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Rational design and facile synthesis of efficient environmentally friendly all-inorganic lead-free halide perovskite catalysts are of great significance in photocatalytic CO2 reduction. Aiming at photogenerated charge carrier separation and CO2 reaction dynamics, in this paper, a CsCuCl3 /Cu nanocrystals (NCs) heterojunction catalyst is designed and synthesized via a simple acid-etching solution process by using Cu2 O as the sacrificed template. Due to the disproportionation reaction of Cu2 O induced by concentrated hydrochloric acid, Cu NCs can be deposited onto the surface of CsCuCl3 microcrystals directly and tightly. As revealed by photoelectrochemical analysis, in situ Fourier transform infrared spectra, etc., the Cu NCs contribute a lot to extracting photoelectrons of CsCuCl3 to improve the charge separation efficiency, regulating the CO2 adsorption and activation, and also stabilizing the reaction intermediates. Therefore, CsCuCl3 /Cu heterojunction exhibits a total electron consumption rate of 58.77 µmol g-1 h-1 , which is 2.9-fold of that of single CsCuCl3 . Moreover, high CH4 selectivity of up to 92.7% is achieved, which is much higher than that of CsCuCl3 (50.4%) and most lead-free halide perovskite-based catalysts. This work provides an ingenious but simple strategy to rationally design cocatalysts in situ decorated perovskite catalysts for manipulating both the catalytic activity and the product selectivity.

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In view of the toxicity of the Pb element, exploring eco-friendly Pb-free halide perovskites with excellent photoelectric properties is of great research and practical application significance. Herein, copper-based halide perovskite CsCuCl3 and the corresponding Br--substituted sample (CsCuCl2Br) are designed and explored as the catalysts for photocatalytic CO2 reduction for the first time. A facile antisolvent recrystallization process with pre-prepared single crystals as the precursor is employed to controllably synthesize CsCuCl3 and CsCuCl2Br microcrystals (MCs). The electronic structure and charge transfer property analysis by theoretical and experimental investigation reveal that CsCuCl3 possesses a satisfying bandgap (1.92 eV) and conduction band minimum (CBM) to harvest the sunlight and drive the conversion of CO2 to CH4 and CO. The Br- substitution can not only narrow the bandgap but also facilitate the transportation of charge carriers. Thus, a total electron consumption rate of 44.71 µmol g-1 h-1 is achieved for CsCuCl2Br MCs, which is much better than that of same-sized CsPbBr3 microcrystals or even better than many perovskite nanocrystal photocatalysts. This study suggests that Cu-based perovskites can serve as promising candidates for artificial photosynthesis or other photocatalytic applications, which may propose a new thought to construct lead-free, low-cost photocatalysts.

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Noncompliance issue is common in early phase clinical trials; and may lead to biased estimation of the intent-to-treat effect and incorrect conclusions for the clinical trial. In this work, we propose a Bayesian approach for sequentially monitoring the phase II randomized clinical trials that takes account for the noncompliance information. We adopt the principal stratification framework and propose to use Bayesian additive regression trees for selecting useful baseline covariates and estimating the complier average causal effect (CACE) for both efficacy and toxicity outcomes. The decision of early termination or not is then made adaptively based on the estimated CACE from the accumulated data. Simulation studies have confirmed the excellent performance of the proposed design in the presence of noncompliance.

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In large-scale problems, it is common practice to select important parameters by a procedure such as the Benjamini and Hochberg procedure and construct confidence intervals (CIs) for further investigation while the false coverage-statement rate (FCR) for the CIs is controlled at a desired level. Although the well-known BY CIs control the FCR, they are uniformly inflated. In this paper, we propose two methods to construct shorter selective CIs. The first method produces shorter CIs by allowing a reduced number of selective CIs. The second method produces shorter CIs by allowing a prefixed proportion of CIs containing the values of uninteresting parameters. We theoretically prove that the proposed CIs are uniformly shorter than BY CIs and control the FCR asymptotically for independent data. Numerical results confirm our theoretical results and show that the proposed CIs still work for correlated data. We illustrate the advantage of the proposed procedures by analyzing the microarray data from a HIV study.

