Four lectures on secant varieties

This paper is based on the first author's lectures at the 2012 University of Regina Workshop "Connections Between Algebra and Geometry". Its aim is to provide an introduction to the theory of higher secant varieties and their applications. Several references and solved exercises are also included.Comment: Lectures notes to appear in PROMS (Springer Proceedings in Mathematics & Statistics), Springer/Birkhause

Efeitos da nutrição mineral sobre o crescimento, aspecto, composição elementar e fixação de nitrogênio em Azolla

The mineral nutrition of Azolla feliculoides Lam was studied in solutions deficient in phosphorus, potassium, calcium, magnesium, sulfur, iron and molybdenum, and in excess of Mn and Al. Dry weight, N2 fixation and mineral composition of Azolla were determined after 3 weeks. Phosphorus, potassium, calcium and magnesium deficiencies and excess of manganese and aluminium decressed growth severely and also depressed the activity of nitrogenase. Phosphorus deficiency improved the uptake of iron and zinc. Potassium deficiency increased the levels of phosphorus in dry matter. Magnesium deficiency caused lower uptake of K and better uptake of Ca, Fe and Mn. Sulfur deficiency reduced aluminium uptake and promoted the best growth. Positive correlations were found between: N content and dry matter, nitrogenase activity and N content.Azolla filiculoides Lam foi cultivado em solução nutritiva arejada, sempre desprovida de N combinado, sendo submetida aos seguintes tratamentos: omissão de P, K, Ca, Mg, S, Fe e Mo, excesso de Mn e Al. As plantas foram colhidas depois de 3 semanas da inoculação. Verificou-se que as deficiências de P, K, Ca e Mg provocaram diminuição na produção de matéria seca e na atividade de nitrogenase. A análise mineral mostrou que: a falta de um elemento provoca redução no seu teor; grande acumulo de Mo; diminuição no teor de Al (do inóculo ou contaminação) no tratamento menos S que garantiu o maior crescimento; efeitos inibitórios ou sinergísticos semelhantes aos descritos no caso de plantas superiores. A toxidez de Al e Mn causou, principalmente a primeira, redução no crescimento e na atividade da nitrogenase. Houve correlações positivas entre: N total e crescimento, atividade de nitrogenase e N total

Whole-genome characterization of lung adenocarcinomas lacking the RTK/RAS/RAF pathway

RTK/RAS/RAF pathway alterations (RPAs) are a hallmark of lung adenocarcinoma (LUAD). In this study, we use whole-genome sequencing (WGS) of 85 cases found to be RPA(−) by previous studies from The Cancer Genome Atlas (TCGA) to characterize the minority of LUADs lacking apparent alterations in this pathway. We show that WGS analysis uncovers RPA(+) in 28 (33%) of the 85 samples. Among the remaining 57 cases, we observe focal deletions targeting the promoter or transcription start site of STK11 (n = 7) or KEAP1 (n = 3), and promoter mutations associated with the increased expression of ILF2 (n = 6). We also identify complex structural variations associated with high-level copy number amplifications. Moreover, an enrichment of focal deletions is found in TP53 mutant cases. Our results indicate that RPA(−) cases demonstrate tumor suppressor deletions and genome instability, but lack unique or recurrent genetic lesions compensating for the lack of RPAs. Larger WGS studies of RPA(−) cases are required to understand this important LUAD subset. © 2021 The AuthorsCarrot-Zhang et al. perform whole-genome characterization of lung adenocarcinomas (LUADs) lacking RTK/RAS/RAF pathway alterations (RPAs) and identify mutations or structural variants in both coding and non-coding spaces that define a unique entity of RPA(−) LUADs and potentially explain the underlying biology of this disease