Shadow Energy Functionals and Potentials in Born-Oppenheimer Molecular Dynamics

In Born-Oppenheimer molecular dynamics (BOMD) simulations based on density functional theory (DFT), the potential energy and the interatomic forces are calculated from an electronic ground state density that is determined by an iterative self-consistent field optimization procedure, which in practice never is fully converged. The calculated energies and the forces are therefore only approximate, which may lead to an unphysical energy drift and instabilities. Here we discuss an alternative shadow BOMD approach that is based on a backward error analysis. Instead of calculating approximate solutions for an underlying exact regular BO potential, we do the opposite. Instead, we calculate the exact electron density, energies, and forces, but for an underlying approximate shadow BO potential. In this way the calculated forces are conservative with respect to the shadow potential and generate accurate molecular trajectories with long-term energy stability. We show how such shadow BO potentials can be constructed at different levels of accuracy as a function of the integration time step, dt, from the minimization of a sequence of systematically improvable, but approximate, shadow energy density functionals. For each functional there is a corresponding ground state BO potential. These pairs of shadow energy functionals and potentials are higher-level generalizations of the original "0th-level" shadow energy functionals and potentials used in extended Lagrangian BOMD [Eur. Phys. J. B vol. 94, 164 (2021)]. The proposed shadow energy functionals and potentials are useful only within this dynamical framework, where also the electronic degrees of freedom are propagated together with the atomic positions and velocities. The theory is general and can be applied to MD simulations using approximate DFT, Hartree-Fock or semi-empirical methods, as well as to coarse-grained flexible charge models.Comment: 16 pages, 3 figure

Matrix Diagonalization as a Board Game: Teaching an Eigensolver the Fastest Path to Solution

Matrix diagonalization is at the cornerstone of numerous fields of scientific computing. Diagonalizing a matrix to solve an eigenvalue problem requires a sequential path of iterations that eventually reaches a sufficiently converged and accurate solution for all the eigenvalues and eigenvectors. This typically translates into a high computational cost. Here we demonstrate how reinforcement learning, using the AlphaZero framework, can accelerate Jacobi matrix diagonalizations by viewing the selection of the fastest path to solution as a board game. To demonstrate the viability of our approach we apply the Jacobi diagonalization algorithm to symmetric Hamiltonian matrices that appear in quantum chemistry calculations. We find that a significant acceleration can often be achieved. Our findings highlight the opportunity to use machine learning as a promising tool to improve the performance of numerical linear algebra.Comment: 14 page

Pair distribution function in a two-dimensional electron gas

We calculate the pair distribution function, $g(r)$, in a two-dimensional electron gas and derive a simple analytical expression for its value at the origin as a function of $r_s$. Our approach is based on solving the Schr\"{o}dinger equation for the two-electron wave function in an appropriate effective potential, leading to results that are in good agreement with Quantum Monte Carlo data and with the most recent numerical calculations of $g(0)$. [C. Bulutay and B. Tanatar, Phys. Rev. B {\bf 65}, 195116 (2002)] We also show that the spin-up spin-down correlation function at the origin, $g_{\uparrow \downarrow}(0)$, is mainly independent of the degree of spin polarization of the electronic system.Comment: 5 figures, pair distribution dependence with distance is calculate

Diabetes in Danish Bank Voles (M. glareolus): Survivorship, Influence on Weight, and Evaluation of Polydipsia as a Screening Tool for Hyperglycaemia

BACKGROUND: Previous studies have concluded that the development of polydipsia (PD, a daily water intake ≥ 21 ml) among captive Danish bank voles, is associated with the development of a type 1 diabetes (T1D), based on findings of hyperglycaemia, glucosuria, ketonuria/-emia, lipemia, destroyed beta cells, and presence of autoantibodies against GAD65, IA-2, and insulin. AIM AND METHODS: We retrospectively analysed data from two separate colonies of Danish bank voles in order to 1) estimate survivorship after onset of PD, 2) evaluate whether the weight of PD voles differed from non-PD voles, and, 3), evaluate a state of PD as a practical and non-invasive tool to screen for voles with a high probability of hypeglycaemia. In addition, we discuss regional differences related to the development of diabetes in Scandinavian bank voles and the relevance of the Ljungan virus as proposed etiological agent. RESULTS: We found that median survival after onset of PD is at least 91 days (lower/upper quartiles = 57/134 days) with a maximum recording of at least 404 days survivorship. The development of PD did not influence the weight of Danish bank voles. The measures of accuracy when using PD as predictor of hyperglycaemia, i.e. sensitivity, specificity, positive predictive value, and negative predictive value, equalled 69%, 97%, 89%, and 89%, respectively. CONCLUSION: The relatively long survival of Danish PD bank voles suggests potentials for this model in future studies of the long-term complications of diabetes, of which some observations are mentioned. Data also indicates that diabetes in Danish bank is not associated with a higher body weight. Finally, the method of using measurements of daily water intake to screen for voles with a high probability of hyperglycaemia constitutes a considerable refinement when compared to the usual, invasive, methods

Optomagnetic composite medium with conducting nanoelements

A new type of metal-dielectric composites has been proposed that is characterised by a resonance-like behaviour of the effective permeability in the infrared and visible spectral ranges. This material can be referred to as optomagnetic medium. The analytical formalism developed is based on solving the scattering problem for considered inclusions with impedance boundary condition, which yields the current and charge distributions within the inclusions. The presence of the effective magnetic permeability and its resonant properties lead to novel optical effects and open new possible applications.Comment: 48 pages, 13 figures. accepted to Phys. Rev. B; to appear vol. 66, 200

Association between proton pump inhibitor therapy and clostridium difficile infection: a contemporary systematic review and meta-analysis.

Abstract Introduction Emerging epidemiological evidence suggests that proton pump inhibitor (PPI) acid-suppression therapy is associated with an increased risk of Clostridium difficile infection (CDI). Methods Ovid MEDLINE, EMBASE, ISI Web of Science, and Scopus were searched from 1990 to January 2012 for analytical studies that reported an adjusted effect estimate of the association between PPI use and CDI. We performed random-effect meta-analyses. We used the GRADE framework to interpret the findings. Results We identified 47 eligible citations (37 case-control and 14 cohort studies) with corresponding 51 effect estimates. The pooled OR was 1.65, 95% CI (1.47, 1.85), I2 = 89.9%, with evidence of publication bias suggested by a contour funnel plot. A novel regression based method was used to adjust for publication bias and resulted in an adjusted pooled OR of 1.51 (95% CI, 1.26–1.83). In a speculative analysis that assumes that this association is based on causality, and based on published baseline CDI incidence, the risk of CDI would be very low in the general population taking PPIs with an estimated NNH of 3925 at 1 year. Conclusions In this rigorously conducted systemic review and meta-analysis, we found very low quality evidence (GRADE class) for an association between PPI use and CDI that does not support a cause-effect relationship