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1. Loop expansion and the bosonic representation of loop quantum gravity

   https://doi.org/10.1103/PhysRevD.94.086009  

   Bianchi, E.; Guglielmon, J.; Hackl, L.; Yokomizo, N. (October 2016, Physical Review D)
2. Learning Loop Invariants

   https://doi.org/10.1145/3328778.3372715  

   Fowler, Megan (February 2020, SIGCSE '20: Proceedings of the 51st ACM Technical Symposium on Computer Science Education)

   One aspect of developing correct code, code that functions as specified, is annotating loops with suitable invariants. Loop invariants are useful for human reasoning and are necessary for tool-assisted automated reasoning. Writing loop invariants can be a difficult task for all students, especially beginning software engineering students. In helping students learn to write adequate invariants, we need to understand not only what errors they make, but also why they make them. This poster discusses the use of a Web IDE backed by the RESOLVE verification engine to aid students in developing loop invariants and to collect performance data. In addition to collecting submitted invariant answers, students are asked to provide their steps or thought processes regarding how they arrived at their answers for each submission. The answers and reasons are then analyzed using a mixed-methods approach. Resulting categories of answers indicate that students are able to use formal method concepts with which they are already familiar, such as, pre and post-conditions as a starting place to develop adequate loop invariants. Additionally, some common trouble spots in learning to write invariants are identified. The results will be useful to guide classroom instruction and automated tutoring. 

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3. Dynamical loop equation

   https://doi.org/10.1214/24-AOP1685  

   Gorin, Vadim; Huang, Jiaoyang (September 2024, The Annals of Probability)
4. Closing the Loop on Exoskeleton Motor Controllers: Benefits of Regression-Based Open-Loop Control

   https://doi.org/10.1109/LRA.2020.3011370  

   Orekhov, Greg; Luque, Jason; Lerner, Zachary F. (October 2020, IEEE Robotics and Automation Letters)

   null (Ed.)
5. An off-shell Wilson loop

   https://doi.org/10.1007/JHEP04(2023)071  

   Belitsky, A. V.; Smirnov, V. A. (April 2023, Journal of High Energy Physics)

   A bstract It is well-known that on-shell maximally helicity-violating gluon scattering amplitudes in planar maximally supersymmetric Yang-Mills theory are dual to a bosonic Wilson loop on a null-polygonal contour. The light-like nature of the intervals is a reflection of the mass-shell condition for massless gluons involved in scattering. Presently, we introduce a Wilson loop prototype on a piece-wise curvilinear contour that can be interpreted in the T-dual language to correspond to nonvanishing gluon off-shellness. We analyze it first for four sites at one loop and demonstrate that it coincides with the four-gluon amplitude on the Coulomb branch. Encouraged by this fact, we move on to the two-loop order. To simplify our considerations, we only focus on the Sudakov asymptotics of the Wilson loop, when the off-shellness goes to zero. The latter serves as a regulator of short-distance divergences around the perimeter of the loop, i.e., divergences when gluons are integrated over a small vicinity of the Wilson loop cusps. It does not however regulate conventional ultraviolet divergences of interior closed loops. This unavoidably introduces a renormalization scale dependence and thus scheme dependence into the problem. With a choice of the scale setting and a finite renormalization, we observe exponentiation of the double logarithmic scaling of the Wilson loop with the accompanying exponent being given by the so-called hexagon anomalous dimension, which recently made its debut in the origin limit of six-leg gluon amplitudes. This is contrary to the expectation for the octagon anomalous dimension to rather emerge from our analysis suggesting that the current object encodes physics different from the Coulomb branch scattering amplitudes. 

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