Three projects in arithmetic geometry: torsion points and curves of low genus

2019 Fall.Includes bibliographical references.This paper is an exposition of three different projects in arithmetic geometry. All of them consider problems related to smooth curves with low genus and the torsion points of their Jacobians. The first project studies curves over finite fields and two invariants of the p-torsion part of their Jacobians: the a-number (a) and p-rank (f). There are many open questions in the literature about the existence of curves with a certain genus g and given values of a and f. In particular, not much is known when g = 4 and the curve is non-hyperelliptic. This is the case that we focus on here; we collect and analyze statistical data of curves over Fp for p = 3, 5, 7, 11 and their invariants. Then, we study the existence of Cartier points, which are also related to the structure of J[p]. For curves with 0 ≤ a < g, the number of Cartier points is bounded, and it depends on a and f. The second project addresses the problem of computing the endomorphism ring of a supersingular elliptic curve. This question has gained recent interest as the basis of alternative cryptosystems that hope to be resistant to quantum attacks. Our strategy is to generate these endomorphism rings by finding cycles in the l-isogeny graph which correspond to generators of the ring. We were able to find a condition for cycles to be linearly independent and an obstruction for two of them to be generators. Finally, the last chapter considers the Galois representations associated to the n-torsion points of elliptic curves over Q. In concrete, we construct models for the modular curves associated to applicable subgroups of GL₂(Z/nZ) and find the rational points on all of those which result in genus 0 or 1 curves, or prove that they have infinitely many. We also analyze the curves with a hyperelliptic genus 2 model and provably find the rational points on all but seven of them

Formación del concepto límite mediante dos registros de representación: representaciones gráficas y el uso algebraico

Uno de los problemas centrales que se presentan, para abordar el tema de límite, es sin duda cuando nos enfrentamos al concepto de infinito. Generalmente el docente al enseñar el concepto de infinito utiliza metáforas didácticas basadas en conjuntos muy grandes, esto para fijar la idea de infinitud. De acuerdo con la real academia española, esto permite crear la noción de infinito en un lenguaje cotidiano, lo que lleva a generar una mala formación de este concepto, dentro de un lenguaje matemático, ya que la imprecisión del lenguaje cotidiano hace ver al concepto de infinito muy vago y se aleja de la idea matemática como unidad total (Ortiz, 1994). El interés de nuestro trabajo se centra precisamente en el diseño de actividades, donde el estudiante pueda realizar y observar un proceso infinito, a través de ejemplos geométricos donde se presente la situación límite (proceso infinito culminado), permitiendo la formación del concepto de límite

Formulación de un plan de optimización enfocado al área de ventas para el Grupo Purdy Motor

Proyecto de graduación (Bachillerato en Administración de Empresas) Instituto Tecnológico de Costa Rica, Escuela de Administración de Empresas, 2013Las estrategias contribuyen a implementar acciones planificadas sistemáticamente en las empresas, con el fin de lograr la meta u objetivos propuestos. El presente trabajo pretende brindar a Purdy Motor San Carlos, un plan de optimización para el departamento de ventas, con el propósito de mejorar la eficiencia de los procesos, en conjunto con la localización de deficiencias e imperfecciones que podrían estar dificultando el crecimiento de las ventas en la sucursal. Complementando la investigación, se desarrolla un análisis de la atención del servicio al cliente de la competencia directa, con el objetivo de evaluar comparativamente entre el servicio brindado por dichas sucursales y la sucursal de Purdy Motor San Carlos. Además, se considera evaluar la atención al cliente que ofrecen actualmente los asesores de ventas de la sucursal mediante clientes incógnitos, y por medio de las opiniones brindadas por los clientes actuales, con la intención de retroalimentar dicha área. Además, se pretende la captación de nuevos clientes a corto plazo, mediante el hallazgo de las variables más importantes que los clientes potenciales consideran en el momento de adquirir un vehículo nuevo. Por otra parte, también se realiza un análisis de la percepción de los colaboradores con el servicio que se presta y las condiciones actuales de la empresa. Definiendo dichos análisis se pretende generar estrategias, dichas estrategias cuentan con sus respectivas acciones y actividades a concretar, ofreciendo así de una manera sencilla y concisa cúales son las modificaciones que debe realizar Purdy Motor San Carlos.Grupo Purdy Motor Instituto Tecnológico de Costa Rica. Sede San Carlos. Escuela de Administración de Empresa

