328 research outputs found

    Equalities of ideals associated with two projections in rings with involution

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    In this article we study various right ideals associated with two projections (self-adjoint idempotents) in a ring with involution. Results of O.M. Baksalary, G. Trenkler, R. Piziak, P.L. Odell and R. Hahn about orthogonal projectors (complex matrices which are Hermitian and idempotent) are considered in the setting of rings with involution. New proofs based on algebraic arguments, rather than finite-dimensional and rank theory, are given.The authors thank the anonymous reviewer for his\her useful suggestions, which helped to improve the original version of this article. The second author is supported by Grant No. 174007 of the Ministry of Science, Technology and Development, Republic of Serbia.Benítez López, J.; Cvetkovic-Ilic, D. (2013). Equalities of ideals associated with two projections in rings with involution. Linear and Multilinear Algebra. 61(10):1419-1435. doi:10.1080/03081087.2012.743026S141914356110Baksalary, O. M., & Trenkler, G. (2009). Column space equalities for orthogonal projectors. Applied Mathematics and Computation, 212(2), 519-529. doi:10.1016/j.amc.2009.02.042Benítez, J. (2008). Moore–Penrose inverses and commuting elements of C∗-algebras. Journal of Mathematical Analysis and Applications, 345(2), 766-770. doi:10.1016/j.jmaa.2008.04.062Green, J. A. (1951). On the Structure of Semigroups. The Annals of Mathematics, 54(1), 163. doi:10.2307/1969317Harte, R. (1992). On generalized inverses in C*-algebras. Studia Mathematica, 103(1), 71-77. doi:10.4064/sm-103-1-71-77Harte, R. (1993). Generalized inverses in C*-algebras II. Studia Mathematica, 106(2), 129-138. doi:10.4064/sm-106-2-129-138Koliha, J. J. (2000). Elements of C*-algebras commuting with their Moore-Penrose inverse. Studia Mathematica, 139(1), 81-90. doi:10.4064/sm-139-1-81-90Koliha, J. J., Cvetković-Ilić, D., & Deng, C. (2012). Generalized Drazin invertibility of combinations of idempotents. Linear Algebra and its Applications, 437(9), 2317-2324. doi:10.1016/j.laa.2012.06.005Koliha, J. J., & Rakočević, V. (2003). Invertibility of the Difference of Idempotents. Linear and Multilinear Algebra, 51(1), 97-110. doi:10.1080/030810802100023499Mary, X. (2011). On generalized inverses and Green’s relations. Linear Algebra and its Applications, 434(8), 1836-1844. doi:10.1016/j.laa.2010.11.045Von Neumann, J. (1936). On Regular Rings. Proceedings of the National Academy of Sciences, 22(12), 707-713. doi:10.1073/pnas.22.12.707Patrı́cio, P., & Puystjens, R. (2004). Drazin–Moore–Penrose invertibility in rings. Linear Algebra and its Applications, 389, 159-173. doi:10.1016/j.laa.2004.04.006Piziak, R., Odell, P. L., & Hahn, R. (1999). Constructing projections on sums and intersections. Computers & Mathematics with Applications, 37(1), 67-74. doi:10.1016/s0898-1221(98)00242-

    Quantifying single nucleotide variant detection sensitivity in exome sequencing

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    BACKGROUND: The targeted capture and sequencing of genomic regions has rapidly demonstrated its utility in genetic studies. Inherent in this technology is considerable heterogeneity of target coverage and this is expected to systematically impact our sensitivity to detect genuine polymorphisms. To fully interpret the polymorphisms identified in a genetic study it is often essential to both detect polymorphisms and to understand where and with what probability real polymorphisms may have been missed. RESULTS: Using down-sampling of 30 deeply sequenced exomes and a set of gold-standard single nucleotide variant (SNV) genotype calls for each sample, we developed an empirical model relating the read depth at a polymorphic site to the probability of calling the correct genotype at that site. We find that measured sensitivity in SNV detection is substantially worse than that predicted from the naive expectation of sampling from a binomial. This calibrated model allows us to produce single nucleotide resolution SNV sensitivity estimates which can be merged to give summary sensitivity measures for any arbitrary partition of the target sequences (nucleotide, exon, gene, pathway, exome). These metrics are directly comparable between platforms and can be combined between samples to give “power estimates” for an entire study. We estimate a local read depth of 13X is required to detect the alleles and genotype of a heterozygous SNV 95% of the time, but only 3X for a homozygous SNV. At a mean on-target read depth of 20X, commonly used for rare disease exome sequencing studies, we predict 5–15% of heterozygous and 1–4% of homozygous SNVs in the targeted regions will be missed. CONCLUSIONS: Non-reference alleles in the heterozygote state have a high chance of being missed when commonly applied read coverage thresholds are used despite the widely held assumption that there is good polymorphism detection at these coverage levels. Such alleles are likely to be of functional importance in population based studies of rare diseases, somatic mutations in cancer and explaining the “missing heritability” of quantitative traits