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Leaf morphology, particularly in crop, is one of the most important agronomic traits because it influences the yield through the manipulation of photosynthetic capacity and transpiration. To understand the regulatory mechanism of leaf morphogenesis, an Oryza sativa dominant mutant, rolled and erect leaf 1 (rel1) has been characterized. This mutant has a predominant rolled leaf, increased leaf angle, and reduced plant height phenotype that results in a reduction in grain yield. Electron microscope observations indicated that the leaf incurvations of rel1 dominant mutants result from the alteration of the size and number of bulliform cells. Molecular cloning revealed that the rel1 dominant mutant phenotype is caused by the activation of the REL1 gene, which encodes a novel unknown protein, despite its high degree of conservation among monocot plants. Moreover, the downregulation of the REL1 gene in the rel1 dominant mutant restored the phenotype of this dominant mutant. Alternatively, overexpression of REL1 in wild-type plants induced a phenotype similar to that of the dominant rel1 mutant, indicating that REL1 plays a positive role in leaf rolling and bending. Consistent with the observed rel1 phenotype, the REL1 gene was predominantly expressed in the meristem of various tissues during plant growth and development. Nevertheless, the responsiveness of both rel1 dominant mutants and REL1-overexpressing plants to exogenous brassinosteroid (BR) was reduced. Moreover, transcript levels of BR response genes in the rel1 dominant mutants and REL1-overexpressing lines were significantly altered. Additionally, seven REL1-interacting proteins were also identified from a yeast two-hybrid screen. Taken together, these findings suggest that REL1 regulates leaf morphology, particularly in leaf rolling and bending, through the coordination of BR signalling transduction.

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In many applications, researchers are interested in making q pairwise comparisons among k test groups on the basis of m outcome variables. Often, m is very large. For example, such situations arise in gene expression microarray studies involving several experimental groups. Researchers are often not only interested in identifying differentially expressed genes between a given pair of experimental groups, but are also interested in making directional inferences such as whether a gene is up- or downregulated in one treatment group relative to another. In such situations, in addition to the usual errors such as false positive (Type I error) and false negative (Type II error), one may commit directional error (Type III error). For example, in a dose response microarray study, a gene may be declared to be upregulated in the high dose group compared to the low dose group when it is not. In this paper, we introduce a mixed directional false discovery rate (mdFDR) controlling procedure using weighted p-values to select positives in different directions. The weights are defined as the inverse of two times the proportion of either positive or negative discoveries. The proposed procedure has been proved mathematically to control the mdFDR at level α and to have a larger power (which is defined as the expected proportion of nontrue null hypotheses) than the GSP10 procedure proposed by Guo et al. (2010). Simulation studies and real data analysis are also conducted to show the outperformance of the proposed procedure than the GSP10 procedure.

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Coherence and consonance are the two important concepts to ensure consistent conclusions drawn from multiple tests. Unlike coherence, consonance of a multiple testing procedure (MTP) has not yet received much attention. Although most of the MTPs used in practice are consonant, cases still exist that dissonant tests have to be used due to their unique advantages, for example, the likelihood ratio tests and sum tests. Consonance adjustments are necessary for such tests to avoid difficulty in interpretation. Moreover, in terms of detecting elementary hypotheses, a consonant test procedure is uniformly more powerful than the corresponding dissonant one. In this paper, several general methods using the partitioning principle to construct (strongly) consonant and strongly coherent MTPs are proposed. As a result, any dissonant (but coherent) multiple level α test can be improved by a consonant one without any cost in terms of inferences on elementary hypotheses.

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In microarray experiments, the goal is often to examine many genes, and select some of them for additional investigation. Traditionally, such a selection problem has been formulated as a multiple testing problem. When the genes of interest are genes with unequal distribution of gene expression under different conditions, multiple testing methods provide an appropriate framework for addressing the selection problems. However, when the genes of interest are a set of genes with the largest difference in gene expression under different conditions, multiple testing methods do not directly address the selection goal and sometimes lead to biased conclusions. For such cases, we propose two methods based on the statistical ranking and selection framework to directly address the selection goal. The proposed methods have an inherent optimization nature in that the selection is optimized according to either a prespecified minimum correct selection ratio (r* selection) or probability of making a correct selection (P* selection). These methods are compared with the multiple testing method that controls the tail probability of the proportion of false positives. Both simulation studies and real data applications provide insight into the fundamental difference between the multiple testing methods and the proposed methods in the way of addressing different selection goals. It has been shown that the proposed methods provide a clear advantage over the multiple testing methods when the goal is to select the most significant genes (not all the significant genes). When the goal is to select all the significant genes, the proposed methods perform equally well as the current multiple testing methods. Another advantage provided by the proposed methods is their ability to detect noisy data and therefore suggest no sensible selection can be made.

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An analytical method has been developed for directly calculating the principal angle theta(p) at which the phase difference between the two reflection coefficients is equal to 90 degrees and at which the ratio of /r(p)/ to /r(s)/ is equal or close to a minimum. The equations given here can be used in many optical applications. For example, ellipsometric data measured at an incidence angle theta(p) will have higher precision than data measured at other incidence angles. theta(p) is the principal angle. Instead of three principal angles, there is only one principal angle, which can be found in the region of 0 < or = theta(p) < or = 90 degrees for most metallic materials used in applications. Results show good agreement between the measured and the calculated spectra of delta(p) and rho(po).