Comparing Galois representations and the Faltings-Serre-Livné method

Treballs finals del Màster en Matemàtica Avançada, Facultat de Matemàtiques, Universitat de Barcelona: Curs: 2019-2020. Director: L. V. Dieulefait i Nuno FreitasIn 1984, Jean-Pierre Serre, based on the ideas of Gerd Faltings, explained in his course at the Collège de France a method for comparing irreducible $\ell$-adic Galois representations. This method would later be anointed as the Faltings-Serre method by the mathematical community. In 1987 Ron Livné gave an algorithm to compare the case of 2-dimensional 2-adic Galois representations with even trace. In 2008 Gabriel Chênevert generalised it erasing the condition on the traces. In this thesis we are going to draw on his work to explore and formalise Serre’s ideas. In addition, we are going to collect some examples from Serre himself in the case of 2-dimensional 2-adic Galois representations from elliptic curves to understand the use of it and we are going to explain them in detail. Finally, we are also going to study Livné’s approach and give an example of this as well

Infinite Galois theory

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2018, Director: Teresa Crespo Vicente[en] For a finite Galois extension $K | k$, the fundamental theorem of classical Galois theory establishes a one-to-one correspondence between the intermediate fields $E | k$ and the subgroups of Gal $( K | k )$ , the Galois group of the extension. With this correspondence, we can examine the finite field extension by using group theory, which is, in some sense, better understood. A natural question may arise: does this correspondence still hold for infinite Galois extensions? It is very tempting to assume the correspondence still exists. Unfortunately, this correspondence between the intermediate fields of $K | k$ and the subgroups of Gal $( K | k )$ does not necessarily hold when $K | k$ is an infinite Galois extension. A naive approach to why this correspondence fails is to observe that Gal $( K | k )$ has "too many" subgroups, so there is no subfield E of K containing k that can correspond to most of its subgroups. Therefore, it is necessary to find a way to only look at the "relevant subgroups" of the infinite Galois group. This is where topology comes to the rescue, letting us introduce a topology on an arbitrary group and study its subgroups with a different perspective. This new study of groups with a topological perspective will lead to our main goal for this work, the discovery that the fundamental theorem of classical Galois theory holds for infinite Galois extensions $K | k$, whenever we associate a particular topology to the Galois group Gal $( K | k )$. After this theorem is proved, we are going give some examples, two of them with more details than the others. We are going to first characterize the absolute Galois group, that is, the Galois group of the extension $\bar{k} | k$, where $\bar{k}$ is the algebraic closure of $k$. This will be achieved by the means of the Artin-Shreier theorem. Then, we are going to explore the field of $p$-adic numbers, $\mathbb{Q}_p$ . We will briefly discuss the structures of the Galois extensions of this field. In this dissertation we assume some previous knowledge. This previous knowledge corresponds to the subjects taught at the University of Barcelona: Algebraic Structures, Algebraic Equations, Toplogy and Mathematical Analysis

Reproducible science: What, why, how

Most scientific papers are not reproducible: it is really hard, if not impossible, to understand how results are derived from data, and being able to regenerate them in the future (even by the same researchers). However, traceability and reproducibility of results are indispensable elements of highquality science, and an increasing requirement of many journals and funding sources. Reproducible studies include code able to regenerate results from the original data. This practice not only provides a perfect record of the whole analysis but also reduces the probability of errors and facilitates code reuse, thus accelerating scientific progress. But doing reproducible science also brings many benefits to the individual researcher, including saving time and effort, improved collaborations, and higher quality and impact of final publications. In this article we introduce reproducible science, why it is important, and how we can improve the reproducibility of our work. We introduce principles and tools for data management, analysis, version control, and software management that help us achieve reproducible workflows in the context of ecology.Peer Reviewe

Ecoinformática: Nuevo grupo de trabajo de la asociación Española de ecología terrestre

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Alzheimer’s Disease Dementia Guidelines for Diagnostic Testing: A Systematic Review

Alzheimer’s disease dementia (AD dementia) is one of the most common neurodegenerative diseases worldwide, with a growing incidence during the last decades. Clinical diagnosis of cognitive impairment and presence of AD biomarkers have become important issues for early and adequate treatment. We performed a systematic literature search and quality appraisal of AD dementia guidelines, published between 2005 and 2011, which contained diagnostic recommendations on AD dementia. We also analyzed diagnostic recommendations related to the use of brief cognitive tests, neuropsychological evaluation, and AD biomarkers. Of the 537 retrieved references, 15 met the selection criteria. We found that Appraisal of Guidelines Research and Evaluation (AGREE)-II domains such as applicability and editorial independence had the lowest scores. The wide variability on assessment of quality of evidence and strength of recommendations were the main concerns identified regarding diagnostic testing. Although the appropriate methodology for clinical practice guideline development is well known, the quality of diagnostic AD dementia guidelines can be significantly improved

