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1. 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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2. ChemML : A machine learning and informatics program package for the analysis, mining, and modeling of chemical and materials data

   https://doi.org/10.1002/wcms.1458  

   Haghighatlari, Mojtaba; Vishwakarma, Gaurav; Altarawy, Doaa; Subramanian, Ramachandran; Kota, Bhargava U.; Sonpal, Aditya; Setlur, Srirangaraj; Hachmann, Johannes (January 2020, WIREs Computational Molecular Science)

   Abstract ChemMLis an open machine learning (ML) and informatics program suite that is designed to support and advance the data‐driven research paradigm that is currently emerging in the chemical and materials domain.ChemMLallows its users to perform various data science tasks and execute ML workflows that are adapted specifically for the chemical and materials context. Key features are automation, general‐purpose utility, versatility, and user‐friendliness in order to make the application of modern data science a viable and widely accessible proposition in the broader chemistry and materials community.ChemMLis also designed to facilitate methodological innovation, and it is one of the cornerstones of the software ecosystem for data‐driven in silico research. This article is categorized under:Software > Simulation MethodsComputer and Information Science > ChemoinformaticsStructure and Mechanism > Computational Materials ScienceSoftware > Molecular Modeling 

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3. 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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4. 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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5. Reverse shortest path problem for unit-disk graphs

   Wang, Haitao; Zhao, Yiming (April 2023, Journal of computational geometry)

   Given a set P of n points in the plane, the unit-disk graph Gr(P) with respect to a parameter r is an undirected graph whose vertex set is P such that an edge connects two points p, q in P if the Euclidean distance between p and q is at most r (the weight of the edge is 1 in the unweighted case and is the distance between p and q in the weighted case). Given a value \lambda>0 and two points s and t of P, we consider the following reverse shortest path problem: computing the smallest r such that the shortest path length between s and t in Gr(P) is at most \lambda. In this paper, we present an algorithm of O(\lfloor \lambda \rfloor \cdot n log n) time and another algorithm of O(n^{5/4} log^{7/4} n) time for the unweighted case, as well as an O(n^{5/4} log^{5/2} n) time algorithm for the weighted case. We also consider the L1 version of the problem where the distance of two points is measured by the L1 metric; we solve the problem in O(n log^3 n) time for both the unweighted and weighted cases. 

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