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Matrix-valued data, where the sampling unit is a matrix consisting of rows and columns of measurements, are emerging in numerous scientific and business applications. Matrix Gaussian graphical models are a useful tool to characterize the conditional dependence structure of rows and columns. We employ non-convex penalization to tackle the estimation of multiple graphs from matrix-valued data under a matrix normal distribution. We propose a highly efficient non-convex optimization algorithm that can scale up for graphs with hundreds of nodes. We establish the asymptotic properties of the estimator, which requires less stringent conditions and has a sharper probability error bound than existing results. We demonstrate the efficacy of our proposed method through both simulations and real functional magnetic resonance imaging analyses.

With the recent explosion of scientific data of unprecedented size and complexity, feature ranking and screening are playing an increasingly important role in many scientific studies. In this article, we propose a novel feature screening procedure under a unified model framework, which covers a wide variety of commonly used parametric and semiparametric models. The new method does not require imposing a specific model structure on regression functions, and thus is particularly appealing to ultrahigh-dimensional regressions, where there are a huge number of candidate predictors but little information about the actual model forms. We demonstrate that, with the number of predictors growing at an exponential rate of the sample size, the proposed procedure possesses consistency in ranking, which is both useful in its own right and can lead to consistency in selection. The new procedure is computationally efficient and simple, and exhibits a competent empirical performance in our intensive simulations and real data analysis.

We introduce a principal support vector machine (PSVM) approach that can be used for both linear and nonlinear sufficient dimension reduction. The basic idea is to divide the response variables into slices and use a modified form of support vector machine to find the optimal hyperplanes that separate them. These optimal hyperplanes are then aligned by the principal components of their normal vectors. It is proved that the aligned normal vectors provide an unbiased, $\\sqrt n $ -consistent, and asymptotically normal estimator of the sufficient dimension reduction space. The method is then generalized to nonlinear sufficient dimension reduction using the reproducing kernel Hubert space. In that context, the aligned normal vectors become functions and it is proved that they are unbiased in the sense that they are functions of the true nonlinear sufficient predictors. We compare PSVM with other sufficient dimension reduction methods by simulation and in real data analysis, and through both comparisons firmly establish its practical advantages.

Aiming at abundant scientific and engineering data with not only high dimensionality but also complex structure, we study the regression problem with a multidimensional array (tensor) response and a vector predictor. Applications include, among others, comparing tensor images across groups after adjusting for additional covariates, which is of central interest in neuroimaging analysis. We propose parsimonious tensor response regression adopting a generalized sparsity principle. It models all voxels of the tensor response jointly, while accounting for the inherent structural information among the voxels. It effectively reduces the number of free parameters, leading to feasible computation and improved interpretation. We achieve model estimation through a nascent technique called the envelope method, which identifies the immaterial information and focuses the estimation based upon the material information in the tensor response. We demonstrate that the resulting estimator is asymptotically efficient, and it enjoys a competitive finite sample performance. We also illustrate the new method on two real neuroimaging studies. Supplementary materials for this article are available online.

Existing sufficient dimension reduction methods suffer from the fact that each dimension reduction component is a linear combination of all the original predictors, so that it is difficult to interpret the resulting estimates. We propose a unified estimation strategy, which combines a regression-type formulation of sufficient dimension reduction methods and shrinkage estimation, to produce sparse and accurate solutions. The method can be applied to most existing sufficient dimension reduction methods such as sliced inverse regression, sliced average variance estimation and principal Hessian directions. We demonstrate the effectiveness of the proposed method by both simulations and real data analysis.

Cancer remains one of the leading causes of death worldwide. The severe adverse reactions and toxic side effects associated with conventional treatments such as surgery, radiotherapy, and chemotherapy pose significant challenges for researchers and clinical practitioners. These limitations have driven the pursuit of more advanced and effective therapeutic approaches. In recent years, natural products have attracted considerable attention in the field of disease treatment and have become an important source for new drug development. Matrine, a major active component of the traditional medicinal plant Sophora flavescens , exhibits a broad range of pharmacological activities, particularly notable antitumor effects. Its antitumor mechanisms include the induction of apoptosis, autophagy, and ferroptosis in tumor cells, as well as the inhibition of tumor cell proliferation, migration, and invasion. With the continuous advancement of therapeutic technologies and the emergence of novel drug delivery strategies, the integration of natural products into cancer therapy has gained renewed significance in the context of innovative delivery systems. Based on this, the present review comprehensively discusses and analyzes the antitumor mechanisms of matrine and its application in nano-delivery systems, highlighting their progress and potential in major disease intervention strategies. This provides new insights for the development and application of advanced drug delivery strategies and technologies in both basic and clinical pharmaceutical research.

