Tootfinder

This https://arxiv.org/abs/2402.16776 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On the length of directed paths in digraphs
Thomassé conjectured the following strengthening of the well-known Caccetta-Haggkvist Conjecture: any digraph with minimum out-degree $δ$ and girth $g$ contains a directed path of length $δ(g-1)$. Bai and Manoussakis gave counterexamples to Thomassé's conjecture for every even $g\geq 4$. In this note, we first generalize their counterexamples to show that Thomassé's conjecture is false for every $g\geq 4$. We also obtain the positive result that any digraph with minimum out-degree $δ$ and…

This slipped my mind, but there's something that crossed my mind after Main Story III.2 about Kamlanage. #clae_ae
Thing is, while we know Hollow Chronos' goal to some degree (to release the Hollow Time Layer from its seal), we don't know yet exactly *how* he plans to use Kamlanage.
But that's beside the point. The main point is: see how suspiciously similar Kamlanage's designated role and situation is with Eden? Which comes to the following...

I've been reading "On Green” (https://joecarlsmith.com/2024/03/21/on-green) and its following article, “On Attunement” with some interest today. I am uninterested in the ways he is focused on “AGI”, but that might actually be part of what he's saying and missing.
They talk about the philosophy of green in the "magic the gathering" sense, which has five core modes of things, and being a game, designed to balance. It's an attractive system and not without merit as a philosophical labeling system. In short: white, moral; blue, knowledge and rationality; red, passion and desire; black, power and achievement. And green. Green is the subject they can't identify clearly.
I don't think they really understand green. (They come from a very rationalist place, and that's not a good mode to understand Green)
Green is the domain of systems thinking and of ecology. It's one of flexible boundaries and hierarchies that vanish when you look at them for long. They talk about philosophical agents and try to fit a green philosophical stance into that framework, but it misses: the very idea of a self is nebulous in a green philosophy. Yes, it obviously exists, we are all separate from each other. But also we are inseparable from each other. Green is a philosophy of relationality and multiple perspectives and ever shifting viewpoints. It's not just yin, passive, permissive, but holistic. It's not that it lets the Other in, it's that it actively is in relation with the Other. The other is the self, the self is the other.
The essays also label green as conservative, and this is not quite true. It is not about being slow or regressive or traditional, but about being whole. They can't quite see that green's willingness to accept death and pain as things that happen and also its strong preservationist stance are not opposed to each other. It seems incoherent, but it's not: death and pain are things that happen to living parts of an ecosystem. They matter, but so too does the whole matter. Where so many blue rationalists see statistical and demographic counts of deaths and "sentient beings harmed”, green sees a whole ecosystem where some of that is deeply natural. It's unnatural, ecosystem-harming deaths that are disasters in the green philosophy. Wholesale extinctions. Protracted, painful deaths, as much for the wound they cause outside the individual as the individual suffering as well. But we all come to an end, and to change that wholesale would end so many kinds of relationship, so many things.
Green revels in the illegible, the incomplete, and the connected. It's easy to be green-blind, to ignore the subtle systemic effects. So many of us want simple cause and effect, rather than action and plurality of reactions.
Green's ability to embrace the illegible lets it deal with Red chaos; its resilience tempers red passion. It can ally with White philosophies into a pastoral, conservative, moralistic framework. It ends up at odds with the rationalist Blue and the power-hungry Black, because they drive disequilibrium, but more than just transition to new stable ecologies, they drive systems permanently out of stability, destroying relationships in their path. When confronted with this, they will deny it because the objects are still there. Preserved. Catalogued. Legible and accounted for. Perhaps used instrumentally. Perhaps wrecked for some "greater purpose” but only acknowledged as objects. The relationships between things remain illegible.

This https://arxiv.org/abs/2402.16776 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On the length of directed paths in digraphs
Thomassé conjectured the following strengthening of the well-known Caccetta-Haggkvist Conjecture: any digraph with minimum out-degree $δ$ and girth $g$ contains a directed path of length $δ(g-1)$. Bai and Manoussakis gave counterexamples to Thomassé's conjecture for every even $g\geq 4$. In this note, we first generalize their counterexamples to show that Thomassé's conjecture is false for every $g\geq 4$. We also obtain the positive result that any digraph with minimum out-degree $δ$ and…

Marburg!
Als ob es dort absolut keine Versorgung gäbe: ".... muss dieses Auto hier stehen, schönen Tag noch".
Eigentlich müsste dieser Tag mit 70€ (eigentlich sogar 140€, wegen Vorsatz) und einem Punkt in Flensburg "verschönt" werden.
#runtervomgehweg

This https://arxiv.org/abs/2402.02905 has been replaced.
link: https://scholar.google.com/scholar?q=a

Variational discretizations of ideal magnetohydrodynamics in smooth regime using finite element exterior calculus
We propose a new class of finite element approximations to ideal compressible magnetohydrodynamic equations in smooth regime. Following variational approximations developed for fluid models in the last decade, our discretizations are built via a discrete variational principle mimicking the continuous Euler-Poincaré principle, and to further exploit the geometrical structure of the problem, vector fields are represented by their action as Lie derivatives on differential forms of any degree. The…

Star Trek kehrt als Prequel zum Prequel ins Kino zurück
Paramount hat bestätigt, dass noch 2024 die Produktion eines neuen Trek-Films beginnt. Dieser soll vor dem Reboot von 2009 spielen.
https://www.

This https://arxiv.org/abs/2402.02905 has been replaced.
link: https://scholar.google.com/scholar?q=a

Variational discretizations of ideal magnetohydrodynamics in smooth regime using finite element exterior calculus
We propose a new class of finite element approximations to ideal compressible magnetohydrodynamic equations in smooth regime. Following variational approximations developed for fluid models in the last decade, our discretizations are built via a discrete variational principle mimicking the continuous Euler-Poincaré principle, and to further exploit the geometrical structure of the problem, vector fields are represented by their action as Lie derivatives on differential forms of any degree. The…

On the length of directed paths in digraphs
Yangyang Cheng, Peter Keevash
https://arxiv.org/abs/2402.16776 https://arxiv.org/pdf/2402…

On the length of directed paths in digraphs
Thomassé conjectured the following strengthening of the well-known Caccetta-Haggkvist Conjecture: any digraph with minimum out-degree $δ$ and girth $g$ contains a directed path of length $δ(g-1)$. Bai and Manoussakis gave counterexamples to Thomassé's conjecture for every even $g\geq 4$. In this note, we first generalize their counterexamples to show that Thomassé's conjecture is false for every $g\geq 4$. We also obtain the positive result that any digraph with minimum out-degree $δ$ and…

A Caro-Wei bound for induced linear forests in graphs
Gwena\"el Joret, Robin Petit
https://arxiv.org/abs/2403.17568 https://arxi…

A Caro-Wei bound for induced linear forests in graphs
A well-known result due to Caro (1979) and Wei (1981) states that every graph $G$ has an independent set of size at least $\sum_{v\in V(G)} \frac{1}{d(v) + 1}$, where $d(v)$ denotes the degree of vertex $v$. Alon, Kahn, and Seymour (1987) showed the following generalization: For every $k\geq 0$, every graph $G$ has a $k$-degenerate induced subgraph with at least $\sum_{v \in V(G)}\min\{1, \frac {k+1}{d(v)+1}\}$ vertices. In particular, for $k=1$, every graph $G$ with no isolated vertices has an…