Hyperspaces, shape theory and computational topology

Esta tesis trata sobre aproximaciones de espacios métricos compactos. La aproximación y reconstrucción de espacios topológicos mediante otros más sencillos es un tema antigüo en topología geométrica. La idea es construir un espacio muy sencillo lo más parecido posible al espacio original. Como es muy difícil (o incluso no tiene sentido) intentar obtener una copia homeomorfa, el objetivo será encontrar un espacio que preserve algunas propriedades topológicas (algebraicas o no) como compacidad, conexión, axiomas de separación, tipo de homotopía, grupos de homotopía y homología, etc. Los primeros candidatos como espacios sencillos con propiedades del espacio original son los poliedros. Ver el artículo [45] para los resultados principales. En el germen de esta idea, destacamos los estudios de Alexandroff en los años 20, relacionando la dimensión del compacto métrico con la dimensión de ciertos poliedros a través de aplicaciones con imágenes o preimágenes controladas (en términos de distancias). En un contexto más moderno, la idea de aproximación puede ser realizada construyendo un complejo simplicial basado en el espacio original, como el complejo de Vietoris-Rips o el complejo de Cech y comparar su realización con él. En este sentido, tenemos el clásico lema del nervio [12, 21] el cual establece que para un recubrimiento por abiertos “suficientemente bueno" del espacio (es decir, un recubrimiento con miembros e intersecciones contractibles o vacías), el nervio del recubrimiento tiene el tipo de homotopía del espacio original. El problema es encontrar estos recubrimientos (si es que existen). Para variedades Riemannianas, existen algunos resultados en este sentido, utilizando los complejos de Vietoris-Rips. Hausmann demostró [35] que la realización del complejo de Vietoris-Rips de la variedad, para valores suficientemente bajos del parámetro, tiene el tipo de homotopía de dicha variedad. En [40], Latschev demostró una conjetura establecida por Hausmann: El tipo de homotopía de la variedad se puede recuperar utilizando un conjunto finito de puntos (suficientemente denso) para el complejo de Vietoris-Rips. Los resultados de Petersen [58], comparando la distancia Gromov-Hausdorff de los compactos métricos con su tipo de homotopía, son también interesantes. Aquí, los poliedros salen a relucir en las demostraciones, no en los resultados...

Discovery and validation of serologic biomarkers for the diagnosis and prognosis of invasive candidiasis by computational immunomics

Invasive candidiasis (IC) is an opportunistic systemic mycosis caused by Candida species (commonly Candida albicans) that continues to pose a significant public health problem worldwide. Despite great advances in antifungal therapy and changes in clinical practices, IC remains a major infectious cause of morbidity and mortality in severely immunocompromised or critically ill patients, and further accounts for substantial healthcare costs. Its impact on patient clinical outcome and economic burden could be ameliorated by timely initiation of appropriate antifungal therapy. However, early detection of IC is extremely difficult because of its unspecific clinical signs and symptoms, and the inadequate accuracy and time delay of the currently available diagnostic or risk stratification methods. In consequence, the diagnosis of IC is often attained in advanced stages of infection (leading to delayed therapeutic interventions and ensuing poor clinical outcomes) or, unfortunately, at autopsy. In addition to the difficulties encountered in diagnosing IC at an early stage, the initial therapeutic decision-making process is also hindered by the insufficient accuracy of the currently available tools for predicting clinical outcomes in individual IC patients at presentation. Therefore, it is not surprising that clinicians are generally unable to early detect IC, and identify those IC patients who are most likely to suffer fatal clinical outcomes and may benefit from more personalized therapeutic strategies at presentation. Better diagnostic and prognostic biomarkers for IC are thus needed to improve the clinical management of this life-threatening and costly opportunistic fungal infection...

Thematic patterning in English and Spanish: contrastive annotation of a bilingual newspaper corpus for liguistic and computational applications

Thematization is recognized as a fundamental phenomenon in the construction of messages and texts by di erent linguistic schools. This location within a text privileges the elements that guide the reader in the orientation and interpretation of discourse at di erent levels. Thematizing a linguistic unit by locating it in the rst-initial position of a clause, paragraph, or text, confers upon it a special status: a signal of the organizational strategy which characterizes di erent text types playing a role as a variable in the distinction of registers, text types and genres. However, in spite of the importance of the study of thematization for message and textual structuring, to date there are no linguistic studies that have undertook the task of validating its aspects in a comparative manner, either for linguistic or computational purposes. This study, therefore, lls a research gap by implementing a methodology based on contrastive corpus annotation, which allows to empirically validate aspects of the phenomenon of Thematization in English and Spanish, it also seeks to develop a bilingual English-Spanish comparable corpus of newspaper texts automatically annotated with thematic features at clausal and discourse levels. The empirically validated categories (Thematic Field and its elements: Textual Theme, Interpersonal Theme, PreHead and Head) are used to annotate a larger corpus of three newspaper genres news reports, editorials and letters to the editor in terms of thematic choices. This characterization, reveals interesting results, such as the use of genre-speci c strategies in thematic position. In addition, the thesis investigates the possibility to automate the annotation of thematic features in the bilingual corpus through the development of a set of JAVA rules implemented in GATE. It also shows the e cacy of this method in comparison with the manual annotation results...