We demonstrate that the processes underlying on-line auction price bids and many other longitudinal data can be represented by an empirical first order stochastic ordinary differential equation with time-varying coefficients and a smooth drift process. This equation may be empirically obtained from longitudinal observations for a sample of subjects and does not presuppose specific knowledge of the underlying processes. For the nonparametric estimation of the components of the differential equation, it suffices to have available sparsely observed longitudinal measurements which may be noisy and are generated by underlying smooth random trajectories for each subject or experimental unit in the sample. The drift process that drives the equation determines how closely individual process trajectories follow a deterministic approximation of the differential equation. We provide estimates for trajectories and especially the variance function of the drift process. At each fixed time point, the proposed empirical dynamic model implies a decomposition of the derivative of the process underlying the longitudinal data into a component explained by a linear component determined by a varying coefficient function dynamic equation and an orthogonal complement that corresponds to the drift process. An enhanced perturbation result enables us to obtain improved asymptotic convergence rates for eigenfunction derivative estimation and consistency for the varying coefficient function and the components of the drift process. We illustrate the differential equation with an application to the dynamics of on-line auction data.

Bayes classifiers for functional data pose a challenge. This is because probability density functions do not exist for functional data. As a consequence, the classical Bayes classifier using density quotients needs to be modified. We propose to use density ratios of projections on a sequence of eigenfunctions that are common to the groups to be classified. The density ratios can then be factored into density ratios of individual functional principal components whence the classification problem is reduced to a sequence of nonparametric one-dimensional density estimates. This is an extension to functional data of some of the very earliest nonparametric Bayes classifiers that were based on simple density ratios in the one-dimensional case. By means of the factorization of the density quotients the curse of dimensionality that would otherwise severely affect Bayes classifiers for functional data can be avoided. We demonstrate that in the case of Gaussian functional data, the proposed functional Bayes classifier reduces to a functional version of the classical quadratic discriminant. A study of the asymptotic behavior of the proposed classifiers in the large sample limit shows that under certain conditions the misclassification rate converges to zero, a phenomenon that has been referred to as "perfect classification". The proposed classifiers also perform favorably in finite sample applications, as we demonstrate in comparisons with other functional classifiers in simulations and various data applications, including wine spectral data, functional magnetic resonance imaging (fMRI) data for attention deficit hyperactivity disorder (ADHD) patients, and yeast gene expression data.

Bronchopulmonary dysplasia (BPD) is a neonatal chronic lung disease characterized by an arrest in alveolar and vascular development. BPD is secondary to lung immaturity, ventilator-induced lung injury, and exposure to hyperoxia in extremely premature infants, leading to a lifelong impairment of lung function. Recent studies indicate that the lung plays an important role in platelet biogenesis. However, the dynamic change of platelet production during lung development and BPD pathogenesis remains to be elucidated. We investigated the dynamic change of platelet parameters in extremely premature infants during BPD development, and in newborn rats during their normal development from birth to adulthood. We further studied the effect of hyperoxia exposure on platelet production and concomitant pulmonary maldevelopment in an experimental BPD rat model induced by prolonged exposure to hyperoxia. We detected a physiological increase in platelet count from birth to 36 weeks postmenstrual age in extremely premature infants, but platelet counts in extremely premature infants who developed BPD were persistently lower than gestational age-matched controls. In line with clinical findings, exposure to hyperoxia significantly decreased the platelet count in neonatal rats. Lung morphometry analysis demonstrated that platelet counts stabilized with the completion of lung alveolarization in rats. Our findings indicate a close association between platelet biogenesis and alveolarization in the developing lung. This phenomenon might explain the reduced platelet count in extremely premature infants with BPD.

Formamidinium lead iodide (FAPbI₃) perovskites are promising emitters for near-infrared light-emitting diodes. However, their performance is still limited by defect-assisted nonradiative recombination and band offset-induced carrier aggregation at the interface. Herein, we introduce a couple of cadmium salts with acetate or halide anion into the FAPbI₃ perovskite precursors to synergistically passivate the material defects and optimize the device band structure. Particularly, the perovskite analogs, containing zero-dimensional formamidinium cadmium iodide, one-dimensional δ-FAPbI₃, two-dimensional FA₂FA_n-1Pb_nI_3n+1, and three-dimensional α-FAPbI₃, can be obtained in one pot and play a pivotal and positive role in energy transfer in the formamidinium iodide-rich lead-based perovskite films. As a result, the near-infrared FAPbI₃-based devices deliver a maximum external quantum efficiency of 24.1% together with substantially improved operational stability. Combining our findings on defect passivation and energy transfer, we also achieve near-infrared light communication with device twins of light emitting and unprecedented self-driven detection.