Tootfinder

📢 Drei Festnahmen im Zusammenhang mit mutmaßlichen Sabotageanschlägen
Die Bundesanwaltschaft hat drei ukrainische Staatsbürger wegen des Verdachts der Agententätigkeit festnehmen lassen. Ihnen werde "Agententätigkeit zu Sabotagezwecken" vorgeworfen, teilte die Behörde mit.
➡️ h…

Drei Festnahmen im Zusammenhang mit mutmaßlichen Sabotageanschlägen
Die Bundesanwaltschaft hat drei ukrainische Staatsbürger wegen des Verdachts der Agententätigkeit festnehmen lassen. Ihnen werde "Agententätigkeit zu Sabotagezwecken" vorgeworfen, teilte die Behörde mit.

Het zijn de laatste dagen van mijn campagne en jouw laatste kans om een exemplaar van mijn nieuwe boek over plezier te pre-orderen en daarmee ook een uitnodiging voor de boeklancering te scoren https://www.voordekunst.nl/projecten/18850-meer-genieten-van-plezier-steun…

Grens tussen Gibraltar en Spanje verdwijnt, Britse apenrots wordt deel van Europese markt | de #Volkskrant
https://www.volkskran…

Upper cluster structure on Kac--Moody Richardson varieties
Huanchen Bao, Jeff York Ye
https://arxiv.org/abs/2506.10382 https://arxiv.…

Upper cluster structure on Kac--Moody Richardson varieties
We show coordinate rings of open Richardson varieties are upper cluster algebras for any symmetrizable Kac--Moody type. We further show the coordinate rings of (generalized) open Richardson varieties on the twisted product of flag varieties are upper cluster algebras for any symmetrizable Kac--Moody type. This includes, as special cases, reduced double Bruhat cells, Bott-Samelson varieties, braid varieties. Our results generalize various results by Casals--Gorsky--Gorsky--Le--Shen--Simental and…

us_roads: United States roads (2000)
The road networks of the 50 US States and the District of Columbia based on UA Census 2000 TIGER/Line Files. Edges are stretches of road and vertices are intersections of roads. The data sets were assembled by Dominik Schultes. The 'merged' network contains all the states merged together.
This network has 308401 nodes and 385164 edges.
Tags: Transportation, Roads, Unweighted

Vortex-magnetic competition and regime transitions in antiparallel flux tubes
Weiyu Shen, Rodolfo Ostilla-M\'onico, Xiaojue Zhu
https://arxiv.org/abs/2506.10648

Vortex-magnetic competition and regime transitions in antiparallel flux tubes
Vortex-magnetic interactions shape magnetohydrodynamic (MHD) turbulence, influencing energy transfer in astrophysical, geophysical, and industrial systems. On the Sun, granular-scale vortex flows couple strongly with magnetic fields, channelling energy into the corona. At high Reynolds numbers, vorticity and magnetic fields are nearly frozen into the charged fluid, and MHD flows emerge from the interplay between vortex dynamics and Lorentz forces. To probe this competition in a controlled setti…

The Classification of Graphs on $8$ vertices with Coinciding Zero Forcing number and Maximum Nullity
Wayne Barrett, Mark Hunnell, John Hutchens, John Sinkovic
https://arxiv.org/abs/2506.10726

The Classification of Graphs on $8$ vertices with Coinciding Zero Forcing number and Maximum Nullity
We study the minimum rank of a (simple, undirected) graph, which is the minimum rank among all matrices in a space determined by the graph. We determine the exact set of graphs on eight vertices for which the nullity of a minimum rank matrix does not coincide with a bound determined by the zero forcing number of a graph. Although our goal was to determine which eight-vertex graphs satisfy maximum nullity equal to the zero forcing number, we also established several additional methods to assist …

Virasoro constraints for Hodge integrals
Xin Wang
https://arxiv.org/abs/2506.10033 https://arxiv.org/pdf/2506.10033

Virasoro constraints for Hodge integrals
The purpose of this paper is to study Virasoro constraints for Hodge integrals in Gromov-Witten theory of any target varieties. Results consist of the following: Firstly, we propose Virasoro conjecture for Hodge integrals in Gromov-Witten theory of any target varieties; Secondly, we prove Virasoro constraints for Hodge integrals in genus zero of any target varieties; Thirdly, we prove the genus-1 $L_1^{\mathbb{E}}$ constraint with one Hodge character class insertion for any target varieties; La…

roadnet: U.S. roads (CA, PA, TX)
Road networks from three US states (CA, PA, TX), in which edges are stretches of road and vertices are intersections of roads.
This network has 1090920 nodes and 3083796 edges.
Tags: Transportation, Roads, Unweighted
https://networks.skewed.de/net/roadnet

Proof of a conjecture on isolation of graphs with a universal vertex
Peter Borg, Alastair Farrugia
https://arxiv.org/abs/2506.09290 https://

Proof of a conjecture on isolation of graphs with a universal vertex
A copy of a graph $F$ is called an $F$-copy. For any graph $G$, the $F$-isolation number of $G$, denoted by $ι(G,F)$, is the size of a smallest subset $D$ of the vertex set of $G$ such that the closed neighbourhood $N[D]$ of $D$ in $G$ intersects the vertex sets of the $F$-copies contained by $G$ (equivalently, $G-N[D]$ contains no $F$-copy). Thus, $ι(G,K_1)$ is the domination number $γ(G)$ of $G$, and $ι(G,K_2)$ is the vertex-edge domination number of $G$. Settling a conjecture of Zhang an…