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1. The joint automated repository for various integrated simulations (JARVIS) for data-driven materials design

   https://doi.org/10.1038/s41524-020-00440-1  

   Choudhary, Kamal; Garrity, Kevin F.; Reid, Andrew C.; DeCost, Brian; Biacchi, Adam J.; Hight Walker, Angela R.; Trautt, Zachary; Hattrick-Simpers, Jason; Kusne, A. Gilad; Centrone, Andrea; et al (December 2020, npj Computational Materials)

   null (Ed.)

   Abstract The Joint Automated Repository for Various Integrated Simulations (JARVIS) is an integrated infrastructure to accelerate materials discovery and design using density functional theory (DFT), classical force-fields (FF), and machine learning (ML) techniques. JARVIS is motivated by the Materials Genome Initiative (MGI) principles of developing open-access databases and tools to reduce the cost and development time of materials discovery, optimization, and deployment. The major features of JARVIS are: JARVIS-DFT, JARVIS-FF, JARVIS-ML, and JARVIS-tools. To date, JARVIS consists of ≈40,000 materials and ≈1 million calculated properties in JARVIS-DFT, ≈500 materials and ≈110 force-fields in JARVIS-FF, and ≈25 ML models for material-property predictions in JARVIS-ML, all of which are continuously expanding. JARVIS-tools provides scripts and workflows for running and analyzing various simulations. We compare our computational data to experiments or high-fidelity computational methods wherever applicable to evaluate error/uncertainty in predictions. In addition to the existing workflows, the infrastructure can support a wide variety of other technologically important applications as part of the data-driven materials design paradigm. The JARVIS datasets and tools are publicly available at the website: https://jarvis.nist.gov . 

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2. Repeat bleaching of a central Pacific coral reef overthe past six decades (1960–2016)

   https://doi.org/10.1038/s42003-018-01  

   Hannah C. Barkley1, 6 (October 2018, Communications biology)

   The oceans are warming and coral reefs are bleaching with increased frequency and severity,fueling concerns for their survival through this century. Yet in the central equatorial Pacific,some of the world’s most productive reefs regularly experience extreme heat associated with El Niño. Here we use skeletal signatures preserved in long-lived corals on Jarvis Island to evaluate the coral community response to multiple successive heatwaves since 1960. By tracking skeletal stress band formation through the 2015-16 El Nino, which killed 95% of Jarvis corals, we validate their utility as proxies of bleaching severity and show that 2015-16was not the first catastrophic bleaching event on Jarvis. Since 1960, eight severe (>30%bleaching) and two moderate (<30% bleaching) events occurred, each coinciding with ElNiño. While the frequency and severity of bleaching on Jarvis did not increase over this time period, 2015–16 was unprecedented in magnitude. The trajectory of recovery of this historically resilient ecosystem will provide critical insights into the potential for coral reef resilience in a warming world. 

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3. Fourier restriction above rectangles

   https://doi.org/10.1007/s00208-021-02202-w  

   Schwend, Jeremy; Stovall, Betsy (May 2021, Mathematische Annalen)

   null (Ed.)

   In this article, we study the problem of obtaining Lebesgue space inequalities for the Fourier restriction operator associated to rectangular pieces of the paraboloid and perturbations thereof. We state a conjecture for the dependence of the operator norms in these inequalities on the sidelengths of the rectangles, prove that this conjecture follows from (a slight reformulation of the) restriction conjecture for elliptic hypersurfaces, and prove that, if valid, the conjecture is essentially sharp. Such questions arise naturally in the study of restriction inequalities for degenerate hypersurfaces; we demonstrate this connection by using our positive results to prove new restriction inequalities for a class of hypersurfaces having some additive structure. 

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4. The chromatic number of {ISK4, diamond, bowtie}‐free graphs

   https://doi.org/10.1002/jgt.22631  

   Chen, Guantao; Chen, Yuan; Cui, Qing; Feng, Xing; Liu, Qinghai (October 2020, Journal of Graph Theory)

   Abstract A graph is said to be ‐free if it does not contain any subdivision of as an induced subgraph. Lévêque, Maffray and Trotignon conjectured that every ‐free graph is 4‐colorable. In this paper, we show that this conjecture is true for the class of {, diamond, bowtie}‐free graphs, where a diamond is the graph obtained from by removing one edge and a bowtie is the graph consisting of two triangles with one vertex identified. 

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5. Blaschke Products, Level Sets, and Crouzeix’s Conjecture

   https://doi.org/10.1007/s11854-023-0295-y  

   Bickel, Kelly; Gorkin, Pamela (April 2024, Journal d'Analyse Mathématique)

   We study several problems motivated by Crouzeix’s conjecture, which we consider in the special setting of model spaces and compressions of the shift with finite Blaschke products as symbols. We pose a version of the conjecture in this setting, called the level set Crouzeix (LSC) conjecture, and establish structural and uniqueness properties for (open) level sets of finite Blaschke products that allow us to prove the LSC conjecture in several cases. In particular, we use the geometry of the numerical range to prove the LSC conjecture for compressions of the shift corresponding to unicritical Blaschke products of degree 4. 

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