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1. Perdew Festschrift editorial

   https://doi.org/10.1063/5.0217719  

   Burke, Kieron; Sun, Jianwei; Yang, Weitao (June 2024, The Journal of Chemical Physics)

   This Special Issue of the Journal of Chemical Physics is dedicated to the work and life of John P. Perdew. A short bio is available within the issue [J. P. Perdew, J. Chem. Phys. 160, 010402 (2024)]. Here, we briefly summarize key publications in density functional theory by Perdew and his collaborators, followed by a structured guide to the papers contributed to this Special Issue. 

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2. The Terminator: An Integration of Inner and Outer Approximations for Solving Wasserstein Distributionally Robust Chance Constrained Programs via Variable Fixing

   https://doi.org/10.1287/ijoc.2023.0299  

   Jiang, Nan; Xie, Weijun (June 2024, INFORMS Journal on Computing)

   We present a novel approach aimed at enhancing the efficacy of solving both regular and distributionally robust chance constrained programs using an empirical reference distribution. In general, these programs can be reformulated as mixed-integer programs (MIPs) by introducing binary variables for each scenario, indicating whether a scenario should be satisfied. Whereas existing methods have focused predominantly on either inner or outer approximations, this paper bridges this gap by studying a scheme that effectively combines these approximations via variable fixing. By checking the restricted outer approximations and comparing them with the inner approximations, we derive optimality cuts that can notably reduce the number of binary variables by effectively setting them to either one or zero. We conduct a theoretical analysis of variable fixing techniques, deriving an asymptotic closed-form expression. This expression quantifies the proportion of binary variables that should be optimally fixed to zero. Our empirical results showcase the advantages of our approach in terms of both computational efficiency and solution quality. Notably, we solve all the tested instances from literature to optimality, signifying the robustness and effectiveness of our proposed approach. History: Accepted by Andrea Lodi/Design & Analysis of Algorithms — Discrete. Funding: This work was supported by Office of Naval Research [N00014-24-1-2066]; Division of Civil, Mechanical and Manufacturing Innovation [2246414]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0299 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0299 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ . 

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3. Desingularization and p-Curvature of Recurrence Operators

   https://doi.org/10.1145/3476446.3535478  

   Zhou, Yi; van Hoeij, Mark (July 2022, ISSAC'2022)

   Linear recurrence operators in characteristic p are classified by their p-curvature. For a recurrence operator L, denote by χ(L) the characteristic polynomial of its p-curvature. We can obtain information about the factorization of L by factoring χ(L). The main theorem of this paper gives an unexpected relation between χ(L) and the true singularities of L. An application is to speed up a fast algorithm for computing χ(L) by desingularizing L first. Another contribution of this paper is faster desingularization. 

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4. The Origin of Universality in the Inner Edges of Planetary Systems

   https://doi.org/10.3847/2041-8213/acdb5d  

   Batygin, Konstantin; Adams, Fred C.; Becker, Juliette (July 2023, The Astrophysical Journal Letters)

   Abstract The characteristic orbital period of the innermost objects within the galactic census of planetary and satellite systems appears to be nearly universal, withPon the order of a few days. This paper presents a theoretical framework that provides a simple explanation for this phenomenon. By considering the interplay between disk accretion, magnetic field generation by convective dynamos, and Kelvin–Helmholtz contraction, we derive an expression for the magnetospheric truncation radius in astrophysical disks and find that the corresponding orbital frequency is independent of the mass of the host body. Our analysis demonstrates that this characteristic frequency corresponds to a period ofP∼ 3 days although intrinsic variations in system parameters are expected to introduce a factor of a ∼2–3 spread in this result. Standard theory of orbital migration further suggests that planets should stabilize at an orbital period that exceeds disk truncation by a small margin. Cumulatively, our findings predict that the periods of close-in bodies should spanP∼ 2–12 days—a range that is consistent with observations. 

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5. Acceleration methods for fixed-point iterations

   https://doi.org/10.1017/S0962492924000096  

   Saad, Yousef (July 2025, Acta Numerica)

   A pervasive approach in scientific computing is to express the solution to a given problem as the limit of a sequence of vectors or other mathematical objects. In many situations these sequences are generated by slowly converging iterative procedures, and this led practitioners to seek faster alternatives to reach the limit. ‘Acceleration techniques’ comprise a broad array of methods specifically designed with this goal in mind. They started as a means of improving the convergence of general scalar sequences by various forms of ‘extrapolation to the limit’, i.e. by extrapolating the most recent iterates to the limit via linear combinations. Extrapolation methods of this type, the best-known of which is Aitken’s delta-squared process, require only the sequence of vectors as input. However, limiting methods to use only the iterates is too restrictive. Accelerating sequences generated by fixed-point iterations by utilizing both the iterates and the fixed-point mapping itself has proved highly successful across various areas of physics. A notable example of these fixed-point accelerators (FP-accelerators) is a method developed by Donald Anderson in 1965 and now widely known as Anderson acceleration (AA). Furthermore, quasi-Newton and inexact Newton methods can also be placed in this category since they can be invoked to find limits of fixed-point iteration sequences by employing exactly the same ingredients as those of the FP-accelerators. This paper presents an overview of these methods – with an emphasis on those, such as AA, that are geared toward accelerating fixed-point iterations. We will navigate through existing variants of accelerators, their implementations and their applications, to unravel the close connections between them. These connections were often not recognized by the originators of certain methods, who sometimes stumbled on slight variations of already established ideas. Furthermore, even though new accelerators were invented in different corners of science, the underlying principles behind them are strikingly similar or identical. The plan of this article will approximately follow the historical trajectory of extrapolation and acceleration methods, beginning with a brief description of extrapolation ideas, followed by the special case of linear systems, the application to self-consistent field (SCF) iterations, and a detailed view of Anderson acceleration. The last part of the paper is concerned with more recent developments, including theoretical aspects, and a few thoughts on accelerating machine learning algorithms. 

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