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1. Galois Symmetry Induced by Hecke Relations in Rational Conformal Field Theory and Associated Modular Tensor Categories

   https://doi.org/10.1088/1751-8121/ab8e03  

   Harvey, J.A.; Hu, Y.; Wu, Y. (January 2020, Journal of physics)

   null (Ed.)

   Hecke operators relate characters of rational conformal field theories (RCFTs) with different central charges, and extend the previously studied Galois symmetry of modular representations and fusion algebras. We show that the conductor N of an RCFT and the quadratic residues modulo N play an important role in the computation and classification of Galois permutations. We establish a field correspondence in different theories through the picture of effective central charge, which combines Galois inner automorphisms and the structure of simple currents. We then make a first attempt to extend Hecke operators to the full data of modular tensor categories. The Galois symmetry encountered in the modular data transforms the fusion and the braiding matrices as well, and yields isomorphic structures in theories related by Hecke operators. 

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2. BERM: a Belowground Ecosystem Resiliency Model for estimating Spartina alterniflora belowground biomass

   https://doi.org/10.1111/nph.17607  

   O’Connell, Jessica L.; Mishra, Deepak R.; Alber, Merryl; Byrd, Kristin B. (August 2021, New Phytologist)

   Summary Spatiotemporal patterns ofSpartina alterniflorabelowground biomass (BGB) are important for evaluating salt marsh resiliency. To solve this, we created the BERM (Belowground Ecosystem Resiliency Model), which estimates monthly BGB (30‐m spatial resolution) from freely available data such as Landsat‐8 and Daymet climate summaries.Our modeling framework relied on extreme gradient boosting, and used field observations from four Georgia salt marshes as ground‐truth data. Model predictors included estimated tidal inundation, elevation, leaf area index, foliar nitrogen, chlorophyll, surface temperature, phenology, and climate data. The final model included 33 variables, and the most important variables were elevation, vapor pressure from the previous four months, Normalized Difference Vegetation Index (NDVI) from the previous five months, and inundation.Root mean squared error for BGB from testing data was 313 g m⁻²(11% of the field data range), explained variance (R²) was 0.62–0.77. Testing data results were unbiased across BGB values and were positively correlated with ground‐truth data across all sites and years (r = 0.56–0.82 and 0.45–0.95, respectively).BERM can estimate BGB withinSpartina alterniflorasalt marshes where environmental parameters are within the training data range, and can be readily extended through a reproducible workflow. This provides a powerful approach for evaluating spatiotemporal BGB and associated ecosystem function. 

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3. Quadrilateral mesh generation II: Meromorphic quartic differentials and Abel–Jacobi condition

   https://doi.org/112980  

   Lei, Na; Zheng, Xiaopeng; Luo, Zhongxuan; Luo, Feng; Gu, Xianfeng (July 2020, Computer methods in applied mechanics and engineering)

   null (Ed.)

   This work discovers the equivalence relation between quadrilateral meshes and meromorphic quartic differentials. Each quad-mesh induces a conformal structure of the surface, and a meromorphic quartic differential, where the configuration of singular vertices corresponds to the configurations of the poles and zeros (divisor) of the meromorphic differential. Due to Riemann surface theory, the configuration of singularities of a quad-mesh satisfies the Abel–Jacobi condition. Inversely, if a divisor satisfies the Abel–Jacobi condition, then there exists a meromorphic quartic differential whose divisor equals the given one. Furthermore, if the meromorphic quartic differential is with finite trajectories, then it also induces a quad-mesh, the poles and zeros of the meromorphic differential correspond to the singular vertices of the quad-mesh. Besides the theoretic proofs, the computational algorithm for verification of Abel–Jacobi condition is also explained in detail. Furthermore, constructive algorithm of meromorphic quartic differential on genus zero surfaces is proposed, which is based on the global algebraic representation of meromorphic differentials. Our experimental results demonstrate the efficiency and efficacy of the algorithm. This opens up a novel direction for quad-mesh generation using algebraic geometric approach. 

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4. Quantum codes and irreducible products of characters

   https://doi.org/10.1007/s10623-025-01599-8  

   Kubischta, Eric; Teixeira, Ian (April 2025, Designs, Codes and Cryptography)

   Abstract In a recent paper, we defined a type of weighted unitary design called a twisted unitary 1-group and showed that such a design automatically induced error-detecting quantum codes. We also showed that twisted unitary 1-groups correspond to irreducible products of characters thereby reducing the problem of code-finding to a computation in the character theory of finite groups. Using a combination of GAP computations and results from the mathematics literature on irreducible products of characters, we identify many new non-trivial quantum codes with unusual transversal gates. Transversal gates are of significant interest to the quantum information community for their central role in fault tolerant quantum computing. Most unitary$$\text {t}$$ $\text{t}$-designs have never been realized as the transversal gate group of a quantum code. We, for the first time, find nontrivial quantum codes realizing nearly every finite group which is a unitary 2-design or better as the transversal gate group of some error-detecting quantum code. 

