Tootfinder

RE: https://mastodon.social/@firefoxwebdevs/116680726980295049
It’s important to know (IMO) that headings can never go beyond level 9 with this feature:

Extreme dominance of Earth-origin heavy ions in the intense #RingCurrent near the Earth during the May 2024 super #GeomagneticStorm: #ionosphere supplied vast majority of ring current ions during May 2024 super geomagnetic storm, study finds: https://en.nagoya-u.ac.jp/news/articles/earths-ionosphere-supplied-vast-majority-of-ring-current-ions-during-may-2024-super-geomagnetic-storm-study-finds/ - despite the dense solar wind, solar wind ion contributions to the ring current during the May 2024 superstorm were minimal; the first simultaneous observation of ring current ions and solar wind during a storm this large.

Cheeger Inequalities for the Persistent Laplacian
Magnus Bakke Botnan, Rui Dong
https://arxiv.org/abs/2606.02846 https://arxiv.org/pdf/2606.02846 https://arxiv.org/html/2606.02846
arXiv:2606.02846v1 Announce Type: new
Abstract: We study Cheeger-type inequalities for persistent Laplacians associated with inclusions of simplicial complexes $\mathcal{K}\hookrightarrow \mathcal{L}$. We introduce a persistent up $p$-Laplacian $\Delta_{q,p,\mathrm{up}}^{\mathcal{K},\mathcal{L}}$ for $p\geq 1$. For $p=2$, this recovers the usual persistent up Laplacian, while for $p=1$ it yields a nonzero persistent Cheeger constant $\varphi_q^{\mathcal{K},\mathcal{L}}$. We prove a Cheeger-type inequality relating $\varphi_q^{\mathcal{K},\mathcal{L}}$ to the smallest nonzero eigenvalue of $\Delta_{q,\mathrm{up}}^{\mathcal{K},\mathcal{L}}$. This gives a persistent extension of recent work by Jost and Zhang (Ann. Sc. Norm. Super. Pisa Cl. Sci., 2024; arXiv:2302.01069).
We then study two more structured settings. Under a locally complete $q$-skeleton assumption on $\mathcal{K}$, we extend the complete-skeleton isoperimetric inequality of Parzanchevski--Rosenthal--Tessler (Combinatorica, 2016; arXiv:1207.0638) to the persistent setting. For orientable $(q 1)$-dimensional pseudomanifolds, we prove a Kron-type reduction of the persistent up Laplacian to a vertex- and edge-weighted graph Laplacian, possibly with Dirichlet boundary terms, and obtain two-sided Cheeger inequalities; this is related to the dual-graph perspective in the work of Steenbergen--Klivans--Mukherjee (Adv. Appl. Math., 2014; arXiv:1209.5091). We also describe the nonzero persistent Cheeger constant $\varphi_q^{\mathcal{K},\mathcal{L}}$ explicitly in terms of the dual graph in the non-branching pseudomanifold case. Finally, for graph inclusions $H\hookrightarrow G$, we compare the persistent Cheeger constants introduced here with the Kron-reduction Cheeger constants of M\'emoli et al. (SIAM J. Math. Data Sci., 2022; arXiv:2012.02808).
toXiv_bot_toot

Freehand, which builds AI agents to manage supply chain spend and operations for Fortune 500 companies, raised a $75M Series B, after a $25M Series A in 2024 (Mary Ann Azevedo/Crunchbase News)
https://news.crunchbase.com/transportat…

Freehand Raises $75M Series B To Automate Fortune 500 Supply Chain Spend
Freehand has raised $75 million in Series B funding to scale autonomous AI agents that manage supply chain spend and back-office operations for enterprises.

'Why are we talking about this?': Democrats are furious that the Bidens won't go away (Politico)
https://www.politico.com/news/2026/05/28/biden-democrats-2024-election-00942001
http://www.memeorandum.com/260528/p135#a260528p135

2024 global temperature record is consistent with model-predicted warming: #GlobalWarming or the lack thereof see the many links in https://skyweek.wordpress.com/2026/03/12/allgemeines-live-blog-ab-dem-12-marz-2026/ at the very bottom).