Non-orthogonal spin-adaptation and application to coupled cluster up to quadruple excitations

textThe theory of non-orthogonal spin-adaptation for closed-shell molecular systems is presented, with an emphasis on application to the coupled cluster family of electronic structure methods. To aid in the derivation of efficient and compact working equations, a new diagrammatic interpretation of the Goldstone diagrams is derived which only requires a small number of the many distinct diagrams and which directly produces equations in a factored form in terms of “spin-summed” tensor elements. This diagrammatic interpretation is applied to coupled cluster methods with quadruple excitations (CCSDTQ), including coupled cluster with a perturbative correction for quadruple excitations (CCSDT(Q)) and to CCSDTQ gradients and properties. The advantages of the non-orthogonal spin-adaption with respect to simplification and factorization of the working equations and to efficient implementation are presented and discussed. Additionally, specific optimizations of the implementation for often-overlooked issues such as tensor transposition, disk access, and removal of redundant and/or unnecessary operations are detailed. The resulting algorithm is implemented for the CCSDTQ and CCSDT(Q) methods and compared to existing codes, where a one to two order-of-magnitude improvement in efficiency is observed. The new implementation is also used for calculations on several larger molecular systems to illustrate the scalability of the method.Chemistr

The Pines : A Tone - Poem For Piano

https://digitalcommons.library.umaine.edu/mmb-ps/1149/thumbnail.jp

Variational Bayesian dropout: pitfalls and fixes

Dropout, a stochastic regularisation technique for training of neural networks, has recently been reinterpreted as a specific type of approximate inference algorithm for Bayesian neural networks. The main contribution of the reinterpretation is in providing a theoretical framework useful for analysing and extending the algorithm. We show that the proposed framework suffers from several issues; from undefined or pathological behaviour of the true posterior related to use of improper priors, to an ill-defined variational objective due to singularity of the approximating distribution relative to the true posterior. Our analysis of the improper log uniform prior used in variational Gaussian dropout suggests the pathologies are generally irredeemable, and that the algorithm still works only because the variational formulation annuls some of the pathologies. To address the singularity issue, we proffer Quasi-KL (QKL) divergence, a new approximate inference objective for approximation of high-dimensional distributions. We show that motivations for variational Bernoulli dropout based on discretisation and noise have QKL as a limit. Properties of QKL are studied both theoretically and on a simple practical example which shows that the QKL-optimal approximation of a full rank Gaussian with a degenerate one naturally leads to the Principal Component Analysis solution.Jiri Hron holds a Nokia CASE Studentship. Alexander Matthews and Zoubin Ghahramani acknowledge the support of EPSRC Grant EP/N014162/1 and EPSRC Grant EP/N510129/1 (The Alan Turing Institute)

Development and validation of an obstetric early warning system model for use in low resource settings

Background The use of obstetric early-warning-systems (EWS) has been recommended to improve timely recognition, management and early referral of women who have or are developing a critical illness. Development of such prediction models should involve a statistical combination of predictor clinical observations into a multivariable model which should be validated. No obstetric EWS has been developed and validated for low resource settings. We report on the development and validation of a simple prediction model for obstetric morbidity and mortality in resource-limited settings. Methods We performed a multivariate logistic regression analysis using a retrospective case-control analysis of secondary data with clinical indices predictive of severe maternal outcome (SMO). Cases for design and validation were randomly selected (n = 500) from 4360 women diagnosed with SMO in 42 Nigerian tertiary-hospitals between June 2012 and mid-August 2013. Controls were 1000 obstetric admissions without SMO diagnosis. We used clinical observations collected within 24 h of SMO occurrence for cases, and normal births for controls. We created a combined dataset with two controls per case, split randomly into development (n = 600) and validation (n = 900) datasets. We assessed the model’s validity using sensitivity and specificity measures and its overall performance in predicting SMO using receiver operator characteristic (ROC) curves. We then fitted the final developmental model on the validation dataset and assessed its performance. Using the reference range proposed in the United Kingdom Confidential-Enquiry-into-Maternal-and-Child-Health 2007-report, we converted the model into a simple score-based obstetric EWS algorithm. Results The final developmental model comprised abnormal systolic blood pressure-(SBP > 140 mmHg or  90 mmHg), respiratory rate-(RR > 40/min), temperature-(> 38 °C), pulse rate-(PR > 120/min), caesarean-birth, and the number of previous caesarean-births. The model was 86% (95% CI 81–90) sensitive and 92%- (95% CI 89–94) specific in predicting SMO with area under ROC of 92% (95% CI 90–95%). All parameters were significant in the validation model except DBP. The model maintained good discriminatory power in the validation (n = 900) dataset (AUC 92, 95% CI 88–94%) and had good screening characteristics. Low urine output (300mls/24 h) and conscious level (prolonged unconsciousness-GCS < 8/15) were strong predictors of SMO in the univariate analysis. Conclusion We developed and validated statistical models that performed well in predicting SMO using data from a low resource settings. Based on these, we proposed a simple score based obstetric EWS algorithm with RR, temperature, systolic BP, pulse rate, consciousness level, urinary output and mode of birth that has a potential for clinical use in low-resource settings.