    Primary carbonatite melt from deeply subducted oceanic crust

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    Partial melting in the Earth's mantle plays an important part in generating the geochemical and isotopic diversity observed in volcanic rocks at the surface. Identifying the composition of these primary melts in the mantle is crucial for establishing links between mantle geochemical 'reservoirs' and fundamental geodynamic processes. Mineral inclusions in natural diamonds have provided a unique window into such deep mantle processes. Here we provide experimental and geochemical evidence that silicate mineral inclusions in diamonds from Juina, Brazil, crystallized from primary and evolved carbonatite melts in the mantle transition zone and deep upper mantle. The incompatible trace element abundances calculated for a melt coexisting with a calcium-titanium-silicate perovskite inclusion indicate deep melting of carbonated oceanic crust, probably at transition-zone depths. Further to perovskite, calcic-majorite garnet inclusions record crystallization in the deep upper mantle from an evolved melt that closely resembles estimates of primitive carbonatite on the basis of volcanic rocks. Small-degree melts of subducted crust can be viewed as agents of chemical mass-transfer in the upper mantle and transition zone, leaving a chemical imprint of ocean crust that can possibly endure for billions of years.4 page(s

    Uncoupling of sexual reproduction from homologous recombination in homozygous Oenothera species

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    Salient features of the first meiotic division are independent segregation of chromosomes and homologous recombination (HR). In non-sexually reproducing, homozygous species studied to date HR is absent. In this study, we constructed the first linkage maps of homozygous, bivalent-forming Oenothera species and provide evidence that HR was exclusively confined to the chromosome ends of all linkage groups in our population. Co-segregation of complementary DNA-based markers with the major group of AFLP markers indicates that HR has only a minor role in generating genetic diversity of this taxon despite its efficient adaptation capability. Uneven chromosome condensation during meiosis in Oenothera may account for restriction of HR. The use of plants with ancient chromosomal arm arrangement demonstrates that limitation of HR occurred before and independent from species hybridizations and reciprocal translocations of chromosome arms—a phenomenon, which is widespread in the genus. We propose that consecutive loss of HR favored the evolution of reciprocal translocations, beneficial superlinkage groups and ultimately permanent translocation heterozygosity

    What You Find Depends on How You Measure It: Reactivity of Response Scales Measuring Predecisional Information Distortion in Medical Diagnosis

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    “Predecisional information distortion” occurs when decision makers evaluate new information in a way that is biased towards their leading option. The phenomenon is well established, as is the method typically used to measure it, termed “stepwise evolution of preference” (SEP). An inadequacy of this method has recently come to the fore: it measures distortion as the total advantage afforded a leading option over its competitor, and therefore it cannot differentiate between distortion to strengthen a leading option (“proleader” distortion) and distortion to weaken a trailing option (“antitrailer” distortion). To address this, recent research introduced new response scales to SEP. We explore whether and how these new response scales might influence the very proleader and antitrailer processes that they were designed to capture (“reactivity”). We used the SEP method with concurrent verbal reporting: fifty family physicians verbalized their thoughts as they evaluated patient symptoms and signs (“cues”) in relation to two competing diagnostic hypotheses. Twenty-five physicians evaluated each cue using the response scale traditional to SEP (a single response scale, returning a single measure of distortion); the other twenty-five did so using the response scales introduced in recent studies (two separate response scales, returning two separate measures of distortion: proleader and antitrailer). We measured proleader and antitrailer processes in verbalizations, and compared verbalizations in the single-scale and separate-scales groups. Response scales did not appear to affect proleader processes: the two groups of physicians were equally likely to bolster their leading diagnosis verbally. Response scales did, however, appear to affect antitrailer processes: the two groups denigrated their trailing diagnosis verbally to differing degrees. Our findings suggest that the response scales used to measure information distortion might influence its constituent processes, limiting their generalizability across and beyond experimental studies

    Systems Integration of Biodefense Omics Data for Analysis of Pathogen-Host Interactions and Identification of Potential Targets

