Análisis de tráfico en Internet utilizando distribuciones Alfa estables en procesadores paralelos

En el contexto actual de desarrollo de aplicaciones basadas en TCP/IP (Internet), el análisis del tráfico IP es una necesidad crucial con el objetivo de prever y solucionar posibles problemas de congestión que dificulten el uso adecuado de dichas aplicaciones. La disponibilidad de modelos matemáticos del tráfico permite anticiparse a futuros problemas en las redes de comunicaciones y además automatizar tareas de monitorización y control que forman parte de la gestión de redes actual. En los últimos años se han propuesto modelos estadísticos basados en las distribuciones alfa estables que se han revelado prometedores, pero que demandan una capacidad de cálculo intensa que limita su aplicación en situaciones de control de red en las que las decisiones se deben tomar en tiempo real. El abaratamiento de la tecnología de procesadores paralelos permite acelerar la ejecución de los algoritmos de estimación de parámetros de tráfico y están habilitando la utilización de las distribuciones alfa estables en el análisis y la resolución de problemas de tráfico. El objetivo de este trabajo sería partir de la situación actual en la que se han implantado algoritmos de estimación de parámetros de tráfico basados en el modelo alfa estable y adaptarlos al análisis de tráfico real, de manera que se puedan utilizar para intentar predecir el comportamiento de una red, lo que supondría la posibilidad de detectar anomalías, cambios en la red o incluso, predecir su comportamiento para llegar a prevenir posibles problemas. Para ello se realizará un estudio de la red, en las que se capturarán muestras de tráfico reales que posteriormente serán ajustadas para ser interpretadas usando distribuciones alfa estables.In the current context of developing applications based on TCP / IP (Internet), the analysis of the IP traffic is a necessity in order to anticipate and solve possible congestion problems that hinder the proper use of such applications. The existence of mathematical models of traffic allow to anticipate future problems in the communications networks and also automate monitoring and control tasks that are part of the current network management. In recent years statistical models have been proposed based on stable alpha distributions, which have been promising, but which demand an intense computational capacity that limits its implementation in situations of network control in which decisions must be taken in real time. Cheaper parallel processor technologies make possible the acceleration of the execution of algorithms for estimating traffic parameters and they are enabling the use of stable alpha distributions in the analysis and resolution of traffic problems. The objective of this work is to start from the current situation in which algorithms have been implemented to estimate traffic parameters based on the stable alpha model and to adapt them to the analysis of real traffic. So that they can be used to try to predict the behavior of a network, which would mean the possibility of detecting anomalies, changes in the network or even, predict their behavior in order to prevent potential problems. Therefore, a study of the network will be carried out, in which real traffic samples will be captured and later adjusted to be interpreted using stable alpha distributions

Renormalization of Horava Gravity

We prove perturbative renormalizability of projectable Horava gravity. The key element of the argument is the choice of a gauge which ensures the correct anisotropic scaling of the propagators and their uniform falloff at large frequencies and momenta. This guarantees that the counterterms required to absorb the loop divergences are local and marginal or relevant with respect to the anisotropic scaling. Gauge invariance of the counterterms is achieved by making use of the background-covariant formalism. We also comment on the difficulties of this approach when addressing the renormalizability of the non-projectable model.Comment: 35 pages, no figures; references discussing gauge invariance of counterterms have been added, typos correcte

Renormalization of gauge theories in the background-field approach

Using the background-field method we demonstrate the Becchi-Rouet-Stora-Tyutin (BRST) structure of counterterms in a broad class of gauge theories. Put simply, we show that gauge invariance is preserved by renormalization in local gauge field theories whenever they admit a sensible background-field formulation and anomaly-free path integral measure. This class encompasses Yang-Mills theories (with possibly Abelian subgroups) and relativistic gravity, including both renormalizable and non-renormalizable (effective) theories. Our results also hold for non-relativistic models such as Yang-Mills theories with anisotropic scaling or Horava gravity. They strengthen and generalize the existing results in the literature concerning the renormalization of gauge systems. Locality of the BRST construction is emphasized throughout the derivation. We illustrate our general approach with several explicit examples.Comment: 45 pages, no figures; references added, changes in the Introduction and Conclusion

