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1. North Temperate Lakes LTER: Phytoplankton - Madison Lakes Area 1995 - current

   https://doi.org/10.6073/pasta/bd03330e83fc52a5442bb39e131c95e9  

   Magnuson, John J. ; Carpenter, Stephen R. ; Stanley, Emily H. ( January 2022 , Environmental Data Initiative)

   Phytoplankton samples for the 4 southern Wisconsin LTER lakes (Mendota, Monona, Wingra, Fish) have been collected for analysis by LTER since 1995 (1996 Wingra, Fish) when the southern Wisconsin lakes were added to the North Temperate Lakes LTER project. Samples are collected as a composite whole-water sample and are preserved in gluteraldehyde. Composite sample depths are 0-8 meters for Lake Mendota (to conform to samples collected and analyzed since 1990 for a UW/DNR food web research study), and 0-2 meters for the other three lakes. A tube sampler is used for the 0-8 m Lake Mendota samples; samples for the other lakes are obtained by collecting water at 1-meter intervals using a Kemmerer water sampler and compositing the samples in a bucket. Samples are taken in the deep hole region of each lake at the same time and location as other limnological sampling. Phytoplankton samples are analyzed by PhycoTech, Inc., a private lab specializing in phytoplankton analyses (see data protocol for procedures). Samples for Wingra and Fish lakes are archived but not routinely counted. Permanent slide mounts (3 per sample) are prepared for all analyzed Mendota and Monona samples as well as 6 samples per year for Wingra and Fish; the slide mounts are archived at the University of Wisconsin - Madison Zoology Museum. Phytoplankton are identified to species using an inverted microscope (Utermohl technique) and are reported as natural unit (i.e., colonies, filaments, or single cells) densities per mL, cell densities per mL, and algal biovolume densities per mL. Multiple entries for the same species on the same date may be due to different variants or vegetative states - (e.g., colonial or attached vs. free cell.) Biovolumes for individual cells of each species are determined during the counting procedure by obtaining cell measurements needed to calculate volumes for geometric solids (e.g., cylinders, spheres, truncated cones) corresponding to actual cell shapes. Biovolume concentrations are then computed by mulitplying the average cell biovolume by the cell densities in the water sample. Note that one million cubicMicrometers of biovolume PerMilliliter of water are equal to a biovolume concentration of one cubicMillimeterPerMilliliter. Assuming a cell density equal to water, a cubicMillimeterPerMilliliter of biovolume converts to a biomass concentration of one milligramPerLiter. Sampling Frequency: bi-weekly during ice-free season from late March or early April through early September, then every 4 weeks through late November; sampling is conducted usually once during the winter (depending on ice conditions). Number of sites: 4 Several taxonomic updates have been made to this dataset February 2013, see methods for details. 

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2. Stable homotopy groups of spheres

   https://doi.org/10.1073/pnas.2012335117  

   Isaksen, Daniel C. ; Wang, Guozhen ; Xu, Zhouli ( September 2020 , Proceedings of the National Academy of Sciences)

   We discuss the current state of knowledge of stable homotopy groups of spheres. We describe a computational method using motivic homotopy theory, viewed as a deformation of classical homotopy theory. This yields a streamlined computation of the first 61 stable homotopy groups and gives information about the stable homotopy groups in dimensions 62 through 90. As an application, we determine the groups of homotopy spheres that classify smooth structures on spheres through dimension 90, except for dimension 4. The method relies more heavily on machine computations than previous methods and is therefore less prone to error. The main mathematical tool is the Adams spectral sequence.

    

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3. On the classification of 5d SCFTs

   https://doi.org/10.1007/JHEP09(2020)007  

   Bhardwaj, Lakshya ( September 2019 , ArXivorg)

   We determine all 5d SCFTs upto rank three by studying RG flows of 5d KK theories. Our analysis reveals the existence of new rank one and rank two 5d SCFTs not captured by previous classifications. In addition to that, we provide for the first time a systematic and conjecturally complete classification of rank three 5d SCFTs. Our methods are based on a recently studied geometric description of 5d KK theories, thus demonstrating the utility of these geometric descriptions. It is straightforward, though computationally intensive, to extend this work and systematically classify 5d SCFTs of higher ranks (greater than or equal to four) by using the geometric description of 5d KK theories. 

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4. Two Applications of Nilpotent Higgsing in Class-S

   Distler, Jacques ; Elliot, Grant ( March 2022 , ArXivorg)

   We introduce a class of Higgs-branch RG flows in theories of class-S, which flow between d = 4 N = 2 SCFTs of the same ADE type. We discuss two applications of this class of RG flows: 1) determining the current-algebra levels in SCFTs where they were previously unknown — a program we carry out for the class-S theories of type E6 and E7 — and 2) constructing a multitude of examples of pairs of N = 2 SCFTs whose “conventional invariants” coincide. We disprove the conjecture of [1] that the global form of the flavour symmetry group is a reliable diagnostic for determining when two such theories are isomorphic. 

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5. Punctured groups for exotic fusion systems

   https://doi.org/10.1112/tlm3.12054  

   Henke, Ellen ; Libman, Assaf ; Lynd, Justin ( December 2023 , Transactions of the London Mathematical Society)

   Abstract The transporter systems of Oliver and Ventura and the localities of Chermak are classes of algebraic structures that model the ‐local structures of finite groups. Other than the transporter categories and localities of finite groups, important examples include centric, quasicentric, and subcentric linking systems for saturated fusion systems. These examples are, however, not defined in general on the full collection of subgroups of the Sylow group. We study here punctured groups , a short name for transporter systems or localities on the collection of nonidentity subgroups of a finite ‐group. As an application of the existence of a punctured group, we show that the subgroup homology decomposition on the centric collection is sharp for the fusion system. We also prove a Signalizer Functor Theorem for punctured groups and use it to show that the smallest Benson–Solomon exotic fusion system at the prime 2 has a punctured group, while the others do not. As for exotic fusion systems at odd primes , we survey several classes and find that in almost all cases, either the subcentric linking system is a punctured group for the system, or the system has no punctured group because the normalizer of some subgroup of order is exotic. Finally, we classify punctured groups restricting to the centric linking system for certain fusion systems on extraspecial ‐groups of order . 

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