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

An Algorithm for Cellular Reprogramming

The day we understand the time evolution of subcellular elements at a level of detail comparable to physical systems governed by Newton's laws of motion seems far away. Even so, quantitative approaches to cellular dynamics add to our understanding of cell biology, providing data-guided frameworks that allow us to develop better predictions about and methods for control over specific biological processes and system-wide cell behavior. In this paper we describe an approach to optimizing the use of transcription factors in the context of cellular reprogramming. We construct an approximate model for the natural evolution of a synchronized population of fibroblasts, based on data obtained by sampling the expression of some 22,083 genes at several times along the cell cycle. (These data are based on a colony of cells that have been cell cycle synchronized) In order to arrive at a model of moderate complexity, we cluster gene expression based on the division of the genome into topologically associating domains (TADs) and then model the dynamics of the expression levels of the TADs. Based on this dynamical model and known bioinformatics, we develop a methodology for identifying the transcription factors that are the most likely to be effective toward a specific cellular reprogramming task. The approach used is based on a device commonly used in optimal control. From this data-guided methodology, we identify a number of validated transcription factors used in reprogramming and/or natural differentiation. Our findings highlight the immense potential of dynamical models models, mathematics, and data guided methodologies for improving methods for control over biological processes

Unifying Parsimonious Tree Reconciliation

Evolution is a process that is influenced by various environmental factors, e.g. the interactions between different species, genes, and biogeographical properties. Hence, it is interesting to study the combined evolutionary history of multiple species, their genes, and the environment they live in. A common approach to address this research problem is to describe each individual evolution as a phylogenetic tree and construct a tree reconciliation which is parsimonious with respect to a given event model. Unfortunately, most of the previous approaches are designed only either for host-parasite systems, for gene tree/species tree reconciliation, or biogeography. Hence, a method is desirable, which addresses the general problem of mapping phylogenetic trees and covering all varieties of coevolving systems, including e.g., predator-prey and symbiotic relationships. To overcome this gap, we introduce a generalized cophylogenetic event model considering the combinatorial complete set of local coevolutionary events. We give a dynamic programming based heuristic for solving the maximum parsimony reconciliation problem in time O(n^2), for two phylogenies each with at most n leaves. Furthermore, we present an exact branch-and-bound algorithm which uses the results from the dynamic programming heuristic for discarding partial reconciliations. The approach has been implemented as a Java application which is freely available from http://pacosy.informatik.uni-leipzig.de/coresym.Comment: Peer-reviewed and presented as part of the 13th Workshop on Algorithms in Bioinformatics (WABI2013

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

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

The International Society for Extracellular Vesicles launches the first massive open online course on extracellular vesicles

The International Society for Extracellular Vesicles (ISEV) has organised its first educational online course for students and beginners in the field of extracellular vesicles (EVs). This course, "Basics of Extracellular Vesicles,'' uses recorded lectures from experts in the field and will be open for an unlimited number of participants. The course is divided into 5 modules and can be accessed at www.coursera.org/learn/extracellular-vesicles. The first module is an introduction to the field covering the nomenclature and history of EVs. Module 2 focuses on the biogenesis and uptake mechanisms of EVs, as well as their RNA, protein and lipid cargo. Module 3 covers the collection and processing of cell culture media and body fluids such as blood, breast milk, cerebrospinal fluid and urine prior to isolation of EVs. Modules 4 and 5 present different isolation methods and characterisation techniques utilised in the EV field. Here, differential ultracentrifugation, size-exclusion chromatography, density gradient centrifugation, kit-based precipitation, electron microscopy, cryo-electron microscopy, flow cytometry, atomic-force microscopy and nanoparticle-tracking analysis are covered. This first massive open online course (MOOC) on EVs was launched on 15 August 2016 at the platform "Coursera'' and is free of charge.11Ysciescopu

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.]