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1. Transient angle stability of inverters equipped with robust droop control

   https://doi.org/10.17775/CSEEJPES.2019.03140  

   Chen Qi; Keyou Wang; Qing-Chang Zhong; Jin Xu; Guojie Li (March 2023, CSEE Journal of Power and Energy Systems)

   Transient angle stability of inverters equipped with the robust droop controller is investigated in this work. At first, the conditions on the control references to guarantee the existence of a feasible post-disturbance operating point are derived. Then, the post-disturbance equilibrium points are found and their stability properties are characterized. Furthermore, the attraction regions of the stable equilibrium points are accurately depicted by calculating the stable and unstable manifolds of the surrounding unstable equilibrium points, which presents an explanation to system transient stability. Finally, the transient control considerations are provided to help the inverter ride-through the disturbance and maintain its stability characteristics. It is shown that the transient angle stability is not a serious problem for droop controlled inverters with proper control settings. 

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2. Relating Bond Strength and Nature to the Thermodynamic Stability of Hypervalent Togni‐Type Iodine Compounds

   https://doi.org/10.1002/cplu.202100285  

   Oliveira, Vytor_Pinheiro; Marcial, Bruna_Luana; Machado, Francisco_B_C; Kraka, Elfi (August 2021, ChemPlusChem)

   Abstract The bond strength and nature of a set of 32 Togni‐like reagents have been investigated at the M062X/def2‐TZVP(D) level of theory in acetonitrile described with the SMD continuum solvent model, to rationalize the main factors responsible for their thermodynamic stability in different conformations, and trifluoromethylation capabilities. For the assessment of bond strength, we utilized local stretching force constants and associated bond strength orders, complemented with local features of the electron density to access the nature of the bonds. Bond dissociation energies varied from 31.6 to 79.9 kcal/mol depending on the polarizing power of the ligand trans to CF₃. Based on the analysis of the Laplacian of the density, we propose that the charge‐shift bond character plays an important role in the stability of the molecules studied, especially for those containing I−O bonds. New insights on the trans influence and on possible ways to fine‐tune the stability of these reagents are provided. 

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3. K-stability of Fano varieties via admissible flags

   https://doi.org/10.1017/fmp.2022.11  

   Abban, Hamid; Zhuang, Ziquan (January 2022, Forum of Mathematics, Pi)

   Abstract We develop a general approach to prove K-stability of Fano varieties. The new theory is used to (a) prove the existence of Kähler-Einstein metrics on all smooth Fano hypersurfaces of Fano index two, (b) compute the stability thresholds for hypersurfaces at generalised Eckardt points and for cubic surfaces at all points, and (c) provide a new algebraic proof of Tian’s criterion for K-stability, amongst other applications. 

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4. Learning to Optimize Differentiable Games

   Chen, Xuxi; Vadori, Nelson; Chen, Tianlong; Wang, Zhangyang (July 2023, International Conference on Machine Learning)

   Many machine learning problems can be abstracted in solving game theory formulations and boil down to optimizing nested objectives, such as generative adversarial networks (GANs) and multi-agent reinforcement learning. Solving these games requires finding their stable fixed points or Nash equilibrium. However, existing algorithms for solving games suffer from empirical instability, hence demanding heavy ad-hoc tuning in practice. To tackle these challenges, we resort to the emerging scheme of Learning to Optimize (L2O), which discovers problem-specific efficient optimization algorithms through data-driven training. Our customized L2O framework for differentiable game theory problems, dubbed “Learning to Play Games" (L2PG), seeks a stable fixed point solution, by predicting the fast update direction from the past trajectory, with a novel gradient stability-aware, sign-based loss function. We further incorporate curriculum learning and self-learning to strengthen the empirical training stability and generalization of L2PG. On test problems including quadratic games and GANs, L2PG can substantially accelerate the convergence, and demonstrates a remarkably more stable trajectory. Codes are available at https://github.com/VITA-Group/L2PG. 

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5. Computing and optimizing over all fixed-points of discrete systems on large networks

   https://doi.org/10.1098/rsif.2020.0126  

   Riehl, James R.; Zimmerman, Maxwell I.; Singh, Matthew F.; Bowman, Gregory R.; Ching, ShiNung (September 2020, Journal of The Royal Society Interface)

   Equilibria, or fixed points, play an important role in dynamical systems across various domains, yet finding them can be computationally challenging. Here, we show how to efficiently compute all equilibrium points of discrete-valued, discrete-time systems on sparse networks. Using graph partitioning, we recursively decompose the original problem into a set of smaller, simpler problems that are easy to compute, and whose solutions combine to yield the full equilibrium set. This makes it possible to find the fixed points of systems on arbitrarily large networks meeting certain criteria. This approach can also be used without computing the full equilibrium set, which may grow very large in some cases. For example, one can use this method to check the existence and total number of equilibria, or to find equilibria that are optimal with respect to a given cost function. We demonstrate the potential capabilities of this approach with examples in two scientific domains: computing the number of fixed points in brain networks and finding the minimal energy conformations of lattice-based protein folding models. 

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