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1. Pairing symmetry and fermion projective symmetry groups

   https://doi.org/10.21468/SciPostPhys.17.6.161  

   Yang, Xu; Biswas, Sayak; Lu, Shuangyuan; Randeria, Mohit; Lu, Yuan-Ming (January 2024, SciPost Physics)

   The Ginzburg-Landau (GL) theory is very successful in describing the pairing symmetry, a fundamental characterization of the broken symmetries in a paired superfluid or superconductor. However, GL theory does not describe fermionic excitations such as Bogoliubov quasiparticles or Andreev bound states that are directly related to topological properties of the superconductor. In this work, we show that the symmetries of the fermionic excitations are captured by a Projective Symmetry Group (PSG), which is a group extension of the bosonic symmetry group in the superconducting state. We further establish a correspondence between the pairing symmetry and the fermion PSG. When the normal and superconducting states share the same spin rotational symmetry, there is a simpler correspondence between the pairing symmetry and the fermion PSG, which we enumerate for all 32 crystalline point groups. We also discuss the general framework for computing PSGs when the spin rotational symmetry is spontaneously broken in the superconducting state. This PSG formalism leads to experimental consequences, and as an example, we show how a given pairing symmetry dictates the classification of topological superconductivity. 

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2. Any-axis Tensegrity Rolling via Bootstrapped Learning and Symmetry Reduction

   Surovik, David; Bruce, Jonathan; Wang, Kun; Vespignani, Massimo; Bekris, Kostas E (November 2018, International Symposium on Experimental Robotics (ISER))

   Tensegrity rovers incorporate design principles that give rise to many desirable properties, such as adaptability and robustness, while also creating challenges in terms of locomotion control. A recent milestone in this area combined reinforcement learning and optimal control to effect fixed-axis rolling of NASA’s 6-bar spherical tensegrity rover prototype, SUPERball, with use of 12 actuators. The new 24-actuator version of SUPERball presents the potential for greatly increased locomotive abilities, but at a drastic nominal increase in the size of the data-driven control problem. This paper is focused upon unlocking those abilities while crucially moderating data requirements by incorporating symmetry reduction into the controller design pipeline, along with other new considerations. Experiments in simulation and on the hardware prototype demonstrate the resulting capability for any-axis rolling on the 24-actuator version of SUPERball, such that it may utilize diverse ground-contact patterns to smoothly locomote in arbitrary directions. 

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3. Geolocating Tweets in any Language at any Location

   https://doi.org/10.1145/3357384.3357926  

   Izbicki, Mike; Papalexakis, Vagelis; Tsotras, Vassilis (November 2019, Proceedings of the 28th ACM International Conference on Information and Knowledge Management)
4. Omniflow: Any-to-any generation with multi-modal rectified flows

   Li, Shufan; Kallidromitis, Konstantinos; Gokul, Akash; Liao, Zichun; Kato, Yusuke; Kozuka, Kazuki; Grover, Aditya (June 2025, IEEE / CVF Computer Vision and Pattern Recognition Conference)
5. Any-Width Networks

   https://doi.org/10.1109/CVPRW50498.2020.00360  

   Vu, Thanh; Eder, Marc; Price, True; Frahm, Jan-Michael (June 2020, he IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops)

   null (Ed.)

   Despite remarkable improvements in speed and accuracy, convolutional neural networks (CNNs) still typically operate as monolithic entities at inference time. This poses a challenge for resource-constrained practical applications, where both computational budgets and performance needs can vary with the situation. To address these constraints, we propose the Any-Width Network (AWN), an adjustable-width CNN architecture and associated training routine that allow for fine-grained control over speed and accuracy during inference. Our key innovation is the use of lower-triangular weight matrices which explicitly address width-varying batch statistics while being naturally suited for multi-width operations. We also show that this design facilitates an efficient training routine based on random width sampling. We empirically demonstrate that our proposed AWNs compare favorably to existing methods while providing maximally granular control during inference. 

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