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5. Preliminary Findings of Usability Studies on an Ontology-Aware Taxon-by-Character Matrix Editor

   https://doi.org/10.3897/biss.6.90949  

   Cui, Hong; Ford, Bruce; Starr, Julian; Reznicek, Anton; Zhou, Yuxuan; Gan, Quan; Léveillé-Bourret, Étienne; Lacroix-Carignan, Étienne; Macklin, James; Cayouette, Jacques; et al (August 2022, Biodiversity Information Science and Standards)

   Taxonomic treatments start with the creation of taxon-by-character matrices. Systematics authors recognized data ambiguity issues in published phenotypic characters and are willing to adopt an ontology-aware authoring tool (Cui et al. 2022). To promote interoperable and reusable taxonomic treatments, we have developed two research prototypes: a web-based application, Character Recorder (http://chrecorder.lusites.xyz/login), to faciliate the use and addition of ontology terms by Carex systematist authors while building their matrices, and a mobile application, Conflict Resolver (Android, https://tinyurl.com/5cfatrz8), to identify potential conflicts among the terms added by the authors and facilitate the resolution of the conflicts. We have completed two usability studies on Character Recorder. a web-based application, Character Recorder (http://chrecorder.lusites.xyz/login), to faciliate the use and addition of ontology terms by Carex systematist authors while building their matrices, and a mobile application, Conflict Resolver (Android, https://tinyurl.com/5cfatrz8), to identify potential conflicts among the terms added by the authors and facilitate the resolution of the conflicts. We have completed two usability studies on Character Recorder. In the one-hour Student Usabiilty Study, 16 third-year biology students with a general introduction to Carex used Character Recorder and Excel to record a set of 11 given characters for two samples (shape of sheath summits = U-shaped/U shaped). In the three-day Expert Usability Study, 7 established Carex systematists and 1 graduate student with expert-level knowledge used Character Recorder to record characters for 1 sample each of Carex canesens and Carex rostrata as they would in their professional life, using real mounted specimens, microscope, reticles, and rulers. Experts activities were not timed but they spent roughly 1.5 days on recording the characters and the rest of time discussing features and improvements. Features of Character Recorder have been reported in 2021 TDWG meeting and we included here only a few figures to highlight its interoperability and reusability features at the time of the usability studies (Fig. 1, Fig. 2, and Fig. 3). The Carex Ontology accompanying Character Recorder was created by extracting terms from Carex treatments of Flora of China and Flora of North America using Explorer of Taxon Concept (Cui et al. 2016) with subsequent manual edits. The design principle of Character Recorder is to encourage standardization and also leave the authors the freedom to do their work. While it took students an average of 6 minutes to recover all the given characters using Microsoft® Excel®, as opposed to 11 minutes using Character Recorder, the total number of unique meaning-bearing words used in their characters was 116 with Excel versus 30 with Character Recorder, showing the power of the latter in reducing synonyms and spelling variations. All students reported that they learned to use Character Recorder quickly and some even thought their use was as fast or faster than using Excel. All preferred Character Recorder to Excel for teaching students to record character data. Nearly all of the students found Character Recorder was more useful for recording clear and consistent data and all students agreed that participating in this study raised their awareness of data variation issues. The expert group consisted of 3, 2, 1, 3 experts in age ranges 20-49, 50-59, 60-69, and >69, respectively. They each recorded over 100 characters for two or more samples. Detailed analysis of their characters is pending, but we have noticed color characters have more variations than other characters (Fig. 4). All experts reported that they learned to use Character Recorder quickly, and 6 out of 8 believed they would not need a tutorial the next time they used it. One out of 8 experts somewhat disliked the feature of reusing others' values ("Use This" in Fig. 2) as it may undermine the objectivity and independence of an author. All experts used Recommended Set of Characters and they liked the term suggestion and illustration features shown in Figs 2, 3. All experts would recommend that their colleagues try Character Recorder and recommended that it be further developed and integrated into every taxonomist's toolbox. Student and expert responses to the National Aeronautics and Space Administration Task Load Index (NASA-TLX, Hart and Staveland 1988) are summarized in Fig. 5, which suggests that, while Character Recorder may incur in a slightly higher cost, the performance it supports outweighs its cost, especially for students. Every piece of the software prototypes and associated resources are open for anyone to access or further develop. We thank all student and expert participants and US National Science Foundation for their support in this research. We thank Harris & Harris and Presses de l'Université Laval for the permissions to use their phenotype illustrations in Character Recorder. 

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