EVIDENT 3 study: A randomized, controlled clinical trial to reduce inactivity and caloric intake in sedentary and overweight or obese people using a smartphone application study protocol

FUNDAMENTOS: La tecnología móvil, cuando se incluye dentro de las intervenciones de componentes múltiples, podría contribuir a una pérdida de peso más efectiva. El objetivo de este proyecto es evaluar el impacto de añadir el uso de la aplicación EVIDENT 3, diseñada para promover la salud a los hábitos de vida, a las estrategias de modificación tradicionales empleadas para la pérdida de peso. También se evaluarán otras conductas específicas (caminar, ingesta de calorías, tiempo sentado) y resultados (calidad de vida, marcadores inflamatorios, mediciones del envejecimiento arterial). MÉTODOS: Ensayo clínico aleatorio y multicéntrico con 2 grupos paralelos. El estudio se llevará a cabo en el ámbito de la atención primaria e incluirá 700 sujetos de 20 a 65 años, con un índice de masa corporal (27,5-40kg/m2), que están clínicamente clasificados como sedentarios. El resultado primario será la pérdida de peso. Los resultados secundarios incluirán cambios en la forma de caminar (pasos/d), el tiempo de permanencia sentado (min/sem), la ingesta calórica (kcal/d), la calidad de vida, el envejecimiento arterial (índice de aumento) y los niveles de marcadores proinflamatorios. Los resultados se medirán en la línea de base, después de 3 meses y después de 1 año. Los participantes serán asignados aleatoriamente al grupo de intervención (IG) o al grupo de control (CG). Ambos grupos recibirán el asesoramiento tradicional de estilo de vida de atención primaria antes de la asignación al azar. A los sujetos del IG se les prestará un teléfono inteligente y una banda inteligente por un período de 3 meses, correspondiente a la duración de la intervención. La aplicación del EVIDENTE 3 integra la información recogida por la banda inteligente sobre la actividad física y la información autodeclarada por los participantes sobre la ingesta diaria de alimentos. Utilizando esta información, la aplicación genera recomendaciones y objetivos personalizados para la pérdida de peso. DISCUSIÓN: Hay una gran diversidad en las aplicaciones utilizadas obteniendo diferentes resultados en la mejora del estilo de vida y la pérdida de peso. Las poblaciones estudiadas no son homogéneas y generan resultados diferentes. Los resultados de este estudio ayudarán a nuestra comprensión de la eficacia de las nuevas tecnologías, combinadas con el asesoramiento tradicional, para reducir la obesidad y permitir estilos de vida más saludables.INTRODUCTION: Mobile technology, when included within multicomponent interventions, could contribute to more effective weight loss. The objective of this project is to assess the impact of adding the use of the EVIDENT 3 application, designed to promote healthy living habits, to traditional modification strategies employed for weight loss. Other targeted behaviors (walking, caloric-intake, sitting time) and outcomes (quality of life, inflammatory markers, measurements of arterial aging) will also be evaluated. METHODS: Randomized, multicentre clinical trial with 2 parallel groups. The study will be conducted in the primary care setting and will include 700 subjects 20 to 65 years, with a body mass index (27.5–40kg/m2), who are clinically classified as sedentary. The primary outcome will be weight loss. Secondary outcomes will include change in walking (steps/d), sitting time (min/wk), caloric intake (kcal/d), quality of life, arterial aging (augmentation index), and pro-inflammatory marker levels. Outcomes will be measured at baseline, after 3 months, and after 1 year. Participants will be randomly assigned to either the intervention group (IG) or the control group (CG). Both groups will receive the traditional primary care lifestyle counseling prior to randomization. The subjects in the IG will be lent a smartphone and a smartband for a 3-month period, corresponding to the length of the intervention. The EVIDENT 3 application integrates the information collected by the smartband on physical activity and the self-reported information by participants on daily food intake. Using this information, the application generates recommendations and personalized goals for weight loss. DISCUSSION: There is a great diversity in the applications used obtaining different results on lifestyle improvement and weight loss. The populations studied are not homogeneous and generate different results. The results of this study will help our understanding of the efficacy of new technologies, combined with traditional counseling, towards reducing obesity and enabling healthier lifestyles.• Ministerio de Ciencia e Innovación y el Instituto de Salud Carlos III/Europa y Fondo de Desarrollo Regional (FEDER). Proyectos PI16/00101, PI16/00952, PI16/00765, PI16/00659, PI16/00421, PI16/00170 • Junta de Castilla y León. Ayuda GRS 1277/B/16peerReviewe

Streptococcus rupicaprae sp. nov., isolated from a Pyrenean chamois (Rupicapra pyrenaica)

