Tootfinder

I spot a tankie from a mile away, and I’m never falling for their revisionist garbage. Two insta-blocks in one day? Absolutely glorious. No platform for authoritarian apologists, win win.
#AntiTankieAction #Tankies

Rumors on evolving graphs through stationary times
Vicenzo Bonasorte
https://arxiv.org/abs/2506.04386 https://arxiv.org/pdf/2506.0438…

Rumors on evolving graphs through stationary times
We study rumor spreading in dynamic random graphs. Starting with a single informed vertex, the information flows until it reaches all the vertices of the graph (completion), according to the following process. At each step $k$, the information is propagated to neighbors of the informed vertices, in the $k$-th generated random graph. The way this information propagates from vertex to vertex at each step will depend on the ``protocol". We provide a method based on strong stationary times to study…

This https://arxiv.org/abs/2504.21059 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A remark on the number of automorphisms of some algebraic structures
In these notes we look at the following question. Given a category $\mathcal C$ of algebraic structure (e.g. the category of groups, monoids, partial groups, ...) and a rational $r\in \mathbb Q$, does there exists an element $x\in \mathcal C$ such that the size of its automorphism group $\text{Aut}_{\mathcal C} (x)$ divided by the size of $x$ (whatever that would means) is equal to $r$\,? To our knowledge, this question was introduced by Tărnăuceanu in the category of groups. Here, we answer …

My wife currently messages me the increasing number of noise sources at home:
Chainsaw to cut bushes, roadworks with jackhammer and rock cutting saw, and now the garbage truck beeping while reversing in our road.
I get a play-by-play description of what keeps her from sleeping in, and I'm torn between laughing, emphasizing and thinking "What happens if she goes all Michael Douglas in Falling Down?"

The stability of independence polynomials of complete bipartite graphs
Guo Chen, Bo Ning, Jianhua Tu
https://arxiv.org/abs/2505.24381 https://

The stability of independence polynomials of complete bipartite graphs
The independence polynomial of a graph is termed {\it stable} if all its roots are located in the left half-plane $\{z \in \mathbb{C} : \mathrm{Re}(z) \leq 0\}$, and the graph itself is also referred to as stable. Brown and Cameron (Electron. J. Combin. 25(1) (2018) \#P1.46) proved that the complete bipartite graph $K_{1,n}$ is stable and posed the question: \textbf{Are all complete bipartite graphs stable?} We answer this question by establishing the following results: \begin{itemize} \i…

Existence of normalized solutions to nonlinear Schr\"odinger equations on lattice graphs
Zhentao He, Chao Ji, Yifan Tao
https://arxiv.org/abs/2507.01591

Existence of normalized solutions to nonlinear Schrödinger equations on lattice graphs
In this paper, using a discrete Schwarz rearrangement on lattice graphs developed in \cite{DSR}, we study the existence of global minimizers for the following functional $I:H^1\left(\mathbb{Z}^N\right)\to \R$, $$I(u)=\frac{1}{2} \int_{\mathbb{Z}^N}|\nabla u|^2 \,dμ-\int_{\mathbb{Z}^N} F(u)\, dμ,$$ constrained on $S_m:=\left\{u \in H^1\left(\mathbb{Z}^N\right) \mid\|u\|_{\ell^2\left(\mathbb{Z}^N\right)}^2=m\right\}$, where $N \geq 2$, $m>0$ is prescribed, $f \in C(\mathbb{R…

We in Game Workers Unite Ireland stand in solidarity with Animation Workers of Ireland, and the international trade union coalition happening to organise against the threat of AI in the animation industry, and we support their call to acton.
Join them Thursday 12 June at 14:00 at the Pâquier in Annecy!!
#Animation

Decoupling for degenerate hypersurfaces
Jianhui Li, Tongou Yang
https://arxiv.org/abs/2507.02134 https://arxiv.org/pdf/2507.02134

Decoupling for degenerate hypersurfaces
We utilise the two principles of decoupling introduced in arXiv:2407.16108 to prove the following conditional result: assuming uniform decoupling for graphs of polynomials in all dimensions with identically zero Gaussian curvature, we can prove decoupling for all smooth hypersurfaces in all dimensions. Moreover, we are able to prove (unconditional) decoupling for all smooth hypersurfaces in $\mathbb R^4$ and graphs of homogeneous polynomials in $\mathbb R^5$.

Hausdorff Dimension of non-conical and Myrberg limit sets
Mahan Mj, Wenyuan Yang
https://arxiv.org/abs/2506.04955 https://arxiv.org/p…

Hausdorff Dimension of non-conical and Myrberg limit sets
In this paper, we develop techniques to study the Hausdorff dimensions of non-conical and Myrberg limit sets for groups acting on negatively curved spaces. We establish maximality of the Hausdorff dimension of the non-conical limit set of $G$ in the following cases. 1. $M$ is a finite volume complete Riemannian manifold of pinched negative curvature and $G$ is an infinite normal subgroups of infinite index in $π_1(M)$. 2. $G$ acts on a regular tree $X$ with $X/G$ infinite and amenable (dimensi…

Ransomware Group Anubis has leaked what they extracted from Disneyland Paris
#ransomware

Ransomware.live 👀
Ransomware.live tracks ransomware groups and their activity. It was created by Julien Mousqueton, a security researcher. The website provides information on the groups' infrastructure, victims, and payment demands. It also includes a live map that shows the latest ransomware attacks.