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1. Adelic Rogers integral formula

   https://doi.org/10.1112/jlms.12830  

   Kim, Seungki (January 2024, Journal of the London Mathematical Society)

   Abstract We formulate and prove the extension of the Rogers integral formula (Rogers [Acta Math.94(1955), 249–287]) to the adeles of number fields. We also prove the second moment formulas for a few important cases, enabling a number of classical and recent applications of the formula to extend immediately to any number field. 

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2. Methods for Discerning the Impact of Mucus on Host Defenses Against Viral Infection

   https://doi.org/10.1002/cpz1.70201  

   Corkran, Maria; Boboltz, Allison; Duncan, Gregg A; Scull, Margaret A (September 2025, Current Protocols)

   Abstract Mucus is an important component of airway host defenses that acts by enabling the trapping and clearance of infectious materials such as bacteria and viruses. It can be difficult, however, to design experiments that independently determine the extent to which mucus contributes to innate barrier functions in the lung. Here, we provide detailed protocols to collect mucus from human airway epithelial cultures and evaluate how the properties of mucus impact mucociliary transport and protection from viral infection. We include recommended test parameters depending on the specific research question as it relates to respiratory infectious diseases. © 2025 The Author(s). Current Protocols published by Wiley Periodicals LLC. Basic Protocol 1: Analysis of mucociliary transport and ciliary beat frequency in HAE cultures Basic Protocol 2: Collection of mucus from HAE cultures Basic Protocol 3: Transplantation of mucus to HAE cultures and infection with virus 

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3. Piikun: an information theoretic toolkit for analysis and visualization of species delimitation metric space

   https://doi.org/10.1186/s12859-024-05997-y  

   Sukumaran, Jeet; Meila, Marina (December 2024, BMC Bioinformatics)

   Abstract <bold>Background</bold>Existing software for comparison of species delimitation models do not provide a (true) metric or distance functions between species delimitation models, nor a way to compare these models in terms of relative clustering differences along a lattice of partitions. <bold>Results</bold>is a Python package for analyzing and visualizing species delimitation models in an information theoretic framework that, in addition to classic measures of information such as the entropy and mutual information [1], provides for the calculation of the Variation of Information (VI) criterion [2], a true metric or distance function for species delimitation models that is aligned with the lattice of partitions. <bold>Conclusions</bold>is available under the MIT license from its public repository (https://github.com/jeetsukumaran/piikun), and can be installed locally using the Python package manager ‘pip‘. 

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4. Infinite flags and Schubert polynomials

   https://doi.org/10.1017/fms.2024.99  

   Anderson, David (January 2025, Forum of Mathematics, Sigma)

   Abstract We study Schubert polynomials using geometry of infinite-dimensional flag varieties and degeneracy loci. Applications include Graham-positivity of coefficients appearing in equivariant coproduct formulas and expansions of back-stable and enriched Schubert polynomials. We also construct an embedding of the type C flag variety and study the corresponding pullback map on (equivariant) cohomology rings. 

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5. Green and Atom Economical Route to High Compressive Strength Lignin Oil-Sulfur Composites

   https://doi.org/10.1007/s10924-024-03287-5  

   Tisdale, Katelyn A; Dona, Nawoda_L Kapuge; Maladeniya, Charini P; Smith, Rhett C (April 2024, Journal of Polymers and the Environment)

   Abstract Lignin is the most abundant natural source of aromatics but remains underutilized. Elemental sulfur is a plentiful by-product of fossil fuel refining. Herein we report a strategy for preparing a durable composite by the one-pot reaction of elemental sulfur and lignin oil comprising lower molecular weight lignin derivatives. A lignin oil-sulfur composite (LOS₉₀) was prepared by reacting 10 wt. % lignin oil with 90 wt. % elemental sulfur. The composite could be remelted and reshaped over several cycles without loss of properties. Results from the study showed thatLOS₉₀has properties competitive with or exceeding values for commercial ordinary Portland cement and brick formulations. For example,LOS₉₀displayed impressive compressive strength (22.1 MPa) and flexural strength (5.7 MPa).LOS₉₀is prepared entirely from waste materials with 98.5% atom economy of composite synthesis, a lowEfactor of 0.057, and lignin char as the only waste product of the process for its preparation. These results suggest the potential applications of lignin and waste sulfur in the continuous efforts to develop more recyclable and sustainable materials. 

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