Human milk fatty acid composition varies during lactation and is influenced by maternal diet, maternal lifestyle-related factors and genetic background. This is one of the first studies to investigate a period effect, that is, the impact of lifestyle-related changes on human milk fatty acid composition, in two different cohorts. Lactating women were recruited from the general population a decade apart in Ulm, Germany, using similar methodology. Human milk samples collected 6 weeks postpartum were analysed (Ulm Birth Cohort Study (UBCS (2000)), n 567; Ulm SPATZ Health Study (SPATZ (2012)), n 458). Centred log ratio transformation was applied to fatty acid data. Principal component analysis was used to determine study-dependent fatty acid profiles. A general linear model was used to determine the study (or period) effect on fatty acid profiles adjusting for duration of gestation, age, education, delivery mode, smoking and pre-pregnancy BMI. Two principal components were retained (PC1 and PC2). PC1 was associated with UBCS, while PC2 was associated with SPATZ. PC1 comprised high SFA, and low MUFA, n-6 and n-3 long-chain PUFA (LCPUFA). The inverse was true for PC2. Although human milk remains a source of essential fatty acids, infants could be at risk of inadequate n-3 and n-6 LCPUFA intake through human milk. The differences in the human milk fatty acid profiles also reflect changes in maternal dietary habits in the more recent cohort, which may comprise lower intakes of dietary trans-fatty acids and SFA and higher intakes of vegetable oils.

The current research paper describes the lateral-directional parameter estimation from flight data of a miniature Unmanned Aerial Vehicle (UAV) using Maximum Likelihood (ML), and Neural-Gauss-Newton (NGN) methods. An unmanned configuration with a cropped delta planform and thin rectangular cross-section has been designed, fabricated and instrumented. Exhaustive full-scale wind-tunnel tests were performed on the UAV to extract the form of aerodynamic model that has to be postulated a priori for parameter estimation. Rigorous flight tests have been performed to acquire the flight data for several prescribed manoeuvres. Four sets of compatible flight data have been used to carry out parameter estimation using classical ML and neural-network-based NGN methods. It is observed that the estimated parameters are consistent and the lower values of the Cramer-Rao bound for the corresponding estimates have shown significant confidence in the obtained parameters. Furthermore, to validate the aerodynamic model used and to enhance the confidence in the estimated parameters, a proof of match exercise has been carried out.

In this work, we concern with the numerical comparison between different kinds of design points in least square (LS) approach on polynomial spaces. Such a topic is motivated by uncertainty quantification (UQ). Three kinds of design points are considered, which are the Sparse Grid (SG) points, the Monte Carlo (MC) points and the Quasi Monte Carlo (QMC) points. We focus on three aspects during the comparison: (i) the convergence properties; (ii) the stability, i.e. the properties of the resulting condition number of the design matrix; (iii) the robustness when numerical noises are present in function values. Several classical high dimensional functions together with a random ODE model are tested. It is shown numerically that (i) neither the MC sampling nor the QMC sampling introduce the low convergence rate, namely, the approach achieves high order convergence rate for all cases provided that the underlying functions admit certain regularity and enough design points are used; (ii)The use of SG points admits better convergence properties only for very low dimensional problems (say d ≤ 2); (iii)The QMC points, being deterministic, seem to be a good choice for higher dimensional problems not only for better convergence properties but also in the stability point of view.

Least squares regression is commonly used in metrology for calibration and estimation. Inregression relating a response y to a predictor x, thepredictor x is often measured with error that is ignored in analysis.Practitioners wondering how to proceed when x has non-negligible errorface a daunting literature, with a wide range of notation, assumptions, and approaches.For the model ytrue = β0 + β1   xtrue,we provide simple expressions for errors in predictors (EIP) estimators \hbox{$\Hat{{\beta }}_{0, {\rm EIP}} $}β̂0, EIP for β0 and \hbox{$\Hat{{\beta }}_{1, {\rm EIP}} $}β̂1, EIP for β1 and for anapproximation to covariance (\hbox{$\Hat{{\beta }}_{0, {\rm EIP}} $}β̂0, EIP, \hbox{$\Hat{{\beta }}_{1, {\rm EIP}} $}β̂1, EIP). It is assumed that there are measured datax = xtrue + ex,andy = ytrue + eywith errors ex in x andey in y and thevariances of the errors ex andey are allowed to depend onxtrue and ytrue, respectively.This paper also investigates the accuracy of the estimated cov(\hbox{$\Hat{{\beta }}_{0, {\rm EIP}} $}β̂0, EIP, \hbox{$\Hat{{\beta }}_{1, {\rm EIP}} $}β̂1, EIP) and provides a numerical Bayesian alternative usingMarkov Chain Monte Carlo, which is recommended particularly for small sample sizes wherethe approximate expression is shown to have lower accuracy than desired.