Trajectory modeling of gestational weight: A functional principal component analysis approach - Fig 3

<p>(a) Scree plot of the weight data and (b–d) The first, second and third principle component (PC) functions for the weight data which account for 95.7%, 2.8%, and 1.1% of the total variation, respectively.</p

Estimated weight trajectories of four subjects, one from each prepregnancy weight categories.

<p>Estimated weight trajectories of four subjects, one from each prepregnancy weight categories.</p

Comparison of the regression models with different forms of responses and predictors.

<p>Comparison of the regression models with different forms of responses and predictors.</p

Functional linear quantile regression on a two-dimensional domain

This article considers the functional linear quantile regression which models the conditional quantile of a scalar response given a functional predictor over a two-dimensional domain. We propose an estimator for the slope function by minimizing the penalized empirical check loss function. Under the framework of reproducing kernel Hilbert space, the minimax rate of convergence for the regularized estimator is established. Using the theory of interpolation spaces on a two- or multi-dimensional domain, we develop a novel result on simultaneous diagonalization of the reproducing and covariance kernels, revealing the interaction of the two kernels in determining the optimal convergence rate of the estimator. Sufficient conditions are provided to show that our analysis applies to many situations, for example, when the covariance kernel is from the Matérn class, and the slope function belongs to a Sobolev space. We implement the interior point method to compute the regularized estimator and illustrate the proposed method by applying it to the hippocampus surface data in the ADNI study. </p

AgCu Nanoparticles as an Antibacterial Coating for Wood

Nano inorganic antibacterial materials (such as nano silver and nano copper) are popular in preventing the spread of bacteria on wood and protecting human health. However, their antibacterial activity and cost are always difficult to balance, and their leachability during the applied procedure impedes service life. Herein, a low-cost nano AgCu alloy with high antibacterial activity is synthesized by a liquid reduction method and further physically mixed with waterborne paint to fabricate the composite paint. The obtained nano AgCu alloy is demonstrated to possess superior antibacterial performance against Escherichia coli and Staphylococcus aureus with a low concentration (10 ppm), a short time (1 min), and a 100% antibacterial rate, due to the synergistic effect between Ag and Cu, and the promoted release of Ag ion. Meanwhile, the composite coating containing nano AgCu alloy could endow the effective migration of Ag ions and further facilitate the high durability and maintain the lasting antibacterial effect on the wood surface by reducing the leaching rate of nano alloy particles from 1.58% to 0.62%. This work provides a reference for future research and development on antibacterial coatings of wood surfaces