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    The NIAID (National Institute for Allergy and Infectious Diseases) Biodefense Proteomics program aims to identify targets for potential vaccines, therapeutics, and diagnostics for agents of concern in bioterrorism, including bacterial, parasitic, and viral pathogens. The program includes seven Proteomics Research Centers, generating diverse types of pathogen-host data, including mass spectrometry, microarray transcriptional profiles, protein interactions, protein structures and biological reagents. The Biodefense Resource Center (www.proteomicsresource.org) has developed a bioinformatics framework, employing a protein-centric approach to integrate and support mining and analysis of the large and heterogeneous data. Underlying this approach is a data warehouse with comprehensive protein + gene identifier and name mappings and annotations extracted from over 100 molecular databases. Value-added annotations are provided for key proteins from experimental findings using controlled vocabulary. The availability of pathogen and host omics data in an integrated framework allows global analysis of the data and comparisons across different experiments and organisms, as illustrated in several case studies presented here. (1) The identification of a hypothetical protein with differential gene and protein expressions in two host systems (mouse macrophage and human HeLa cells) infected by different bacterial (Bacillus anthracis and Salmonella typhimurium) and viral (orthopox) pathogens suggesting that this protein can be prioritized for additional analysis and functional characterization. (2) The analysis of a vaccinia-human protein interaction network supplemented with protein accumulation levels led to the identification of human Keratin, type II cytoskeletal 4 protein as a potential therapeutic target. (3) Comparison of complete genomes from pathogenic variants coupled with experimental information on complete proteomes allowed the identification and prioritization of ten potential diagnostic targets from Bacillus anthracis. The integrative analysis across data sets from multiple centers can reveal potential functional significance and hidden relationships between pathogen and host proteins, thereby providing a systems approach to basic understanding of pathogenicity and target identification

    Effects of Elevated Temperature and Carbon Dioxide on the Growth and Survival of Larvae and Juveniles of Three Species of Northwest Atlantic Bivalves

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    Rising CO2 concentrations and water temperatures this century are likely to have transformative effects on many coastal marine organisms. Here, we compared the responses of two life history stages (larval, juvenile) of three species of calcifying bivalves (Mercenaria mercenaria, Crassostrea virginica, and Argopecten irradians) to temperatures (24 and 28°C) and CO2 concentrations (∼250, 390, and 750 ppm) representative of past, present, and future summer conditions in temperate estuaries. Results demonstrated that increases in temperature and CO2 each significantly depressed survival, development, growth, and lipid synthesis of M. mercenaria and A. irradians larvae and that the effects were additive. Juvenile M. mercenaria and A. irradians were negatively impacted by higher temperatures while C. virginica juveniles were not. C. virginica and A. irradians juveniles were negatively affected by higher CO2 concentrations, while M. mercenaria was not. Larvae were substantially more vulnerable to elevated CO2 than juvenile stages. These findings suggest that current and future increases in temperature and CO2 are likely to have negative consequences for coastal bivalve populations

    Vaccinia Virus Protein C6 Is a Virulence Factor that Binds TBK-1 Adaptor Proteins and Inhibits Activation of IRF3 and IRF7

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    Recognition of viruses by pattern recognition receptors (PRRs) causes interferon-β (IFN-β) induction, a key event in the anti-viral innate immune response, and also a target of viral immune evasion. Here the vaccinia virus (VACV) protein C6 is identified as an inhibitor of PRR-induced IFN-β expression by a functional screen of select VACV open reading frames expressed individually in mammalian cells. C6 is a member of a family of Bcl-2-like poxvirus proteins, many of which have been shown to inhibit innate immune signalling pathways. PRRs activate both NF-κB and IFN regulatory factors (IRFs) to activate the IFN-β promoter induction. Data presented here show that C6 inhibits IRF3 activation and translocation into the nucleus, but does not inhibit NF-κB activation. C6 inhibits IRF3 and IRF7 activation downstream of the kinases TANK binding kinase 1 (TBK1) and IκB kinase-ε (IKKε), which phosphorylate and activate these IRFs. However, C6 does not inhibit TBK1- and IKKε-independent IRF7 activation or the induction of promoters by constitutively active forms of IRF3 or IRF7, indicating that C6 acts at the level of the TBK1/IKKε complex. Consistent with this notion, C6 immunoprecipitated with the TBK1 complex scaffold proteins TANK, SINTBAD and NAP1. C6 is expressed early during infection and is present in both nucleus and cytoplasm. Mutant viruses in which the C6L gene is deleted, or mutated so that the C6 protein is not expressed, replicated normally in cell culture but were attenuated in two in vivo models of infection compared to wild type and revertant controls. Thus C6 contributes to VACV virulence and might do so via the inhibition of PRR-induced activation of IRF3 and IRF7
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