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1. The eigensplitting of the fiber of the cyclotomic trace for the sphere spectrum

   https://doi.org/10.1090/tran/8822  

   Blumberg, Andrew; Mandell, Michael (January 2022, Transactions of the American Mathematical Society)

   Let p ∈ Z p\in {\mathbb {Z}} be an odd prime. We show that the fiber sequence for the cyclotomic trace of the sphere spectrum S {\mathbb {S}} admits an “eigensplitting” that generalizes known splittings on K K -theory and T C TC . We identify the summands in the fiber as the covers of Z p {\mathbb {Z}}_{p} -Anderson duals of summands in the K ( 1 ) K(1) -localized algebraic K K -theory of Z {\mathbb {Z}} . Analogous results hold for the ring Z {\mathbb {Z}} where we prove that the K ( 1 ) K(1) -localized fiber sequence is self-dual for Z p {\mathbb {Z}}_{p} -Anderson duality, with the duality permuting the summands by i ↦ p − i i\mapsto p-i (indexed mod p − 1 p-1 ). We explain an intrinsic characterization of the summand we call Z Z in the splitting T C ( Z ) p ∧ ≃ j ∨ Σ j ′ ∨ Z TC({\mathbb {Z}})^{\wedge }_{p}\simeq j \vee \Sigma j’\vee Z in terms of units in the p p -cyclotomic tower of Q p {\mathbb {Q}}_{p} . 

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2. THE BOUNDARY OF THE p -RANK STRATUM OF THE MODULI SPACE OF CYCLIC COVERS OF THE PROJECTIVE LINE

   https://doi.org/10.1017/nmj.2022.12  

   OZMAN, EKIN; PRIES, RACHEL; WEIR, COLIN (December 2022, Nagoya Mathematical Journal)

   Abstract. We study the p-rank stratification of the moduli space of cyclic degree ! covers of the projective line in characteristic p for distinct primes p and !. The main result is about the intersection of the p-rank 0 stratum with the boundary of the moduli space of curves. When ! = 3 and p ≡ 2 mod 3 is an odd prime, we prove that there exists a smooth trielliptic curve in characteristic p, for every genus g, signature type (r,s), and p-rank f satisfying the clear necessary conditions. 

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3. Mapping the uneven geographies of digital phenomena: The case of blockchain

   https://doi.org/10.1111/cag.12738  

   Zook, Matthew; McCanless, Michael (December 2021, Canadian Geographies / Géographies canadiennes)

   Key messages Grounding practices within the materiality of geography is an important technique for studying the complexity of digital phenomena.The DIGO (Discourses, Infrastructures, Groupings, and Outcomes) framework uses these categories to guide data selection for locating digital phenomenon in material geographies.This article applies the DIGO framework to blockchain (using data about tweets, miners, firms, and ICOs) to show how this digital practice connects to and across material geographies. 

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4. The application of metacommunity theory to the management of riverine ecosystems

   https://doi.org/10.1002/wat2.1557  

   Patrick, Christopher J.; Anderson, Kurt E.; Brown, Brown L.; Hawkins, Charles P.; Metcalfe, Anya; Saffarinia, Parsa; Siqueira, Tadeu; Swan, Christopher M.; Tonkin, Jonathan D.; Yuan, Lester L. (September 2021, WIREs Water)

   Abstract River managers strive to use the best available science to sustain biodiversity and ecosystem function. To achieve this goal requires consideration of processes at different scales. Metacommunity theory describes how multiple species from different communities potentially interact with local‐scale environmental drivers to influence population dynamics and community structure. However, this body of knowledge has only rarely been used to inform management practices for river ecosystems. In this article, we present a conceptual model outlining how the metacommunity processes of local niche sorting and dispersal can influence the outcomes of management interventions and provide a series of specific recommendations for applying these ideas as well as research needs. In all cases, we identify situations where traditional approaches to riverine management could be enhanced by incorporating an understanding of metacommunity dynamics. A common theme is developing guidelines for assessing the metacommunity context of a site or region, evaluating how that context may affect the desired outcome, and incorporating that understanding into the planning process and methods used. To maximize the effectiveness of management activities, scientists, and resource managers should update the toolbox of approaches to riverine management to reflect theoretical advances in metacommunity ecology. This article is categorized under:Water and Life > Nature of Freshwater EcosystemsWater and Life > Conservation, Management, and AwarenessWater and Life > Methods 

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5. The determination of leaf size on the basis of developmental traits

   https://doi.org/10.1111/nph.20461  

   Ma, Zeqing; Buckley, Thomas_N; Sack, Lawren (February 2025, New Phytologist)

   Summary Mature leaf area (LA) is a showcase of diversity – varying enormously within and across species, and associated with the productivity and distribution of plants and ecosystems. Yet, it remains unclear how developmental processes determine variation in LA.We introduce a mathematical framework pinpointing the origin of variation in LA by quantifying six epidermal ‘developmental traits’: initial mean cell size and number (approximating values within the leaf primordium), and the maximum relative rates and durations of cell proliferation and expansion until leaf maturity. We analyzed a novel database of developmental trajectories of LA and epidermal anatomy, representing 12 eudicotyledonous species and 52 Arabidopsis experiments.Within and across species, mean primordium cell number and maximum relative cell proliferation rate were the strongest developmental determinants of LA. Trade‐offs between developmental traits, consistent with evolutionary and metabolic scaling theory, strongly constrain LA variation. These include trade‐offs between primordium cell number vs cell proliferation, primordium mean cell size vs cell expansion, and the durations vs maximum relative rates of cell proliferation and expansion. Mutant and wild‐type comparisons showed these trade‐offs have a genetic basis in Arabidopsis.Analyses of developmental traits underlying LA and its diversification highlight mechanisms for leaf evolution, and opportunities for breeding trait shifts. 

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