Although increasing hidden layers can improve the ability of a neural network in modeling complex nonlinear relationships, deep layers may result in degradation of accuracy due to the problem of vanishing gradient. Accuracy degradation limits the applications of deep neural networks to predict continuous variables with a small sample size and/or weak or little invariance to translations. Inspired by residual convolutional neural network in computer vision, we developed an encoder-decoder full residual deep network to robustly regress and predict complex spatiotemporal variables. We embedded full shortcuts from each encoding layer to its corresponding decoding layer in a systematic encoder-decoder architecture for efficient residual mapping and error signal propagation. We demonstrated, theoretically and experimentally, that the proposed network structure with full residual connections can successfully boost the backpropagation of signals and improve learning outcomes. This novel method has been extensively evaluated and compared with four commonly used methods (i.e., plain neural network, cascaded residual autoencoder, generalized additive model, and XGBoost) across different testing cases for continuous variable predictions. For model evaluation, we focused on spatiotemporal imputation of satellite aerosol optical depth with massive nonrandomness missingness and spatiotemporal estimation of atmospheric fine particulate matter [Formula: see text] (PM_2.5). Compared with the other approaches, our method achieved the state-of-the-art accuracy, had less bias in predicting extreme values, and generated more realistic spatial surfaces. This encoder-decoder full residual deep network can be an efficient and powerful tool in a variety of applications that involve complex nonlinear relationships of continuous variables, varying sample sizes, and spatiotemporal data with weak or little invariance to translation.

As hypothetical topological defects in the geometry of spacetime, vortex strings could have played many roles in cosmology, and their distinct features can provide observable clues about the early universes evolution. A key feature of vortex strings is that they can interact with Weyl fermionic modes and support massless chiral-anomaly states along strings. To date, despite many attempts to detect vortex strings in astrophysics or to emulate them in artificially created systems, observation of these vortex-string chiral modes remains experimentally elusive. Here we report experimental observations of vortex-string chiral modes using a metamaterial system. This is implemented by inhomogeneous perturbation of Yang-monopole phononic metamaterials. The measured linear dispersion and modal profiles confirm the existence of topological modes bound to and propagating along the string with the chiral anomaly. Our work provides a platform for studying diverse cosmic topological defects in astrophysics and offers applications as topological fibres in communication techniques.

PURPOSE: To compare the evaluation metrics for deep learning methods that were developed using imbalanced imaging data in osteoarthritis studies. MATERIALS AND METHODS: This retrospective study utilized 2996 sagittal intermediate-weighted fat-suppressed knee MRIs with MRI Osteoarthritis Knee Score readings from 2467 participants in the Osteoarthritis Initiative study. We obtained probabilities of the presence of bone marrow lesions (BMLs) from MRIs in the testing dataset at the sub-region (15 sub-regions), compartment, and whole-knee levels based on the trained deep learning models. We compared different evaluation metrics (e.g., receiver operating characteristic (ROC) and precision-recall (PR) curves) in the testing dataset with various class ratios (presence of BMLs vs. absence of BMLs) at these three data levels to assess the models performance. RESULTS: In a subregion with an extremely high imbalance ratio, the model achieved a ROC-AUC of 0.84, a PR-AUC of 0.10, a sensitivity of 0, and a specificity of 1. CONCLUSION: The commonly used ROC curve is not sufficiently informative, especially in the case of imbalanced data. We provide the following practical suggestions based on our data analysis: 1) ROC-AUC is recommended for balanced data, 2) PR-AUC should be used for moderately imbalanced data (i.e., when the proportion of the minor class is above 5% and less than 50%), and 3) for severely imbalanced data (i.e., when the proportion of the minor class is below 5%), it is not practical to apply a deep learning model, even with the application of techniques addressing imbalanced data issues.