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1. Reconstruction of the Crossing Type of a Point Set from the Compatible Exchange Graph of Noncrossing Spanning Trees

   https://doi.org/10.1007/978-3-030-14085-4_19  

   Marcos Oropeza, Csaba D. (February 2019, International Conference on Discrete Geometry for Computer Imagery)

   Let P be a set of n points in the plane in general position. The order type of P specifies, for every ordered triple, a positive or negative orientation; and the x-type (a.k.a. crossing type) of P specifies, for every unordered 4-tuple, whether they are in convex position. Geometric algorithms on P typically rely on primitives involving the order type or x-type (i.e., triples or 4-tuples). In this paper, we show that the x-type of P can be reconstructed from the compatible exchange graph G1(P) of noncrossing spanning trees on P. This extends a recent result by Keller and Perles (2016), who proved that the x-type of P can be reconstructed from the exchange graph G0(P) of noncrossing spanning trees, where G1(P) is a subgraph of G0(P) . A crucial ingredient of our proof is a structure theorem on the maximal sets of pairwise noncrossing edges (msnes) between two components of a planar straight-line graph on the point set P. 

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2. Data from: Ecological diversification in an adaptive radiation of plants: the role of de novo mutation and introgression

   https://doi.org/10.6084/m9.figshare.24480499  

   Stone, Benjamin; Wessinger, Carolyn A. (January 2023, figshare)

   Data from: Stone and Wessinger 2023, "Ecological diversification in an adaptive radiation of plants: the role of de novo mutation and introgression"DOI: 10.1101/2023.11.01.565185The code used to conduct analyses from this study can be found here: https://github.com/benstemon/MBE-23-0936The raw sequencing reads generated from this study have been deposited on the SRA under Project number: PRJNA1057825This repository contains a README.md file, which contains information on all files included. 

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3. An update of the development of motor behavior

   https://doi.org/10.1002/wcs.1682  

   Franchak, John_M; Adolph, Karen_E (June 2024, WIREs Cognitive Science)

   Abstract This primer describes research on the development of motor behavior. We focus on infancy when basic action systems are acquired—posture, locomotion, manual actions, and facial actions—and we adopt a developmental systems perspective to understand the causes and consequences of developmental change. Experience facilitates improvements in motor behavior and infants accumulate immense amounts of varied everyday experience with all the basic action systems. At every point in development, perception guides behavior by providing feedback about the results of just prior movements and information about what to do next. Across development, new motor behaviors provide new inputs for perception. Thus, motor development opens up new opportunities for acquiring knowledge and acting on the world, instigating cascades of developmental changes in perceptual, cognitive, and social domains. This article is categorized under:Cognitive Biology > Cognitive DevelopmentPsychology > Motor Skill and PerformanceNeuroscience > Development 

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4. Cellular pavings of fibers of convolution morphisms

   https://doi.org/10.46298/epiga.2024.12352  

   Haines, Thomas J (May 2025, Épijournal de Géométrie Algébrique)

   This article proves, in the case of split groups over arbitrary fields, that all fibers of convolution morphisms attached to parahoric affine flag varieties are paved by products of affine lines and affine lines minus a point. This applies in particular to the affine Grassmannian and to the convolution morphisms in the context of the geometric Satake correspondence. The second part of the article extends these results over $$\mathbb Z$$. Those in turn relate to the recent work of Cass-van den Hove-Scholbach on the geometric Satake equivalence for integral motives, and provide some alternative proofs for some of their results. Comment: 24 pages. Minor error corrected with the addition of Lemma 7.2. Lemma 7.3 added. Material on triviality of morphisms added to section 5. Minor changes in notation. Published version 

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5. On L ₁ -Embeddability of Unions of L ₁ -Embeddable Metric Spaces and of Twisted Unions of Hypercubes

   https://doi.org/10.1515/agms-2022-0145  

   Ostrovskii, Mikhail I.; Randrianantoanina, Beata (January 2022, Analysis and Geometry in Metric Spaces)

   Abstract We study properties of twisted unions of metric spaces introduced in [Johnson, Lindenstrauss, and Schechtman 1986], and in [Naor and Rabani 2017]. In particular, we prove that under certain natural mild assumptions twisted unions of L 1 -embeddable metric spaces also embed in L 1 with distortions bounded above by constants that do not depend on the metric spaces themselves, or on their size, but only on certain general parameters. This answers a question stated in [Naor 2015] and in [Naor and Rabani 2017]. In the second part of the paper we give new simple examples of metric spaces such that their every embedding into L p , 1 ≤ p < ∞, has distortion at least 3, but which are a union of two subsets, each isometrically embeddable in L p . This extends the result of [K. Makarychev and Y. Makarychev 2016] from Hilbert spaces to L p -spaces, 1 ≤ p < ∞. 

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