Genetic transformation is a pivotal approach in plant genetic engineering. Peanut ( Arachis hypogaea L.) is an important oil and cash crop, but the stable genetic transformation of peanut is still difficult and inefficient. Recently, the pollen tube injection pathway has been shown to be effective for the genetic transformation of peanut. However, the poor reproducibility of this pathway is still controversial. In this study, the appropriate time and location of injection, along with transgenic screening, were systematically investigated in the pollen tube mediated peanut genetic transformation. Our findings revealed that Agrobacterium injections could be conducted within a time window of two to three hours preceding and succeeding the blooming process. Among the various selective markers evaluated, the Basta screening emerged as the most expedient, followed closely by the DsRed visual screening. According to resistance screening and molecular identification, the average transformation efficiency was 2.6% in the heritable transgenic progenies, which was more likely affected by individual operation by style cavity injection. Furthermore, the use of synergistic FT artificially regulated the blooming of peanuts under indoor conditions, facilitating operations involving keel petal injection and ultimately enhancing the genetic transformation efficiency. Thus, our study systematically validated the feasibility of peanut genetic transformation through an optimized pollen-tube injection technique without tissue culture, potentially guiding future advancements in peanut engineering and molecular breeding programs.

The rise of network data in many different domains has offered researchers new insights into the problem of modeling complex systems and propelled the development of numerous innovative statistical methodologies and computational tools. In this paper, we primarily focus on two types of biological networks, gene networks and brain networks, where statistical network modeling has found both fruitful and challenging applications. Unlike other network examples such as social networks where network edges can be directly observed, both gene and brain networks require careful estimation of edges using measured data as a first step. We provide a discussion on existing statistical and computational methods for edge estimation and subsequent statistical inference problems in these two types of biological networks.

Modern technologies are producing a wealth of data with complex structures. For instance, in two‐dimensional digital imaging, flow cytometry and electroencephalography, matrix‐type covariates frequently arise when measurements are obtained for each combination of two underlying variables. To address scientific questions arising from those data, new regression methods that take matrices as covariates are needed, and sparsity or other forms of regularization are crucial owing to the ultrahigh dimensionality and complex structure of the matrix data. The popular lasso and related regularization methods hinge on the sparsity of the true signal in terms of the number of its non‐zero coefficients. However, for the matrix data, the true signal is often of, or can be well approximated by, a low rank structure. As such, the sparsity is frequently in the form of low rank of the matrix parameters, which may seriously violate the assumption of the classical lasso. We propose a class of regularized matrix regression methods based on spectral regularization. A highly efficient and scalable estimation algorithm is developed, and a degrees‐of‐freedom formula is derived to facilitate model selection along the regularization path. Superior performance of the method proposed is demonstrated on both synthetic and real examples.

L‐5‐Methyltetrahydrofolate (L‐5‐MTHF) is the only biologically active form of folate in the human body. Production of L‐5‐MTHF by using microbes is an emerging consideration for green synthesis. However, microbes naturally produce only a small amount of L‐5‐MTHF. Here, Escherichia coli BL21(DE3) was engineered to increase the production of L‐5‐MTHF by overexpressing the intrinsic genes of dihydrofolate reductase and methylenetetrahydrofolate (methylene‐THF) reductase, introducing the genes encoding formate‐THF ligase, formyl‐THF cyclohydrolase and methylene‐THF dehydrogenase from the one‐carbon metabolic pathway of Methylobacterium extorquens or Clostridium autoethanogenum and disrupting the gene of methionine synthase involved in the consumption and synthesis inhibition of the target product. Thus, upon its native pathway, an additional pathway for L‐5‐MTHF synthesis was developed in E. coli, which was further analysed and confirmed by qRT‐PCR, enzyme assays and metabolite determination. After optimizing the conditions of induction time, temperature, cell density and concentration of IPTG and supplementing exogenous substances (folic acid, sodium formate and glucose) to the culture, the highest yield of 527.84 μg g−1 of dry cell weight for L‐5‐MTHF was obtained, which was about 11.8 folds of that of the original strain. This study paves the way for further metabolic engineering to improve the biosynthesis of L‐5‐MTHF in E. coli. L ‐5‐Methyltetrahydrofolate (L‐5‐MTHF) is the only biologically active form of folate in the human body. Production of L‐5‐MTHF by using microbes is an emerging consideration for green synthesis. Here, Escherichia coli BL21(DE3) was engineered to increase the production of L‐5‐MTHF. After optimizing the conditions and supplementing exogenous substances, the highest yield of 527.84 µg∙g‐1 of dry cell weight for L‐5‐MTHF was obtained, which was about 11.8 folds of that of the original strain.