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Hierarchical data analysis is crucial in various fields for making discoveries. The linear mixed model is often used for training hierarchical data, but its parameter estimation is computationally expensive, especially with big data. Subsampling techniques have been developed to address this challenge. However, most existing subsampling methods assume homogeneous data and do not consider the possible heterogeneity in hierarchical data. To address this limitation, we develop a new approach called group-orthogonal subsampling (GOSS) for selecting informative subsets of hierarchical data that may exhibit heterogeneity. GOSS selects subdata with balanced data size among groups and combinatorial orthogonality within each group, resulting in subdata that are D- and A-optimal for building linear mixed models. Estimators of parameters trained on GOSS subdata are consistent and asymptotically normal. GOSS is shown to be numerically appealing via simulations and a real data application. Theoretical proofs, R codes, and supplementary numerical results are accessible online as . [ABSTRACT FROM AUTHOR]

Strong orthogonal arrays are suitable designs for computer experiments because of stratification in low‐dimensional projections. However, strong orthogonal arrays may be very expensive for a moderate number of factors. In this article, we develop a method for constructing space‐filling designs with more economical run sizes. These designs are not only column‐orthogonal but also enjoy a large proportion of low‐dimensional stratification properties that strong orthogonal arrays ought to have. Moreover, a class of proposed designs can be 3‐orthogonal. In addition, some theoretical results on regular fractional factorial designs are obtained as a by‐product. [ABSTRACT FROM AUTHOR]

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A supersaturated design (SSD) is a factorial design whose run size is not enough for estimating all the main effects. Such designs have received much recent interest because of their potential in factor screening experiments. This paper first shows that the design obtained by the Kronecker sum of a balanced design and a generalized Hadamard matrix (i.e., a matrix with both itself and its transpose being difference matrices) has some nice properties. Based on these findings, some new methods for constructing E (f NOD) -optimal SSDs via generalized Hadamard matrices are developed. Meanwhile, the non-orthogonality of the proposed designs is well controlled by the source designs. In addition, some generalized Hadamard matrices with nice properties are constructed for obtaining E (f NOD) -optimal SSDs. The proposed methods are easy to implement and many new SSDs can then be constructed. [ABSTRACT FROM AUTHOR]

Space-filling designs are widely used in both computer and physical experiments. Column-orthogonality, maximin distance, and projection uniformity are three basic and popular space-filling criteria proposed from different perspectives, but their relationships have been rarely investigated. We show that the average squared correlation metric is a function of the pairwise L2-distances between the rows only. We further explore the connection between uniform projection designs and maximin L1-distance designs. Based on these connections, we develop new lower and upper bounds for column-orthogonality and projection uniformity from the perspective of distance between design points. These results not only provide new theoretical justifications for each criterion but also help in finding better space-filling designs under multiple criteria. for this article are available online. [ABSTRACT FROM AUTHOR]

An order-of-addition experiment is a kind of experiment in which the response is affected by the addition order of materials or components. In many situations, performing the full design with all possible permutations of components is unaffordable, especially when the number of components is larger than four. We introduce a component-position model for analyzing data from such experiments and study associated problems. We further propose a new type of design, called component orthogonal array, as a fraction of the full design for order-of-addition experiments. It is shown that component orthogonal arrays have the same D-efficiency as the full design under our proposed model. Component orthogonal arrays also perform well under the existing pairwise ordering model. Two drug combination experiments are used to show the effectiveness of the proposed model and designs. Supplementary materials for this paper are available online. [ABSTRACT FROM AUTHOR]

Abstract: Factorial designs are arguably the most widely used designs in scientific investigations. Generalized minimum aberration (GMA) and uniformity are two important criteria for evaluating both regular and non-regular designs. The generation of GMA designs is a non-trivial problem due to the sequential optimization nature of the criterion. Based on an analytical expression between the generalized wordlength pattern and a uniformity measure, this paper converts the generation of GMA designs to a constrained optimization problem, and provides effective algorithms for solving this particular problem. Moreover, many new designs with GMA or near-GMA are reported, which are also (nearly) optimal under the uniformity measure. [Copyright &y& Elsevier]

Halophytes are remarkable plants that can tolerate extremely high-salinity conditions, and have different salinity tolerance mechanisms from those of glycophytic plants. In this work, we investigated the mechanisms of salinity tolerance of an extreme halophyte, Kochia sieversiana (Pall.) C. A. M, using RNA sequencing and physiological tests. The results showed that moderate salinity stimulated the growth and water uptake of K. sieversiana and, even under 480-mM salinity condition, K. sieversiana maintained an extremely high water content. This high water content may be a specific adaptive strategy of K. sieversiana to high salinity. The physiological analysis indicated that increasing succulence and great accumulations of sodium, alanine, sucrose, and maltose may be favorable to the water uptake and osmotic regulation of K. sieversiana under high-salinity stress. Transcriptome data indicated that some aquaporin genes and potassium (K + ) transporter genes may be important for water uptake and ion balance, respectively, while different members of those gene families were employed under low- and high-salinity stresses. In addition, several aquaporin genes were up-regulated in low- but not high-salinity stressed roots. The highly expressed aquaporin genes may allow low-salinity stressed K. sieversiana plants to uptake more water than control plants. The leaf K + /root K + ratio was enhanced under low- but not high-salinity stress, which suggested that low salinity might promote K + transport from the roots to the shoots. Hence, we speculated that low salinity might allow K. sieversiana to uptake more water and transport more K + from roots to shoots, increasing the growth rate of K. sieversiana .