A framework to select tuning parameters for nonparametric derivative estimation.

In this paper, we propose a general framework to select tuning parameters for the nonparametric derivative estimation. The new framework broadens the scope of the previously proposed generalized C p $C_p$ criterion by replacing the empirical derivative with any other linear nonparametric smoother. We provide the theoretical support of the proposed derivative estimation in a random design and justify it through simulation studies. The practical application of the proposed framework is demonstrated in the study of the age effect on hippocampal gray matter volume in healthy adults from the IXI dataset and the study of the effect of age and body mass index on blood pressure from the Pima Indians dataset.

Robust functional principal component analysis via a functional pairwise spatial sign operator.

Functional principal component analysis (FPCA) has been widely used to capture major modes of variation and reduce dimensions in functional data analysis. However, standard FPCA based on the sample covariance estimator does not work well if the data exhibits heavy-tailedness or outliers. To address this challenge, a new robust FPCA approach based on a functional pairwise spatial sign (PASS) operator, termed PASS FPCA, is introduced. We propose robust estimation procedures for eigenfunctions and eigenvalues. Theoretical properties of the PASS operator are established, showing that it adopts the same eigenfunctions as the standard covariance operator and also allows recovering ratios between eigenvalues. We also extend the proposed procedure to handle functional data measured with noise. Compared to existing robust FPCA approaches, the proposed PASS FPCA requires weaker distributional assumptions to conserve the eigenspace of the covariance function. Specifically, existing work are often built upon a class of functional elliptical distributions, which requires inherently symmetry. In contrast, we introduce a class of distributions called the weakly functional coordinate symmetry (weakly FCS), which allows for severe asymmetry and is much more flexible than the functional elliptical distribution family. The robustness of the PASS FPCA is demonstrated via extensive simulation studies, especially its advantages in scenarios with nonelliptical distributions. The proposed method was motivated by and applied to analysis of accelerometry data from the Objective Physical Activity and Cardiovascular Health Study, a large-scale epidemiological study to investigate the relationship between objectively measured physical activity and cardiovascular health among older women.

MEScan: a powerful statistical framework for genome-scale mutual exclusivity analysis of cancer mutations.

MOTIVATION: Cancer somatic driver mutations associated with genes within a pathway often show a mutually exclusive pattern across a cohort of patients. This mutually exclusive mutational signal has been frequently used to distinguish driver from passenger mutations and to investigate relationships among driver mutations. Current methods for de novo discovery of mutually exclusive mutational patterns are limited because the heterogeneity in background mutation rate can confound mutational patterns, and the presence of highly mutated genes can lead to spurious patterns. In addition, most methods only focus on a limited number of pre-selected genes and are unable to perform genome-wide analysis due to computational inefficiency. RESULTS: We introduce a statistical framework, MEScan, for accurate and efficient mutual exclusivity analysis at the genomic scale. Our framework contains a fast and powerful statistical test for mutual exclusivity with adjustment of the background mutation rate and impact of highly mutated genes, and a multi-step procedure for genome-wide screening with the control of false discovery rate. We demonstrate that MEScan more accurately identifies mutually exclusive gene sets than existing methods and is at least two orders of magnitude faster than most methods. By applying MEScan to data from four different cancer types and pan-cancer, we have identified several biologically meaningful mutually exclusive gene sets. AVAILABILITY AND IMPLEMENTATION: MEScan is available as an R package at https://github.com/MarkeyBBSRF/MEScan. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Efficient frequency conversion induced by quantum constructive interference.

We demonstrate in experiment an efficient cw four-wave mixing scheme with maximal intensity conversion efficiency up to 73% in a double-Λ system of hot rubidium atoms. Relevant theoretical analysis shows that this high conversion efficiency benefits greatly from the constructive interference between two four-wave mixing channels, characterized by two different space-dependent phases.

Dual-channel all-optical wavelength conversion switching by four-wave mixing.

We report an experimental demonstration of dual-channel all-optical wavelength conversion switching in hot Rb vapor. In a four-level atomic system, a coupling field and a pump field interact with both (87)Rb and (85)Rb isotopes simultaneously and facilitate the generation of two nonlinear signals when the probe field is applied to the corresponding transition. Each nonlinear signal is switched on and off separately by the pump field at different frequencies based on four-wave mixing and isotope shifts.