Developing Purposeful Mathematical Thinking : a Curious Tale of Apple Trees. 'Desarrollo de un pensamiento matemático intencionado : un relato curioso de manzanos'.

Resumen basado en el de la publicación

Multi-objective optimization scheme for static and dynamic multicast flows

Muchas de las nuevas aplicaciones emergentes de Internet tales como TV sobre Internet, Radio sobre Internet,Video Streamming multi-punto, entre otras, necesitan los siguientes requerimientos de recursos: ancho de banda consumido, retardo extremo-a-extremo, tasa de paquetes perdidos, etc. Por lo anterior, es necesario formular una propuesta que especifique y provea para este tipo de aplicaciones los recursos necesarios para su buen funcionamiento. En esta tesis, proponemos un esquema de ingeniería de tráfico multi-objetivo a través del uso de diferentes árboles de distribución para muchos flujos multicast. En este caso, estamos usando la aproximación de múltiples caminos para cada nodo egreso y de esta forma obtener la aproximación de múltiples árboles y a través de esta forma crear diferentes árboles multicast. Sin embargo, nuestra propuesta resuelve la fracción de la división del tráfico a través de múltiples árboles. La propuesta puede ser aplicada en redes MPLS estableciendo rutas explícitas en eventos multicast. En primera instancia, el objetivo es combinar los siguientes objetivos ponderados dentro de una métrica agregada: máxima utilización de los enlaces, cantidad de saltos, el ancho de banda total consumido y el retardo total extremo-a-extremo. Nosotros hemos formulado esta función multi-objetivo (modelo MHDB-S) y los resultados obtenidos muestran que varios objetivos ponderados son reducidos y la máxima utilización de los enlaces es minimizada. El problema es NP-duro, por lo tanto, un algoritmo es propuesto para optimizar los diferentes objetivos. El comportamiento que obtuvimos usando este algoritmo es similar al que obtuvimos con el modelo. Normalmente, durante la transmisión multicast los nodos egresos pueden salir o entrar del árbol y por esta razón en esta tesis proponemos un esquema de ingeniería de tráfico multi-objetivo usando diferentes árboles para grupos multicast dinámicos. (en el cual los nodos egresos pueden cambiar durante el tiempo de vida de la conexión). Si un árbol multicast es recomputado desde el principio, esto podría consumir un tiempo considerable de CPU y además todas las comuicaciones que están usando el árbol multicast serán temporalmente interrumpida. Para aliviar estos inconvenientes, proponemos un modelo de optimización (modelo dinámico MHDB-D) que utilice los árboles multicast previamente computados (modelo estático MHDB-S) adicionando nuevos nodos egreso. Usando el método de la suma ponderada para resolver el modelo analítico, no necesariamente es correcto, porque es posible tener un espacio de solución no convexo y por esta razón algunas soluciones pueden no ser encontradas. Adicionalmente, otros tipos de objetivos fueron encontrados en diferentes trabajos de investigación. Por las razones mencionadas anteriormente, un nuevo modelo llamado GMM es propuesto y para dar solución a este problema un nuevo algoritmo usando Algoritmos Evolutivos Multi-Objetivos es propuesto. Este algoritmo esta inspirado por el algoritmo Strength Pareto Evolutionary Algorithm (SPEA). Para dar una solución al caso dinámico con este modelo generalizado, nosotros hemos propuesto un nuevo modelo dinámico y una solución computacional usando Breadth First Search (BFS) probabilístico. Finalmente, para evaluar nuestro esquema de optimización propuesto, ejecutamos diferentes pruebas y simulaciones. Las principales contribuciones de esta tesis son la taxonomía, los modelos de optimización multi-objetivo para los casos estático y dinámico en transmisiones multicast (MHDB-S y MHDB-D), los algoritmos para dar solución computacional a los modelos. Finalmente, los modelos generalizados también para los casos estático y dinámico (GMM y GMM Dinámico) y las propuestas computacionales para dar slución usando MOEA y BFS probabilístico.

A collocation method for high frequency scattering by convex polygons

We consider the problem of scattering of a time-harmonic acoustic incident plane wave by a sound soft convex polygon. For standard boundary or finite element methods, with a piecewise polynomial approximation space, the computational cost required to achieve a prescribed level of accuracy grows linearly with respect to the frequency of the incident wave. Recently Chandler–Wilde and Langdon proposed a novel Galerkin boundary element method for this problem for which, by incorporating the products of plane wave basis functions with piecewise polynomials supported on a graded mesh into the approximation space, they were able to demonstrate that the number of degrees of freedom required to achieve a prescribed level of accuracy grows only logarithmically with respect to the frequency. Here we propose a related collocation method, using the same approximation space, for which we demonstrate via numerical experiments a convergence rate identical to that achieved with the Galerkin scheme, but with a substantially reduced computational cost.

