Tootfinder

Good morning gang! Let’s solve the mystery of the missing funnel steps!

Oh wow I’ve amassed over 2000 followers on the Fediverse! That‘s absolutely ludicrous 😍

faculty_hiring_us: Faculty hiring networks in the US (2022)
Networks of faculty hiring for all PhD-granting US universities over the decade 2011–2020. Each node is a PhD-granting institution, and a directed edge (i,j) indicates that a person received their PhD from node i and was tenure-track faculty at node j during time of collection (2011-2020). This dataset is divided into separate networks for all 107 fields, as well as aggregate networks for 8 domains, and an overall network for …

Heute vor 61 Jahren: Am 22.04.1965 zündeten die #USA im Rahmen von Operation Whetstone die 39. Atombombe "Chenille". Whetstone war eine Serie von #Kernwaffentests bei der 1964/65 insgesamt 46 Bomben größtenteils im Testgebiet in

„Eichhörnchen sind ja auch nur kleine Nussfüchse“

Add richer tooltips to ggiraph with kableExtra and friends: #dataviz

🇺🇦 #NowPlaying on KEXP's #AfternoonShow
Portishead:
🎵 Wandering Star
#Portishead
https://andrewcolohan.bandcamp.com/track/portishead-wandering-star-cover-2022
https://open.spotify.com/track/7h14W1uQK7sjpVI1oVTobt

I remember watching the 2022 documentary
"Aşk, Mark ve Ölüm"
(Love, Deutschmarks and Death) by Cem Kaya
with awe and shame at how much I had not known.
The film looks at the difficult lives of Turkish workers in Germany through the music they produced.
One widely popular song, sung by Yüksel Özkasap, included the lines:
“Germany, everything about you is a lie. You have stolen my life and taken my love.”
The language textbook
"Türk…

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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Girls just wanna have Pfand