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Zirconium is a silvery-white malleable and ductile metal at room temperature with a crustal abundance of 162 ppm. Its compounds, showing Lewis acidic behavior and high catalytic performance, have been recognized as a relatively cheap, low-toxicity, stable, green, and efficient catalysts for various important organic transformations. Commercially available inorganic zirconium chloride was widely applied as a catalyst to accelerate amination, Michael addition, and oxidation reactions. Well-designed zirconocene perfluorosulfonates can be applied in allylation, acylation, esterification, etc. N-Chelating oganozirconium complexes accelerate polymerization, hydroaminoalkylation, and CO

Learning from large-scale and high-dimensional data still remains a computationally challenging problem, though it has received increasing interest recently. To address this issue, randomized reduction methods have been developed by either reducing the dimensionality or reducing the number of training instances to obtain a small sketch of the original data. In this paper, we focus on recovering a high-dimensional classification/regression model from random sketched data. We propose to exploit the intrinsic sparsity of optimal solutions and develop novel methods by increasing the regularization parameter before the sparse regularizer. In particular, (i) for high-dimensional classification problems, we leverage randomized reduction methods to reduce the dimensionality of data and solve a dual formulation on the random sketched data with an introduced sparse regularizer on the dual solution; (ii) for high-dimensional sparse least-squares regression problems, we employ randomized reduction methods to reduce the scale of data and solve a formulation on the random sketched data with an increased regularization parameter before the sparse regularizer. For both classes of problems, by exploiting the intrinsic sparsity of the optimal dual solution or the optimal primal solution we provide formal theoretical guarantee on the recovery error of learned models in comparison with the optimal models that are learned from the original data. Compared with previous studies on randomized reduction for machine learning, the present work enjoy several advantages: (i) the proposed formulations enjoys intuitive geometric explanations; (ii) the theoretical guarantee does not rely on any stringent assumptions about the original data (e.g., low-rankness of the data matrix or the data are linearly separable); (iii) the theory covers both smooth and non-smooth loss functions for classification; (iv) the analysis is applicable to a broad class of randomized reduction methods as long as the reduction matrices admit the Johnson–Lindenstrauss type of lemma. We also present empirical studies to support the proposed methods and the presented theory.

In this paper, we present novel yet simple homotopy proximal mapping algorithms for reconstructing a sparse signal from (noisy) linear measurements of the signal or for learning a sparse linear model from observed data, where the former task is well-known in the field of compressive sensing and the latter task is known as model selection in statistics and machine learning. The algorithms adopt a simple proximal mapping of the $$\ell _1$$ norm at each iteration and gradually reduces the regularization parameter for the $$\ell _1$$ norm. We prove a global linear convergence of the proposed homotopy proximal mapping (HPM) algorithms for recovering the sparse signal under three different settings (i) sparse signal recovery under noiseless measurements, (ii) sparse signal recovery under noisy measurements, and (iii) nearly-sparse signal recovery under sub-Gaussian noisy measurements. In particular, we show that when the measurement matrix satisfies restricted isometric properties (RIP), one of the proposed algorithms with an appropriate setting of a parameter based on the RIP constants converges linearly to the optimal solution up to the noise level. In addition, in setting (iii), a practical variant of the proposed algorithms does not rely on the RIP constants and our results for sparse signal recovery are better than the previous results in the sense that our recovery error bound is smaller. Furthermore, our analysis explicitly exhibits that more observations lead to not only more accurate recovery but also faster convergence. Finally our empirical studies provide further support for the proposed homotopy proximal mapping algorithm and verify the theoretical results.

