Geometric Approach to Pontryagin's Maximum Principle

Since the second half of the 20th century, Pontryagin's Maximum Principle has been widely discussed and used as a method to solve optimal control problems in medicine, robotics, finance, engineering, astronomy. Here, we focus on the proof and on the understanding of this Principle, using as much geometric ideas and geometric tools as possible. This approach provides a better and clearer understanding of the Principle and, in particular, of the role of the abnormal extremals. These extremals are interesting because they do not depend on the cost function, but only on the control system. Moreover, they were discarded as solutions until the nineties, when examples of strict abnormal optimal curves were found. In order to give a detailed exposition of the proof, the paper is mostly self\textendash{}contained, which forces us to consider different areas in mathematics such as algebra, analysis, geometry.Comment: Final version. Minors changes have been made. 56 page

Role of age and comorbidities in mortality of patients with infective endocarditis

Purpose: The aim of this study was to analyse the characteristics of patients with IE in three groups of age and to assess the ability of age and the Charlson Comorbidity Index (CCI) to predict mortality. Methods: Prospective cohort study of all patients with IE included in the GAMES Spanish database between 2008 and 2015. Patients were stratified into three age groups:<65 years, 65 to 80 years, and = 80 years.The area under the receiver-operating characteristic (AUROC) curve was calculated to quantify the diagnostic accuracy of the CCI to predict mortality risk. Results: A total of 3120 patients with IE (1327 < 65 years;1291 65-80 years;502 = 80 years) were enrolled.Fever and heart failure were the most common presentations of IE, with no differences among age groups.Patients =80 years who underwent surgery were significantly lower compared with other age groups (14.3%, 65 years; 20.5%, 65-79 years; 31.3%, =80 years). In-hospital mortality was lower in the <65-year group (20.3%, <65 years;30.1%, 65-79 years;34.7%, =80 years;p < 0.001) as well as 1-year mortality (3.2%, <65 years; 5.5%, 65-80 years;7.6%, =80 years; p = 0.003).Independent predictors of mortality were age = 80 years (hazard ratio [HR]:2.78;95% confidence interval [CI]:2.32–3.34), CCI = 3 (HR:1.62; 95% CI:1.39–1.88), and non-performed surgery (HR:1.64;95% CI:11.16–1.58).When the three age groups were compared, the AUROC curve for CCI was significantly larger for patients aged <65 years(p < 0.001) for both in-hospital and 1-year mortality. Conclusion: There were no differences in the clinical presentation of IE between the groups. Age = 80 years, high comorbidity (measured by CCI), and non-performance of surgery were independent predictors of mortality in patients with IE.CCI could help to identify those patients with IE and surgical indication who present a lower risk of in-hospital and 1-year mortality after surgery, especially in the <65-year group

A922 Sequential measurement of 1 hour creatinine clearance (1-CRCL) in critically ill patients at risk of acute kidney injury (AKI)

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Theodor and Marcella Boveri : chromosomes and cytoplasm in heredity and development

The chromosome theory of heredity, developed in 1902–1904, became one of the foundation stones of twentieth-century genetics. It is usually referred to as the Sutton-Boveri theory after Walter Sutton and Theodor Boveri. However, the contributions of Theodor Boveri and his co-worker, Marcella O’Grady Boveri (also his wife), to the understanding of heredity and development go beyond the localization of the Mendelian hereditary factors onto the chromosomes. They investigated the interaction of cytoplasm and chromosomes, and demonstrated its relevance in heredity and development

Flora y vegetación de suelos crioturbados y hábitats asociados en la Cordillera Blanca, Ancash, Perú

Since 2006 to 2008, floristic and vegetational studies on cryoturbed soils and its associated habitats were carried out in four sites above 4500 m, at Cordillera Blanca (Ancash, Peru). Botanical collections and intersection-line transects were made. The space (in cm) occupied by each species were measurement. A total of 136 species, in 65 genera and 26 families, were recorded. Magnoliopsida (Dicots) were the most diverse (97 spp.), followed by the Liliopsida (Monocots) (36 spp.). The highest species richness was found in the Asteraceae and Poaceae families (40,63%). The most diverse genera was Senecio (18) and Calamagrostis (12 ). We registered 76 species (54,82%) in cryoturbed soils and associates habitats, while 60 species (44,11%) were recorded for the adjacent vegetation. From the total, 95,56% of the species were perennials herbs. Four types of plants comunities were characterized: a) community of cryoturbed soil proper, b) community of cryoturbed soil associated with grassland, c) community of cryoturbed soil associated with dry rocky areas, and d) community of cryoturbed soil associated with humid rocky areas. Species associated to each community are given.Entre los años 2006 y 2008, se llevaron a cabo estudios florístico y de vegetación de los suelos crioturbados y hábitats asociados en cuatro localidades de la Cordillera Blanca (Ancash, Perú) localizadas por encima de los 4500 m. Se realizaron recolectas botánicas además de transectos de intersección-línea, en los cuales se midió el espacio (en cm) ocupado por cada especie. Fueron determinadas 136 especies de plantas vasculares, agrupadas en 65 géneros y 26 familias. Las Magnoliópsida (dicotiledóneas) fueron las más diversas con 97 especies, seguidas de las Liliópsidas (Monocotiledóneas) con 36. La mayor diversidad está concentrada en las familias Asteraceae y Poaceae (40,63%). Los géneros con mayor riqueza de especies fueron Senecio (18) y Calamagrostis (12). Se registraron 76 especies (54,82%) en suelos crioturbados y hábitats asociados; mientras que 60 especies (44,11%) fueron colectadas en la vegetación adyacente. El 95,56% de las especies reportadas fueron hierbas perennes. Se caracterizaron cuatro tipos de comunidades vegetales: a) comunidad de suelos crioturbados propiamente dicha, b) comunidad de suelos crioturbados asociada a pajonal, c) comunidad de suelos crioturbados asociada a roquedal seco y d) comunidad de suelos crioturbados asociadas a roquedal húmedo. Se indícan las especies características de cada comunidad

Azorella cushion plants and aridity are important drivers of soil microbial communities in Andean ecosystems

Cushion plants are specialized keystone species of alpine environments that can have a positive effect on ecosystem structure and function. However, we know relatively little about how cushion plants regulate the diversity and composition of soil microbial communities, major drivers of soil processes and ecosystem functioning. Identifying what factors drive the diversity and composition of soil microbial communities in high-elevation ecosystems is also fundamental to predict how global changes will affect their conservation and the services and functions they provide. Thus, we sampled four sites along the southern Andes following the vegetation belt of Azorella cushion species. The field sites spread along a latitudinal gradient and had contrasting levels of aridity, UV-B radiation, mean temperature and soil properties. Overall, Azorella, as well as aridity and UV-B radiation, were the major drivers of the distribution, composition and diversity of soil microbial communities in the studied ecosystems of the Chilean Andes. UV-B radiation affected particularly soil fungi, while soil properties such as pH, total C and N content, essential predictors of microbial diversity globally, had a much lower effect on the composition of soil microbial communities. Understanding the factors driving the structure and composition of microbial communities, particularly the role of cushion plants and the feedbacks between plant, climate and soil is of uttermost importance for the preservation of the functionality of high-elevation ecosystems threatened by climate change