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Free-form concrete panels (FCPs) require precise lower-shape implementation because lower-shape errors directly affect thickness quality, geometric accuracy, and constructability. Although previous studies have developed several lower-mold systems, the sectional behavior of lower-shape errors and their deformation tendencies under concrete load have not been sufficiently clarified. Therefore, this study investigates the sectional shape error characteristics of the lower silicone mold (LSM) before casting and of the lower shape of the FCP after casting under combined curvature and thickness conditions. Single-curved FCPs were designed with curvatures of 20, 25, and 30 mm and thicknesses of 20, 30, and 40 mm. The lower geometry was divided into middle and edge sections, and statistical analyses were conducted to examine curvature-dependent deformation and load-induced error behavior. Before casting, the mean error of the LSM increased from 0.289 mm to 0.345 mm and 0.425 mm as curvature increased. After casting, the lower-shape error of the manufactured FCPs ranged from 0.313 mm to 0.444 mm. Under the 30 mm curvature and 20 mm thickness condition, the error decreased after casting, indicating partial load compensation, whereas manufacture was not possible under the 30 mm curvature and 40 mm thickness condition because of excessive side-mold displacement. These results provide quantitative evidence for deformation behavior under load and support the need for FCP-specific quality criteria.

We consider the problem of nonparametric regression when the covariate is d dimensional, where d ≥ 1. In this paper, we introduce and study two non-parametric least squares estimators (LSEs) in this setting—the entirely monotonic LSE and the constrained Hardy–Krause variation LSE. We show that these two LSEs are natural generalizations of univariate isotonic regression and univariate total variation denoising, respectively, to multiple dimensions. We discuss the characterization and computation of these two LSEs obtained from n data points. We provide a detailed study of their risk properties under the squared error loss and fixed uniform lattice design. We show that the finite sample risk of these LSEs is always bounded from above by n −2/3 modulo logarithmic factors depending on d; thus these nonparametric LSEs avoid the curse of dimensionality to some extent. We also prove nearly matching minimax lower bounds. Further, we illustrate that these LSEs are particularly useful in fitting rectangular piecewise constant functions. Specifically, we show that the risk of the entirely monotonic LSE is almost parametric (at most 1/n up to logarithmic factors) when the true function is well approximable by a rectangular piecewise constant entirely monotone function with not too many constant pieces. A similar result is also shown to hold for the constrained Hardy–Krause variation LSE for a simple subclass of rectangular piecewise constant functions. We believe that the proposed LSEs yield a novel approach to estimating multivariate functions using convex optimization that avoid the curse of dimensionality to some extent.

Methods for statistically analyzing patient-specific data that vary both spatially and over time are currently either limited to summary statistics or require elaborate surface registration. We propose a new method, called correspondence-based network analysis, which leverages particle-based shape modeling to establish correspondence across a population and preserve patient-specific measurements and predictions through statistical analysis. Herein, we evaluated this method using three published datasets of the hip describing cortical bone thickness of the proximal femur, cartilage contact stress, and dynamic joint space between control and patient cohorts to evaluate activity- and group-based differences, as applicable, using traditional statistical parametric mapping (SPM) and our proposed spatially considerate correspondence-based network analysis approach. The network approach was insensitive to correspondence density, while the traditional application of SPM showed decreasing area of the region of significance with increasing correspondence density. In comparison to SPM, the network approach identified broader and more connected regions of significance for all three datasets. The correspondence-based network analysis approach identified differences between groups and activities without loss of subject and spatial specificity which could improve clinical interpretation of results.

Rapid generation of lower limb musculoskeletal models is essential for clinically applicable patient-specific gait modeling. Estimation of muscle and joint contact forces requires accurate representation of bone geometry and pose, as well as their muscle attachment sites, which define muscle moment arms. Motion-capture is a routine part of gait assessment but contains relatively sparse geometric information. Standard methods for creating customized models from motion-capture data scale a reference model without considering natural shape variations. We present an articulated statistical shape model of the left lower limb with embedded anatomical landmarks and muscle attachment regions. This model is used in an automatic workflow, implemented in an easy-to-use software application, that robustly and accurately estimates realistic lower limb bone geometry, pose, and muscle attachment regions from seven commonly used motion-capture landmarks. Estimated bone models were validated on noise-free marker positions to have a lower (p=0.001) surface-to-surface root-mean-squared error of 4.28mm, compared to 5.22mm using standard isotropic scaling. Errors at a variety of anatomical landmarks were also lower (8.6mm versus 10.8mm, p=0.001). We improve upon standard lower limb model scaling methods with shape model-constrained realistic bone geometries, regional muscle attachment sites, and higher accuracy.

Abnormal postoperative global sagittal alignment (GSA) is associated with an increased risk of mechanical complications after spinal surgery. Typical assessment of sagittal alignment relies on a few selected measures, disregarding global complexity and variability of the sagittal curvature. The normative range of spinal loads associated with GSA has not yet been considered in clinical evaluation. The study objectives were to develop a new GSA assessment method that holistically describes the inherent relationships within GSA and to estimate the related spinal loads. Vertebral endplates were annotated on radiographs of 85 non-pathological subjects. A Principal Component Analysis (PCA) was performed to derive a Statistical Shape Model (SSM). Associations between identified GSA variability modes and conventional alignment measures were assessed. Simulations of respective Shape Modes (SMs) were performed using an established musculoskeletal AnyBody model to estimate normal variation in cervico-thoraco-lumbar loads. The first six principal components explained 97.96% of GSA variance. The SSM provides the normative range of GSA and a visual representation of the main variability modes. Normal variation relative to the population mean in identified alignment features was found to influence spinal loads, e.g. the lower bound of the second shape mode (SM2-2σ) corresponds to an increase in L4L5-compression by 378.64 N (67.86%). Six unique alignment features were sufficient to describe GSA almost entirely, demonstrating the value of the proposed method for an objective and comprehensive analysis of GSA. The influence of these features on spinal loads provides a normative biomechanical reference, eventually guiding surgical planning of deformity correction in the future.