Background Hydroxycinnamoyl-spermine conjugates (HCSpm) are a class of hydroxycinnamic acid amides (HCAAs), which not only are instrumental in plant development and stress response, but also benefit human health. However, HCSpm are not commonly produced in plants, and the mechanism of their biosynthesis remains unclear. In previous investigations of phenolics in Solanum fruits related to eggplant (Solanum melongena L.), we discovered that Solanum richardii, an African wild relative of eggplant, was rich in HCSpms in fruits. Results The putative spermine hydroxycinnamoyl transferase (HT) SpmHT was isolated from S. richardii and eggplant. SrSpmHT expression was high in flowers and fruit, and was associated with HCSpm accumulation in S. richardii; however, SpmHT was hardly detected in eggplant cultivars and other wild relatives. Recombinant SpmHT exclusively selected spermine as the acyl acceptor substrate, while showing donor substrate preference in the following order: caffeoyl-CoA, feruloyl-CoA, and p-coumaroyl-CoA. Molecular docking revealed that substrate binding pockets of SpmHT could properly accommodate spermine but not the shorter, more common spermidine. Conclusion SrSpmHT is a novel spermine hydroxycinnamoyl transferase that uses Spm exclusively as the acyl acceptor substrate to produce HCSpms. Our findings shed light on the HCSpm biosynthetic pathway that may allow an increase of health beneficial metabolites in Solanum crops via methods such as introgression or engineering HCAA metabolism. Electronic supplementary material The online version of this article (10.1186/s12870-019-1846-3) contains supplementary material, which is available to authorized users.

Polyphenols are secondary metabolites widely present in plants which benefit to human health. In the present study we analyzed the changes of polyphenol contents during strawberry fruit development as well as changes of polyphenol oxidase (PPO). The results depicted that the polyphenol content showed a decreasing trend with the fruit development. The pH value impacts the PPO activity, and in strawberry fruit the optimal pH for the PPO activity was 4.5. Meanwhile, PPO activity kept decreasing with the development of the fruit flesh and achenes. The damaged fruit enhanced the PPO activity. We found four PPO genes encoding the PPO in the strawberry that had different expression levels in tissues. The overexpression of the FaPPO1 genes improved the PPO activity in strawberry fruit and delays the fungus infection process. The FaPPO1 gene expression changes had affected the pathogen-related gene expression, such as PAL, SOD, POD, BG, and Chitinase genes. The fruit damage induced the FaPPO1 gene expression, and the abscisic acid and methyl jasmonic were also involved in the regulation of FaPPO1 gene expression. The FaPPO1 and FaPPO2 gene expressions were regulated both by abiotic stresses of low temperature, NaCl, and H2O2 and biotic stresses of powdery mildew and gray mold. Understanding the regulation mechanism of PPO will be helpful and provide meaningful ideas in future for strawberry breeders.

We study the non-smooth optimization problems in machine learning, where both the loss function and the regularizer are non-smooth functions. Previous studies on efficient empirical loss minimization assume either a smooth loss function or a strongly convex regularizer, making them unsuitable for non-smooth optimization. We develop a simple yet efficient method for a family of non-smooth optimization problems where the dual form of the loss function is bilinear in primal and dual variables. We cast a non-smooth optimization problem into a minimax optimization problem, and develop a primal dual prox method that solves the minimax optimization problem at a rate of $$O(1/T)$$O(1/T) assuming that the proximal step can be efficiently solved, significantly faster than a standard subgradient descent method that has an $$O(1/\sqrt{T})$$O(1/T) convergence rate. Our empirical studies verify the efficiency of the proposed method for various non-smooth optimization problems that arise ubiquitously in machine learning by comparing it to the state-of-the-art first order methods.

Recently, it has been shown that the regret of the Follow the Regularized Leader (FTRL) algorithm for online linear optimization can be bounded by the total variation of the cost vectors rather than the number of rounds. In this paper, we extend this result to general online convex optimization. In particular, this resolves an open problem that has been posed in a number of recent papers. We first analyze the limitations of the FTRL algorithm as proposed by Hazan and Kale (in Machine Learning 80(2---3), 165---188, 2010) when applied to online convex optimization, and extend the definition of variation to a gradual variation which is shown to be a lower bound of the total variation. We then present two novel algorithms that bound the regret by the gradual variation of cost functions. Unlike previous approaches that maintain a single sequence of solutions, the proposed algorithms maintain two sequences of solutions that make it possible to achieve a variation-based regret bound for online convex optimization. To establish the main results, we discuss a lower bound for FTRL that maintains only one sequence of solutions, and a necessary condition on smoothness of the cost functions for obtaining a gradual variation bound. We extend the main results three-fold: (i) we present a general method to obtain a gradual variation bound measured by general norm; (ii) we extend algorithms to a class of online non-smooth optimization with gradual variation bound; and (iii) we develop a deterministic algorithm for online bandit optimization in multipoint bandit setting.

