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Summary: Synthetic genomics involves the design, assembly, and transfer of artificially synthesized DNA fragments into target hosts to replace the native genome and construct viable forms of life. With advances in DNA synthesis and assembly techniques, the application of synthetic genomics in viruses, bacteria, and yeast has improved our knowledge of genome organization and function. Multicellular eukaryotic organisms are characterized by larger genomes, more complex epigenetic regulation, and widespread transposable elements, making genome synthesis challenging. Recently, the first synthetic multicellular eukaryotic organism was generated in the model plant Physcomitrium patens with a partially synthetic chromosome arm. Here, we introduce the design and assembly principles of moss genome synthesis. We also discuss the remaining technical barriers in the application of synthetic genomics in seed plants. [ABSTRACT FROM AUTHOR]

Plants or tissues can be regenerated through various pathways. Like animal regeneration, cell totipotency and pluripotency are the molecular basis of plant regeneration. Detailed systematic studies on Arabidopsis thaliana gradually unravel the fundamental mechanisms and principles underlying plant regeneration. Specifically, plant hormones, cell division, epigenetic remodeling, and transcription factors play crucial roles in reprogramming somatic cells and reestablishing meristematic cells. Recent research on basal non-vascular plants and monocot crops has revealed that plant regeneration differs among species, with various plant species using distinct mechanisms and displaying significant differences in regenerative capacity. Conducting multi-omics studies at the single-cell level, tracking plant regeneration processes in real-time, and deciphering the natural variation in regenerative capacity will ultimately help understand the essence of plant regeneration, improve crop regeneration efficiency, and contribute to future crop design. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study multiple structural changes that occur at unknown locations in high-dimensional linear regression. We consider a structural change model where the parameters are subject to shifts at possibly different locations. We propose a penalized least squares approach, combined with a temporal difference penalty term for the difference between the coefficients at successive points for identifying latent change points, as well as a common sparsity penalty to detect important covariates. This procedure automatically estimates the number and the locations of the change-points and the parameters in each corresponding segment. To implement the proposed approach, we devise an alternating direction method of multipliers (ADMM) algorithm. We demonstrate the convergence of the proposed ADMM algorithm in the present setting. We also establish an oracle inequality for the proposed estimator. We carry out simulation studies to evaluate the finite sample performance of the proposed method and illustrate its application on a data set. [ABSTRACT FROM AUTHOR]

This article, published in the journal Molecular Horticulture, explores the role of cytokinin in the patterning of adventitious root apical meristem (adRAM) from leaf cuttings. The study focuses on Arabidopsis thaliana leaf cuttings and reveals that cytokinin is required for the tissue differentiation of the adRAM. The researchers conducted experiments using cytokinin inhibitors and mutants, and observed adverse effects on root regeneration. They also analyzed the expression patterns of auxin and cytokinin markers during adventitious root organogenesis, which indicated that auxin and cytokinin function antagonistically in different steps and cells during cell fate transition and differentiation. The findings suggest that cytokinin contributes to the elimination of the stem cell niche identity and tissue differentiation in the adRAM, ensuring its maturation. [Extracted from the article]

In this paper, we investigate solving the elliptical multiple eigenvalue (EME) problems using a Feedforward Neural Network. Firstly, we propose a general formulation for computing EME based on penalized variational forms of elliptical eigenvalue problems. Next, we solve the penalized variational form using the Deep Ritz Method. We establish an upper bound on the error between the estimated eigenvalues and true ones in terms of the depth D , width W of the neural network, and training sample size n. By exploring the regularity of the EME and selecting an appropriate depth D and width W , we demonstrate that the desired bound enjoys a convergence rate of O (1 / n 16) , which circumvents the curse of dimensionality. We also present several high-dimensional simulation results to illustrate the effectiveness of our proposed method and support our theoretical findings. [ABSTRACT FROM AUTHOR]

Using deep neural networks to solve partial differential equations (PDEs) has attracted a lot of attention recently. However, why the deep learning method works is falling far behind its empirical success. In this paper, we provide a rigorous numerical analysis on the deep Ritz method (DRM) for second-order elliptic equations with Dirichlet, Neumann and Robin boundary conditions, respectively. We establish the first nonasymptotic convergence rate in H 1 norm for DRM using deep neural networks with smooth activation functions including logistic and hyperbolic tangent functions. Our results show how to set the hyper-parameter of depth and width to achieve the desired convergence rate in terms of the number of training samples. [ABSTRACT FROM AUTHOR]

