerian graph with a specified set of edges $S \subseteq E(G)$, and let $b$ be a vertex of $G$. Then what is the maximum integer $k$ so that the edge-set of $G$ can be partitioned into $k$ non-zero $b$-trails? That is, each trail must begin and end at $b$ and contain an odd number of edges from~$S$. This theorem is motivated by a connection to vertex-minors and yields two conjectures of Máčajová and Škoviera as cor…

🇺🇦 #NowPlaying on KEXP's #MiddayShow
Flying Mojito Bros:
🎵 Glitter
#FlyingMojitoBros
https://flyingmojitobros.bandcamp.com/album/glitter
https://open.spotify.com/track/7jNsuvcAbrJjUeAY1UugmX
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Unknottedness of symplectic submanifold fillings
Zhengyi Zhou
https://arxiv.org/abs/2506.06807 https://arxiv.org/pdf/2506.06807

Unknottedness of symplectic submanifold fillings
We show that any symplectic filling of the standard contact submanifold $(\mathbb{S}^{2n-1},ξ_{\mathrm{std}})$ of $(\mathbb{S}^{2n+1},ξ_{\mathrm{std}})$ in $(\mathbb{D}^{n+1},ω_{\mathrm{std}})$ is smoothly unknotted if $n\ge 2$. We also give a self-contained proof of the Siefring intersection formula between punctured holomorphic curves and holomorphic hypersurfaces used in the proof using the $L$-simple setup of Bao-Honda.

From @… - False UFO stories created by military... sometimes intentionally terrorizing their own soldiers https://n…

How False UFO Stories Were Created - Sometimes Deliberately - by the US Military - Slashdot
Last year's Pentagon report reviewing UFO reports "left out the truth behind some of the foundational myths about UFOs," reports the Wall Street Journal. "The Pentagon itself sometimes deliberately fanned the flames, in what amounted to the U.S. government targeting its own citizens with disinforma...

This https://arxiv.org/abs/2501.16144 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A Survey of the Holroyd-Talbot Conjecture
A family of sets is intersecting if every pair of its members has an element in common. Such a family of sets is called a star if some element is in every set of the family. Given a graph $G$, let $μ(G)$ denote the size of the smallest maximal independent set of $G$. In 2005, Holroyd and Talbot conjectured the following generalization of the Erdős-Ko-Rado Theorem: for $1\le r\le μ(G)/2$, there is a maximum size intersecting family of independent $r$-sets that is a star. In this paper we pres…

Failure of Bott vanishing for (co)adjoint partial flag varieties
Pieter Belmans
https://arxiv.org/abs/2506.09811 https://arxiv.org/pd…

Failure of Bott vanishing for (co)adjoint partial flag varieties
Bott vanishing is a strong vanishing result for the cohomology of exterior powers of the cotangent bundle twisted by ample line bundles. Buch-Thomsen-Lauritzen-Mehta conjectured that partial flag varieties (which are not products of projective spaces) do not satisfy Bott vanishing, despite all their other nice properties. The cominuscule case is an easy application of the Borel-Weil-Bott theorem, following results of Snow. We show that the (co)adjoint partial flag varieties of all classical and…

This https://arxiv.org/abs/2410.13695 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Zarankiewicz bounds from distal regularity lemma
Since Kővári, Sós, and Turán proved upper bounds for the Zarankiewicz problem in 1954, much work has been undertaken to improve these bounds, and some have done so by restricting to particular classes of graphs. In 2017, Fox, Pach, Sheffer, Suk, and Zahl proved better bounds for semialgebraic binary relations, and this work was extended by Do in the following year to arbitrary semialgebraic relations. In this paper, we show that Zarankiewicz bounds in the shape of Do's are enjoyed by all re…