Full Three Dimensional Orbits For Multiple Stars on Close Approaches to the Central Supermassive Black Hole

With the advent of adaptive optics on the W. M. Keck 10 m telescope, two significant steps forward have been taken in building the case for a supermassive black hole at the center of the Milky Way and understanding the black hole's effect on its environment. Using adaptive optics and speckle imaging to study the motions of stars in the plane of sky with +-~2 mas precision over the past 7 years, we have obtained the first simultaneous orbital solution for multiple stars. Among the included stars, three are newly identified (S0-16, S0-19, S0-20). The most dramatic orbit is that of the newly identified star S0-16, which passed a mere 60 AU from the central dark mass at a velocity of 9,000 km/s in 1999. The orbital analysis results in a new central dark mass estimate of 3.6(+-0.4)x10^6(D/8kpc)^3 Mo. This dramatically strengthens the case for a black hole at the center of our Galaxy, by confining the dark matter to within a radius of 0.0003 pc or 1,000 Rsh and thereby increasing the inferred dark mass density by four orders of magnitude compared to earlier estimates. With the introduction of an adaptive-optics-fed spectrometer, we have obtained the spectra of these high-velocity stars, which suggest that they are massive (~15 Mo), young (<10 Myr) main sequence stars. This presents a major challenge to star formation theories, given the strong tidal forces that prevail over all distances reached by these stars in their current orbits and the difficulty in migrating these stars inward during their lifetime from further out where tidal forces should no longer preclude star formation.Comment: 7 pages, 5 figures (abridged abstract

Annealed Flow Transport Monte Carlo

Annealed Importance Sampling (AIS) and its Sequential Monte Carlo (SMC) extensions are state-of-the-art methods for estimating normalizing constants of probability distributions. We propose here a novel Monte Carlo algorithm, Annealed Flow Transport (AFT), that builds upon AIS and SMC and combines them with normalizing flows (NFs) for improved performance. This method transports a set of particles using not only importance sampling (IS), Markov chain Monte Carlo (MCMC) and resampling steps - as in SMC, but also relies on NFs which are learned sequentially to push particles towards the successive annealed targets. We provide limit theorems for the resulting Monte Carlo estimates of the normalizing constant and expectations with respect to the target distribution. Additionally, we show that a continuous-time scaling limit of the population version of AFT is given by a Feynman--Kac measure which simplifies to the law of a controlled diffusion for expressive NFs. We demonstrate experimentally the benefits and limitations of our methodology on a variety of applications

Characterization of SiGe thin films using a laboratory X-ray instrument

The technique of reciprocal space mapping using X-rays is a recognized tool for the nondestructive characterization of epitaxial films. X-ray scattering from epitaxial Si0.4Ge0.6 films on Si(100) substrates using a laboratory X-ray source was investigated. It is shown that a laboratory source with a rotating anode makes it possible to investigate the material parameters of the super-thin 2–6 nm layers. For another set of partially relaxed layers, 50–200 nm thick, it is shown that from a high-resolution reciprocal space map, conditioned from diffuse scattering on dislocations, it is possible to determine quantitatively from the shape of a diffraction peak (possessing no thickness fringes) additional parameters such as misfit dislocation density and layer thickness as well as concentration and relaxation

Petrological evidence in support of the death mask model for Ediacaran soft-bodied preservation in South Australia

Microbially mediated early diagenetic pyrite formation in the immediate vicinity of organic material has been the favoured mechanism by which to explain widespread preservation of soft-bodied organisms in late Ediacaran sedimentary successions, but an alternative rapid silicification model has been proposed for macrofossil preservation in sandstones of the Ediacara Member in South Australia. We here provide petrological evidence from Nilpena National Heritage Site and Ediacara Conservation Park to demonstrate the presence of grain-coating iron oxides, framboidal hematite, and clay minerals along Ediacara Member sandstone bedding planes, including fossil-bearing bed soles. SEM and petrographic data reveal that framboids and grain coatings, which we interpret as oxidized pyrite, formed before the precipitation of silica cements. In conjunction with geochemical and taphonomic considerations, our data suggest that anactualistically high concentrations of silica need not be invoked to explain Ediacara Member fossil preservation: we conclude that the pyritic ‘death mask’ model remains compelling.AGL is funded by the Natural Environment Research Council [grant number NE/L011409/2]. SM acknowledges support from the European Union’s Horizon 2020 Research and Innovation Programme under Marie Skłodowska-Curie grant agreement 747877 ... JJM recognises support from Mitacs ..