The shoot meristem generates the entire shoot system and is precisely maintained throughout the life cycle under various environmental challenges. In this study, we identified a prion-like domain (PrD) in the key shoot meristem regulator SHOOT MERISTEMLESS (STM), which distinguishes STM from other related KNOX1 proteins. We demonstrated that PrD stimulates STM to form nuclear condensates, which are required for maintaining the shoot meristem. STM nuclear condensate formation is stabilized by selected PrD-containing STM-interacting BELL proteins in vitro and in vivo. Moreover, condensation of STM promotes its interaction with the Mediator complex subunit MED8 and thereby enhances its transcriptional activity. Thus, condensate formation emerges as a novel regulatory mechanism of shoot meristem functions. Furthermore, we found that the formation of STM condensates is enhanced upon salt stress, which allows enhanced salt tolerance and increased shoot branching. Our findings highlight that the transcription factor partitioning plays an important role in cell fate determination and might also act as a tunable environmental acclimation mechanism. Condensate formation is essential for STM to function as a shoot meristem regulator. Condensation of STM promotes its transcriptional activity to ensure meristem maintenance. Salt treatment enhances condensate formation and promotes accessory axillary bud formation. [ABSTRACT FROM AUTHOR]

We propose a deep generative approach to sampling from a conditional distribution based on a unified formulation of conditional distribution and generalized nonparametric regression function using the noise-outsourcing lemma. The proposed approach aims at learning a conditional generator, so that a random sample from the target conditional distribution can be obtained by transforming a sample drawn from a reference distribution. The conditional generator is estimated nonparametrically with neural networks by matching appropriate joint distributions using the Kullback-Liebler divergence. An appealing aspect of our method is that it allows either of or both the predictor and the response to be high-dimensional and can handle both continuous and discrete type predictors and responses. We show that the proposed method is consistent in the sense that the conditional generator converges in distribution to the underlying conditional distribution under mild conditions. Our numerical experiments with simulated and benchmark image data validate the proposed method and demonstrate that it outperforms several existing conditional density estimation methods. for this article are available online. [ABSTRACT FROM AUTHOR]

In this paper, we consider recovering n - dimensional signals from m binary measurements corrupted by noises and sign flips under the assumption that the target signals have low generative intrinsic dimension, i.e., the target signals can be approximately generated via an L-Lipschitz generator G : R k → R n , k ≪ n . Although the binary measurements model is highly nonlinear, we propose a least square decoder and prove that, up to a constant c, with high probability, the least square decoder achieves a sharp estimation error C k log (L n) m as long as m ≥ C (k log (L n)) . Extensive numerical simulations and comparisons with state-of-the-art methods demonstrated the least square decoder is robust to noise and sign flips, as indicated by our theory. By constructing a ReLU network with properly chosen depth and width, we verify the (approximately) deep generative prior, which is of independent interest. [ABSTRACT FROM AUTHOR]

During their postembryonic development, plants continuously form branches to conquer more space and adapt to changing environments. In seed plants, this is achieved by lateral branching, in which axillary meristems (AMs) initiate at the leaf axils to form axillary buds. The developmental potential of AMs to form shoot branches is the same as that of embryonic shoot apical meristems (SAMs). Recent studies in Arabidopsis thaliana have revealed the cellular origin of AMs and have identified transcription factors and phytohormones that regulate sequential steps leading to AM initiation. In particular, a group of meristematic cells detached from the SAM are key to AM initiation, which constitutes an excellent system for understanding stem cell fate and de novo meristem formation. [ABSTRACT FROM AUTHOR]

