Tootfinder

Mutation of $n$-cotorsion pairs in extriangulated categories
Huimin Chang, Yu Liu, Panyue Zhou
https://arxiv.org/abs/2506.16188 https://

Mutation of $n$-cotorsion pairs in extriangulated categories
In this article, we introduce the notion of $n$-cotorsion pairs in extriangulated categories, which extends both the cotorsion pairs established by Nakaoka and Palu and the $n$-cotorsion pairs in triangulated categories developed by Chang and Zhou. We further prove that any mutation of an $n$-cotorsion pair remains an $n$-cotorsion pair. As applications, we provide a geometric characterization of $n$-cotorsion pairs in $n$-cluster categories of type $A_{\infty}$, and we realize mutations of $n$…

Complete systems of solutions, transmutations and Darboux transform for Sturm-Liouville equations in impedance form
V\'ictor A. Vicente-Ben\'itez
https://arxiv.org/abs/2506.16604

Complete systems of solutions, transmutations and Darboux transform for Sturm-Liouville equations in impedance form
We present the construction of a complete system of functions associated with the Sturm-Liouville equation in impedance form on a finite interval $I$, given an impedance function $a\in L^2(I)$. The system, known as the formal powers, is generated through recursive integration of the impedance function $a$ and its reciprocal. We establish the completeness of this system in the space $L^p$ with the weight function $a^2$. Under additional conditions on $a$, we extend the completeness of this compl…

Hopf-Induced Desynchronization
Seungjae Lee, Lennart J. Kuklinski, Moritz Th\"umler, Marc Timme
https://arxiv.org/abs/2506.16845 https://

Hopf-Induced Desynchronization
The emergence of synchrony essentially underlies the functionality of many systems across physics, biology and engineering. In all established synchronization phase transitions so far, a stable synchronous state is connected to a stable incoherent state: For continuous transitions, stable synchrony directly connects to stable incoherence at a critical point, whereas for discontinuous transitions, stable synchrony is connected to stable incoherence via an additional unstable branch. Here we pres…

"Anyone you’re talking to has had decreased funding, or lost almost all of their funding, or is having trouble continuing their funding...
That, along with the pretty pervasive and growing anti-science establishment narrative … have been strong motivators to look elsewhere,” Eric Schuster said.
Schuster is one of many budding academics reflecting what could become a significant American brain drain,
sending the brightest minds in the country to flee the US and take their…

Spain's national power blackout: investigation results.
One non-renewable power station not available (for grid stabilisation).
Other power stations not complying with contractual requirements on frequency stabilisation.
We don't know which ones.
This on top of a speculatively unplanned power system.
So a cascade of effects leading to rapid shutdown.
(#Press rep…

El informe del apagón detecta centrales que “no estaban regulando tensión” y una desconexión “indebida” de instalaciones
El histórico cero energético se debió a “una combinación de factores”: había centrales “disponibles” para regular tensión que no lo estaban haciendo “según lo previsto por la normativa” y hubo plantas que se desconectaron de forma “indebida”, según Aagesen

Filing: neobank Chime plans to sell 26M shares in its IPO at $24 to $26, giving it a valuation between $10.3B and $11.1B; its two co-founders own 4% to 5% each (Cory Weinberg/The Information)
https://www.theinformation.com/briefings/chime-sets-ipo-…

Chime Sets Tentative IPO Price at Around $10.7 Billion
Banking app Chime plans to sell shares in an initial public offering at a price that would value it at between $10.3 billion and $11.1 billion, on a fully-diluted basis, the company said in a new securities filing Monday. The company set the price range ahead of a roadshow to meet investors over the next week, ahead of its IPO. The per-share price of the range, between $24 and $26, is more

140 media organizations call on Israel to LIFT its BAN on international journalists entering Gaza.
There is NO excuse for not allowing international media to enter #Gaza.
"Absolutely unprecedented in modern warfare". #PressFreedom

Press freedom groups demand open access to Gaza – DW – 06/08/2025
More than 140 media organizations are calling on Israel to lift its ban on international journalists entering Gaza. The lack of foreign journalists allows misinformation to flourish, said Jodie Ginsberg, CEO of the Committee to Protect Journalists and one of the signatories of the appeal.

Reason why there's Putins in the world:
Half of the I-do-my-own-reasearch comments: “But what would the lions eat now that they can't eat the villagers‘ cattle?” [Video literally shows zebras in the Nairobi National Park.]
Other half of comments: “$24 for 1 Lion Light ... Nice scam!” [Video produced by a corporation giving funds to other established non-profits; literally states the Lion Lights have motherboards.)
->
The genius invention that made peace wit…

Lexicographic products and lexicographic powers of graphs -- a walk matrix approach
Domingos M. Cardoso, Paula Carvalho, Helena Gomes, Sofia J. Pinheiro, Paula Rama
https://arxiv.org/abs/2506.12168

Lexicographic products and lexicographic powers of graphs -- a walk matrix approach
The characteristic polynomial and the spectrum of the lexicographic product of graphs $H[G]$, a specific instance of the generalized composition (also called $H$-join), are explicitly determined for arbitrary graphs $H$ and $G$, in terms of the eigenvalues of $G$ and an $H[G]$ associated matrix $\widetilde{\bf W}$, which relates $H$ with $G$. This study also establishes conditions under which a main eigenvalue of $G$ is a main or non-main eigenvalue of the matrix $\widetilde{\bf W}$, when the n…

✨ Spring SIGs wrapped! ✨
From Prague to Paris to Ispra, 4 GÉANT Special Interest Groups (SIGs) met to explore AI, Time & Frequency networks, service strategy development, and network operations.
Spring days packed with great ideas, useful insights, new collaborations, and our beloved Lightning Talks.
👏 Big thanks to CESNET, RENATER, EC JRC & all who joined in-person and online.
Catch up on all the highlights and takeaways here 👉

GÉANT Community Programme | GÉANT CONNECT Online
The GÉANT community programme supports research and education through the activities of Special Interest Groups and Task Forces and connects academia, the business community and governmental organisations.