33 research outputs found

    Commuting UU-operators in Jordan algebras

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    GROWING HEARTS IN ASSOCIATIVE SYSTEMS

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    Follow-Up Study Confirms the Presence of Gastric Cancer DNA Methylation Hallmarks in High-Risk Precursor Lesions

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    Intestinal metaplasia confers an increased risk of progression to gastric cancer. However, some intestinal metaplasia patients do not develop cancer. The development of robust molecular biomarkers to stratify patients with advanced gastric precursor lesions at risk of cancer progression will contribute to guiding programs for prevention. Starting from a genome-wide methylation study, we have simplified the detection method regarding candidate-methylation tests to improve their applicability in the clinical environment. We identified CpG methylation at the ZNF793 and RPRM promoters as a common event in intestinal metaplasia and intestinal forms of gastric cancer. Furthermore, we also showed that Helicobacter pylori infection influences DNA methylation in early precursor lesions but not in intestinal metaplasia, suggesting that therapeutic strategies to prevent epigenome reprogramming toward a cancer signature need to be adopted early in the precursor cascade. To adopt prevention strategies in gastric cancer, it is imperative to develop robust biomarkers with acceptable costs and feasibility in clinical practice to stratified populations according to risk scores. With this aim, we applied an unbiased genome-wide CpG methylation approach to a discovery cohort composed of gastric cancer (n = 24), and non-malignant precursor lesions (n = 64). Then, candidate-methylation approaches were performed in a validation cohort of precursor lesions obtained from an observational longitudinal study (n = 264), with a 12-year follow-up to identify repression or progression cases. H. pylori stratification and histology were considered to determine their influence on the methylation dynamics. As a result, we ascertained that intestinal metaplasia partially recapitulates patterns of aberrant methylation of intestinal type of gastric cancer, independently of the H. pylori status. Two epigenetically regulated genes in cancer, RPRM and ZNF793, consistently showed increased methylation in intestinal metaplasia with respect to earlier precursor lesions. In summary, our result supports the need to investigate the practical utilities of the quantification of DNA methylation in candidate genes as a marker for disease progression. In addition, the H. pylori-dependent methylation in intestinal metaplasia suggests that pharmacological treatments aimed at H. pylori eradication in the late stages of precursor lesions do not prevent epigenome reprogramming toward a cancer signature

    Idempotents and Peirce gradings of Jordan algebras

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    AbstractIn this paper we find a necessary and sufficient condition for a Peirce grading of a Jordan algebra J to come from a Peirce decomposition with respect to an idempotent of a Jordan algebra J˜ containing J as a subalgebra. We also show that the above condition holds automatically when J is nondegenerate

    Primitive Jordan Pairs and Triple Systems

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    Local and Subquotient Inheritance of Simplicity in Jordan Systems

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    AbstractIn this paper we prove that the local algebras of a simple Jordan pair are simple. Jordan pairs all of which local algebras are simple are also studied, showing that they have a nonzero simple heart, which is described in terms of powers of the original pair. Similar results are given for Jordan triple systems and algebras. Finally, we characterize the inner ideals of a simple pair which determine simple subquotients, answering the question posed by O. Loos and E. Neher (1994, J. Algebra166, 255–295)
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