Tootfinder

Props to the people working on @… and @… for making Element Call.
I deployed the LiveKit backend on my Matrix server which was, frankly, quite tricky.
Once it's set up, though, it works super well. I've been…

Great read by Sarahanne Field and Madeleine Pownall:
Subjectivity is a Feature, not a Flaw: A Call to Unsilence the Human Element in Science
#OpenScience includes practices such as #reflexivity in order to increase the transparancy of the research process.

An equality for balanced digraphs
Darij Grinberg, Benjamin Liber
https://arxiv.org/abs/2507.22388 https://arxiv.org/pdf/2507.22388

An equality for balanced digraphs
Consider a directed multigraph $D$ that is balanced (i.e., at each vertex, the indegree equals the outdegree). Let $A$ be its set of arcs. Fix an integer $k$. Let $s$ be a vertex of $D$. We show that the number of $k$-element subsets $B$ of $A$ that contain no cycles but contain a path from each vertex to $s$ (we call them "$s$-convergences") is independent on $s$. This generalizes known facts about spanning arborescences, acyclic orientations and maximal acyclic subdigraphs (or, equivalently, …

Zero Insertive Nil Clean Rings
Sanjiv Subba, Tikaram Subedi
https://arxiv.org/abs/2508.01333 https://arxiv.org/pdf/2508.01333

Zero Insertive Nil Clean Rings
This paper investigates key properties of ZINC rings and their relationships with semicommutative and weakly semicommutative rings. We call an element $x$ of a ring $R$ zero insertive if $x=arb$ for some $a,b,r\in R$ such that $ab=0$ and $ZI(R)$ denotes the set of all zero insertive elements of $R$. We establish that a ring $R$ is semicommutative if and only if $ZI(R) \subseteq E(R)$, and weakly semicommutative if and only if $ZI(R) \subseteq N(R)$, where $E(R)$ and $N(R)$ denote respectively t…