Joint Laver diamonds and grounded forcing axioms

I explore two separate topics: the concept of jointness for set-theoretic guessing principles, and the notion of grounded forcing axioms. A family of guessing sequences is said to be joint if all of its members can guess any given family of targets independently and simultaneously. I primarily investigate jointness in the case of various kinds of Laver diamonds. In the case of measurable cardinals I show that, while the assertions that there are joint families of Laver diamonds of a given length get strictly stronger with increasing length, they are all equiconsistent. This is contrasted with the case of partially strong cardinals, where we can derive additional consistency strength, and ordinary diamond sequences, where large joint families exist whenever even one diamond sequence does. Grounded forcing axioms modify the usual forcing axioms by restricting the posets considered to a suitable ground model. I focus on the grounded Martin's axiom which states that Martin's axioms holds for posets coming from some ccc ground model. I examine the new axiom's effects on the cardinal characteristics of the continuum and show that it is quite a bit more robust under mild forcing than Martin's axiom itself.Comment: This is my PhD dissertatio

Ideal Projections and Forcing Projections

It is well known that saturation of ideals is closely related to the “antichain-catching” phenomenon from Foreman-Magidor-Shelah [10]. We consider several antichain-catching properties that are weaker than saturation, and prove: (1) If I is a normal ideal on ω2 which satisfies stationary antichain catching, then there is an inner model with a Woodin cardinal; (2) For any n ∈ ω, it is consistent relative to large cardinals that there is a normal ideal I on ωn which satisfies projective antichain catching, yet I is not saturated (or even strong). This provides a negative answer to Open Question number 13 from Foreman’s chapter in the Handbook of Set Theory ([7])

Stable modification of relative curves

We generalize theorems of Deligne-Mumford and de Jong on semi-stable modifications of families of proper curves. The main result states that after a generically \'etale alteration of the base any (not necessarily proper) family of multipointed curves with semi-stable generic fiber admits a minimal semi-stable modification. The latter can also be characterized by the property that its geometric fibers have no certain exceptional components. The main step of our proof is uniformization of one-dimensional extensions of valued fields. Riemann-Zariski spaces are then used to obtain the result over any integral base.Comment: 60 pages, third version, the paper was revised due to referee's report, section 2 was divided into sections 2 and 6, to appear in JA

An Unsolicited Soliloquy on Dependency Parsing

Programa Oficial de Doutoramento en Computación . 5009V01[Abstract] This thesis presents work on dependency parsing covering two distinct lines of research. The first aims to develop efficient parsers so that they can be fast enough to parse large amounts of data while still maintaining decent accuracy. We investigate two techniques to achieve this. The first is a cognitively-inspired method and the second uses a model distillation method. The first technique proved to be utterly dismal, while the second was somewhat of a success. The second line of research presented in this thesis evaluates parsers. This is also done in two ways. We aim to evaluate what causes variation in parsing performance for different algorithms and also different treebanks. This evaluation is grounded in dependency displacements (the directed distance between a dependent and its head) and the subsequent distributions associated with algorithms and the distributions found in treebanks. This work sheds some light on the variation in performance for both different algorithms and different treebanks. And the second part of this area focuses on the utility of part-of-speech tags when used with parsing systems and questions the standard position of assuming that they might help but they certainly won’t hurt.[Resumen] Esta tesis presenta trabajo sobre análisis de dependencias que cubre dos líneas de investigación distintas. La primera tiene como objetivo desarrollar analizadores eficientes, de modo que sean suficientemente rápidos como para analizar grandes volúmenes de datos y, al mismo tiempo, sean suficientemente precisos. Investigamos dos métodos. El primero se basa en teorías cognitivas y el segundo usa una técnica de destilación. La primera técnica resultó un enorme fracaso, mientras que la segunda fue en cierto modo un ´éxito. La otra línea evalúa los analizadores sintácticos. Esto también se hace de dos maneras. Evaluamos la causa de la variación en el rendimiento de los analizadores para distintos algoritmos y corpus. Esta evaluación utiliza la diferencia entre las distribuciones del desplazamiento de arista (la distancia dirigida de las aristas) correspondientes a cada algoritmo y corpus. También evalúa la diferencia entre las distribuciones del desplazamiento de arista en los datos de entrenamiento y prueba. Este trabajo esclarece las variaciones en el rendimiento para algoritmos y corpus diferentes. La segunda parte de esta línea investiga la utilidad de las etiquetas gramaticales para los analizadores sintácticos.[Resumo] Esta tese presenta traballo sobre análise sintáctica, cubrindo dúas liñas de investigación. A primeira aspira a desenvolver analizadores eficientes, de maneira que sexan suficientemente rápidos para procesar grandes volumes de datos e á vez sexan precisos. Investigamos dous métodos. O primeiro baséase nunha teoría cognitiva, e o segundo usa unha técnica de destilación. O primeiro método foi un enorme fracaso, mentres que o segundo foi en certo modo un éxito. A outra liña avalúa os analizadores sintácticos. Esto tamén se fai de dúas maneiras. Avaliamos a causa da variación no rendemento dos analizadores para distintos algoritmos e corpus. Esta avaliaci´on usa a diferencia entre as distribucións do desprazamento de arista (a distancia dirixida das aristas) correspondentes aos algoritmos e aos corpus. Tamén avalía a diferencia entre as distribucións do desprazamento de arista nos datos de adestramento e proba. Este traballo esclarece as variacións no rendemento para algoritmos e corpus diferentes. A segunda parte desta liña investiga a utilidade das etiquetas gramaticais para os analizadores sintácticos.This work has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (FASTPARSE, grant agreement No 714150) and from the Centro de Investigación de Galicia (CITIC) which is funded by the Xunta de Galicia and the European Union (ERDF - Galicia 2014-2020 Program) by grant ED431G 2019/01.Xunta de Galicia; ED431G 2019/0