Biochemical and molecular genetic studies were performed on an unknown Gram-stain-positive, catalase-negative, coccus-shaped organism isolated from clinical samples of a Pyrenean chamois. The micro-organism was identified as a streptococcal species based on its cellular morphological and biochemical tests. 16S rRNA gene sequence comparison studies confirmed its identification as a member of the genus Streptococcus, but the organism did not correspond to any species of this genus. The nearest phylogenetic relative of the unknown coccus from chamois was Streptococcus ovis (95.9 % 16S rRNA gene sequence similarity). The rpoB and sodA sequence analysis showed sequence similarity values of less than 85.7 % and 83.0 %, respectively, with the currently recognized species of the genus Streptococcus. The novel bacterial isolate was distinguished from S. ovis and other species of the genus Streptococcus using biochemical tests. Based on both phenotypic and phylogenetic findings, it is proposed that the unknown bacterium be classified as a novel species of the genus Streptococcus, Streptococcus rupicaprae sp. nov., with the type strain 2777-2-07(T) (= CECT 7718(T) = CCUG 59652(T))

Septicemic salmonellosis caused by Salmonella Hessarek in wintering and migrating song thrushes (turdus philomelos) in Spain

We investigated two mortality events in wintering and migrating Song Thrushes (Turdus philomelos) in Catalonia, northeastern Spain in 2009 and 2010. Both episodes occurred in late February to mid-March during the spring migration. Salmonellosis produced by the serotype Salmonella enterica subsp. enterica serotype Hessarek (S. Hessarek) was identified as the cause of death in both episodes. Poor body condition, marked splenomegaly, and microscopic disseminated intravascular coagulation with numerous intravascular and tissular bacteria were the most consistent findings. Macro-restriction profiling by pulsed-field gel electrophoresis (PFGE) using XbaI was performed for epidemiologic typing of the S. Hessarek isolates. Two clusters were discernible, that are possibly related, with a similarity of 82.8%. Analysis comparing pectoral muscle and subcutaneous fat scores from the Song Thrushes that died from S. Hessarek with those from healthy Song Thrushes from nearby areas during 2009 and 2010 suggest that poor body condition was associated with the S. Hessarek infection

Síntomas psicopatológicos en pacientes afectos de cefalea crónica con o sin fibromialgia

La presencia de sintomatología psicopatológica, como la ansiedad y la depresión, en las cefaleas crónicas y en la fibromialgia es común. Objetivos. Estudiar si existen diferencias en el perfil psicopatológico entre pacientes con cefalea crónica y fibromialgia (CCFM) y pacientes con cefalea crónica sin fibromialgia (CC), y si existen diferencias en la respuesta al tratamiento entre ambos grupos. Pacientes y métodos. Se administra una batería de test de evaluación de síntomas psicopatológicos a 30 pacientes con CC y a 30 pacientes con CCFM diagnosticados por un reumatólogo. Incluimos en la CC a pacientes con migraña crónica y cefalea tensional crónica. El diseño es con datos apareados de edad y sexo. Se comparan las puntuaciones de depresión, ansiedad, obsesión y perfil de sintomatología psicopatológica -inventario multifásico de personalidad de Minnessota (MMPI-2) y cuestionario de 90 síntomas revisado (SCL-90-R)- (prueba t). Se correlacionan los datos con la respuesta al tratamiento. Resultados. Los pacientes con CCFM muestran puntuaciones significativamente superiores en las escalas de hipocondriasis, depresión, histeria, paranoia, psicastenia y esquizofrenia (MMPI-2), y más somatizaciones, obsesión y ansiedad según el SCL-90-R. La respuesta favorable al tratamiento es inferior en el grupo CCFM (17,85%) que en el CC (42,85%). La hipocondriasis se correlaciona con una peor respuesta (regresión logística). Conclusiones. Los pacientes con CCFM muestran un perfil psicopatológico con mayores puntuaciones y síntomas que los pacientes sin fibromialgia. Esta diferencia se correlaciona con la respuesta terapéutic

The Emissivity Of Foam-Covered Water Surface At L-Band: Theoretical Modeling And Experimental Results From The FROG 2003 Field Experiment

Sea surface salinity can be measured by microwave radiometry at L-band (1400-1427 MHz). This frequency is a compromise between sensitivity to the salinity, small atmospheric perturbation, and reasonable pixel resolution. The description of the ocean emission depends on two main factors: (1) the sea water permittivity, which is a function of salinity, temperature, and frequency, and (2) the sea surface state, which depends on the wind-induced wave spectrum, swell, and rain-induced roughness spectrum, and by the foam coverage and its emissivity. This study presents a simplified two-layer emission model for foam-covered water and the results of a controlled experiment to measure the foam emissivity as a function of salinity, foam thickness, incidence angle, and polarization. Experimental results are presented, and then compared to the two-layer foam emission model with the measured foam parameters used as input model parameters. At 37 psu salt water the foam-induced emissivity increase is /spl sim/0.007 per millimeter of foam thickness (extrapolated to nadir), increasing with increasing incidence angles at vertical polarization, and decreasing with increasing incidence angles at horizontal polarization.Peer Reviewe