Optimal error analysis of spectral methods with emphasis on non-constant coefficients and deformed geometries

The numerical analysis of spectral methods when non-constant coefficients appear in the equation, either due to the original statement of the equations or to take into account the deformed geometry, is presented. Particular attention is devoted to the optimality of the discretization even for low values of the discretization parameter. The effect of some overintegration is also addressed, in order to possibly improve the accuracy of the discretization

A well-posed optimal spectral element approximation for the Stokes problem

A method is proposed for the spectral element simulation of incompressible flow. This method constitutes in a well-posed optimal approximation of the steady Stokes problem with no spurious modes in the pressure. The resulting method is analyzed, and numerical results are presented for a model problem

Realist Legitimacy

This thesis is an investigation of realist theories of political legitimacy, with a particular focus on two realist accounts of legitimacy – those of Amanda Greene (2019) and Bernard Williams (2005). Many theorists have taken the view that realist accounts of legitimacy clearly provide an insufficient normative standard of legitimacy. This thesis provides a challenge to such critics by offering a partial defence of (some kinds of) realist accounts of legitimacy as providing a viable normative standard of legitimacy. The thesis argues, first, that realist theories of legitimacy have more impressive normative implications than might be thought, and second, that there are good reasons to reject forms of critique of realist legitimacy based on ‘external’ moral standards. This latter argument is based on an understanding of realist legitimacy as offering an ‘internalist’ standard for the moral evaluation of states’ rule

Spectral element methods: Algorithms and architectures

Spectral element methods are high-order weighted residual techniques for partial differential equations that combine the geometric flexibility of finite element methods with the rapid convergence of spectral techniques. Spectral element methods are described for the simulation of incompressible fluid flows, with special emphasis on implementation of spectral element techniques on medium-grained parallel processors. Two parallel architectures are considered: the first, a commercially available message-passing hypercube system; the second, a developmental reconfigurable architecture based on Geometry-Defining Processors. High parallel efficiency is obtained in hypercube spectral element computations, indicating that load balancing and communication issues can be successfully addressed by a high-order technique/medium-grained processor algorithm-architecture coupling

Nuevas soluciones a viejos problemas: taxones de amplia distribución, distribuciones redundantes y áreas ausentes en la biogeografía cladista de procesos

Area cladograms are widely used in historical biogeography to summarize area relationships. Constructing such cladograms is complicated by the existence of widespread taxa (terminal taxa distributed in more than one area), redundant distributions (areas harboring more than one taxon) and missing areas (areas of interest absent from some of the compared cladograms). These problems have traditionally been dealt with using Assumptions 0, 1, and 2, but the assumptions are inapplicable to event–based methods of biogeographic analysis because they do not specify the costs of alternative solutions and may result in non–overlapping solution sets. The present paper presents the argument that only widespread terminals pose a problem to event–based methods, and three possible solutions are described. Under the recent option, the widespread distribution is assumed to be the result of recent dispersal. The ancient option assumes that the widespread distribution is the result of a failure to vicariate, and explains any mismatch between the distribution and the area cladogram by extinction. The free option treats the widespread taxon as an unresolved higher taxon consisting of one lineage occurring in each area, and permits any combination of events and any resolution of the terminal polytomy in explaining the widespread distribution. Algorithms implementing these options are described and applied to Rosen (1978)’s classical data set on Heterandria and Xiphophorus.El análisis biogeográfico cladista se basa en la comparación de cladogramas de áreas de organismos que habitan una misma región (sustituyendo el nombre de los taxones en la filogenia por las áreas que éstos ocupan) para obtener un patrón común, el cladograma general de áreas. La construcción del cladograma de áreas se complica cuando existen taxones presentes en más de un área de distribución (“taxones de amplia distribución”), áreas que albergan más de un taxón (“distribuciones redundantes”), o áreas que no están presentes en alguno de los grupos (“áreas ausentes”). En biogeografía cladista de procesos, los taxones de amplia distribución se resuelven aplicando las Asunciones: 0, 1, y 2, que difieren en la relación cladogenética permitida entre las áreas donde se distribuye el taxon. Se proponen tres nuevas soluciones para abordar este problema dentro de un nuevo enfoque en biogeografía cladista que incorpora los procesos al análisis biogeográfico: “biogeografía cladista de procesos”. Estas opciones difieren no sólo en las relaciones entre las áreas implicadas sino ambién en los procesos biogeográficos que pudieron haber dado lugar a la distribución. La opción recent considera la amplia distribución como si fuera de origen reciente y la explica por dispersión. La opción ancient considera que la amplia distribución es ancestral y la explica mediante vicarianza y extinción. La opción free considera la amplia distribución como un taxón de alto rango con un linaje en cada una de las áreas implicadas y cuyas relaciones no han sido establecidas, permitiendo cualquier combinación de procesos biogeográficos y cualquier solución de la politomía para explicar la distribución. Se comparan estas opciones utilizando el famoso análisis de Rosen (1978) sobre Heterandria y Xiphophorus. También se discute brevemente como tratar las distribuciones redundantes y las áreas usentes dentro de este nuevo enfoque

RevBayes: Bayesian Phylogenetic Inference Using Graphical Models and an Interactive Model-Specification Language.

Programs for Bayesian inference of phylogeny currently implement a unique and fixed suite of models. Consequently, users of these software packages are simultaneously forced to use a number of programs for a given study, while also lacking the freedom to explore models that have not been implemented by the developers of those programs. We developed a new open-source software package, RevBayes, to address these problems. RevBayes is entirely based on probabilistic graphical models, a powerful generic framework for specifying and analyzing statistical models. Phylogenetic-graphical models can be specified interactively in RevBayes, piece by piece, using a new succinct and intuitive language called Rev. Rev is similar to the R language and the BUGS model-specification language, and should be easy to learn for most users. The strength of RevBayes is the simplicity with which one can design, specify, and implement new and complex models. Fortunately, this tremendous flexibility does not come at the cost of slower computation; as we demonstrate, RevBayes outperforms competing software for several standard analyses. Compared with other programs, RevBayes has fewer black-box elements. Users need to explicitly specify each part of the model and analysis. Although this explicitness may initially be unfamiliar, we are convinced that this transparency will improve understanding of phylogenetic models in our field. Moreover, it will motivate the search for improvements to existing methods by brazenly exposing the model choices that we make to critical scrutiny. RevBayes is freely available at http://www.RevBayes.com [Bayesian inference; Graphical models; MCMC; statistical phylogenetics.]