Sparse Model Identification and Learning for Ultra-high-dimensional Additive Partially Linear Models

The additive partially linear model (APLM) combines the flexibility of nonparametric regression with the parsimony of regression models, and has been widely used as a popular tool in multivariate nonparametric regression to alleviate the "curse of dimensionality". A natural question raised in practice is the choice of structure in the nonparametric part, that is, whether the continuous covariates enter into the model in linear or nonparametric form. In this paper, we present a comprehensive framework for simultaneous sparse model identification and learning for ultra-high-dimensional APLMs where both the linear and nonparametric components are possibly larger than the sample size. We propose a fast and efficient two-stage procedure. In the first stage, we decompose the nonparametric functions into a linear part and a nonlinear part. The nonlinear functions are approximated by constant spline bases, and a triple penalization procedure is proposed to select nonzero components using adaptive group LASSO. In the second stage, we refit data with selected covariates using higher order polynomial splines, and apply spline-backfitted local-linear smoothing to obtain asymptotic normality for the estimators. The procedure is shown to be consistent for model structure identification. It can identify zero, linear, and nonlinear components correctly and efficiently. Inference can be made on both linear coefficients and nonparametric functions. We conduct simulation studies to evaluate the performance of the method and apply the proposed method to a dataset on the Shoot Apical Meristem (SAM) of maize genotypes for illustration

Magnetic Resonance imaging (MRI) in detection of _Bifidobacterium longum_ and _Clostridium novyi-NT_ labeled with superparamagnetic iron oxide (SPIO) nanoparticle

*Purpose:* To investigate the MR imaging of _Bifidobacterium longum_ and _Clostridium novyi-NT_ labeling with superparamagnetic iron oxide (SPIO) nanoparticles.

*Materials and methods:* Tubes containing _B. longum_-SPIO, Free-SPIO, _B. longum_ and PYG Medium were incubated under anaerobic condition in _in vitro_ experiment. Transmission electron microscope and Prussian blue staining were used to demonstrate intra-bacteria nanoparticles. R~2~^*^ mapping and R~2~ mapping were reconstructed after MR scanning. _B. longum_-SPIO and _C. novyi_-NT-SPIO were injected respectively _in vivo_ to show whether it might be traced by MR imaging.

*Results:* Magnetosomes in bacteria were observed by electron microscopic and stained by Prussian blue staining. At the same concentration of SPIOs, the R~2~^*^ value of _B. longum_-SPIO was significantly higher than that of Free-SPIO (P<0.001), however, the R~2~ value was lower comparing with Free-SPIO (P<0.001). After injection with _B. longum_-SPIO, they could present in tumor and shorten T~2~^*^.

*Conclusion:* _B. longum_ and _C. novyi_-NT could be labeled by SPIO and then traced by MRI