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1. Dedekind sums arising from newform Eisenstein series

   https://doi.org/10.1142/S1793042120501092  

   Stucker, T.; Vennos, A.; Young, M. P. (November 2020, International Journal of Number Theory)

   For primitive nontrivial Dirichlet characters [Formula: see text] and [Formula: see text], we study the weight zero newform Eisenstein series [Formula: see text] at [Formula: see text]. The holomorphic part of this function has a transformation rule that we express in finite terms as a generalized Dedekind sum. This gives rise to the explicit construction (in finite terms) of elements of [Formula: see text]. We also give a short proof of the reciprocity formula for this Dedekind sum. 

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2. Scattering diagrams, tight gradings, and generalized positivity

   https://doi.org/10.1073/pnas.2422893122  

   Burcroff, Amanda; Lee, Kyungyong; Mou, Lang (May 2025, Proceedings of the National Academy of Sciences)

   In 2013, Lee, Li, and Zelevinsky introduced combinatorial objects called compatible pairs to construct the greedy bases for rank-2 cluster algebras, consisting of indecomposable positive elements including the cluster monomials. Subsequently, Rupel extended this construction to the setting of generalized rank-2 cluster algebras by defining compatible gradings. We find a class of combinatorial objects which we call tight gradings. Using this, we give a directly computable, manifestly positive, and elementary but highly nontrivial formula describing rank-2 consistent scattering diagrams. This allows us to show that the coefficients of the wall-functions on a generalized cluster scattering diagram of any rank are positive, which implies the Laurent positivity for generalized cluster algebras and the strong positivity of their theta bases. 

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3. New structure on the quantum alcove model with applications to representation theory and Schubert calculus

   https://doi.org/10.4171/JCA/77  

   Kouno, Takafumi; Lenart, Cristian; Naito, Satoshi (November 2023, Journal of Combinatorial Algebra)

   NA (Ed.)

   The quantum alcove model associated to a dominant weight plays an important role in many branches of mathematics, such as combinatorial representation theory, the theory of Macdonald polynomials, and Schubert calculus. For a dominant weight, it is proved by Lenart–Lubovsky that the quantum alcove model does not depend on the choice of a reduced alcove path, which is a shortest path of alcoves from the fundamental one to its translation by the given dominant weight. This is established through quantum Yang–Baxter moves, which biject the objects of the models associated to two such alcove paths, and can be viewed as a generalization of jeu de taquin slides to arbitrary root systems. The purpose of this paper is to give a generalization of quantum Yang–Baxter moves to the quantum alcove model corresponding to an arbitrary weight, which was used to express a general Chevalley formula for the equivariantK-group of semi-infinite flag manifolds. The generalized quantum Yang–Baxter moves give rise to a “sijection” (bijection between signed sets), and are shown to preserve certain important statistics, including weights and heights. As an application, we prove that the generating function of these statistics does not depend on the choice of a reduced alcove path. Also, we obtain an identity for the graded characters of Demazure submodules of level-zero extremal weight modules over a quantum affine algebra, which can be thought of as a representation-theoretic analogue of the mentioned Chevalley formula. 

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4. Dynamic capillary stalls in reperfused ischemic penumbra contribute to injury: A hyperacute role for neutrophils in persistent traffic jams

   https://doi.org/10.1177/0271678X20914179  

   Erdener, Şefik E; Tang, Jianbo; Kılıç, Kıvılcım; Postnov, Dmitry; Giblin, John T; Kura, Sreekanth; Chen, I-chun A; Vayisoğlu, Tuğberk; Sakadžić, Sava; Schaffer, Chris B; et al (February 2021, Journal of Cerebral Blood Flow & Metabolism)

   null (Ed.)

   Ever since the introduction of thrombolysis and the subsequent expansion of endovascular treatments for acute ischemic stroke, it remains to be identified why the actual outcomes are less favorable despite recanalization. Here, by high spatio-temporal resolution imaging of capillary circulation in mice, we introduce the pathological phenomenon of dynamic flow stalls in cerebral capillaries, occurring persistently in salvageable penumbra after reperfusion. These stalls, which are different from permanent cellular plugs of no-reflow, were temporarily and repetitively occurring in the capillary network, impairing the overall circulation like small focal traffic jams. In vivo microscopy in the ischemic penumbra revealed leukocytes traveling slowly through capillary lumen or getting stuck, while red blood cell flow was being disturbed in the neighboring segments under reperfused conditions. Stall dynamics could be modulated, by injection of an anti-Ly6G antibody specifically targeting neutrophils. Decreased number and duration of stalls were associated with improvement in penumbral blood flow within 2–24 h after reperfusion along with increased capillary oxygenation, decreased cellular damage and improved functional outcome. Thereby, dynamic microcirculatory stall phenomenon can be a contributing factor to ongoing penumbral injury and is a potential hyperacute mechanism adding on previous observations of detrimental effects of activated neutrophils in ischemic stroke. 

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5. Enhanced Three-minute Oscillation above a Sunspot during a Solar Flare

   https://doi.org/10.3847/1538-4357/ad10a9  

   Wang, Ya; Fletcher, Lyndsay; Mulay, Sargam; Ji, Haisheng; Cao, Wenda (January 2024, The Astrophysical Journal)

   Abstract Three-minute oscillations are a common phenomenon in the solar chromosphere above a sunspot. Oscillations can be affected by the energy release process related to solar flares. In this paper, we report on an enhanced oscillation in flare event SOL2012-07-05T21:42 with a period of around 3 minutes that occurred at the location of a flare ribbon at a sunspot umbral–penumbral boundary and was observed in both chromospheric and coronal passbands. An analysis of this oscillation was carried out using simultaneous ground-based observations from the Goode Solar Telescope at the Big Bear Solar Observatory and space-based observations from the Solar Dynamics Observatory. A frequency shift was observed before and after the flare, with the running penumbral wave that was present with a period of about 200 s before the flare coexisting with a strengthened oscillation with a period of 180 s at the same locations after the flare. We also found a phase difference between different passbands, with the oscillation occurring from high-temperature to low-temperature passbands. Theoretically, the change in frequency was strongly dependent on the variation of the inclination of the magnetic field and the chromospheric temperature. Following an analysis of the properties of the region, we found the frequency change was caused by a slight decrease of the magnetic inclination angle with respect to the local vertical. In addition, we suggest that the enhanced 3 minute oscillation was related to the additional heating, maybe due to the downflow, during the EUV late phase of the flare. 

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