Tootfinder

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?"

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 $\mathbb R^5$.

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…

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…

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

Aid charities unanimously calling it
"Over 500 Palestinians have been killed while seeking aid since the GHF started operating in late May, following Israel's three-month blockade of Gaza, the organisations said. Almost 4,000 have been injured.
The organisations, including Oxfam, Save the Children and Amnesty, say Israeli forces and armed groups "routinely" open fire on Palestinians seeking aid."
Israeli, US-backed Gaza aid group must end, say 130 cha…

Israeli, US-backed Gaza aid group must end, say 130 charities
The call from some of the world's top aid organisations and charities comes after reports of soldiers killing hundreds of of Palestinians at aid sites.

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.

Faster Algorithm for Second (s,t)-mincut and Breaking Quadratic barrier for Dual Edge Sensitivity for (s,t)-mincut
Surender Baswana, Koustav Bhanja, Anupam Roy
https://arxiv.org/abs/2507.01366

Faster Algorithm for Second (s,t)-mincut and Breaking Quadratic barrier for Dual Edge Sensitivity for (s,t)-mincut
We study (s,t)-cuts of second minimum capacity and present the following algorithmic and graph-theoretic results. 1. Vazirani and Yannakakis [ICALP 1992] designed the first algorithm for computing an (s,t)-cut of second minimum capacity using $O(n^2)$ maximum (s,t)-flow computations. For directed integer-weighted graphs, we significantly improve this bound by designing an algorithm that computes an $(s,t)$-cut of second minimum capacity using $O(\sqrt{n})$ maximum (s,t)-flow computations w.h.…

Localized atomic vibrations caused by point impurity in long chains of noble gas atoms adsorbed in outer grooves of carbon nanobundle
E. V. Manzhelii, S. B. Feodosyev
https://arxiv.org/abs/2505.24497

Localized atomic vibrations caused by point impurity in long chains of noble gas atoms adsorbed in outer grooves of carbon nanobundle
The characteristics of discrete vibrational levels caused by a point three-parameter substitutional impurity in long linear chain of inert gas atoms adsorbed in groove on the surface of carbon nanobundle are studied. The impurity atom differs from the atoms of the chain in the following parameters: the mass, the parameter of interaction with neighboring atoms and the parameter of interaction with the substrate. Analytical expressions for the frequencies of the localized vibrations and the inten…

Cardinalities of the total number of independent sets
Benedek Kov\'acs, Zolt\'an L\'or\'ant Nagy
https://arxiv.org/abs/2505.24794 https://

Cardinalities of the total number of independent sets
We study the set of numbers the total number of independent sets can admit in $n$-vertex graphs. In this paper, we prove that the cardinality of this set $\mathcal{N}i(n)$ is very close to $2^n$ in the following sense: $\mathcal{N}i(n)/2^n = O(n^{-1/5})$ while for infinitely many $n$, we have $\log_2(\mathcal{N}i(n)/2^n)\ge -2^{(1+o(1)\sqrt{\log_2 n}}$. This set is also precisely the set of possible values of the independence polynomial $I_G(x)$ at $x=1$ for $n$-vertex graphs $G$. As an applica…