In contemporary scientific research, it is of great interest to predict a categorical response based on a high-dimensional tensor (i.e. multi-dimensional array) and additional covariates. This mixture of different types of data leads to challenges in statistical analysis. Motivated by applications in science and engineering, we propose a comprehensive and interpretable discriminant analysis model, called CATCH model (in short for Covariate-Adjusted Tensor Classification in High-dimensions), which efficiently integrates the covariates and the tensor to predict the categorical outcome. The CATCH model jointly models the relationships among the covariates, the tensor predictor, and the categorical response. More importantly, it preserves and utilizes the structures of the data for maximum interpretability and optimal prediction. To tackle the new computational and statistical challenges arising from the intimidating tensor dimensions, we propose a penalized approach to select a subset of tensor predictor entries that has direct discriminative effect after adjusting for covariates. We further develop an efficient algorithm that takes advantage of the tensor structure. Theoretical results confirm that our method achieves variable selection consistency and optimal classification error, even when the tensor dimension is much larger than the sample size. The superior performance of our method over existing methods is demonstrated in extensive simulated and real data examples.

The effect of volcanic aerosols on China's monsoon precipitation over the past 700 years has been studied using two independently compiled histories of volcanism combined with the Monsoon Asia Drought Atlas. For both reconstructions, four categories of eruptions are distinguished based on the character of their Northern Hemisphere (NH) injection; then Superposed Epoch Analysis (SEA) with a 10,000 Monte Carlo resampling procedure is undertaken for each category and also each individual grid. Results show a statistically significant (at 90% confidence level) drying trend over mainland China from year 1 to year 4 after the eruptions, and the more sulfate aerosol that is injected into the NH stratosphere, the more severe this drying trend. In comparison, a minor wetting trend is observed in the years following Southern Hemisphere-only injections. Results from spatial distribution of the SEA show (1) a southward movement of the significant dry areas in eastern China from year 0 to year 2 after volcanic perturbations that are either equal to or double the size of the 1991 Mount Pinatubo eruption (15 T sulfate aerosols in NH) and (2) northeast and northwest China experienced substantial droughts in years 2 to 5. These results are in good agreement with a SEA analysis of the Chinese Historical Drought Disaster Index compiled from historical meteorological records. Our findings illustrate the important role stratospheric aerosols have played in altering China's precipitation during the summer monsoon season and can shed new light on the possible effects that stratospheric geoengineering may have on China's precipitation.

State or societal collapses are often described as featuring rapid reductions in socioeconomic complexity, population loss or displacement, and/or political discontinuity, with climate thought to contribute mainly by disrupting a society’s agroecological base. Here we use a state-of-the-art multi-ice-core reconstruction of explosive volcanism, representing the dominant global external driver of severe short-term climatic change, to reveal a systematic association between eruptions and dynastic collapse across two millennia of Chinese history. We next employ a 1,062-year reconstruction of Chinese warfare as a proxy for political and socioeconomic stress to reveal the dynamic role of volcanic climatic shocks in collapse. We find that smaller shocks may act as the ultimate cause of collapse at times of high pre-existing stress, whereas larger shocks may act with greater independence as proximate causes without substantial observed pre-existing stress. We further show that post-collapse warfare tends to diminish rapidly, such that collapse itself may act as an evolved adaptation tied to the influential “mandate of heaven” concept in which successive dynasties could claim legitimacy as divinely sanctioned mandate holders, facilitating a more rapid restoration of social order.

The incidence of obesity and associated metabolic diseases is increasing globally, adversely affecting human health. Dietary fats, especially triglycerides, are an important source of energy for the body, and the intestine absorbs lipids through a series of orderly and complex steps. A long-term high-fat diet leads to intestinal dysfunction, inducing obesity and metabolic disorders. Therefore, regulating dietary triglycerides absorption is a promising therapeutic strategy. In this review, we will discuss diverse aspects of the dietary triglycerides hydrolysis, fatty acid uptake, triglycerides resynthesis, chylomicron assembly, trafficking, and secretion processes in intestinal epithelial cells, as well as potential targets in this process that may influence dietary fat-induced obesity and metabolic diseases. We also mention the possible shortcomings and deficiencies in modulating dietary lipid absorption targets to provide a better understanding of their administrability as drugs in obesity and related metabolic disorders.

For a multivariate random walk with i.i.d. jumps satisfying the Cramér moment condition and having mean vector with at least one negative component, we derive the exact asymptotics of the probability of ever hitting the positive orthant that is being translated to infinity along a fixed vector with positive components. This problem is motivated by and extends results from a paper by F. Avram et al. (2008) on a two-dimensional risk process. Our approach combines the large deviation techniques from a series of papers by A. Borovkov and A. Mogulskii from around 2000 with new auxiliary constructions, which enable us to extend their results on hitting remote sets with smooth boundaries to the case of boundaries with a "corner" at the "most probable hitting point". We also discuss how our results can be extended to the case of more general target sets.