2026-07-16 10:00:00
All the talks from rstudio::conf 2022: https://www.rstudio.com/conference/2022/2022-conf-talks/ 👩🏫 Keynotes: https://www.
All the talks from rstudio::conf 2022: https://www.rstudio.com/conference/2022/2022-conf-talks/ 👩🏫 Keynotes: https://www.
Nvidia acquired Kumo, which sells predictive AI software to enterprises, a source says for $400M ; PitchBook: Kumo raised $37M at a $250M valuation in 2022 (The Information)
https://www.theinformation.com/articles/nvidia-buys-enterprise-mo…
Girls just wanna have Pfand
In the Summer of 2022, Greek politician Stelios Kouloglou was investigating how intrusive spyware had been used to hack business leaders, law enforcement officials, and politicians.
As part of the European Parliament’s PEGA Committee,
set up to investigate the use of the notorious Pegasus spyware and other variants,
Kouloglou travelled to interview spyware victims and probe high-profile cases.
That fall, according to a new forensic analysis,
💥Kouloglou’s iPhone …
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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