Tootfinder

"A federal appeals court on Monday refused to throw out an $83.3 million jury verdict against U.S. President Donald Trump for damaging the reputation of the writer E. Jean Carroll in 2019 when he denied her rape claim.
The 2nd U.S. Circuit Court of Appeals in Manhattan rejected Trump's argument that the January 2024 verdict should be overturned because he deserved presidential immunity from Carroll's lawsuit."

Trump fails to overturn E. Jean Carroll's $83 million verdict
A federal appeals court on Monday refused to throw out an $83.3 million jury verdict against U.S. President Donald Trump for damaging the reputation of the...

Comparing cluster algebras on braid varieties
Roger Casals, Pavel Galashin, Mikhail Gorsky, Linhui Shen, Melissa Sherman-Bennett, Jos\'e Simental
https://arxiv.org/abs/2508.03816

Comparing cluster algebras on braid varieties
Braid varieties parametrize linear configurations of flags with transversality conditions dictated by positive braids. They include and generalize reduced double Bruhat cells, positroid varieties, open Bott-Samelson varieties, and Richardson varieties, among others. Recently, two cluster algebra structures were independently constructed in the coordinate rings of braid varieties: one using weaves and the other using Deodhar geometry. The main result of the article is that these two cluster alge…

Talking points der Union
„Seither ist bei vielen Kritikern von "Massenüberwachung" die Rede. Die will auch das EU-Parlament ausschließen. Es hat sich schon vor knapp zwei Jahren mit breiter Mehrheit auf eine Position geeinigt, betont die CDU-Europaabgeordnete Lena Düpont. Danach soll ein Scannen der Nachricht nur als letztes Mittel bei konkretem Verdacht möglich sein.“
Der 'konkrete Verdacht' trifft dann eben sehr, sehr viele.
Debatte über “

Google announces Veo updates: support for vertical video and 1080p, lower pricing, and general availability of Veo 3 and Veo 3 Fast in the Gemini API (Google Developers Blog)
https://developers.googleblog.com/en/veo-3-and-veo-3-…

Veo 3 and Veo 3 Fast – new pricing, new configurations and better resolution- Google Developers Blog
Today, we’re launching three big Veo updates: support for vertical format outputs (9:16 aspect ratio...

Geometrically expanding the BPS vortex of a non-canonical multi-field theory
F. C. E. Lima
https://arxiv.org/abs/2510.03237 https://arxiv.org/pdf/2510.0323…

Geometrically expanding the BPS vortex of a non-canonical multi-field theory
Considering a non-canonical multi-field theory, we propose a mechanism of geometric expansion for Abrikosov-Nielsen-Olesen (ANO) vortices. One builds the general setup adopting a non-canonical O(3)-sigma model, non-minimally coupled through an anomalous magnetic dipole interaction to a gauge and real scalar field. By embracing a hyperbolic non-canonical extension, one finds that self-dual vortex configurations undergo geometric expansion, deforming ANO-like vortices into disk-like structures, m…

Court rejects Trump’s attempt to overturn E Jean Carroll’s $83m verdict
#news

Strong hub cover pebbling number
Runze Wang
https://arxiv.org/abs/2510.05170 https://arxiv.org/pdf/2510.05170

Strong hub cover pebbling number
In a graph $G$, we define a set of vertices to be a \emph{strong hub set} if for any two vertices in $G$, we can find a path between them whose internal vertices are all in this set. We define the \emph{strong hub cover pebbling number} of $G$, denoted by $h_s^*(G)$, to be the smallest $t$ such that for any initial configuration with $t$ pebbles on $G$, we can make some pebbling moves (a pebbling move consists of removing two pebbles from a vertex $v$ and adding one pebble to another vertex adj…

Det är obegripligt för mig varför IMY valde att slå ihop de här två ämnena till samma artikel.

https://www.imy.se/blogg/var-saker-pa-natet--om-kakor-och-ai-i-vardagen/

Subgroup perfect codes of $S_n$ in Cayley sum graphs
Ankan Shaw, Biswajit Mondal, Satya Bagchi
https://arxiv.org/abs/2509.05069 https://arxiv.org/pdf/2509.…

Subgroup perfect codes of $S_n$ in Cayley sum graphs
A perfect code in a graph $Γ= (V, E)$ is a subset $C$ of $V$ such that no two vertices in $C$ are adjacent, and every vertex in $V \setminus C$ is adjacent to exactly one vertex in $C$. Let $ G $ be a finite group, and let $ S $ be a square-free normal subset of $ G $. The Cayley sum graph of $ G $ with respect to $ S $ is a simple graph with vertex set $ G $ and two vertices $ x $ and $ y $ are adjacent if $ xy\in S .$ A subset $ C $ of $ G $ is called perfect code of $ G $ if there exists a …

Vertex-ordering and arc-partitioning problems
N\'ora A. Borsik, P\'eter Madarasi
https://arxiv.org/abs/2509.05245 https://arxiv.org/pdf/2509.05245

Vertex-ordering and arc-partitioning problems
We study vertex-ordering problems in loop-free digraphs subject to constraints on the left-going arcs, focusing on existence conditions and computational complexity. As an intriguing special case, we explore vertex-specific lower and upper bounds on the left-outdegrees and right-indegrees. We show, for example, that deciding whether the left-going arcs can form an in-branching is solvable in polynomial time and provide a necessary and sufficient condition, while the analogous problem for an in-…