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There is a growing need for flexible general frameworks that integrate individual‐level data with external summary information for improved statistical inference. External information relevant for a risk prediction model may come in multiple forms, through regression coefficient estimates or predicted values of the outcome variable. Different external models may use different sets of predictors and the algorithm they used to predict the outcome Y given these predictors may or may not be known. The underlying populations corresponding to each external model may be different from each other and from the internal study population. Motivated by a prostate cancer risk prediction problem where novel biomarkers are measured only in the internal study, this paper proposes an imputation‐based methodology, where the goal is to fit a target regression model with all available predictors in the internal study while utilizing summary information from external models that may have used only a subset of the predictors. The method allows for heterogeneity of covariate effects across the external populations. The proposed approach generates synthetic outcome data in each external population, uses stacked multiple imputation to create a long dataset with complete covariate information. The final analysis of the stacked imputed data is conducted by weighted regression. This flexible and unified approach can improve statistical efficiency of the estimated coefficients in the internal study, improve predictions by utilizing even partial information available from models that use a subset of the full set of covariates used in the internal study, and provide statistical inference for the external population with potentially different covariate effects from the internal population.

Since its advent in the 1970s, optical tweezers have been widely deployed as a preferred non-contact technique for manipulating microscale objects. On-chip integrated optical tweezers, which afford significant size, weight, and cost benefits, have been implemented, relying upon near-field evanescent waves. As a result, these tweezers are only capable of manipulation in near-surface regions and often demand high power since the evanescent interactions are relatively weak. We introduce on-chip optical tweezers based on freeform micro-optics, which comprise optical reflectors or refractive lenses integrated on waveguide end facets via two-photon polymerization. The freeform optical design offers unprecedented degrees of freedom to design optical fields with strong three-dimensional intensity gradients, useful for trapping and manipulating suspended particles in an integrated chip-scale platform. We demonstrate the design, fabrication, and measurement of both reflective and refractive micro-optical tweezers. The reflective tweezers feature a remarkably low trapping threshold power, and the refractive tweezers are particularly useful for multiparticle trapping and interparticle interaction analysis. Our integrated micro-optical tweezers uniquely combine a compact footprint, broadband operation, high trapping efficiency, and scalable integration with planar photonic circuits. This class of tweezers is promising for on-chip sensing, cell assembly, particle dynamics analysis, and ion trapping.

The extraordinary optical properties of single-layer graphene have spurred the development of a variety of photonic components. We have previously demonstrated a scalable and versatile platform to facilitate the integration of graphene and other 2-D materials with chalcogenide glass-based planar photonics. In this paper, we detail the design criteria and optimization guidelines towards high-performance graphene-integrated thermo-optic (TO) switches based on the chalcogenide glass-on-graphene platform. Notably, absorption loss of graphene can be reduced to < 20 dB/cm when it is sandwiched inside photonic structures capitalizing on the anisotropic absorption property of graphene. We quantify energy efficiency of the TO switch, showing that the choice of cladding materials plays a critical role in improving device efficiency. Furthermore, we report a record TO switching efficiency of 10 nm/mW via judicious engineering of the overlap between optical mode and thermal profile.

We consider a situation where rich historical data are available for the coefficients and their standard errors in an established regression model describing the association between a binary outcome variable Y and a set of predicting factors X, from a large study. We would like to utilize this summary information for improving estimation and prediction in an expanded model of interest, Y|X,B. The additional variable B is a new biomarker, measured on a small number of subjects in a new data set. We develop and evaluate several approaches for translating the external information into constraints on regression coefficients in a logistic regression model of Y|X,B. Borrowing from the measurement error literature we establish an approximate relationship between the regression coefficients in the models Pr(Y=1|X,β), Pr(Y=1|X,B,γ) and E(B|X,θ) for a Gaussian distribution of B. For binary B we propose an alternative expression. The simulation results comparing these methods indicate that historical information on Pr(Y=1|X,β) can improve the efficiency of estimation and enhance the predictive power in the regression model of interest Pr(Y=1|X,B,γ). We illustrate our methodology by enhancing the high grade prostate cancer prevention trial risk calculator, with two new biomarkers: prostate cancer antigen 3 and TMPRSS2:ERG.

On-chip spectrometers have the potential to offer dramatic size, weight, and power advantages over conventional benchtop instruments for many applications such as spectroscopic sensing, optical network performance monitoring, hyperspectral imaging, and radio-frequency spectrum analysis. Existing on-chip spectrometer designs, however, are limited in spectral channel count and signal-to-noise ratio. Here we demonstrate a transformative on-chip digital Fourier transform spectrometer that acquires high-resolution spectra via time-domain modulation of a reconfigurable Mach-Zehnder interferometer. The device, fabricated and packaged using industry-standard silicon photonics technology, claims the multiplex advantage to dramatically boost the signal-to-noise ratio and unprecedented scalability capable of addressing exponentially increasing numbers of spectral channels. We further explore and implement machine learning regularization techniques to spectrum reconstruction. Using an ‘elastic-D₁’ regularized regression method that we develop, we achieved significant noise suppression for both broad (>600 GHz) and narrow (<25 GHz) spectral features, as well as spectral resolution enhancement beyond the classical Rayleigh criterion.