Retrieving high-precision concentrations of atmospheric trace gases from FTIR (Fourier transform infrared) spectrometry requires a precise knowledge of the instrumental performance. In this context, this paper examines the impact on the ozone (O3) retrievals of several approaches used to characterize the instrumental line shape (ILS) function of ground-based FTIR spectrometers within NDACC (Network for the Detection of Atmospheric Composition Change). The analysis has been carried out at the subtropical Izaña Observatory (IZO, Spain) by using the 20-year time series of the high-resolution FTIR solar absorption spectra acquired between 1999 and 2018. The theoretical quality assessment and the comparison to independent O3 observations available at IZO (Brewer O3 total columns and electrochemical concentration cell, ECC, sondes) reveal consistent findings. The inclusion of a simultaneous retrieval of the ILS parameters in the O3 retrieval strategy allows, on the one hand, a rough instrumental characterization to be obtained and, on the other hand, the precision of the FTIR O3 products to be slightly improved. The improvement is of special relevance above the lower stratosphere, where the cross-interference between the O3 vertical distribution and the instrumental performance is more significant. However, it has been found that the simultaneous ILS retrieval leads to a misinterpretation of the O3 variations on daily and seasonal scales. Therefore, in order to ensure the independence of the O3 retrievals and the instrumental response, the optimal approach to deal with the FTIR instrumental characterization is found to be the continuous monitoring of the ILS function by means of independent observations, such as gas cell measurements.

Phacopid trilobites are well documented during the Paleozoic. Nevertheless, while 2D quantitative analyses have advanced our understanding of the morphological relationships among trilobites, the quantification of their morphological traits in 3D remains rarely documented. Based on two sets of morphological data (head and tail), 2D versus 3D shape quantification approaches were used to explore shape allometries as well as to explore how the shape variations can be explained by the phylogenetic relationships among phacopid trilobite species for the first time. We demonstrate that (1) there are similar patterns of morphological variability across taxa in 3D and 2D; (2) there are rather congruent results between 3D and 2D to discriminate taxa; (3) 2D and 3D landmarks capture different levels of detail, and the third dimension in 3D is very important for making taxonomic distinctions at the genus level; (4) there is congruity between 2D and 3D datasets for allometric patterns with results showing similar allometric slopes among species exhibiting a glabellar length decrease during growth leading to wider cephala; (5) the phylomorphospaces show tree branches that do not intersect, suggesting possible phylogenetic constraints on morphospace occupation for each species and supporting the idea that the Austerops and Morocops groups are sister clades that experienced different modes of morphological evolution; and (6) the morphological descriptors in morphometric analyses in 2D and 3D throughout phacopid evolution are effective.

Many applications, including rank aggregation, crowd-labeling and graphon estimation, can be modeled in terms of a bivariate isotonic matrix with unknown permutations acting on its rows and/or columns. We consider the problem of estimating an unknown matrix in this class, based on noisy observations of (possibly, a subset of) its entries. We design and analyze polynomial-time algorithms that improve upon the state of the art in two distinct metrics, showing, in particular, that minimax optimal, computationally efficient estimation is achievable in certain settings. Along the way, we prove matching upper and lower bounds on the minimax radii of certain cone testing problems, which may be of independent interest.

For the first time, the lower bound shakedown theorem is integrated into a level set–based topology optimization framework to identify lightweight elastoplastic designs. Shakedown is a cyclic elastoplastic behavior in which, upon cycling beyond the elastic limit, the accumulation of plastic strain arrests and purely elastic behavior is recovered. In contrast to most elastoplastic topology optimization, the use of a lower bound shakedown limit allows elastoplastic shakedown limits to be rigorously estimated using only the elastic solution. Under small deformation assumptions, this amounts to solving one simple partial differential equation, avoiding the non-linearity associated with plasticity, and thus simplifying the resolution process. Numerical results are provided for several benchmark examples. The results highlight the design performance enhancements attributed to allowing elastoplastic shakedown to occur instead of designing to first yield. In particular, up to 10% reduction in weight is found for the simple structures considered.

We consider a two-component mixture model with one known component. We develop methods for estimating the mixing proportion and the unknown distribution non-parametrically, given independent and identically distributed data from the mixture model, using ideas from shape-restricted function estimation. We establish the consistency of our estimators. We find the rate of convergence and asymptotic limit of the estimator for the mixing proportion. Completely automated distribution-free honest finite sample lower confidence bounds are developed for the mixing proportion. Connection to the problem of multiple testing is discussed. The identifiability of the model and the estimation of the density of the unknown distribution are also addressed. We compare the estimators proposed, which are easily implementable, with some of the existing procedures through simulation studies and analyse two data sets: one arising from an application in astronomy and the other from a microarray experiment.