Efficiency and accuracy of GPU-parallelized Fourier spectral methods for solving phase-field models

Phase-field models are widely employed to simulate microstructure evolution during processes such as solidification or heat treatment. The resulting partial differential equations, often strongly coupled together, may be solved by a broad range of numerical methods, but this often results in a high computational cost, which calls for advanced numerical methods to accelerate their resolution. Here, we quantitatively test the efficiency and accuracy of semi-implicit Fourier spectral-based methods, implemented in Python programming language and parallelized on a graphics processing unit (GPU), for solving a phase-field model coupling Cahn-Hilliard and Allen-Cahn equations. We compare computational performance and accuracy with a standard explicit finite difference (FD) implementation with similar GPU parallelization on the same hardware. For a similar spatial discretization, the semi-implicit Fourier spectral (FS) solvers outperform the FD resolution as soon as the time step can be taken 5 to 6 times higher than afforded for the stability of the FD scheme. The accuracy of the FS methods also remains excellent even for coarse grids, while that of FD deteriorates significantly. Therefore, for an equivalent level of accuracy, semi-implicit FS methods severely outperform explicit FD, by up to 4 orders of magnitude, as they allow much coarser spatial and temporal discretization

Simulation guided design of globular single-chain nanoparticles by tuning the solvent quality

The control of primary and further structures of individual folded/collapsed synthetic polymers has received significant attention in recent years. However, the synthesis of single-chain nanoparticles (SCNPs) showing a compact, globular conformation in solution has turned out so far to be highly elusive. By means of simulations, we propose two methods for obtaining globular SCNPs in solution. The first synthesis route is performed in the bad solvent, with the precursor anchored to a surface. In the second route we use a random copolymer precursor with unreactive solvophilic and reactive solvophobic units, which form a single core-shell structure. Both protocols prevent intermolecular cross-linking. After recovering good solvent conditions, the swollen nanoparticles maintain their globular character. The proposed methods are experimentally realizable and do not require specific sequence control of the precursors. Our results pave the way for the synthesis via solvent-assisted design of a new generation of globular soft nanoparticles mimicking global conformations of native proteins in solution.We acknowledge financial support from the Projects MAT2012-31088 (MINECO) and T-654-13 (GV).Peer Reviewe

Favourable areas for co-occurrence of parapatric species: niche conservatism and niche divergence in Iberian tree frogs and midwife toads

Aim Predicting species responses to global change is one of the most pressing issues in conservation biogeography. A key part of the problem is understanding how organisms have reacted to climatic changes in the past. Here we use species distribution modelling to infer the effects of climate changes since the Last Interglacial (LIG, about 130,000 ybp) on patterns of genetic structure and diversity in the Western Spadefoot toad (Pelobates cultripes) in combination with spatially-explicit phylogeographic analyses. Location Iberian Peninsula and mainland France. Methods 524 individuals from 54 populations across the species range were sampled to document patterns of genetic diversity and infer their evolutionary history based on data from mtDNA and fourteen polymorphic microsatellites. Generalized linear models based on distribution data were used to infer climatic favourability for the species in the present and in paleoclimatic simulations for the LIG, the Mid Holocene and the last glacial maximum (LGM). Results Estimates of genetic diversity show a decreasing trend from south to north, suggesting persistence of high historical population sizes in the southern Iberian Peninsula. Species distribution models show differences in climatic favourability through time, with significant correlations between historically stable favourable areas and current patterns of genetic diversity. These results are corroborated by Bayesian Skyline Plots and continuous diffusion phylogeographic analyses. Main conclusions The results indicate the presence of southern refugia, with moderate recent expansions at the northern end of the species’ range. Toads at the northern range margin exhibit the lowest genetic diversity and occupy areas of high past climate variability, classified as marginal in terms of favourability, rendering these populations most vulnerable to climate-mediated changes in the long term

Large-scale linkage analysis of 1302 affected relative pairs with rheumatoid arthritis

Rheumatoid arthritis is the most common systematic autoimmune disease and its etiology is believed to have both strong genetic and environmental components. We demonstrate the utility of including genetic and clinical phenotypes as covariates within a linkage analysis framework to search for rheumatoid arthritis susceptibility loci. The raw genotypes of 1302 affected relative pairs were combined from four large family-based samples (North American Rheumatoid Arthritis Consortium, United Kingdom, European Consortium on Rheumatoid Arthritis Families, and Canada). The familiality of the clinical phenotypes was assessed. The affected relative pairs were subjected to autosomal multipoint affected relative-pair linkage analysis. Covariates were included in the linkage analysis to take account of heterogeneity within the sample. Evidence of familiality was observed with age at onset (p << 0.001) and rheumatoid factor (RF) IgM (p << 0.001), but not definite erosions (p = 0.21). Genome-wide significant evidence for linkage was observed on chromosome 6. Genome-wide suggestive evidence for linkage was observed on chromosomes 13 and 20 when conditioning on age at onset, chromosome 15 conditional on gender, and chromosome 19 conditional on RF IgM after allowing for multiple testing of covariates

Combining linkage data sets for meta-analysis and mega-analysis: the GAW15 rheumatoid arthritis data set

We have used the genome-wide marker genotypes from Genetic Analysis Workshop 15 Problem 2 to explore joint evidence for genetic linkage to rheumatoid arthritis across several samples. The data consisted of four high-density genome scans on samples selected for rheumatoid arthritis. We cleaned the data, removed intermarker linkage disequilibrium, and assembled the samples onto a common genetic map using genome sequence positions as a reference for map interpolation. The individual studies were combined first at the genotype level (mega-analysis) prior to a multipoint linkage analysis on the combined sample, and second using the genome scan meta-analysis method after linkage analysis of each sample. The two approaches were compared, and give strong support to the HLA locus on chromosome 6 as a susceptibility locus. Other regions of interest include loci on chromosomes 11, 2, and 12