Motivation The findings from genome-wide association studies (GWASs) have greatly helped us to understand the genetic basis of human complex traits and diseases. Despite the tremendous progress, much effects are still needed to address several major challenges arising in GWAS. First, most GWAS hits are located in the non-coding region of human genome, and thus their biological functions largely remain unknown. Second, due to the polygenicity of human complex traits and diseases, many genetic risk variants with weak or moderate effects have not been identified yet. Results To address the above challenges, we propose a powerful and adaptive latent model (PALM) to integrate cell-type/tissue-specific functional annotations with GWAS summary statistics. Unlike existing methods, which are mainly based on linear models, PALM leverages a tree ensemble to adaptively characterize non-linear relationship between functional annotations and the association status of genetic variants. To make PALM scalable to millions of variants and hundreds of functional annotations, we develop a functional gradient-based expectation–maximization algorithm, to fit the tree-based non-linear model in a stable manner. Through comprehensive simulation studies, we show that PALM not only controls false discovery rate well, but also improves statistical power of identifying risk variants. We also apply PALM to integrate summary statistics of 30 GWASs with 127 cell type/tissue-specific functional annotations. The results indicate that PALM can identify more risk variants as well as rank the importance of functional annotations, yielding better interpretation of GWAS results. Availability and implementation The source code is available at https://github.com/YangLabHKUST/PALM. Supplementary information Supplementary data are available at Bioinformatics online. [ABSTRACT FROM AUTHOR]

Spatially resolved transcriptomics involves a set of emerging technologies that enable the transcriptomic profiling of tissues with the physical location of expressions. Although a variety of methods have been developed for data integration, most of them are for single-cell RNA-seq datasets without consideration of spatial information. Thus, methods that can integrate spatial transcriptomics data from multiple tissue slides, possibly from multiple individuals, are needed. Here, we present PRECAST, a data integration method for multiple spatial transcriptomics datasets with complex batch effects and/or biological effects between slides. PRECAST unifies spatial factor analysis simultaneously with spatial clustering and embedding alignment, while requiring only partially shared cell/domain clusters across datasets. Using both simulated and four real datasets, we show improved cell/domain detection with outstanding visualization, and the estimated aligned embeddings and cell/domain labels facilitate many downstream analyses. We demonstrate that PRECAST is computationally scalable and applicable to spatial transcriptomics datasets from different platforms. Methods that perform data integration are needed to analyse spatial transcriptomics data from multiple tissue slides. Here, the authors present PRECAST, an efficient data integration method for multiple spatial transcriptomics datasets with complex batch or biological effects between slides. [ABSTRACT FROM AUTHOR]

Spatially resolved transcriptomics involves a set of emerging technologies that enable the transcriptomic profiling of tissues with the physical location of expressions. Although a variety of methods have been developed for data integration, most of them are for single-cell RNA-seq datasets without consideration of spatial information. Thus, methods that can integrate spatial transcriptomics data from multiple tissue slides, possibly from multiple individuals, are needed. Here, we present PRECAST, a data integration method for multiple spatial transcriptomics datasets with complex batch effects and/or biological effects between slides. PRECAST unifies spatial factor analysis simultaneously with spatial clustering and embedding alignment, while requiring only partially shared cell/domain clusters across datasets. Using both simulated and four real datasets, we show improved cell/domain detection with outstanding visualization, and the estimated aligned embeddings and cell/domain labels facilitate many downstream analyses. We demonstrate that PRECAST is computationally scalable and applicable to spatial transcriptomics datasets from different platforms.Methods that perform data integration are needed to analyse spatial transcriptomics data from multiple tissue slides. Here, the authors present PRECAST, an efficient data integration method for multiple spatial transcriptomics datasets with complex batch or biological effects between slides. [ABSTRACT FROM AUTHOR]

SUMMARY: Single‐cell sequencing approaches reveal the intracellular dynamics of individual cells and answer biological questions with high‐dimensional catalogs of millions of cells, including genomics, transcriptomics, chromatin accessibility, epigenomics, and proteomics data across species. These emerging yet thriving technologies have been fully embraced by the field of plant biology, with a constantly expanding portfolio of applications. Here, we introduce the current technical advances used for single‐cell omics, especially single‐cell genome and transcriptome sequencing. Firstly, we overview methods for protoplast and nucleus isolation and genome and transcriptome amplification. Subsequently, we use well‐executed benchmarking studies to highlight advances made through the application of single‐cell omics techniques. Looking forward, we offer a glimpse of additional hurdles and future opportunities that will introduce broad adoption of single‐cell sequencing with revolutionary perspectives in plant biology. Significance Statement: In this review, we introduce the current technical advances in single‐cell omics, especially single‐cell genome and transcriptome sequencing. Firstly, we overview methods for protoplast and nucleus isolation and genome and transcriptome amplification. Subsequently, we use well‐executed benchmarking studies to highlight advances made through the application of single‐cell omics techniques. [ABSTRACT FROM AUTHOR]