Guía de atención integral (GAI). Detección temprana y diagnóstico del cáncer de colon y recto. Atención integral, seguimiento y rehabilitación de pacientes con diagnóstico de cáncer de colon y recto

El cáncer color rectal (CCR) es el cuarto tipo más común de cáncer alrededor del mundo y en las dos últimas décadas ha venido en aumento en Colombia. En la actualidad no se cuenta con una guía de atención integral que permita aclarar las recomendaciones frente al manejo de individuos asintomáticos en relación con las estrategias de tamización, terapias biológicas o el uso de quimioterapia. El desarrollo de una guía de atención integral permitirá es una necesidad urgente en nuestro medio para este tipo de tumor ya que permitirá hacer uso de la evidencia disponible y de esta manera estandarizar la atención integral de los pacientes desde la detección temprana, el diagnóstico, tratamiento endoscópico, estatificación, tratamiento quirúrgico , rehabilitación y seguimient

The Role of P2X7 Receptor Signaling in Regulation of Rhythmic Astrocyte Physiology in Mouse Suprachiasmatic Nucleus Cells

Mammalian circadian rhythms are controlled by the suprachiasmatic nuclei (SCN) of the hypothalamus. While neural circuits influence SCN entrainment, cells within the SCN also act as individual oscillators. Research on mechanisms that regulate synchronization of ensemble SCN rhythms has mainly focused on neuronal populations. However, astrocytes are just as abundant in the SCN and display circadian rhythms in clock gene expression and extracellular accumulation of ATP. Rhythmic accumulation of ATP in the rat SCN in vivo has also been described to occur during the night. Nonetheless, it remains unclear whether or not astrocytic ATP release functions as a synchronizing signal in the SCN and contributes to ensemble neural activities such as inflammatory signaling. Preliminary studies on SCN cell cultures and purinergic inhibitors disrupt ATP accumulation and clock gene expression rhythms. Further, clock-defective astrocytes are unable to accumulate ATP rhythmically. I tested the hypothesis that ATP signaling mediates rhythms in astrocytic physiology through P2X7 receptor. First, I tested whether rhythmic ATP release may synchronize individual oscillators in the SCN cells. I also tested the effectiveness of BzATP, a P2X7R agonist, in inducing release of ATP in mouse SCN cells. I tested if P2X7R, GFAP overall protein expression and astrocytic activation markers such as GFAP, are rhythmic in mouse SCN cells. I demonstrate that ATP signaling among astrocytes is a good candidate for a coordinating mechanism that synchronizes clock-controlled physiological responses in the SCN and other brain regions. Furthermore, I present data indicating that clock-controlled ATP signaling rhythms are involved in modulating neuroinflammatory signaling. Since BzATP proved to be an effective P2X7R agonist with regard to potentiating ATP release from mouse SCN cells, further experiments with other agonists and antagonists can provide evidence for the role of ATP and P2X7R signaling rhythms, their circadian regulation, and their influence on astrocytic physiology and brain health

Oportunidades en la implementación de la metodología BIM en los Llanos orientales: ¿continuar en el confort de lo conocido o evolucionar hacia las nuevas tecnologías?

El artículo estudia las oportunidades de mejora del sector de la construcción en los Llanos orientales a partir de la metodología building information modeling. Esto para buscar estrategias innovadoras que les permita la optimización de los recursos financieros

Síntesis y caracterización de un material compuesto de aluminio-cobre (al-cu) reforzado con partículas cerámicas de carburo de titanio (TIC)