Although a large body of work is devoted to finding communities in static social networks, only a few studies examined the dynamics of communities in evolving social networks. In this paper, we propose a dynamic stochastic block model for finding communities and their evolution in a dynamic social network. The proposed model captures the evolution of communities by explicitly modeling the transition of community memberships for individual nodes in the network. Unlike many existing approaches for modeling social networks that estimate parameters by their most likely values (i.e., point estimation), in this study, we employ a Bayesian treatment for parameter estimation that computes the posterior distributions for all the unknown parameters. This Bayesian treatment allows us to capture the uncertainty in parameter values and therefore is more robust to data noise than point estimation. In addition, an efficient algorithm is developed for Bayesian inference to handle large sparse social networks. Extensive experimental studies based on both synthetic data and real-life data demonstrate that our model achieves higher accuracy and reveals more insights in the data than several state-of-the-art algorithms.

Intracellular calcium transients during plant-pathogen interactions are necessary early events leading to local and systemic acquired resistance. Salicylic acid, a critical messenger, is also required for both of these responses, but whether and how salicylic acid level is regulated by Ca(2+) signalling during plant-pathogen interaction is unclear. Here we report a mechanism connecting Ca(2+) signal to salicylic-acid-mediated immune response through calmodulin, AtSR1 (also known as CAMTA3), a Ca(2+)/calmodulin-binding transcription factor, and EDS1, an established regulator of salicylic acid level. Constitutive disease resistance and elevated levels of salicylic acid in loss-of-function alleles of Arabidopsis AtSR1 suggest that AtSR1 is a negative regulator of plant immunity. This was confirmed by epistasis analysis with mutants of compromised salicylic acid accumulation and disease resistance. We show that AtSR1 interacts with the promoter of EDS1 and represses its expression. Furthermore, Ca(2+)/calmodulin-binding to AtSR1 is required for suppression of plant defence, indicating a direct role for Ca(2+)/calmodulin in regulating the function of AtSR1. These results reveal a previously unknown regulatory mechanism linking Ca(2+) signalling to salicylic acid level.

Legumes, such as Medicago truncatula, form mutualistic symbiotic relationships with nitrogen-fixing rhizobial bacteria. This occurs within specialized root organs--nodules--that provide the conditions required for nitrogen fixation. A rhizobium-derived signalling molecule, Nod factor, is required to establish the symbiosis. Perception of Nod factor in the plant leads to the induction of Ca2+ oscillations, and the transduction of this Ca2+ signal requires DMI3 (refs 2, 3), which encodes the protein kinase Ca2+/calmodulin-dependent protein kinase (CCaMK). Central to the regulation of CCaMK is an autoinhibitory domain that negatively regulates kinase activity. Here we show that the specific removal of the autoinhibition domain leads to the autoactivation of the nodulation signalling pathway in the plant, with the resultant induction of nodules and nodulation gene expression in the absence of bacterial elicitation. This autoactivation requires nodulation-specific transcriptional regulators in the GRAS family. This work demonstrates that the release of autoinhibition from CCaMK after calmodulin binding is a central switch that is sufficient to activate nodule morphogenesis. The fact that a single regulation event is sufficient to induce nodulation highlights the possibility of transferring this process to non-legumes.