Aiming at improving assembly line efficiency and flexibility, a balancing method of parallel U-shaped assembly line system is proposed. Based on the improved product priority diagram, the bidirectional priority value formula is obtained. Then, assembly lines are partitioned into z-q partitions and workstations are defined. After that, the mathematical model of the parallel U-shaped assembly line balancing problem is established. A heuristic algorithm based on bidirectional priority values is used to solve explanatory examples and test examples. It can be seen from the results and the effect indicators of the assembly line balancing problem that the heuristic algorithm is suitable for large balancing problems. The proposed method has higher calculation accuracy and shorter calculation time. The balancing effect of the parallel U-shaped assembly line is better than that of single U-shaped assembly line, which verifies the superiority of the parallel U-type assembly line and effectiveness of the proposed method. It provides a theoretical and practical reference for parallel U-type assembly line balancing problem. [ABSTRACT FROM AUTHOR]

We propose a fast Newton algorithm for ℓ 0 regularized high-dimensional generalized linear models based on support detection and root finding. We refer to the proposed method as GSDAR. GSDAR is developed based on the KKT conditions for ℓ 0 -penalized maximum likelihood estimators and generates a sequence of solutions of the KKT system iteratively. We show that GSDAR can be equivalently formulated as a generalized Newton algorithm. Under a restricted invertibility condition on the likelihood function and a sparsity condition on the regression coefficient, we establish an explicit upper bound on the estimation errors of the solution sequence generated by GSDAR in supremum norm and show that it achieves the optimal order in finite iterations with high probability. Moreover, we show that the oracle estimator can be recovered with high probability if the target signal is above the detectable level. These results directly concern the solution sequence generated from the GSDAR algorithm, instead of a theoretically defined global solution. We conduct simulations and real data analysis to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Leaf shape is highly variable within and among plant species, ranging from slender to oval shaped. This is largely determined by the proximodistal axis of growth. However, little is known about how proximal–distal growth is controlled to determine leaf shape. Here, we show that Arabidopsis leaf and sepal proximodistal growth is tuned by two phytohormones. Two class A AUXIN RESPONSE FACTORs (ARFs), ARF6 and ARF8, activate the transcription of DWARF4 , which encodes a key brassinosteroid (BR) biosynthetic enzyme. At the cellular level, the phytohormones promote more directional cell expansion along the proximodistal axis, as well as final cell sizes. BRs promote the demethyl-esterification of cell wall pectins, leading to isotropic in-plane cell wall loosening. Notably, numerical simulation showed that isotropic cell wall loosening could lead to directional cell and organ growth along the proximodistal axis. Taken together, we show that auxin acts through biosynthesis of BRs to determine cell wall mechanics and directional cell growth to generate leaves of variable roundness. Highly variable leaf shape is largely determined by the proximodistal growth. This study reveals that auxin signaling activates the transcription of DWARF4 to promote the brassinosteroid biosynthesis in leaf and sepal epidermis, which modulates the cell wall mechanics and directional cell growth. These findings provide a mechanical perspective of how gene activities regulate the organ shape. [ABSTRACT FROM AUTHOR]

The shape of comparable tissues and organs is consistent among individuals of a given species, but how this consistency or robustness is achieved remains an open question. The interaction between morphogenetic factors determines organ formation and subsequent shaping, which is ultimately a mechanical process. Using a computational approach, we show that the epidermal layer is essential for the robustness of organ geometry control. Specifically, proper epidermal restriction allows organ asymmetry maintenance, and the tensile epidermal layer is sufficient to suppress local variability in growth, leading to shape robustness. The model explains the enhanced organ shape variations in epidermal mutant plants. In addition, differences in the patterns of epidermal restriction may underlie the initial establishment of organ asymmetry. Our results show that epidermal restriction can answer the longstanding question of how cellular growth noise is averaged to produce precise organ shapes, and the findings also shed light on organ asymmetry establishment. [ABSTRACT FROM AUTHOR]