Los materiales compuestos de matriz metálica (MMC’s) reforzados con partículas cerámicas hacen parte de los materiales más apetecidos para aplicaciones que combinen características mecánicas elevadas con una relación de peso considerablemente bajo, como la aeronáutica o el transporte terrestre. Esta rama de los materiales establece un reto importante en su estudio debido a que la meta es crear un material con propiedades imposibles de obtener en un material convencional. En este trabajo se desarrolla la fabricación y caracterización de un material compuesto de matriz metálica reforzado con partículas cerámicas. Por medio de la técnica de infiltración por capilaridad sin presión externa a 1250°C bajo una atmósfera controlada de argón se fabricó el material compuesto de matriz Aluminio-12%Cobre (40%) reforzado con partículas cerámicas de Carburo de Titanio (60%). El tamaño de partícula del refuerzo de TiC fue en promedio de 2,262 μm, el valor de la dureza fue de 374,75 HV y el módulo elástico de 249,9 GPa. El análisis por microscopía electrónica de barrido muestra una distribución de fase

Multimodal examination of emotion processing systems associated with negative affectivity across early childhood

High Temperamental Negative Affectivity in early childhood has been found to predict later emotion dysregulation. While much work has been conducted to separately probe bio-behavioral systems associated with Negative Affectivity, very little work has examined the relations among multiple systems across age. In this study, we use multi-modal methods to index neurobiological systems associated with Negative Affectivity in 53 4-7-year-old children. Prefrontal activation during emotion regulation was measured using functional near-infrared spectroscopy over the lateral prefrontal cortex (PFC) while children played a game designed to elicit frustration in Social (Happy and Angry faces) and Nonsocial contexts. Gaze behaviors while free-viewing Happy and Angry faces were also measured. Finally, Negative Affectivity was indexed using a score composite based on factor analysis of parent-reported temperament. Using mixed-effects linear models, we found an age-dependent association between Negative Affectivity and both PFC activation during frustration and fixation duration on the mouth area of Happy faces, such that older children high in Negative Affectivity spent less time looking at the mouths of Happy faces and had lower PFC activation in response to frustration (ps\u3c0.034). These results provide further insight to how Negative Affectivity may be associated with changes in affective neurobiological systems across early childhood

Decreased levels of serum glutathione peroxidase 3 are associated with papillary serous ovarian cancer and disease progression

<p>Abstract</p> <p>Background</p> <p>Glutathione peroxidase 3 (GPX3) is a selenocysteine-containing antioxidant enzyme that reacts with hydrogen peroxide and soluble fatty acid hydroperoxides, thereby helping to maintain redox balance within cells. Serum levels of GPX3 have been found to be reduced in various cancers including prostrate, thyroid, colorectal, breast and gastric cancers. Intriguingly, GPX3 has been reported to be upregulated in clear cell ovarian cancer tissues and thus may have implications in chemotherapeutic resistance. Since clear cell and serous subtypes of ovarian cancer represent two distinct disease entities, the aim of this study was to determine GPX3 levels in serous ovarian cancer patients and establish its potential as a biomarker for detection and/or surveillance of papillary serous ovarian cancer, the most frequent form of ovarian tumors in women.</p> <p>Patients and Methods</p> <p>Serum was obtained from 66 patients (median age: 62 years, range: 22-89) prior to surgery and 65 controls with a comparable age-range (median age: 53 years, range: 25-83). ELISA was used to determine the levels of serum GPX3. The Mann Whitney <it>U </it>test was performed to determine statistical significance between the levels of serum GPX3 in patients and controls.</p> <p>Results</p> <p>Serum levels of GPX3 were found to be significantly lower in patients than controls (p = 1 × 10^-2). Furthermore, this was found to be dependent on the stage of disease. While levels in early stage (I/II) patients showed no significant difference when compared to controls, there was a significant reduction in late stage (III/IV, p = 9 × 10^-4) and recurrent (p = 1 × 10^-2) patients. There was a statistically significant reduction in levels of GPX3 between early and late stage (p = 5 × 10^-4) as well as early and recurrent (p = 1 × 10^-2) patients. Comparison of women and controls stratified to include only women at or above 50 years of age shows that the same trends were maintained and the differences became more statistically significant.</p> <p>Conclusions</p> <p>Serum GPX3 levels are decreased in women with papillary serous ovarian cancer in a stage-dependent manner and also decreased in women with disease recurrence. Whether this decrease represents a general feature in response to the disease or a link to the progression of the cancer is unknown. Understanding this relationship may have clinical and therapeutic consequences for women with papillary serous adenocarcinoma.</p