We present a numerical scheme for approximating the incompressible Navier-Stokes equations based on an auxiliary variable associated with the total system energy. By introducing a dynamic equation for the auxiliary variable and reformulating the Navier-Stokes equations into an equivalent system, the scheme satisfies a discrete energy stability property in terms of a modified energy and it allows for an efficient solution algorithm and implementation. Within each time step, the algorithm involves the computations of two pressure fields and two velocity fields by solving several de-coupled individual linear algebraic systems with constant coefficient matrices, together with the solution of a nonlinear algebraic equation about a scalar number involving a negligible cost. A number of numerical experiments are presented to demonstrate the accuracy and the performance of the presented algorithm.

Collecting comprehensive data sets of the same subject has become a standard in neuroscience research and uncovering multivariate relationships among collected data sets have gained significant attentions in recent years. Canonical correlation analysis (CCA) is one of the powerful multivariate tools to jointly investigate relationships among multiple data sets, which can uncover disease or environmental effects in various modalities simultaneously and characterize changes during development, aging, and disease progressions comprehensively. In the past 10 years, despite an increasing number of studies have utilized CCA in multivariate analysis, simple conventional CCA dominates these applications. Multiple CCA‐variant techniques have been proposed to improve the model performance; however, the complicated multivariate formulations and not well‐known capabilities have delayed their wide applications. Therefore, in this study, a comprehensive review of CCA and its variant techniques is provided. Detailed technical formulation with analytical and numerical solutions, current applications in neuroscience research, and advantages and limitations of each CCA‐related technique are discussed. Finally, a general guideline in how to select the most appropriate CCA‐related technique based on the properties of available data sets and particularly targeted neuroscience questions is provided.

Understanding charge separation and charge transport in mesoporous semiconductor films is crucial to designing high efficiency photoelectrochemical water splitting cells. In the present work, we systematically study the origin of the higher photoelectrochemical performance of mesoporous BiVO 4 film under FTOside illumination (F-illumination) than that under BiVO 4 -side illumination (Billumination). Via intensity-modulated photocurrent spectroscopy in conjunction with modeling simulation of electron diffusion inside mesoporous BiVO 4 films with different thicknesses, we find that the F-illumination is more tolerant to recombination than the B-illumination, leading to a higher charge separation efficiency of the former. Specifically, we have identified a trap-free electron transport region of BiVO 4 vicinal to the FTO substrate and a trap-limited transport region farther away under F-illumination, whereas only a trap-limited transport exists under B-illumination. Simulated results accord well with the experimental data and further provide a deep insight of the detailed electron transport behavior: it is the higher electron density in the region proximal to the FTO under F-illumination that has led to the greater recombination tolerance than under B-illumination. Such a photogenerated electron transport characteristic in mesoporous films is expected to be common for other semiconductors and will inspire practicle strategies for designing high efficiency semiconductor nanostructure-based photoelectrochemical devices.

This paper presents FriendsQA, a challenging question answering dataset that contains 1,222 dialogues and 10,610 open-domain questions, to tackle machine comprehension on everyday conversations. Each dialogue, involving multiple speakers, is annotated with several types of questions regarding the dialogue contexts, and the answers are annotated with certain spans in the dialogue. A series of crowdsourcing tasks are conducted to ensure good annotation quality, resulting a high inter-annotator agreement of 81.82%. A comprehensive annotation analytics is provided for a deeper understanding in this dataset. Three state-of-the-art QA systems are experimented, R-Net, QANet, and BERT, and evaluated on this dataset. BERT in particular depicts promising results, an accuracy of 74.2% for answer utterance selection and an F1-score of 64.2% for answer span selection, suggesting that the FriendsQA task is hard yet has a great potential of elevating QA research on multiparty dialogue to another level.