A Galerkin boundary element method for high frequency scattering by convex polygons

In this paper we consider the problem of time-harmonic acoustic scattering in two dimensions by convex polygons. Standard boundary or finite element methods for acoustic scattering problems have a computational cost that grows at least linearly as a function of the frequency of the incident wave. Here we present a novel Galerkin boundary element method, which uses an approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh, with smaller elements closer to the corners of the polygon. We prove that the best approximation from the approximation space requires a number of degrees of freedom to achieve a prescribed level of accuracy that grows only logarithmically as a function of the frequency. Numerical results demonstrate the same logarithmic dependence on the frequency for the Galerkin method solution. Our boundary element method is a discretization of a well-known second kind combined-layer-potential integral equation. We provide a proof that this equation and its adjoint are well-posed and equivalent to the boundary value problem in a Sobolev space setting for general Lipschitz domains.

A lightweight supercomputing web portal for inferring phylogenetic trees

In this paper we describe a lightweight Web portal developed for running computational jobs on a IBM JS21 Bladecenter cluster, ThamesBlue, for inferring and analyzing evolutionary histories. We first discuss the need for leveraging HPC as a enabler for molecular phylogenetics research. We go on to describe how the portal is designed to interface with existing open-source software that is typical of a HPC resource configuration, and how by design this portal is generic enough to be portable to other similarly configured compute clusters, and for other applications.

The effectiveness of somatic embryogenesis in eliminating the cocoa swollen shoot virus from infected cocoa trees

Investigations were undertaken on the use of somatic embryogenesis to generate cocoa swollen shoot virus (CSSV) disease free clonal propagules, from infected trees. Polymerase chain reaction (PCR) capillary electrophoresis revealed the presence of CSSV in all the callus tissues induced from the CSSV-infected Amelonado cocoa trees (T1, T2 and T4). The virus was transmitted to primary somatic embryos induced from the infected callus tissues at the rate of 10 (19%), 18 (14%) and 16 (15%) for T1, T2 and T4, respectively. Virus free primary somatic embryos from the infected callus tissues converted into plantlets tested CSSV negative by PCR/capillary electrophoresis 2 years after weaning. Secondary somatic embryos induced from the CSSV-infected primary somatic embryos revealed the presence of viral fragments at the rate of 4 (4%) and 9 (9%) for T2 and T4, respectively. Real-time PCR revealed 23 of the 24 secondary somatic embryos contained no detectable virus. Based on these findings, it is proposed that progressive elimination of the CSSV in infected cocoa trees occurred from primary embryogenesis to secondary embryogenesis. (C) 2008 Elsevier B.V. All rights reserved.

Shoot dieback in clipped young Golden Leyland (Cupressocyparis leylandii) trees - a physiological mechanism?

Shoot dieback is a problem in frequently trimmed Leyland hedges and is increasingly affecting gardeners’ choice of hedge trees, having a negative effect on a conifer nursery industry. Some damage can be attributed to the feeding by aphids, but it is unclear if there are also underlying physiological causes. In this study, we tested the hypothesis that shoot-clipping of conifer trees during adverse growing conditions (i.e. high air temperature and low soil moisture) could be leading to shoot ‘dieback’. Three-year-old Golden Leyland Cypress (x Cupressocyparis leylandii ‘Excalibur Gold’) plants were subjected to either a well-watered or droughted irrigation regime and placed in either a ‘hot’ (average day temperature = 40°C) or a ‘cool’ (average day temperature = 27°C) glasshouse compartment. Half of the plants from each glasshouse were clipped on Day 14 and again on Day 50. Measurements of soil moisture content (SMC), net CO2 assimilation rate (A), stomatal conductance (gs), branchlet xylem water potential (XWP), plant height and foliage colour were made. Within the clipped and unclipped treatments of both glasshouse compartments, plants from the droughted regime had significantly lower values for A, gs and XWP than those from the well-watered regime. However, there was no difference in these parameters between the hot and cool glasshouse compartments. The trends seen for A, gs and XWP of all treatments generally mirrored changes in SMC indicating a direct effect of water supply on these parameters. By the end of the experiment the overall foliage colour of plants from the hot glasshouse was darker than that of plants from the cool glasshouse and the overall foliage colour was also darker following shoot clipping. In general, shoot clipping led to increases in A, gs XWP and SMC. This may be due to the reduction in total leaf area leading to a greater supply of water for the remaining leaves. No shoot ‘dieback’ was observed in any treatment in response to drought stress or shoot-clipping.