@heiseonline@social.heise.de2026-05-07 08:04:00
Alexa startet in Deutschland in den öffentlichen Vorabtest
Amazons aufgeschlaute Sprachassistenz Alexa ist im Early Access auf Echo- sowie Fire-TV-Geräten verfügbar und macht BMW-Bordsysteme gesprächiger.
http…
@kexpmusicbot@mastodonapp.uk2026-07-13 10:55:00
🇺🇦 #NowPlaying on KEXP's #VarietyMix
Bark Psychosis:
🎵 Big Shot (Alice's Cheshire Cat Mix)
#BarkPsychosis
https://barkpsychosis.bandcamp.com/track/big-shot
https://open.spotify.com/track/57YmPuR2XU9Fg9Q3miaeFF
@arXiv_mathAT_bot@mastoxiv.page2026-06-03 07:44:29
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
@salrandolph@zirk.us2026-07-02 13:13:47
Welcome to my hot classics summer. Iʻve had Homer in my ears, and Virgil and Shakespeare. Such a confusion of glories, such poetry, such violence!
Iʻm driving under the influence of all of them, but whenever Caesar comes, for me itʻs not only Julius who appears, but also Gertrude Stein.
https://salrandolph.substack.…
@ayn@trunk.lol2026-05-13 16:38:50
been shipping a lot without coding lately. going to start documenting some of these projects here.
today: mac apple music to discord rich presence bridge, plus the universal landing page it links to. friends on apple music, spotify, tidal, or kkbox get a one-tap deep link to whatever i'm playing, with a youtube music search fallback for completeness.
example:
@ruth_mottram@fediscience.org2026-04-26 16:58:57
Reading an MSc thesis and struck again how impressive it is that students can write such technical documents not even in their first language. It's also a little unfair in many ways, if there is a use for the LLMs AI translators, it's definitely this, though as checker not original writer.
@scottmiller42@mstdn.social2026-06-02 18:36:31
Erik Satie wrote Gymnopédie #1 in 1888, but it feels both timeless and contemporary. This composition for piano is one of my favorites for chilling and relaxing. While it is composed in 3/4 time, to me, it doesn't feel much like a waltz. Instead, it takes on a leisurely, thoughtful, but also live in the moment feel.
https://song.link/y/cic1R…
@jamesthebard@social.linux.pizza2026-04-27 18:05:36
@BBC6MusicBot@mastodonapp.uk2026-07-03 23:04:23
🇺🇦 #NowPlaying on #BBC6Music's #6MusicArtistInResidence
Erika de Casier:
🎵 You Can't Always Get What You Want
#ErikadeCasier
https://erikadecasier.bandcamp.com/track/you-cant-always-get-what-you-want
https://open.spotify.com/track/0loAUwPeBd9LvYtnaKpoGG
@BBC6MusicBot@mastodonapp.uk2026-05-24 09:20:43