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1. The Genus Paronychia (Caryophyllaceae) in South America: Nomenclatural Review and Taxonomic Notes with the Description of a New Species from North Peru

   https://doi.org/10.3390/plants12051064  

   Iamonico, Duilio; Montesinos_Tubée, Daniel B (March 2023, Plants)

   All the names in Paronychia described from South America are investigated. Five names (P. arbuscula, P. brasiliana subsp. brasiliana var. pubescens, P. coquimbensis, P. hieronymi, and P. mandoniana) are lecto- or neotypified on specimens preserved at GOET, K, LP, and P. The typification of nine names, first proposed by Chaudhri in 1968 as the “holotype” are corrected according to Art. 9.10 of ICN. Three second-step typifications (Art. 9.17 of ICN) are proposed for P. camphorosmoides, P. communis, and P. hartwegiana. The following nomenclatural changes are proposed: P. arequipensis comb. et stat. nov. (basionym: P. microphylla subsp. microphylla var. arequepensis), P. compacta nom. nov. pro P. andina (Philippi non Gray; Art. 53.1 of ICN), P. jujuyensis comb. et stat. nov. (basionym: P. hieronymi subsp. hieronymi var. jujuyensis), P. compacta subsp. boliviana comb. nov. (basionym: P. andina subsp. boliviana), and P. compacta subsp. purpurea comb. nov. (basionym: P. andina subsp. purpurea). A new species (P. glabra sp. nov.) is proposed based on our examination of live plants and herbarium specimens. P. johnstonii subsp. johnstonii var. scabrida is synonymized (syn. nov.) with P. johnstonii. Finally, P. argyrocoma subsp. argyrocoma is excluded from South America since it was based on misidentified specimens (deposited at MO) of P. andina subsp. andina. A total of 30 species (43 taxa including subspecies, varieties, subvarieties, and forms) are recognized, highlighting that for some (Paronychia chilensis, P. communis, P. setigera) we provisionally accept Chaudhri’s infraspecific classification, since the high phenotypic variability of these taxa is quite complicated and further investigations need to solve their taxonomy. 

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2. MBSE Online Professional Development Learning Modules Data

   https://doi.org/10.4231/3DR2-VY15  

   Douglas, Kerrie; Huang, Wanju; Li, Tiantian; Marcos, Leonardo; Huang, Wanju (January 2025, Purdue University Research Repository)

   <p>The data was downloaded and captured through MBSE online learning modules. Deidentified learners&#39; activities within the modules, such as clickstreams and assignments, were captured in the data/</p> <p>&bull; All files here are student submissions to one or more of the modules in the MBSE program.</p> <p>&bull; All user data has either been removed or redacted from the submission.</p> <p>&bull; &ldquo;Andrew Hurt&rdquo; is not a student and none of these files came from him. He is the person who did the redaction.</p> <p>&bull; The naming structure of the files is as follows: [Module number]-[Module Offering Date]-[Submission Number]-[Part Number of Submission]. Example: M5-040422-S1-Part3. This file is from Module 5, which was offered on April 4, 2022, it is submission 1, and part 3 of submission 1.</p> <p>&bull; Note that submissions within or between modules are not necessarily connected to specific students. So &ldquo;Submission 1&rdquo; from module 5 is not the same user as &ldquo;Submission 1&rdquo; from module 6.</p> <p>&bull; Not all submissions have multiple parts.</p> <p>&bull; No .mdzip files (proprietary MagicDraw software files) have been included in this list.</p> <p>&bull; If a module or folder in the module is missing content from a particular offering, it is because either no one submitted anything or because the file was a .mdzip file and was not downloaded.</p> <p>&nbsp;</p> 

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3. Bounds for exit times of Brownian motion and the first Dirichlet eigenvalue for the Laplacian

   https://doi.org/10.1090/tran/8903  

   Bañuelos, Rodrigo; Mariano, Phanuel; Wang, Jing (August 2023, Transactions of the American Mathematical Society)

   For domains in R d \mathbb {R}^d , d ≥ 2 d\geq 2 , we prove universal upper and lower bounds on the product of the bottom of the spectrum for the Laplacian to the power p > 0 p>0 and the supremum over all starting points of the p p -moments of the exit time of Brownian motion. It is shown that the lower bound is sharp for integer values of p p and that for p ≥ 1 p \geq 1 , the upper bound is asymptotically sharp as d → ∞ d\to \infty . For all p > 0 p>0 , we prove the existence of an extremal domain among the class of domains that are convex and symmetric with respect to all coordinate axes. For this class of domains we conjecture that the cube is extremal. 

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4. A simple proof of reflexivity and separability of N^{1,p} Sobolev spaces

   https://doi.org/10.54330/afm.127419  

   Alvarado, Ryan; Hajłasz, Piotr; Malý, Lukáš (October 2022, Annales Fennici Mathematici)

   We present an elementary proof of a well-known theorem of Cheeger which states that if a metric-measure space \(X\) supports a \(p\)-Poincaré inequality, then the \(N^{1,p}(X)\) Sobolev space is reflexive and separable whenever \(p\in (1,\infty)\). We also prove separability of the space when \(p=1\). Our proof is based on a straightforward construction of an equivalent norm on \(N^{1,p}(X)\), \(p\in [1,\infty)\), that is uniformly convex when \(p\in (1,\infty)\). Finally, we explicitly construct a functional that is pointwise comparable to the minimal \(p\)-weak upper gradient, when \(p\in (1,\infty)\). 

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5. Optimal Stopping Rules for Sequential Hypothesis Testing

   Daskalakis, Constantinos; Kawase, Yasushi (January 2017, 25th Annual European Symposium on Algorithms (ESA))

   Suppose that we are given sample access to an unknown distribution p over n elements and an explicit distribution q over the same n elements. We would like to reject the null hypothesis“p=q” after seeing as few samples as possible, whenp6=q, while we never want to reject the null, when p=q. Well-known results show thatΘ(√n/2)samples are necessary and sufficient for distinguishing whether p equals q versus p is-far from q in total variation distance. However,this requires the distinguishing radiusto be fixed prior to deciding how many samples to request.Our goal is instead to design sequential hypothesis testers, i.e. online algorithms that request i.i.d.samples from p and stop as soon as they can confidently reject the hypothesis p=q, without being given a lower bound on the distance between p and q, whenp6=q. In particular, we want to minimize the number of samples requested by our tests as a function of the distance between p and q, and if p=q we want the algorithm, with high probability, to never reject the null. Our work is motivated by and addresses the practical challenge of sequential A/B testing in Statistics.We show that, when n= 2, any sequential hypothesis test must seeΩ(1dtv(p,q)2log log1dtv(p,q))samples, with high (constant) probability, before it rejects p=q, where dtv(p,q) is the—unknown to the tester—total variation distance between p and q. We match the dependence of this lower bound ondtv(p,q)by proposing a sequential tester that rejects p=q from at most O(√ndtv(p,q)2log log1dtv(p,q))samples with high (constant) probability. TheΩ(√n)dependence on the support size n is also known to be necessary. We similarly provide two-sample sequential hypothesis testers, when sample access is given to both p and q, and discuss applications to sequential A/B testing. 

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