SUMMARY: Compound leaves are composed of multiple separate blade units termed leaflets. In tomato (Solanum lycopersicum) compound leaves, auxin promotes both leaflet initiation and blade expansion. However, it is unclear how these two developmental processes interact. With highly variable complexity, tomato compound leaves provide an ideal system to address this question. In this study, we obtained and analyzed mutants of the WUSCHEL‐RELATED HOMEOBOX (WOX) family gene SlLAM1 from tomato, whose orthologs in tobacco (Nicotiana sylvestris) and other species are indispensable for blade expansion. We show that SlLAM1 is expressed in the middle and marginal domains of leaves, and is required for blade expansion in leaflets. We demonstrate that sllam1 mutants cause a delay of leaflet initiation and slightly alter the arrangement of first‐order leaflets, whereas the overall leaflet number is comparable to that of wild‐type leaves. Analysis of the genetic interactions between SlLAM1 and key auxin signaling components revealed an epistatic effect of SlLAM1 in determining the final leaf form. Finally, we show that SlLAM1 is also required for floral organ growth and affects the fertility of gametophytes. Our data suggest that SlLAM1 promotes blade expansion in multiple leaf types, and leaflet initiation can be largely uncoupled from blade expansion during compound leaf morphogenesis. Significance Statement: During compound leaf development, small blade units termed leaflets are generated from the leaf margin. It remains unclear whether and how leaflet initiation and blade expansion interact with each other. We identified tomato sllam1 mutant alleles which are impaired in blade expansion in multiple leaf types but have a mild influence on the overall leaflet number. This suggests that the two processes of leaflet initiation and blade expansion are largely uncoupled. [ABSTRACT FROM AUTHOR]

Axillary meristems (AMs) are located in the leaf axil and can establish new growth axes. Whereas their neighboring cells are differentiated, the undifferentiated cells in the AM endow the AM with the same developmental potential as the shoot apical meristem. The AM is, therefore, an excellent system to study stem cell fate maintenance in plants. In this review, we summarize the current knowledge of AM initiation. Recent findings have shown that AMs derive from a stem cell lineage that is maintained in the leaf axil. This review covers AM progenitor cell fate maintenance, reactivation, and meristem establishment. We also highlight recent work that links transcription factors, phytohormones, and epigenetic regulation to AM initiation. [ABSTRACT FROM AUTHOR]

Motivation Although genome-wide association studies (GWAS) have deepened our understanding of the genetic architecture of complex traits, the mechanistic links that underlie how genetic variants cause complex traits remains elusive. To advance our understanding of the underlying mechanistic links, various consortia have collected a vast volume of genomic data that enable us to investigate the role that genetic variants play in gene expression regulation. Recently, a collaborative mixed model (CoMM) was proposed to jointly interrogate genome on complex traits by integrating both the GWAS dataset and the expression quantitative trait loci (eQTL) dataset. Although CoMM is a powerful approach that leverages regulatory information while accounting for the uncertainty in using an eQTL dataset, it requires individual-level GWAS data and cannot fully make use of widely available GWAS summary statistics. Therefore, statistically efficient methods that leverages transcriptome information using only summary statistics information from GWAS data are required. Results In this study, we propose a novel probabilistic model, CoMM-S2, to examine the mechanistic role that genetic variants play, by using only GWAS summary statistics instead of individual-level GWAS data. Similar to CoMM which uses individual-level GWAS data, CoMM-S2 combines two models: the first model examines the relationship between gene expression and genotype, while the second model examines the relationship between the phenotype and the predicted gene expression from the first model. Distinct from CoMM, CoMM-S2 requires only GWAS summary statistics. Using both simulation studies and real data analysis, we demonstrate that even though CoMM-S2 utilizes GWAS summary statistics, it has comparable performance as CoMM, which uses individual-level GWAS data. Availability and implementation The implement of CoMM-S2 is included in the CoMM package that can be downloaded from https://github.com/gordonliu810822/CoMM. Supplementary information Supplementary data are available at Bioinformatics online. [ABSTRACT FROM AUTHOR]

