Determining species tree topologies from clade probabilities under the coalescent

One approach to estimating a species tree from a collection of gene trees is to first estimate probabilities of clades from the gene trees, and then to construct the species tree from the estimated clade probabilities. While a greedy consensus algorithm, which consecutively accepts the most probable clades compatible with previously accepted clades, can be used for this second stage, this method is known to be statistically inconsistent under the multispecies coalescent model. This raises the question of whether it is theoretically possible to reconstruct the species tree from known probabilities of clades on gene trees. We investigate clade probabilities arising from the multispecies coalescent model, with an eye toward identifying features of the species tree. Clades on gene trees with probability greater than 1/3 are shown to reflect clades on the species tree, while those with smaller probabilities may not. Linear invariants of clade probabilities are studied both computationally and theoretically, with certain linear invariants giving insight into the clade structure of the species tree. For species trees with generic edge lengths, these invariants can be used to identify the species tree topology. These theoretical results both confirm that clade probabilities contain full information on the species tree topology and suggest future directions of study for developing statistically consistent inference methods from clade frequencies on gene trees.Comment: 25 pages, 2 figure

Shape optimization with a level set based mesh evolution method

International audienceIn this article, we discuss an approach for geometry and topology optimization of structures which benefits from an accurate description of shapes at each stage of the iterative process - by means of a mesh amenable for mechanical analyses - while retaining the whole versatility of the level set method when it comes to accounting for their evolution. The key ingredients of this method are two operators for switching from a meshed representation of a domain to an implicit one, and conversely; this notably brings into play an algorithm for generating the signed distance function to an arbitrary discrete domain, and a mesh generation algorithm for implicitly-defined geometries

A PDE based approach to multi-domain partitioning and quadrilateral meshing

International audienceIn this paper, we present an algorithm for partitioning any given 2d domain into regions suitable for quadrilateral meshing. It can deal with multi-domain geometries with ease, and is able to preserve the symmetry of the domain. Moreover, this method keeps the number of singularities at the junctions of the regions to a minimum. Each part of the domain, being four-sided, can then be meshed using a structured method. The partitioning stage is achieved by solving a PDE constrained problem based on the geometric properties of the domain boundaries

A mesh evolution algorithm based on the level set method for geometry and topology optimization

An approach for structural optimization is proposed, which combines the versatility of the level set method for handling large deformations and topology changes with the accurate description of the geometry provided by an exact mesh of the shape. The key ingredients of this method are efficient algorithms for (i) moving a level set function on an unstructured mesh, (ii) remeshing the surface corresponding to the zero level set and (iii) simultaneously adaptating the volumic mesh which fits to this surfacic mesh

YAMS A fully Automatic Adaptive Isotropic Surface Remeshing Procedure

This technical note describes the main features of YAMS {This software was registered with the APP under n° IDDN.FR.001.410006.00.R.P. 1999.000.20600 on october 4, 1999.}, an automatic adaptive surface remeshing tool. The aim of the software, the input and output files and the list of error messages are defined in this document. A number of typical application examples are provided to explain the various possibilities of the code. Finally, a short technical description of the algorithm and the various ways to obtain the software are given. YAMS has been developed within the GAMMA research project at INRIA­Rocquen­court. This document describes the features of the current version : V2.1 (June, 2001)

Génération et adaptation de maillages de surfaces à partir de données anatomiques discrètes

Des systèmes de numérisation précis et rapides sont aujourd'hui largement utilisés dans de nombreux domaines de l'ingénierie scientifique et biomédicale- . Les données discrètes en résultant sont généralement directement converties en maillages de surfaces polyédriques, au moyen d'algorithmes de type "brute-force", conduisant à des maillages pouvant souvent contenir plusieurs millions de polygones. De fait, simplifier de tels maillages permet d'en faciliter le stockage et la transmission, et d'en rendre le calcul et le rendu possibles sinon efficaces. Dans ce rapport, on présente un schéma général pour la simplification et l'adaptation de maillages de surfaces basé sur un contrôle de l'approximation géométrique ainsi que la qualité en forme et en taille des éléments (requis dans les simulations numériques). Plusieurs exemples académiques ou relatifs à des géométries anatomiques complexes sont présentés pour illustrer l'efficacité de l'approche proposée

Medit : outil interactif de visualisation de maillages. (version 2.0, nov. 2000)

Ce rapport technique décrit les principales fonctionnalités du logiciel Medit. Ce programme a été développé à l'INRIA pour permettre la visualisation interactive de maillages (plans, de surfaces ou volumiques), spécifiquement dans le contexte d'applications numériques. Basé sur le standard graphique OpenGL, Medit a été conçu pour répondre aux besoins les plus courants des utilisateurs (en général, environ $10$ des possibilités des logiciels de visualisation sont exploitées par $90$ des utilisateurs)

MEDIT : An interactive Mesh visualization Software

This technical report describes the main features of MEDIT (This software wa registered with the APP under n° IDDN.FR.001.410023.00.R.P. 2001.000.10800 on january 25, 2001.), an interactive mesh visualization tool developped in the Gamma project at INRIA-Rocquencourt. Based on the graphic standard OpenGL, this software has been specifically designed to fulfill most of the common requirements of engineers and numericians, in the context of numerical simulations. This program is rather intuitive and, therefore, the user does not really need any specific learning stage prior to be able to play with it. In this document, the user will learn how to visualize and manipulate mesh data structures via the mouse, how to deal with scalar/ten- sor values associated with a mesh and how to deal with more complex features (e.g., animations, postscript or image output creation, etc.). This document describes the features of the current version : release V2.1 (June, 2001) and, as such, replaces the previous document [3]