Aim: To explore changes in body weight and cardiometabolic risk factors after treatment withdrawal in the STEP 1 trial extension.Materials and Methods: STEP 1 (NCT03548935) randomized 1961 adults with a body mass index ≥ 30 kg/m 2 (or ≥ 27 kg/m 2 with ≥ 1 weight-related co-morbidity) without diabetes to 68 weeks of once-weekly subcutaneous semaglutide 2.4 mg (including 16 weeks of dose escalation) or placebo, as an adjunct to lifestyle intervention. At week 68, treatments (including lifestyle intervention) were discontinued. An off-treatment extension assessed for a further year a representative subset of This article has an accompanied Plain Language Summary in the Supporting Information Data S1.

The growing need for uncertainty analysis of complex computational models has led to an expanding use of meta-models across engineering and sciences. The efficiency of meta-modeling techniques relies on their ability to provide statistically-equivalent analytical representations based on relatively few evaluations of the original model. Polynomial chaos expansions (PCE) have proven a powerful tool for developing meta-models in a wide range of applications; the key idea thereof is to expand the model response onto a basis made of multivariate polynomials obtained as tensor products of appropriate univariate polynomials. The classical PCE approach nevertheless faces the "curse of dimensionality", namely the exponential increase of the basis size with increasing input dimension. To address this limitation, the sparse PCE technique has been proposed, in which the expansion is carried out on only a few relevant basis terms that are automatically selected by a suitable algorithm. An alternative for developing meta-models with polynomial functions in high-dimensional problems is offered by the newly emerged low-rank approximations (LRA) approach. By exploiting the tensor-product structure of the multivariate basis, LRA can provide polynomial representations in highly compressed formats. Through extensive numerical investigations, we herein first shed light on issues relating to the construction of canonical LRA with a particular greedy algorithm involving a sequential updating of the polynomial coefficients along separate dimensions. Specifically, we examine the selection of optimal rank, stopping criteria in the updating of the polynomial coefficients and error estimation. In the sequel, we confront canonical LRA to sparse PCE in structural-mechanics and heat-conduction applications based on finite-element solutions. Canonical LRA exhibit smaller errors than sparse PCE in cases when the number of available model evaluations is small with respect to the input dimension, a situation that is often encountered in real-life problems. By introducing the conditional generalization error, we further demonstrate that canonical LRA tend to outperform sparse PCE in the prediction of extreme model responses, which is critical in reliability analysis.Keywords: uncertainty quantification -meta-modeling -sparse polynomial chaos expansions -canonical low-rank approximations -rank selection -meta-model error 1 arXiv:1511.07492v2 [math.NA]

In the context of global sensitivity analysis, the Sobol' indices constitute a powerful tool for assessing the relative significance of the uncertain input parameters of a model. We herein introduce a novel approach for evaluating these indices at low computational cost, by postprocessing the coefficients of polynomial meta-models belonging to the class of low-rank tensor approximations. Meta-models of this class can be particularly efficient in representing responses of high-dimensional models, because the number of unknowns in their general functional form grows only linearly with the input dimension. The proposed approach is validated in example applications, where the Sobol' indices derived from the meta-model coefficients are compared to reference indices, the latter obtained by exact analytical solutions or Monte-Carlo simulation with extremely large samples. Moreover, low-rank tensor approximations are confronted to the popular polynomial chaos expansion meta-models in case studies that involve analytical rank-one functions and finite-element models pertinent to structural mechanics and heat conduction. In the examined applications, indices based on the novel approach tend to converge faster to the reference solution with increasing size of the experimental design used to build the meta-model.

The study makes use of polynomial chaos expansions to compute Sobol' indices within the frame of a global sensitivity analysis of hydrodispersive parameters in a simplified vertical cross-section of a segment of the subsurface of the Paris Basin. Applying conservative ranges, the uncertainty in 78 input variables is propagated upon the mean lifetime expectancy of water molecules departing from a specific location within a highly confining layer situated in the middle of the model domain. Lifetime expectancy is a hydrogeological performance measure pertinent to safety analysis with respect to subsurface contaminants, such as radionuclides. The sensitivity analysis indicates that the variability in the mean lifetime expectancy can be sufficiently explained by the uncertainty in the petrofacies, i.e. the sets of porosity and hydraulic conductivity, of only a few layers of the model. The obtained results provide guidance regarding the uncertainty modeling in future investigations employing detailed numerical models of the subsurface * Corresponding author, e-mail: konakli@ibk.baug.ethz.ch of the Paris Basin. Moreover, the study demonstrates the high efficiency of sparse polynomial chaos expansions in computing Sobol' indices for high-dimensional models.

SUMMARYA method is presented for simulating arrays of spatially varying ground motions, incorporating the effects of incoherence, wave passage, and differential site response. Non-stationarity is accounted for by considering the motions as consisting of stationary segments. Two approaches are developed. In the first, simulated motions are consistent with the power spectral densities of a segmented recorded motion and are characterized by uniform variability at all locations. Uniform variability in the array of ground motions is essential when synthetic motions are used for statistical analysis of the response of multiply-supported structures. In the second approach, simulated motions are conditioned on the segmented record itself and exhibit increasing variance with distance from the site of the observation. For both approaches, example simulated motions are presented for an existing bridge model employing two alternatives for modeling the local soil response: i) idealizing each soil-column as a single-degree-of-freedom oscillator, and ii) employing the theory of vertical wave propagation in a single soil layer over bedrock. The selection of parameters in the simulation procedure and their effects on the characteristics of the generated motions are discussed. The method is validated by comparing statistical characteristics of the synthetic motions with target theoretical models. Response spectra of the simulated motions at each support are also examined.

Fragility curves are commonly used in civil engineering to assess the vulnerability of structures to earthquakes. The probability of failure associated with a prescribed criterion (e.g. the maximal inter-storey drift of a building exceeding a certain threshold) is represented as a function of the intensity of the earthquake ground motion (e.g. peak ground acceleration or spectral acceleration). The classical approach relies on assuming a lognormal shape of the fragility curves;it is thus parametric. In this paper, we introduce two non-parametric approaches to establish the fragility curves without employing the above assumption, namely binned Monte Carlo simulation and kernel density estimation. As an illustration, we compute the fragility curves for a three-storey steel frame using a large number of synthetic ground motions. The curves obtained with the non-parametric approaches are compared with respective curves based on the lognormal assumption. A similar comparison is presented for a case when a limited number of recorded ground motions is available. It is found that the accuracy of the lognormal curves depends on the ground motion intensity measure, the failure criterion and most importantly, on the employed method for estimating the parameters of the lognormal shape.

This paper introduces a generalized formulation of the multiple support response spectrum (MSRS) method (Earthquake Engng Struct. Dyn. 1992; 21:713-740) and extends it by accounting for the quasi-static contributions of truncated modes. The generalized formulation allows consideration of response quantities that involve support degrees of freedom (DOF). This situation arises for many response quantities of interest when rotational DOF are condensed out. New cross-correlation coefficients are introduced in the extended rule and a parametric study is performed to gain insight and identify cases of ground motion spatial variability in which these terms are significant. An efficient computer implementation of the extended MSRS method is described and used for comprehensive analysis of two real bridge models with vastly different structural characteristics. The specified input is in accordance with standards used in engineering practice. The effects of differential support motions, including the influence of spatially varying soil conditions, on the pseudo-static and dynamic components and the total response are examined and the improvement achieved with the extended MSRS method is assessed.

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