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1. Temporal Difference Learning as Gradient Splitting

   Liu, Rui; Olshevsky, Alex (November 2021, International Conference on Machine Learning (ICML))

   Temporal difference learning with linear function approximation is a popular method to obtain a low-dimensional approximation of the value function of a policy in a Markov Decision Process. We give a new interpretation of this method in terms of a splitting of the gradient of an appropriately chosen function. As a consequence of this interpretation, convergence proofs for gradient descent can be applied almost verbatim to temporal difference learning. Beyond giving a new, fuller explanation of why temporal difference works, our interpretation also yields improved convergence times. We consider the setting with 1/T^{1/2} step-size, where previous comparable finite-time convergence time bounds for temporal difference learning had the multiplicative factor 1/(1-\gamma) in front of the bound, with γ being the discount factor. We show that a minor variation on TD learning which estimates the mean of the value function separately has a convergence time where 1/(1-\gamma) only multiplies an asymptotically negligible term. 

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2. Semi-experimental equilibrium ( r e SE) and theoretical structures of hydrazoic acid (HN3)

   https://doi.org/10.1063/5.0101064  

   Owen, Andrew N.; Sahoo, Nitai P.; Esselman, Brian J.; Stanton, John F.; Woods, R. Claude; McMahon, Robert J. (July 2022, The Journal of Chemical Physics)

   Hydrazoic acid (HN3) is used as a case study for investigating the accuracy and precision by which a molecular structure—specifically, a semi-experimental equilibrium structure (reSE)—may be determined using current state-of-the-art methodology. The influence of the theoretical corrections for effects of vibration–rotation coupling and electron-mass distribution that are employed in the analysis is explored in detail. The small size of HN3 allowed us to deploy considerable computational resources to probe the basis-set dependence of these corrections using a series of coupled-cluster single, double, perturbative triple [CCSD(T)] calculations with cc-pCVXZ (X = D, T, Q, 5) basis sets. We extrapolated the resulting corrections to the complete basis set (CBS) limit to obtain CCSD(T)/CBS corrections, which were used in a subsequent reSE structure determination. The reSE parameters obtained using the CCSD(T)/cc-pCV5Z corrections are nearly identical to those obtained using the CCSD(T)/CBS corrections, with uncertainties in the bond distances and angles of less than 0.0006 Å and 0.08°, respectively. The previously obtained reSE structure using CCSD(T)/ANO2 agrees with that using CCSD(T)/cc-pCV5Z to within 0.000 08 Å and 0.016° for bond distances and angles, respectively, and with only 25% larger uncertainties, validating the idea that reSE structure determinations can be carried out with significantly smaller basis sets than those needed for similarly accurate, strictly ab initio determinations. Although the purely computational re structural parameters [CCSD(T)/cc-pCV6Z] fall outside of the statistical uncertainties (2σ) of the corresponding reSE structural parameters, the discrepancy is rectified by applying corrections to address the theoretical limitations of the CCSD(T)/cc-pCV6Z geometry with respect to basis set, electron correlation, relativity, and the Born–Oppenheimer approximation, thereby supporting the contention that the semi-experimental approach is both an accurate and vastly more efficient method for structure determinations than is brute-force computation. 

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3. Reliability of Geosynthetic Reinforced Soil Structure Design with Probabilistic and Finite Element Methods

   Wang, Lei; Tait, Sandae; Shin, Ji Shin; Khoshnevisan, Sara; Gong, Wenping (December 2019, Proceedings of the 7th International Symposium on Geotechnical Safety and Risk (ISGSR))

   Geosynthetic reinforced soil structures are widely used for earth retention and stabilization in many geotechnical and transportation applications. In the traditional design of geosynthetic reinforced soil structures, factor of safety is used to address the uncertainties. However, this approach cannot systematically consider the uncertainties and usually result in over-conservativeness and inconsistence in the design practice. In this paper, a reliability assessment framework of geosynthetic reinforced soil structure design is developed using probabilistic and numerical methods. The geosynthetic reinforced soil structures are modeled using finite element method. In the finite element method, the soil behavior is modelled using the Mohr-Coulomb soil model and a strength reduction method is used to determine the factor of safety value for a given geosynthetic reinforced soil structure. Then the reliability method is combined with the finite element method to obtain the probability curves for the geosynthetic reinforced soil structure. A case study of geosynthetic reinforced soil wall design is used to illustrate the significance of the proposed framework. The reliability assessment framework provides a useful decision making tool for informed design of geosynthetic reinforced soil structures in the face of uncertainties. 

