Modeling across site variation of the substitution process is increasingly recognized as important for obtaining more accurate phylogenetic reconstructions. Both finite and infinite mixture models have been proposed and have been shown to significantly improve on classical single-matrix models. Compared with their finite counterparts, infinite mixtures have a greater expressivity. However, they are computationally more challenging. This has resulted in practical compromises in the design of infinite mixture models. In particular, a fast but simplified version of a Dirichlet process model over equilibrium frequency profiles implemented in PhyloBayes has often been used in recent phylogenomics studies, while more refined model structures, more realistic and empirically more fit, have been practically out of reach. We introduce a message passing interface version of PhyloBayes, implementing the Dirichlet process mixture models as well as more classical empirical matrices and finite mixtures. The parallelization is made efficient thanks to the combination of two algorithmic strategies: a partial Gibbs sampling update of the tree topology and the use of a truncated stick-breaking representation for the Dirichlet process prior. The implementation shows close to linear gains in computational speed for up to 64 cores, thus allowing faster phylogenetic reconstruction under complex mixture models. PhyloBayes MPI is freely available from our website www.phylobayes.org.

The WMAP determination of the baryon−to−photon ratio implies, through Big Bang nucleosynthesis, a cosmological Li abundance larger, by a factor of 2 to 3, than the Li abundance plateau observed in the oldest Pop II stars. It is however inescapable that there be a reduction by a factor of at least 1.6 to 2.0 of the surface Li abundance during the evolution of Pop II field stars with [Fe/H] ≤ −1.5. That the observed Li be lower than cosmologically produced Li is expected from stellar evolution models. Since at turnoff most of the Li abundance reduction is caused by gravitational settling, the presence of 6 Li in some turnoff stars is also understood. Given that the WMAP implications for Li cosmological abundance and the Li Spite plateau can be naturally explained by gravitational settling in the presence of weak turbulence, there appears little need for exotic physics as suggested by some authors. Instead, there is a need for a better understanding of turbulent transport in the radiative zones of stars. This requires simulations from first principles. Rather strict upper limits to turbulent transport are determined for the Sun and Pop II stars.

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A bidomain reaction-diffusion model of the human heart was developed, and potentials resulting from normal depolarization and repolarization were compared with results from a compatible monodomain model. Comparisons were made for an empty isolated heart and for a heart with fluid-filled ventricles. Both sinus rhythm and ectopic activation were simulated. The bidomain model took 2 days on 32 processors to simulate a complete cardiac cycle. Differences between monodomain and bidomain results were extremely small, even for the extracellular potentials, which in case of the monodomain model were computed with a high-resolution forward model. Propagation of activation was 2% faster in the bidomain model than in the monodomain model. Electrograms computed with monodomain and bidomain models were visually indistinguishable. We conclude that, in the absence of applied currents, propagating action potentials on the scale of a human heart can be studied with a monodomain model.

The solar evolution has been calculated including all the e †ects of the di †usion of helium and heavy elements. Monochromatic opacities are used to calculate radiative accelerations and Rosseland opacities at each evolution time step, taking into account the local abundance changes of all important (21) chemical elements. The OPAL monochromatic data are used for the opacities and the radiative accelerations. The Opacity Project data are needed to calculate how chemical species and electrons share the momentum absorbed from the radiation Ñux.A detailed evaluation of the impact of atomic di †usion on solar models is presented. On some elements thermal di †usion adds approximately 50% to the gravitational settling velocity. While gravitational settling had been included in previous solar models, this is the Ðrst time that the impact of radiative accelerations is considered. Radiative accelerations can be up to 40% of gravity below the solar convection zone and thus a †ect chemical element di †usion signiÐcantly, contrary to current belief.Up to the solar age, the abundances of most metals change by 7.5% if complete ionization is assumed, but by 8.5%È10% if detailed ionization of each species is taken into account. If radiative accelerations are included, intermediate values are obtained. Di †usion leads to a change of up to 8% in the Rosseland opacities, compared to those of the original mixture. Most of this e †ect can be taken into account by using tables with several values of Z.If one isolates the e †ects of radiative accelerations, the abundance changes they cause alter the Rosseland opacity by up to 0.5% ; the density is a †ected by up to 0.2% ; the sound speed is a †ected by at most 0.06%. The inclusion of radiative accelerations leads to a reduction of 3% of neutrino Ñuxes measured with 37Cl detectors and 1% measured with 71Ga detectors.The partial transformation of C and O into N by nuclear reactions in the core causes a D1% change in the opacities that cannot be modeled by a change in Z alone.The evolution is allowed to proceed to 1010 yr in order to determine the impact at the end of the main-sequence life of solar-type stars. It is found that immediately below the convection zone, the radiative acceleration on some iron peak elements is within a few percent of gravity. The abundance anomalies reach 18% for He in the convection zone but are kept within 12% and 15% for most because of They would have reached 18% in the absence of g rad . g rad .

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