Ho\v{r}ava gravity is asymptotically free (in 2+1 dimensions)

We compute the $\beta$-functions of marginal couplings in projectable Ho\v{r}ava gravity in $2+1$ spacetime dimensions. We show that the renormalization group flow has an asymptotically-free fixed point in the ultraviolet (UV), establishing the theory as a UV-complete model with dynamical gravitational degrees of freedom. Therefore, this theory may serve as a toy-model to study fundamental aspects of quantum gravity. Our results represent a step forward towards understanding the UV properties of realistic versions of Ho\v{r}ava gravity.Comment: Updated references, minor revisions. Matches journal versio

Reconstructing Detailed Line Profiles of Lamellar Gratings from GISAXS Patterns with a Maxwell Solver

Laterally periodic nanostructures were investigated with grazing incidence small angle X-ray scattering (GISAXS) by using the diffraction patterns to reconstruct the surface shape. To model visible light scattering, rigorous calculations of the near and far field by numerically solving Maxwell's equations with a finite-element method are well established. The application of this technique to X-rays is still challenging, due to the discrepancy between incident wavelength and finite-element size. This drawback vanishes for GISAXS due to the small angles of incidence, the conical scattering geometry and the periodicity of the surface structures, which allows a rigorous computation of the diffraction efficiencies with sufficient numerical precision. To develop dimensional metrology tools based on GISAXS, lamellar gratings with line widths down to 55 nm were produced by state-of-the-art e-beam lithography and then etched into silicon. The high surface sensitivity of GISAXS in conjunction with a Maxwell solver allows a detailed reconstruction of the grating line shape also for thick, non-homogeneous substrates. The reconstructed geometrical line shape models are statistically validated by applying a Markov chain Monte Carlo (MCMC) sampling technique which reveals that GISAXS is able to reconstruct critical parameters like the widths of the lines with sub-nm uncertainty

Heat kernel methods for Lifshitz theories

We study the one-loop covariant effective action of Lifshitz theories using the heat kernel technique. The characteristic feature of Lifshitz theories is an anisotropic scaling between space and time. This is enforced by the existence of a preferred foliation of space-time, which breaks Lorentz invariance. In contrast to the relativistic case, covariant Lifshitz theories are only invariant under diffeomorphisms preserving the foliation structure. We develop a systematic method to reduce the calculation of the effective action for a generic Lifshitz operator to an algorithm acting on known results for relativistic operators. In addition, we present techniques that drastically simplify the calculation for operators with special properties. We demonstrate the efficiency of these methods by explicit applications.Comment: 36 pages, matches journal versio

Desarrollo de la unidad didáctica "La función de nutrición" mediante ABPP

Este Trabajo Fin de Máster tiene su origen e inspiración en gran parte en las actividades realizadas y experiencias vividas a lo largo del practicum II desarrollado en el IES Plaza de la Cruz al llevar a cabo la unidad didáctica de “La Nutrición”. Con esta propuesta didáctica se pretende elaborar un aprendizaje llevado a cabo con la intención de crear conocimiento, construido por el propio sujeto, que ayude a entender y comprender el entorno y la realidad, asimilando así de forma íntegra y duradera el conocimiento adquirido. Consiste en el compendio de actividades propuestas para desarrollar con ellas los principios en los que se basa este trabajo, planteada desde la perspectiva del aprendizaje basado en problemas y proyectos, encuadradas en la unidad didáctica correspondiente a la función de nutrición humana. El método de evaluación de cada actividad se define en la unidad didáctica, incluye métodos autoevaluativos y coevaluativos, así como técnicas para evaluar el éxito o fracaso en el aula de la aplicación del proyecto.Máster Universitario en Profesorado de Educación Secundaria por la Universidad Pública de NavarraBigarren Hezkuntzako Irakasletzako Unibertsitate Masterra Nafarroako Unibertsitate Publikoa