Tootfinder

Revisiting $d$-distance (independent) domination in trees and in bipartite graphs
Csilla Bujt\'as, Vesna Ir\v{s}i\v{c} Chenoweth, Sandi Klav\v{z}ar, Gang Zhang
https://arxiv.org/abs/2508.12804

Revisiting $d$-distance (independent) domination in trees and in bipartite graphs
The $d$-distance $p$-packing domination number $γ_d^p(G)$ of $G$ is the minimum size of a set of vertices of $G$ which is both a $d$-distance dominating set and a $p$-packing. In 1994, Beineke and Henning conjectured that if $d\ge 1$ and $T$ is a tree of order $n \geq d+1$, then $γ_d^1(T) \leq \frac{n}{d+1}$. They supported the conjecture by proving it for $d\in \{1,2,3\}$. In this paper, it is proved that $γ_d^1(G) \leq \frac{n}{d+1}$ holds for any bipartite graph $G$ of order $n \geq d+1$,…

Consider how far a
"use of force authorization" could be read to extend
when it starts with no limiting principle
-- no armed attack, no organized armed group fighting the United States
-- and is in fact explicitly authorizing widespread murder of mere suspects
https://

Ambros im Interview - „Ein Grab am Zentralfriedhof ist wohl reserviert“ #News #Nachrichten

Calibrated Semantic Diffusion: A p-Laplacian Synthesis with Learnable Dissipation, Quantified Constants, and Graph-Aware Calibration
Faruk Alpay, Hamdi Alakkad
https://arxiv.org/abs/2508.13658

Calibrated Semantic Diffusion: A p-Laplacian Synthesis with Learnable Dissipation, Quantified Constants, and Graph-Aware Calibration
We develop a calibrated diffusion framework by synthesizing three established concepts: linear Laplacian smoothing, nonlinear graph p-Laplacian flows, and a learnable dissipation term derived from a strongly convex potential. This synthesis provides a general model for graph-based diffusion with controllable dynamics. Our key theoretical results include a quantified two-regime decay analysis for $p>2$, which provides stronger, p-dependent transient bounds not captured by standard ISS templates,…

Scaling Behaviors in Active Model B via the Functional Renormalization Group
Gergely Fej\H{o}s, Zsolt Sz\'ep, Naoki Yamamoto
https://arxiv.org/abs/2508.12065 https://

Scaling Behaviors in Active Model B+ via the Functional Renormalization Group
We study the scaling behaviors of the Active Model B+ using the functional renormalization group (FRG) approach, based on the nonequilibrium effective action formulated via the Martin-Siggia-Rose path-integral formalism. We derive the $β$ functions for all couplings of the system in generic $d$ dimensions, revealing regulator independence in various contributions to the RG flow at specific values for $d$. After identifying specific regions of the parameter space that define submodels closed un…

Feuerwehr half nicht - Entenküken-Rettung lässt Wogen hochgehen #News #Nachrichten

Homological torsion growth in non-normal chains of graphs of free groups
Dario Ascari, Jonathan Fruchter
https://arxiv.org/abs/2509.15075 https://arxiv.org…

Homological torsion growth in non-normal chains of graphs of free groups
Let $G$ be a hyperbolic group that splits as a graph of free groups with cyclic edge groups, and which is not isomorphic to a free product of free and surface groups. We show that $G$ admits an exhausting, nested sequence of finite-index non-normal subgroups $G\ge G_1 \ge G_2 \ge \cdots$ with exponential homological torsion growth. More specifically, we prove that simultaneously for every prime $p$, $\liminf_{n\rightarrow \infty} \frac{\log \vert \mathrm{Tor}_p(G_n^{\mathrm{ab}})\vert}{[G:G_n]}…

Drama um Tier - Bellende Hunde hetzen Pferd „Maxi“ in den Tod #News #Nachrichten

Tricyclic graphs for which the second largest distance eigenvalue less than $-\frac{1}{2}$
Kexin Yang, Ligong Wang
https://arxiv.org/abs/2509.12640 https://

Tricyclic graphs for which the second largest distance eigenvalue less than $-\frac{1}{2}$
Let $G$ be a simple connected graph with vertex set $V(G)=\{v_{1}, v_{2}, \ldots, v_{n}\}$. The distance $d_G(v_i,v_j)$ between two vertices $v_i$ and $v_j$ of $G$ is the length of a shortest path between $v_i$ and $v_j$. The distance matrix of $G$ is defined as $D(G)=(d_G(v_i,v_j))_{n\times n}$. The second largest distance eigenvalue of \( G \) is the second largest eigenvalues of $D(G)$. Guo and Zhou [Discrete Math. 347(2024), 114082] proved that any connected graph with the second largest di…

Stiller Moment - Trump besuchte Grab von Queen Elizabeth II. #News #Nachrichten