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4. Capturing the electron–electron cusp with the coupling-constant averaged exchange–correlation hole: A case study for Hooke’s atoms

   https://doi.org/10.1063/5.0173370  

   Hou, Lin; Irons, Tom_J_P; Wang, Yanyong; Furness, James_W; Wibowo-Teale, Andrew_M; Sun, Jianwei (January 2024, The Journal of Chemical Physics)

   In density-functional theory, the exchange–correlation (XC) energy can be defined exactly through the coupling-constant (λ) averaged XC hole n̄xc(r,r′), representing the probability depletion of finding an electron at r′ due to an electron at r. Accurate knowledge of n̄xc(r,r′) has been crucial for developing XC energy density-functional approximations and understanding their performance for molecules and materials. However, there are very few systems for which accurate XC holes have been calculated since this requires evaluating the one- and two-particle reduced density matrices for a reference wave function over a range of λ while the electron density remains fixed at the physical (λ = 1) density. Although the coupled-cluster singles and doubles (CCSD) method can yield exact results for a two-electron system in the complete basis set limit, it cannot capture the electron–electron cusp using finite basis sets. Focusing on Hooke’s atom as a two-electron model system for which certain analytic solutions are known, we examine the effect of this cusp error on the XC hole calculated using CCSD. The Lieb functional is calculated at a range of coupling constants to determine the λ-integrated XC hole. Our results indicate that, for Hooke’s atoms, the error introduced by the description of the electron–electron cusp using Gaussian basis sets at the CCSD level is negligible compared to the basis set incompleteness error. The system-, angle-, and coupling-constant-averaged XC holes are also calculated and provide a benchmark against which the Perdew–Burke–Ernzerhof and local density approximation XC hole models are assessed. 

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5. Agrobacterium tumefaciens Growth Pole Ring Protein: C Terminus and Internal Apolipoprotein Homologous Domains Are Essential for Function and Subcellular Localization

   https://doi.org/10.1128/mBio.00764-21  

   Zupan, John; Guo, Zisheng; Biddle, Trevor; Zambryski, Patricia (June 2021, mBio)

   Sloan Siegrist, M. (Ed.)

   ABSTRACT The Agrobacterium growth pole ring (GPR) protein forms a hexameric ring at the growth pole (GP) that is essential for polar growth. GPR is large (2,115 amino acids) and contains 1,700 amino acids of continuous α-helices. To dissect potential GPR functional domains, we created deletions of regions with similarity to human apolipoprotein A-IV (396 amino acids), itself composed of α-helical domains. We also tested deletions of the GPR C terminus. Deletions were inducibly expressed as green fluorescent protein (GFP) fusion proteins and tested for merodiploid interference with wild-type (WT) GPR function, for partial function in cells lacking GPR, and for formation of paired fluorescent foci (indicative of hexameric rings) at the GP. Deletion of domains similar to human apolipoprotein A-IV in GPR caused defects in cell morphology when expressed in trans to WT GPR and provided only partial complementation to cells lacking GPR. Agrobacterium -specific domains A-IV-1 and A-IV-4 contain predicted coiled coil (CC) regions of 21 amino acids; deletion of CC regions produced severe defects in cell morphology in the interference assay. Mutants that produced the most severe effects on cell shape also failed to form paired polar foci. Modeling of A-IV-1 and A-IV-4 reveals significant similarity to the solved structure of human apolipoprotein A-IV. GPR C-terminal deletions profoundly blocked complementation. Finally, peptidoglycan (PG) synthesis is abnormally localized circumferentially in cells lacking GPR. The results support the hypothesis that GPR plays essential roles as an organizing center for membrane and PG synthesis during polar growth. IMPORTANCE Bacterial growth and division are extensively studied in model systems ( Escherichia coli , Bacillus subtilis , and Caulobacter crescentus ) that grow by dispersed insertion of new cell wall material along the length of the cell. An alternative growth mode—polar growth—is used by some Actinomycetales and Proteobacteria species. The latter phylum includes the family Rhizobiaceae , in which many species, including Agrobacterium tumefaciens , exhibit polar growth. Current research aims to identify growth pole (GP) factors. The Agrobacterium growth pole ring (GPR) protein is essential for polar growth and forms a striking hexameric ring structure at the GP. GPR is long (2,115 amino acids), and little is known about regions essential for structure or function. Genetic analyses demonstrate that the C terminus of GPR, and two internal regions with homology to human apolipoproteins (that sequester lipids), are essential for GPR function and localization to the GP. We hypothesize that GPR is an organizing center for membrane and cell wall synthesis during polar growth. 

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