S-Lemma with Equality and Its Applications

Let $f(x)=x^TAx+2a^Tx+c$ and $h(x)=x^TBx+2b^Tx+d$ be two quadratic functions having symmetric matrices $A$ and $B$. The S-lemma with equality asks when the unsolvability of the system $f(x)<0, h(x)=0$ implies the existence of a real number $\mu$ such that $f(x) + \mu h(x)\ge0, ~\forall x\in \mathbb{R}^n$. The problem is much harder than the inequality version which asserts that, under Slater condition, $f(x)<0, h(x)\le0$ is unsolvable if and only if $f(x) + \mu h(x)\ge0, ~\forall x\in \mathbb{R}^n$ for some $\mu\ge0$. In this paper, we show that the S-lemma with equality does not hold only when the matrix $A$ has exactly one negative eigenvalue and $h(x)$ is a non-constant linear function ($B=0, b\not=0$). As an application, we can globally solve $\inf\{f(x)\vert h(x)=0\}$ as well as the two-sided generalized trust region subproblem $\inf\{f(x)\vert l\le h(x)\le u\}$ without any condition. Moreover, the convexity of the joint numerical range $\{(f(x), h_1(x),\ldots, h_p(x)):~x\in\Bbb R^n\}$ where $f$ is a (possibly non-convex) quadratic function and $h_1(x),\ldots,h_p(x)$ are affine functions can be characterized using the newly developed S-lemma with equality.Comment: 34 page

Examining the generalizability of research findings from archival data

This initiative examined systematically the extent to which a large set of archival research findings generalizes across contexts. We repeated the key analyses for 29 original strategic management effects in the same context (direct reproduction) as well as in 52 novel time periods and geographies; 45% of the reproductions returned results matching the original reports together with 55% of tests in different spans of years and 40% of tests in novel geographies. Some original findings were associated with multiple new tests. Reproducibility was the best predictor of generalizability—for the findings that proved directly reproducible, 84% emerged in other available time periods and 57% emerged in other geographies. Overall, only limited empirical evidence emerged for context sensitivity. In a forecasting survey, independent scientists were able to anticipate which effects would find support in tests in new samples

RNA-Seq Analysis of Cocos nucifera: Transcriptome Sequencing and De Novo for Subsequent Functional Genomics Approaches

Background: Cocos nucifera (coconut), a member of the Arecaceae family, is an economically important woody palm grown in tropical regions. Despite its agronomic importance, previous germplasm assessment studies have relied solely on morphological and agronomical traits. Molecular biology techniques have been scarcely used in assessment of genetic resources and for improvement of important agronomic and quality traits in Cocos nucifera, mostly due to the absence of available sequence information. Methodology/Principal Findings: To provide basic information for molecular breeding and further molecular biological analysis in Cocos nucifera, we applied RNA-seq technology and de novo assembly to gain a global overview of the Cocos nucifera transcriptome from mixed tissue samples. Using Illumina sequencing, we obtained 54.9 million short reads and conducted de novo assembly to obtain 57,304 unigenes with an average length of 752 base pairs. Sequence comparison between assembled unigenes and released cDNA sequences of Cocos nucifera and Elaeis guineensis indicated that the assembled sequences were of high quality. Approximately 99.9% of unigenes were novel compared to the released coconut EST sequences. Using BLASTX, 68.2% of unigenes were successfully annotated based on the Genbank non-redundant (Nr) protein database. The annotated unigenes were then further classified using the Gene Ontology (GO), Clusters of Orthologous Groups (COG) and Kyoto Encyclopedia of Genes and Genomes (KEGG) databases. Conclusions/Significance: Our study provides a large quantity of novel genetic information for Cocos nucifera. This information will act as a valuable resource for further molecular genetic studies and breeding in coconut, as well as for isolation and characterization of functional genes involved in different biochemical pathways in this important tropical crop species

Notes for genera – Ascomycota

Knowledge of the relationships and thus the classification of fungi, has developed rapidly with increasingly widespread use of molecular techniques, over the past 10--15 years, and continues to accelerate. Several genera have been found to be polyphyletic, and their generic concepts have subsequently been emended. New names have thus been introduced for species which are phylogenetically distinct from the type species of particular genera. The ending of the separate naming of morphs of the same species in 2011, has also caused changes in fungal generic names. In order to facilitate access to all important changes, it was desirable to compile these in a single document. The present article provides a list of generic names of Ascomycota (approximately 6500 accepted names published to the end of 2016), including those which are lichen-forming. Notes and summaries of the changes since the last edition of `Ainsworth Bisby's Dictionary of the Fungi' in 2008 are provided. The notes include the number of accepted species, classification, type species (with location of the type material), culture availability, life-styles, distribution, and selected publications that have appeared since 2008. This work is intended to provide the foundation for updating the ascomycete component of the ``Without prejudice list of generic names of Fungi'' published in 2013, which will be developed into a list of protected generic names. This will be subjected to the XIXth International Botanical Congress in Shenzhen in July 2017 agreeing to a modification in the rules relating to protected lists, and scrutiny by procedures determined by the Nomenclature Committee for Fungi (NCF). The previously invalidly published generic names Barriopsis, Collophora (as Collophorina), Cryomyces, Dematiopleospora, Heterospora (as Heterosporicola), Lithophila, Palmomyces (as Palmaria) and Saxomyces are validated, as are two previously invalid family names, Bartaliniaceae and Wiesneriomycetaceae. Four species of Lalaria, which were invalidly published are transferred to Taphrina and validated as new combinations. Catenomycopsis Tibell Constant. is reduced under Chaenothecopsis Vain., while Dichomera Cooke is reduced under Botryosphaeria Ces. De Not. (Art. 59)