Tootfinder

The NYT says it is reviewing columnist Nick Kristof's work that favorably mentioned former donors to his 2022 Oregon governor bid, including Bill Gates (Max Tani/Semafor)
https://www.semafor.com/article/06/14/2026/new-york-times-…

Exclusive: New York Times’ Kristof quoted former campaign donors in columns
The paper had promised that Nick Kristof would disclose when someone he reported on was a donor to his Oregon gubernatorial campaign.

Heute vor 3 Jahren: Am 14. Juni 2023 erklärte der belarussische Präsident Aleksander Lukaschenko in einem Fernsehinterview mit dem russischen Staatssender Russia-1, dass #Belarus, wie am 25.03.23 durch Putin angekündigt, #Kernwaffen von Russland erhalten habe.

Heute vor 61 Jahren: Am 11.06.1965 zündeten die #USA im Rahmen von Operation Whetstone die Atombombe "Organdy". Whetstone war eine Serie von #Kernwaffentests bei der 1964/65 insgesamt 46 Bomben größtenteils im Testgebiet in

from my link log —
LEGO rolling ball clock.
https://jkbrickworks.com/rolling-ball-clock/
saved 2022-11-18 https://dotat.at/:/RBDH9.…

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

Heute vor 61 Jahren: Am 11.06.1965 zündeten die #USA im Rahmen von Operation Whetstone die Atombombe "Petrel". Whetstone war eine Serie von #Kernwaffentests bei der 1964/65 insgesamt 46 Bomben größtenteils im Testgebiet in