Tootfinder

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

Ransomware-Verdacht: Französische Polizei verhaftet russischen Basketballer
Laut einem Medienbericht ist ein russischer Basketballspieler auf Antrag der USA in Frankreich festgenommen und inhaftiert worden. Der bestreitet alle Vorwürfe.

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…

The QED photon-fermion vertex from its Dyson-Schwinger equation in 4D: the full vertex, the transverse form factors and the perturbative solution
Orlando Oliveira
https://arxiv.org/abs/2507.06880

The QED photon-fermion vertex from its Dyson-Schwinger equation in 4D: the full vertex, the transverse form factors and the perturbative solution
We investigate the Dyson-Schwinger equation for the photon-fermion one-particle irreducible vertex in QED in linear covariant gauges. The longitudinal component of this vertex is described using the Ball-Chiu basis, while its transverse part is expressed with the Kızılersu-Reenders-Pennington basis. Combining the vertex Ward-Takahashi identity with the vertex equation, we derive a set of exact, non-linear integral equations governing the transverse vertex. These equations hold for any linear …

Shared and diverging neural dynamics underlying false and veridical perception https://www.jneurosci.org/content/early/2025/06/04/JNEUROSCI.1479-24.2025 Now let's "mistake" meaningful noise as meaningful images through enhanced reliance…

Shared and diverging neural dynamics underlying false and veridical perception
We often mistake visual noise for meaningful images, which sometimes appear as convincing as veridical percepts. This suggests considerable overlap between the mechanisms that underlie false and veridical perception. Yet, false percepts must arise at least in part from internally generated signals. Here, we apply multivariate analyses to human MEG data to study the overlap between veridical and false perception across two aspects of perceptual inference: discrimination of content (what did I se…

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…

Hem från Kyiv efter uppdrag för Myndigheten för psykologiskt försvar. Skriver om kontraster. Flyglarmet ljuder medan unga spelar piano på gatan. Om att möta samtiden och framtiden samtidigt. Tillbaka i Kyiv - där vardag är motståndskraft.
https://carlheath.se/tillbaka-i-kyiv-d

Cyberangriff per Telefonkonferenz: Fünf junge Männer unter Verdacht
Fünf junge Männer blockierten die Telefonleitungen von rund 800 Polizeidienststellen. Der verwendete Trick war simpel, sorgte aber für viel Ärger.

Deterministic simplicial complexes
S. N. Dorogovtsev, P. L. Krapivsky
https://arxiv.org/abs/2507.07402 https://arxiv.org/pdf/2507.074…

Deterministic simplicial complexes
We investigate simplicial complexes deterministically growing from a single vertex. In the first step, a vertex and an edge connecting it to the primordial vertex are added. The resulting simplicial complex has a 1-dimensional simplex and two 0-dimensional faces (the vertices). The process continues recursively: On the $n$-th step, every existing $d-$dimensional simplex ($d\leq n-1$) joins a new vertex forming a $(d+1)-$dimensional simplex; all $2^{d+1}-2$ new faces are also added so that the r…

On a conjecture of Faudree and Schelp
Jan Goedgebeur, Jorik Jooken, Michiel Provoost, Carol T. Zamfirescu
https://arxiv.org/abs/2506.09667 https://

On a conjecture of Faudree and Schelp
In 1976 Faudree and Schelp conjectured that in a hamiltonian-connected graph on $n$ vertices, any two distinct vertices are connected by a path of length $k$ for every $k \ge n/2$. In 1978 Thomassen constructed a (non-cubic and non-planar) family of counterexamples, showing that there exist hamiltonian-connected $n$-vertex graphs containing two vertices with no path of length $n-2$ between them. We complement this result by describing cubic planar counterexamples on $6p+16$ vertices, each conta…