Tootfinder

Star decompositions via orientations
Viktor Harangi
https://arxiv.org/abs/2506.05194 https://arxiv.org/pdf/2506.05194

Star decompositions via orientations
A $k$-star decomposition of a graph is a partition of its edges into $k$-stars (i.e., $k$ edges with a common vertex). The paper studies the following problem: given $k \leq d/2$, does the random $d$-regular graph have a $k$-star decomposition (asymptotically almost surely, provided that the number of edges is divisible by $k$)? Delcourt, Greenhill, Isaev, Lidický, and Postle proved the a.a.s. existence for every odd $k$ using earlier results regarding orientations satisfying certain degree co…

There's a lot of fear and panic here in my social circles in #Romania. Very much feels like a rerun of December. I'm actually feeling a bit more optimistic and less afraid than last time. Just a bit though.
There is a path to victory for Nicusor Dan. It relies on expanding the voting base. Not all is lost yet, the sky isn't falling, just need as many Romanians as possible th…

I nearly gave my credit card to a legit-looking Maine business, until I noticed their “privacy policy” linked to Wikipedia. That’s not laziness but AI-generated HTML vibecoded into place without review. And a lot more can go wrong than a missing legal page.
https://www.

Nippon Steel’s $14.9bn acquisition of US Steel closed on Wednesday,
confirming an unusual degree of power for the Trump administration after the Japanese company’s 18-month struggle to close the purchase.
Under the deal terms, Nippon bought 100% of US Steel shares at $55 a share, as it first laid out in its December 2023 offer for the well-known and struggling steelmaker.
A press release on the filing also discloses details of a national security agreement inked with the Tr…

This https://arxiv.org/abs/1807.03420 has been replaced.
link: https://scholar.google.com/scholar?q=a

A JSJ-type decomposition theorem for symplectic fillings
We establish a JSJ-type decomposition theorem for splitting exact symplectic fillings of contact 3-manifolds along \emph{mixed tori} -- these are convex tori satisfying a particular geometric condition. As an application, we show that if $(M,ξ)$ is obtained from $(S^3,ξ_{\mathrm{std}})$ via Legendrian surgery along a knot which has been stabilized both positively and negatively, then $(M,ξ)$ has a unique exact filling.

Local feature filtering for scalable and well-conditioned Random Feature Methods
Jan Willem van Beek, Victorita Dolean, Ben Moseley
https://arxiv.org/abs/2506.17626

Local feature filtering for scalable and well-conditioned Random Feature Methods
In recent years, machine learning has emerged as a powerful tool for solving partial differential equations (PDEs), with randomized neural networks showing remarkable potential. These networks, typically shallow, differ from conventional approaches by randomizing all parameters except those in the final layer. Notably, by integrating techniques inspired by domain decomposition, they achieve improved local accuracy and computational efficiency. Following \cite{chen:2022:BTM}, we refer to these a…

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...

Computer scientist Greg Nelson and I presented "Following AI's Footsteps from School to Society" at the 2025 UMaine Faculty Institute https://mycampus.maine.edu/web/uc-faculty-portal/faculty-institute-2025 including the IMPACT RISK framew…

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…