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1. Quantum extremal modular curvature: modular transport with islands

   https://doi.org/10.1007/JHEP10(2024)006  

   Aalsma, Lars; Keeler, Cynthia; Zukowski, Claire (October 2024, Journal of High Energy Physics)

   Modular Berry transport is a useful way to understand how geometric bulk information is encoded in the boundary CFT: the modular curvature is directly related to the bulk Riemann curvature. We extend this approach by studying modular transport in the presence of a non-trivial quantum extremal surface. Focusing on JT gravity on an AdS background coupled to a non-gravitating bath, we compute the modular curvature of an interval in the bath in the presence of an island: the Quantum Extremal Modular Curvature (QEMC). We highlight some important properties of the QEMC, most importantly that it is non-local in general. In an OPE limit, the QEMC becomes local and probes the bulk Riemann curvature in regions with an island. Our work gives a new approach to probe physics behind horizons. 

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2. Braided Zestings of Verlinde Modular Categories and Their Modular Data

   https://doi.org/10.1007/s00220-024-05097-1  

   Galindo, César; Mora, Giovanny; Rowell, Eric_C (October 2024, Communications in Mathematical Physics)

   Abstract Zesting of braided fusion categories is a procedure that can be used to obtain new modular categories from a modular category with non-trivial invertible objects. In this paper, we classify and construct all possible braided zesting data for modular categories associated with quantum groups at roots of unity. We produce closed formulas, based on the root system of the associated Lie algebra, for the modular data of these new modular categories. 

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3. Modular ontology modeling

   https://doi.org/10.3233/SW-222886  

   Shimizu, Cogan; Hammar, Karl; Hitzler, Pascal (April 2023, Semantic Web)

   Kirrane, Sabrina; Ngonga Ngomo, Axel-Cyrille; Kirrane, Sabrina; Ngonga Ngomo, Axel-Cyrille (Ed.)

   Reusing ontologies for new purposes, or adapting them to new use-cases, is frequently difficult. In our experiences, we have found this to be the case for several reasons: (i) differing representational granularity in ontologies and in use-cases, (ii) lacking conceptual clarity in potentially reusable ontologies, (iii) lack and difficulty of adherence to good modeling principles, and (iv) a lack of reuse emphasis and process support available in ontology engineering tooling. In order to address these concerns, we have developed the Modular Ontology Modeling (MOMo) methodology, and its supporting tooling infrastructure, CoModIDE (the Comprehensive Modular Ontology IDE – “commodity”). MOMo builds on the established eXtreme Design methodology, and like it emphasizes modular development and design pattern reuse; but crucially adds the extensive use of graphical schema diagrams, and tooling that support them, as vehicles for knowledge elicitation from experts. In this paper, we present the MOMo workflow in detail, and describe several useful resources for executing it. In particular, we provide a thorough and rigorous evaluation of CoModIDE in its role of supporting the MOMo methodology’s graphical modeling paradigm. We find that CoModIDE significantly improves approachability of such a paradigm, and that it displays a high usability. 

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4. Modular Conformal Calibration

   Marx, Charles; Zhao, Shengjia; Neiswanger, Willie; Ermon, Stefano (January 2022, International Conference on Machine Learning)
5. Modular Nori Motives

   https://doi.org/10.1134/S2070046623030020  

   Combe, N C; Manin, Yu I; Marcolli, M (September 2023, p-Adic Numbers, Ultrametric Analysis and Applications)