BFDA: A MATLAB Toolbox for Bayesian Functional Data Analysis

We provide a MATLAB toolbox, BFDA, that implements a Bayesian hierarchical model to smooth multiple functional data samples with the assumptions of the same underlying Gaussian process distribution, a Gaussian process prior for the mean function, and an Inverse-Wishart process prior for the covariance function. This model-based approach can borrow strength from all functional data samples to increase the smoothing accuracy, as well as simultaneously estimate the mean-covariance functions. An option of approximating the Bayesian inference process using cubic B-spline basis functions is integrated in BFDA, which allows for efficiently dealing with high-dimensional functional data. Examples of using BFDA in various scenarios and conducting follow-up functional regression are provided. The advantages of BFDA include: (1) simultaneously smooths multiple functional data samples and estimates the mean-covariance functions in a nonparametric way; (2) flexibly deals with sparse and high-dimensional functional data with stationary and nonstationary covariance functions, and without the requirement of common observation grids; (3) provides accurately smoothed functional data for follow-up analysis

Computer-based tracking, analysis, and visualization of linguistically significant nonmanual events in American Sign Language (ASL)

Our linguistically annotated American Sign Language (ASL) corpora have formed a basis for research to automate detection by computer of essential linguistic information conveyed through facial expressions and head movements. We have tracked head position and facial deformations, and used computational learning to discern specific grammatical markings. Our ability to detect, identify, and temporally localize the occurrence of such markings in ASL videos has recently been improved by incorporation of (1) new techniques for deformable model-based 3D tracking of head position and facial expressions, which provide significantly better tracking accuracy and recover quickly from temporary loss of track due to occlusion; and (2) a computational learning approach incorporating 2-level Conditional Random Fields (CRFs), suited to the multi-scale spatio-temporal characteristics of the data, which analyses not only low-level appearance characteristics, but also the patterns that enable identification of significant gestural components, such as periodic head movements and raised or lowered eyebrows. Here we summarize our linguistically motivated computational approach and the results for detection and recognition of nonmanual grammatical markings; demonstrate our data visualizations, and discuss the relevance for linguistic research; and describe work underway to enable such visualizations to be produced over large corpora and shared publicly on the Web

Reflective silicon binary diffraction grating for visible wavelengths

We introduce a new device based on sub-wavelength resonant gratings. We built a silicon-on-oxide reflective binary grating for visible light that mimics the functionality of a blazed diffraction grating in a flat geometry