An iterative Multiscale Finite-Volume algorithm converging to the exact solution

The multiscale finite volume (MsFV) method has been developed to efficiently solve large heterogeneous problems (elliptic or parabolic); it is usually employed for pressure equations and delivers conservative flux fields to be used in transport problems. The method essentially relies on the hypothesis that the (fine-scale) problem can be reasonably described by a set of local solutions coupled by a conservative global (coarse-scale) problem. In most cases, the boundary conditions assigned for the local problems are satisfactory and the approximate conservative fluxes provided by the method are accurate. In numerically challenging cases, however, a more accurate localization is required to obtain a good approximation of the fine-scale solution. In this paper we develop a procedure to iteratively improve the boundary conditions of the local problems. The algorithm relies on the data structure of the MsFV method and employs a Krylov-subspace projection method to obtain an unconditionally stable scheme and accelerate convergence. Two variants are considered: in the first, only the MsFV operator is used; in the second, the MsFV operator is combined in a two-step method with an operator derived from the problem solved to construct the conservative flux field. The resulting iterative MsFV algorithms allow arbitrary reduction of the solution error without compromising the construction of a conservative flux field, which is guaranteed at any iteration. Since it converges to the exact solution, the method can be regarded as a linear solver. In this context, the schemes proposed here can be viewed as preconditioned versions of the Generalized Minimal Residual method (GMRES), with a very peculiar characteristic that the residual on the coarse grid is zero at any iteration (thus conservative fluxes can be obtained).

Methods for testing association between uncertain genotypes and quantitative traits.

Interpretability and power of genome-wide association studies can be increased by imputing unobserved genotypes, using a reference panel of individuals genotyped at higher marker density. For many markers, genotypes cannot be imputed with complete certainty, and the uncertainty needs to be taken into account when testing for association with a given phenotype. In this paper, we compare currently available methods for testing association between uncertain genotypes and quantitative traits. We show that some previously described methods offer poor control of the false-positive rate (FPR), and that satisfactory performance of these methods is obtained only by using ad hoc filtering rules or by using a harsh transformation of the trait under study. We propose new methods that are based on exact maximum likelihood estimation and use a mixture model to accommodate nonnormal trait distributions when necessary. The new methods adequately control the FPR and also have equal or better power compared to all previously described methods. We provide a fast software implementation of all the methods studied here; our new method requires computation time of less than one computer-day for a typical genome-wide scan, with 2.5 M single nucleotide polymorphisms and 5000 individuals.

Sex differences in the computation of traveling distance

Path integration is known to provide information to keep track of spatial location. Surprisingly, few investigations concerning sex differences in computation of the traveling distance have been done. This work was aimed at analyzing the reproduction of both passive and active linear displacements in women and men. To this end, the displacement of blindfolded subjects was done in a wheelchair, then on foot, three times in each condition for a fixed distance. Copies of passive and active traveling distance, distance estimations and pointing responses towards the starting point were analyzed. In passive condition and comparatively to men, women error was larger. Whereas traveling distance was generally underestimated in women, it was overestimated in men. In active condition, no sex differences were observed. When blindfolded subjects have to estimate the traveling distance, the female error was larger than the male one. But, when subjects were asked to indicate the visual cue corresponding to the traveling distance, the male error was larger than the female one. Finally, pointing to the starting point (0°) after a whole-body rotation showed a larger deviation from 0° in men than in women. These results suggest that sex of the subjects influence brain computation of path integration information.

A program for the computation of power and determination of sample size in hierarchical experimental designs.

We have devised a program that allows computation of the power of F-test, and hence determination of appropriate sample and subsample sizes, in the context of the one-way hierarchical analysis of variance with fixed effects. The power at a fixed alternative is an increasing function of the sample size and of the subsample size. The program makes it easy to obtain the power of F-test for a range of values of sample and subsample sizes, and therefore the appropriate sizes based on a desired power. The program can be used for the 'ordinary' case of the one-way analysis of variance, as well as for hierarchical analysis of variance with two stages of sampling. Examples are given of the practical use of the program.

Wheat alleles introgress into selfing wild relatives: empirical estimates from approximate Bayesian computation in Aegilops triuncialis.

Extensive gene flow between wheat (Triticum sp.) and several wild relatives of the genus Aegilops has recently been detected despite notoriously high levels of selfing in these species. Here, we assess and model the spread of wheat alleles into natural populations of the barbed goatgrass (Aegilops triuncialis), a wild wheat relative prevailing in the Mediterranean flora. Our sampling, based on an extensive survey of 31 Ae. triuncialis populations collected along a 60 km × 20 km area in southern Spain (Grazalema Mountain chain, Andalousia, totalling 458 specimens), is completed with 33 wheat cultivars representative of the European domesticated pool. All specimens were genotyped with amplified fragment length polymorphism with the aim of estimating wheat admixture levels in Ae. triuncialis populations. This survey first confirmed extensive hybridization and backcrossing of wheat into the wild species. We then used explicit modelling of populations and approximate Bayesian computation to estimate the selfing rate of Ae. triuncialis along with the magnitude, the tempo and the geographical distance over which wheat alleles introgress into Ae. triuncialis populations. These simulations confirmed that extensive introgression of wheat alleles (2.7 × 10(-4) wheat immigrants for each Ae. triuncialis resident, at each generation) into Ae. triuncialis occurs despite a high selfing rate (Fis ≈ 1 and selfing rate = 97%). These results are discussed in the light of risks associated with the release of genetically modified wheat cultivars in Mediterranean agrosystems.

Predicting drug metabolism: experiment and/or computation?

Drug metabolism can produce metabolites with physicochemical and pharmacological properties that differ substantially from those of the parent drug, and consequently has important implications for both drug safety and efficacy. To reduce the risk of costly clinical-stage attrition due to the metabolic characteristics of drug candidates, there is a need for efficient and reliable ways to predict drug metabolism in vitro, in silico and in vivo. In this Perspective, we provide an overview of the state of the art of experimental and computational approaches for investigating drug metabolism. We highlight the scope and limitations of these methods, and indicate strategies to harvest the synergies that result from combining measurement and prediction of drug metabolism.

Approximate Bayesian Computation Reveals the Crucial Role of Oceanic Islands for the Assembly of Continental Biodiversity.

The perceived low levels of genetic diversity, poor interspecific competitive and defensive ability, and loss of dispersal capacities of insular lineages have driven the view that oceanic islands are evolutionary dead ends. Focusing on the Atlantic bryophyte flora distributed across the archipelagos of the Azores, Madeira, the Canary Islands, Western Europe, and northwestern Africa, we used an integrative approach with species distribution modeling and population genetic analyses based on approximate Bayesian computation to determine whether this view applies to organisms with inherent high dispersal capacities. Genetic diversity was found to be higher in island than in continental populations, contributing to mounting evidence that, contrary to theoretical expectations, island populations are not necessarily genetically depauperate. Patterns of genetic variation among island and continental populations consistently fitted those simulated under a scenario of de novo foundation of continental populations from insular ancestors better than those expected if islands would represent a sink or a refugium of continental biodiversity. We, suggest that the northeastern Atlantic archipelagos have played a key role as a stepping stone for transoceanic migrants. Our results challenge the traditional notion that oceanic islands are the end of the colonization road and illustrate the significant role of oceanic islands as reservoirs of novel biodiversity for the assembly of continental floras.