Discretization of the Region of Interest

[EN]The meccano method was recently introduced to construct simultaneously tetrahedral meshes and volumetric parameterizations of solids. The method requires the information of the solid geometry that is defined by its surface, a meccano, i.e., an outline of the solid defined by connected polyhedral pieces, and a tolerance that fixes the desired approximation of the solid surface. The method builds an adaptive tetrahedral mesh of the solid (physical domain) as a deformation of an appropriate tetrahedral mesh of the meccano (parametric domain). The main stages of the procedure involve an admissible mapping between the meccano and the solid boundaries, the nested Kossaczký’s refinement, and our simultaneous untangling and smoothing algorithm. In this chapter, we focus on the application of the method to build tetrahedral meshes over complex terrain, that is interesting for simulation of environmental processes. A digital elevation map of the terrain, the height of the domain, and the required orography approximation are given as input data. In addition, the geometry of buildings or stacks can be considered. In these applications, we have considered a simple cuboid as meccano.Ministerio de Economía y Competitividad, Gobierno de España; Fondos FEDER; Departamento de Educación, Junta de Castilla y León; CONACYT-SENER, Fondo Sectorial CONACYT SENER HIDROCARBUROS

Primer of adaptive finite element methods

Adaptive finite element methods (AFEM) are a fundamental numerical instrument in science and engineering to approximate partial differential equations. In the 1980s and 1990s a great deal of effort was devoted to the design of a posteriori error estimators, following the pioneering work of Babuska. These are computable quantities, depending on the discrete solution(s) and data, that can be used to assess the approximation quality and improve it adaptively. Despite their practical success, adaptive processes have been shown to converge, and to exhibit optimal cardinality, only recently for dimension d > 1 and for linear elliptic PDE. These series of lectures presents an up-to-date discussion of AFEM encompassing the derivation of upper and lower a posteriori error bounds for residual-type estimators, including a critical look at the role of oscillation, the design of AFEM and its basic properties, as well as a complete discussion of convergence, contraction property and quasi-optimal cardinality of AFEM

Gain-of-function mutations in DNMT3A in patients with paraganglioma

Purpose: The high percentage of patients carrying germline mutations makes pheochromocytomas/paragangliomas the most heritable of all tumors. However, there are still cases unexplained by mutations in the known genes. We aimed to identify the genetic cause of disease in patients strongly suspected of having hereditary tumors. Methods: Whole-exome sequencing was applied to the germlines of a parent–proband trio. Genome-wide methylome analysis, RNA-seq, CRISPR/Cas9 gene editing, and targeted sequencing were also performed. Results: We identified a novel de novo germline mutation in DNMT3A, affecting a highly conserved residue located close to the aromatic cage that binds to trimethylated histone H3. DNMT3A-mutated tumors exhibited significant hypermethylation of homeobox-containing genes, suggesting an activating role of the mutation. CRISPR/Cas9-mediated knock-in in HeLa cells led to global changes in methylation, providing evidence of the DNMT3A-altered function. Targeted sequencing revealed subclonal somatic mutations in six additional paragangliomas. Finally, a second germline DNMT3A mutation, also causing global tumor DNA hypermethylation, was found in a patient with a family history of pheochromocytoma. Conclusion: Our findings suggest that DNMT3A may be a susceptibility gene for paragangliomas and, if confirmed in future studies, would represent the first example of gain-of-function mutations affecting a DNA methyltransferase gene involved in cancer predisposition