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On Website Technicals (2022-08) - Tech updates: FUELINST glitch, review pros and cons, a11y, fanlife, Save-Data, traffic nadir, JXL. - https://www.earth.org.uk/note-on-site-technicals-63.html

On Website Technicals (2022-08)
Tech updates: FUELINST glitch, review pros and cons, a11y, fanlife, Save-Data, traffic nadir, JXL.

„Trotz oder gerade wegen des Krieges sei die Ukraine zu einem Star in der E-Mobilität aufgestiegen. Im Jahr 2022, als Russland die Ukraine angriff, waren noch 48.400 Elektroautos in dem Land zugelassen. Ihr Anteil ist 2025 auf mehr als 252.000 gestiegen.
https://www.zeit.de/mob…

Elektroauto in der Ukraine: Autark durch den Krieg
Ausgerechnet in der Ukraine boomen Elektroautos – trotz der Angriffe auf die Energieversorgung. Reichweitenängste stören offenbar wenig, es zählen andere Qualitäten.

Privacy token Zcash plunges after the disclosure of a 2022 vulnerability in its Orchard shielded pool that could have allowed undetectable ZEC counterfeiting (Akash Girimath/Decrypt)
https://decrypt.co/370105/zec-crashes-38-as-zcash-discloses…

ZEC Crashes 38% as Zcash Discloses ‘Critical Counterfeiting Vulnerability’
An Orchard vulnerability that allowed undetectable counterfeiting of ZEC in its shielded pool has reignited debate over privacy coins.

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.

The recent #Artemis flight made me laugh when I recalled this 2022 episode off @… radio with its reference to #accordion spaceflight
“Then comes the unfurlin…

On Website Technicals (2022-07) - Tech updates: hot, cross (references). - https://www.earth.org.uk/note-on-site-technicals-62.html

On Website Technicals (2022-07)
Tech updates: hot, cross (references).

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).
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