Chimeric Ca(2+)/calmodulin-dependent protein kinase (CCaMK) was cloned from developing anthers of lily (Lilium longiflorum Thumb. cv. Nellie White) and tobacco (Nicotiana tabacum L. cv. Xanthi). Previous biochemical characterization and structure/function studies had revealed that CCaMK has dual modes of regulation by Ca(2+) and Ca(2+)/calmodulin. The unique structural features of CCaMK include a catalytic domain, a calmodulin-binding domain, and a neural visinin-like Ca(2+)-binding domain. The existence of these three features in a single polypeptide distinguishes it from other kinases. Western analysis revealed that CCaMK is expressed in a stage-specific manner in developing anthers. Expression of CCaMK was first detected in pollen mother cells and continued to increase, reaching a peak around the tetrad stage of meiosis. Following microsporogenesis, CCaMK expression rapidly decreased and at later stages of microspore development, no expression was detected. A tobacco genomic clone of CCaMK was isolated and transgenic tobacco plants were produced carrying the CCaMK promoter fused to the beta-glucuronidase reporter gene. Both CCaMK mRNA and protein were detected in the pollen sac and their localizations were restricted to the pollen mother cells and tapetal cells. Consistent results showing a stage-specific expression pattern were obtained by beta-glucuronidase analysis, in-situ hybridization and immunolocalization. The stage- and tissue-specific appearance of CCaMK in anthers suggests that it could play a role in sensing transient changes in free Ca(2+) concentration in target cells, thereby controlling developmental events in the anther.

Recently, we reported on the characterization of the calmodulin (CaM) gene family in wheat [44]. We classified wheat CaM genes into four subfamilies (SFs) designated SF-1 to SF-4, each representing a series of homoeoallelic loci on the homoeologous chromosomes of the three genomes of common wheat. Here we studied the expression of these wheat CaM genes in the course of wheat development. Northern blot analysis using SF-specific probes revealed differences in SF expression levels in different organs and stages of development. Subsequently, cell-specific expression of CaM SFs was investigated by in situ RNA hybridization. In developing seeds, all CaM SFs showed highest expression in the embryo and less in the aleurone and in the starchy endosperm. In primary roots, all four CaM SFs were expressed in the root cap, meristematic regions and in differentiating cells. During development of the roots, expression gradually decreased. The wheat glutenin gene, which was used as a control throughout our experiments, was found to be expressed in the starchy endosperm but not in the aleurone, embryos or vegetative tissues. In stems, at advanced stages of growth, differences in cell-specific expression of CaM SFs were found. For example, SF-2 was highly expressed in differentiating phloem fibers. Thus, CaM genes in common wheat exhibit a developmentally regulated organ-, tissue-, cell- and SF-specific expression patterns.

Background Fruit ripening is a complicated development process affected by a variety of external and internal cues. It is well established that calcium treatment delays fruit ripening and senescence. However, the underlying molecular mechanisms remain unclear. Results Previous studies have shown that calcium/calmodulin-regulated SR/CAMTAs are important for modulation of disease resistance, cold sensitivity and wounding response in vegetative tissues. To study the possible roles of this gene family in fruit development and ripening, we cloned seven SR/CAMTAs, designated as SlSRs, from tomato, a model fruit-bearing crop. All seven genes encode polypeptides with a conserved DNA-binding domain and a calmodulin-binding site. Calmodulin specifically binds to the putative targeting site in a calcium-dependent manner. All SlSRs were highly yet differentially expressed during fruit development and ripening. Most notably, the expression of SlSR2 was scarcely detected at the mature green and breaker stages, two critical stages of fruit development and ripening; and SlSR3L and SlSR4 were expressed exclusively in fruit tissues. During the developmental span from 10 to 50 days post anthesis, the expression profiles of all seven SlSRs were dramatically altered in ripening mutant rin compared with wildtype fruit. By contrast, only minor alterations were noted for ripening mutant nor and Nr fruit. In addition, ethylene treatment of mature green wildtype fruit transiently stimulated expression of all SlSRs within one to two hours. Conclusions This study indicates that SlSR expression is influenced by both the Rin-mediated developmental network and ethylene signaling. The results suggest that calcium signaling is involved in the regulation of fruit development and ripening through calcium/calmodulin/SlSR interactions.