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Brain-effective connectivity analysis quantifies directed influence of one neural element or region over another, and it is of great scientific interest to understand how effective connectivity pattern is affected by variations of subject conditions. Vector autoregression (VAR) is a useful tool for this type of problems. However, there is a paucity of solutions when there is measurement error, when there are multiple subjects, and when the focus is the inference of the transition matrix. In this article, we study the problem of transition matrix inference under the high-dimensional VAR model with measurement error and multiple subjects. We propose a simultaneous testing procedure, with three key components: a modified expectation-maximization (EM) algorithm, a test statistic based on the tensor regression of a bias-corrected estimator of the lagged auto-covariance given the covariates, and a properly thresholded simultaneous test. We establish the uniform consistency for the estimators of our modified EM, and show that the subsequent test achieves both a consistent false discovery control, and its power approaches one asymptotically. We demonstrate the efficacy of our method through both simulations and a brain connectivity study of task-evoked functional magnetic resonance imaging.

 

The electrochemical CO 2 or CO reduction to chemicals and fuels using renewable energy is a promising way to reduce anthropogenic carbon emissions. The gas diffusion electrode (GDE) design enables low-carbon manufacturing of target products at a current density (e.g., 500 mA cm −2 ) relevant to industrial requirements. However, the long-term stability of the GDE is restricted by poor water management and flooding, resulting in a significant hydrogen evolution reaction (HER) within almost an hour. The optimization of water management in the GDE demands a thorough understanding of the role of the gas diffusion layer (GDL) and the catalyst layer (CL) distinctively. Herein, the hydrophobicity of the GDL and CL is independently adjusted to investigate their influence on gas transport efficiency and water management. The gas transport efficiency is more enhanced with the increase in hydrophobicity of the GDL than the CL. Direct visualization of water distribution by optical microscope and micro-computed tomography demonstrates that the water flow pattern transfers from the stable displacement to capillary fingering as GDL hydrophobicity increases. Unfortunately, only increasing the hydrophobicity is not sufficient to prevent flooding. A revolutionary change in the design of the GDE structure is essential to maintain the long-term stability of CO 2 /CO reduction.