Motivation In genome-wide association studies (GWASs) where multiple correlated traits have been measured on participants, a joint analysis strategy, whereby the traits are analyzed jointly, can improve statistical power over a single-trait analysis strategy. There are two questions of interest to be addressed when conducting a joint GWAS analysis with multiple traits. The first question examines whether a genetic loci is significantly associated with any of the traits being tested. The second question focuses on identifying the specific trait(s) that is associated with the genetic loci. Since existing methods primarily focus on the first question, this article seeks to provide a complementary method that addresses the second question. Results We propose a novel method, Variational Inference for Multiple Correlated Outcomes (VIMCO) that focuses on identifying the specific trait that is associated with the genetic loci, when performing a joint GWAS analysis of multiple traits, while accounting for correlation among the multiple traits. We performed extensive numerical studies and also applied VIMCO to analyze two datasets. The numerical studies and real data analysis demonstrate that VIMCO improves statistical power over single-trait analysis strategies when the multiple traits are correlated and has comparable performance when the traits are not correlated. Availability and implementation The VIMCO software can be downloaded from: https://github.com/XingjieShi/VIMCO. Supplementary information Supplementary data are available at Bioinformatics online. [ABSTRACT FROM AUTHOR]

The seamless-L0 (SELO) penalty is a smooth function that very closely resembles the L0 penalty, which has been demonstrated theoretically and practically to be effective in nonconvex penalization for variable selection. In this paper, the authors first generalize the SELO penalty to a class of penalties retaining good features of SELO, and then develop variable selection and parameter estimation in Cox models using the proposed generalized SELO (GSELO) penalized log partial likelihood (PPL) approach. The authors show that the GSELO-PPL procedure possesses the oracle property with a diverging number of predictors under certain mild, interpretable regularity conditions. The entire path of GSELO-PPL estimates can be efficiently computed through a smoothing quasi-Newton (SQN) with continuation algorithm. The authors propose a consistent modified BIC (MBIC) tuning parameter selector for GSELO-PPL, and show that under some regularity conditions, the GSELOPPL- MBIC procedure consistently identifies the true model. Simulation studies and real data analysis are conducted to evaluate the finite sample performance of the proposed method. [ABSTRACT FROM AUTHOR]

The smooth integration of counting and absolute deviation (SICA) penalty has been demonstrated theoretically and practically to be effective in nonconvex penalization for variable selection and parameter estimation. However, solving the nonconvex optimization problem associated with SICA penalty in high-dimensional setting remains to be enriched, mainly due to the singularity at the origin and the nonconvexity of the SICA penalty function. In this paper, we develop a fast primal dual active set (PDAS) with continuation algorithm for solving the nonconvex SICA-penalized least squares in high dimensions. Upon introducing the dual variable, the PDAS algorithm iteratively identify and update the active set in the optimization using both the primal and dual information, and then solve a low-dimensional least square problem on the active set. When combined with a continuation strategy and a high-dimensional Bayesian information criterion (BIC) selector on the tuning parameters, the proposed algorithm is very efficient and accurate. Extensive simulation studies and analysis of a high-dimensional microarray gene expression data are presented to illustrate the performance of the proposed method. [ABSTRACT FROM AUTHOR]

A natural image u is often sparse under a given transformation W, one can use L0 norm of Wu as a regularisation term in image reconstructions. Since minimizing the L0 norm is a NP hard problem, the L1 norm is widely used as an replacement. However, recent studies show that nonconvex penalties, e.g., MCP, enjoy better performance for sparse signal recovery. In this paper, we propose a nonconvex model for image restoration with a minimax concave penalty (MCP). First we establish the existence of a global minimizer for the nonconvex model. Then we solve this model by using the alternating direction method of multipliers algorithm. The convergence of the proposed algorithm is analysed with properly chosen parameters. Numerical experiments show that the MCP model outperforms TV model in terms of efficiency and accuracy. [ABSTRACT FROM AUTHOR]

Correction to: I Nature Communications i https://doi.org/10.1038/s41467-023-35947-w, published online 18 January 2023 In this article, the funding from the 'University Development Fund (UDF01003033) from The Chinese University of Hong Kong, Shenzhen' was omitted. These authors contributed equally: Wei Liu, Xu Liao. [Extracted from the article]

Abstract Plants maintain the ability to form lateral appendages throughout their life cycle and form leaves as the principal lateral appendages of the stem. Leaves initiate at the peripheral zone of the shoot apical meristem and then develop into flattened structures. In most plants, the leaf functions as a solar panel, where photosynthesis converts carbon dioxide and water into carbohydrates and oxygen. To produce structures that can optimally fulfill this function, plants precisely control the initiation, shape, and polarity of leaves. Moreover, leaf development is highly flexible but follows common themes with conserved regulatory mechanisms. Leaves may have evolved from lateral branches that are converted into determinate, flattened structures. Many other plant parts, such as floral organs, are considered specialized leaves, and thus leaf development underlies their morphogenesis. Here, we review recent advances in the understanding of how three-dimensional leaf forms are established. We focus on how genes, phytohormones, and mechanical properties modulate leaf development, and discuss these factors in the context of leaf initiation, polarity establishment and maintenance, leaf flattening, and intercalary growth. This review summarizes recent advances in the understanding of how three-dimensional leaf forms are established through the regulation of leaf initiation, polarity establishment and maintenance, leaf flattening, and intercalary growth, with a focus on how genes, phytohormones, and mechanical properties modulate leaf development. [ABSTRACT FROM AUTHOR]

