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Untargeted metabolomics based on liquid chromatography−mass spectrometry is affected by nonlinear batch effects, which cover up biological effects, result in nonreproducibility, and are difficult to be calibrate. In this study, we propose a novel deep learning model, called Normalization Autoencoder (NormAE), which is based on nonlinear autoencoders (AEs) and adversarial learning. An additional classifier and ranker are trained to provide adversarial regularization during the training of the AE model, latent representations are extracted by the encoder, and then the decoder reconstructs the data without batch effects. The NormAE method was tested on two real metabolomics data sets. After calibration by NormAE, the quality control samples (QCs) for both data sets gathered most closely in a PCA score plot (average distances decreased from 56.550 and 52.476 to 7.383 and 14.075, respectively) and obtained the highest average correlation coefficients (from 0.873 and 0.907 to 0.997 for both). Additionally, NormAE significantly improved biomarker discovery (median number of differential peaks increased from 322 and 466 to 1140 and 1622, respectively). NormAE was compared with four commonly used batch effect removal methods. The results demonstrated that using NormAE produces the best calibration results.

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Abstract:Tunable orbit angular momentum (OAM) of surface plasmon polaritons (SPPs) is theoretically studied with appropriately designed metasurfaces. By controlling both the orientation angle and spatial position of nano aperture array on an ultrathin gold film, the field distributions of the surface waves can be engineered to contain both spin dependent and independent OAM components. Simultaneous control over the geometric phase and optical path difference induced phase (dynamic phase) provides extra degrees of freedom for manipulating OAM of SPPs. We show that arbitrary combination of OAM numbers can be realized for the SPPs excited by incident light of different circular polarizations. The results provide powerful control over the OAM of SPPs, which will have potential applications on optical trapping, imaging, communications and quantum information processing.