Functional single index models for longitudinal data

A new single-index model that reflects the time-dynamic effects of the single index is proposed for longitudinal and functional response data, possibly measured with errors, for both longitudinal and time-invariant covariates. With appropriate initial estimates of the parametric index, the proposed estimator is shown to be $\sqrt{n}$-consistent and asymptotically normally distributed. We also address the nonparametric estimation of regression functions and provide estimates with optimal convergence rates. One advantage of the new approach is that the same bandwidth is used to estimate both the nonparametric mean function and the parameter in the index. The finite-sample performance for the proposed procedure is studied numerically.Comment: Published in at http://dx.doi.org/10.1214/10-AOS845 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Covariate adjusted functional principal components analysis for longitudinal data

Classical multivariate principal component analysis has been extended to functional data and termed functional principal component analysis (FPCA). Most existing FPCA approaches do not accommodate covariate information, and it is the goal of this paper to develop two methods that do. In the first approach, both the mean and covariance functions depend on the covariate $Z$ and time scale $t$ while in the second approach only the mean function depends on the covariate $Z$. Both new approaches accommodate additional measurement errors and functional data sampled at regular time grids as well as sparse longitudinal data sampled at irregular time grids. The first approach to fully adjust both the mean and covariance functions adapts more to the data but is computationally more intensive than the approach to adjust the covariate effects on the mean function only. We develop general asymptotic theory for both approaches and compare their performance numerically through simulation studies and a data set.Comment: Published in at http://dx.doi.org/10.1214/09-AOS742 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Null hypersurface quantization, electromagnetic duality and asymptotic symmetries of Maxwell theory

In this paper we consider introducing careful regularization in the quantization of Maxwell theory in the asymptotic null infinity. This allows systematic discussions of the commutators in various boundary conditions, and application of Dirac brackets accordingly in a controlled manner. This method is most useful when we consider asymptotic charges that are not localized at the boundary $u\to \pm \infty$ like large gauge transformations. We show that our method reproduces the operator algebra in known cases, and it can be applied to other space-time symmetry charges such as the BMS transformations. We also obtain the asymptotic form of the U(1) charge following from the electromagnetic duality in an explicitly EM symmetric Schwarz-Sen type action. Using our regularization method, we demonstrate that the charge generates the expected transformation of a helicity operator. Our method promises applications in more generic theories.Comment: 26 pages, typos correcte

Inverse regression for longitudinal data

Sliced inverse regression (Duan and Li [Ann. Statist. 19 (1991) 505-530], Li [J. Amer. Statist. Assoc. 86 (1991) 316-342]) is an appealing dimension reduction method for regression models with multivariate covariates. It has been extended by Ferr\'{e} and Yao [Statistics 37 (2003) 475-488, Statist. Sinica 15 (2005) 665-683] and Hsing and Ren [Ann. Statist. 37 (2009) 726-755] to functional covariates where the whole trajectories of random functional covariates are completely observed. The focus of this paper is to develop sliced inverse regression for intermittently and sparsely measured longitudinal covariates. We develop asymptotic theory for the new procedure and show, under some regularity conditions, that the estimated directions attain the optimal rate of convergence. Simulation studies and data analysis are also provided to demonstrate the performance of our method.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1193 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org). With Correction

GaN-Based High Efficiency Transmitter for Multiple-Receiver Wireless Power Transfer

Wireless power transfer (WPT) has attracted great attention from industry and academia due to high charging flexibility. However, the efficiency of WPT is lower and the cost is higher than the wired power transfer approaches. Efforts including converter optimization, power delivery architecture improvement, and coils have been made to increase system efficiency.In this thesis, new power delivery architectures in the WPT of consumer electronics have been proposed to improve the overall system efficiency and increase the power density.First, a two-stage transmitter architecture is designed for a 100 W WPT system. After comparing with other topologies, the front-end ac-dc power factor correction (PFC) rectifier employs a totem-pole rectifier. A full bridge 6.78 MHz resonant inverter is designed for the subsequent stage. An impedance matching network provides constant transmitter coil current. The experimental results verify the high efficiency, high PF, and low total harmonic distortion (THD).Then, a single-stage transmitter is derived based on the verified two-stage structure. By integration of the PFC rectifier and full bridge inverter, two GaN FETs are saved and high efficiency is maintained. The integrated DCM operated PFC rectifier provides high PF and low THD. By adopting a control scheme, the transmitter coil current and power are regulated. A simple auxiliary circuit is employed to improve the light load efficiency. The experimental results verify the achievement of high efficiency.A closed-loop control scheme is implemented in the single-stage transmitter to supply multiple receivers simultaneously. With a controlled constant transmitter current, the system provides a smooth transition during dynamically load change. ZVS detection circuit is proposed to protect the transmitter from continuous hard switching operation. The control scheme is verified in the experiments.The multiple-reciever WPT system with the single-stage transmitter is investigated. The system operating range is discussed. The method of tracking optimum system efficiency is studied. The system control scheme and control procedure, targeting at providing a wide system operating range, robust operation and capability of tracking the optimized system efficiency, are proposed. Experiment results demonstrate the WPT system operation