The smooth integration of counting and absolute deviation (SICA) penalty has been demonstrated theoretically and practically to be effective in non-convex penalization for variable selection. However, solving the non-convex optimization problem associated with the SICA penalty when the number of variables exceeds the sample size remains to be enriched due to the singularity at the origin and the non-convexity of the SICA penalty function. In this paper, we develop an efficient and accurate alternating direction method of multipliers with continuation algorithm for solving the SICA-penalized least squares problem in high dimensions. We establish the convergence property of the proposed algorithm under some mild regularity conditions and study the corresponding Karush-Kuhn-Tucker optimality condition. A high-dimensional Bayesian information criterion is developed to select the optimal tuning parameters. We conduct extensive simulations studies to evaluate the efficiency and accuracy of the proposed algorithm, while its practical usefulness is further illustrated with a high-dimensional microarray study. [ABSTRACT FROM AUTHOR]

Leaf adaxial-abaxial polarity refers to the two leaf faces, which have different types of cells performing distinct biological functions. In 1951, Ian Sussex reported that when an incipient leaf primordium was surgically isolated by an incision across the vegetative shoot apical meristem ( SAM), a radialized structure without an adaxial domain would form. This led to the proposal that a signal, now called the Sussex signal, is transported from the SAM to emerging primordia to direct leaf adaxial-abaxial patterning. It was recently proposed that instead of the Sussex signal, polar transport of the plant hormone auxin is critical in leaf polarity formation. However, how auxin polar transport functions in the process is unknown. Through live imaging, we established a profile of auxin polar transport in and around young leaf primordia. Here we show that auxin polar transport in lateral regions of an incipient primordium forms auxin convergence points. We demonstrated that blocking auxin polar transport in the lateral regions of the incipient primordium by incisions abolished the auxin convergence points and caused abaxialized leaves to form. The lateral incisions also blocked the formation of leaf middle domain and margins and disrupted expression of the middle domain/margin-associated marker gene WUSCHEL- RELATED HOMEOBOX 1 ( Sl WOX1). Based on these results we propose that the auxin convergence points are required for the formation of leaf middle domain and margins, and the functional middle domain and margins ensure leaf adaxial-abaxial polarity. How middle domain and margins function in the process is discussed. [ABSTRACT FROM AUTHOR]

In this paper, we propose a lower bound based smoothed quasi-Newton algorithm for computing the solution paths of the group bridge estimator in linear regression models. Our method is based on the quasi-Newton algorithm with a smoothed group bridge penalty in combination with a novel data-driven thresholding rule for the regression coefficients. This rule is derived based on a necessary KKT condition of the group bridge optimization problem. It is easy to implement and can be used to eliminate groups with zero coefficients. Thus, it reduces the dimension of the optimization problem. The proposed algorithm removes the restriction of groupwise orthogonal condition needed in coordinate descent and LARS algorithms for group variable selection. Numerical results show that the proposed algorithm outperforms the coordinate descent based algorithms in both efficiency and accuracy. [ABSTRACT FROM AUTHOR]

In this note, we analyze an iterative soft/hard thresholding algorithm with homotopy continuation for recovering a sparse signal x^\dagger from noisy data of a noise level \epsilon. Under suitable regularity and sparsity conditions, we design a path, along which the algorithm can find a solution x^*, which admits a sharp reconstruction error \Vert x^* - x^\dagger \Vert \ell ^\infty = O(\epsilon) with an iteration complexity O(\frac{\ln \epsilon }{\ln \gamma } np) , where $n$ and $p$ are problem dimensionality and $\gamma \in (0,1)$ controls the length of the path. Numerical examples are given to illustrate its performance. [ABSTRACT FROM PUBLISHER]