Searching for convergence in phylogenetic Markov chain Monte Carlo

Markov chain Monte Carlo (MCMC) is a methodology that is gaining widespread use in the phylogenetics community and is central to phylogenetic software packages such as MrBayes. An important issue for users of MCMC methods is how to select appropriate values for adjustable parameters such as the length of the Markov chain or chains, the sampling density, the proposal mechanism, and, if Metropolis-coupled MCMC is being used, the number of heated chains and their temperatures. Although some parameter settings have been examined in detail in the literature, others are frequently chosen with more regard to computational time or personal experience with other data sets. Such choices may lead to inadequate sampling of tree space or an inefficient use of computational resources. We performed a detailed study of convergence and mixing for 70 randomly selected, putatively orthologous protein sets with different sizes and taxonomic compositions. Replicated runs from multiple random starting points permit a more rigorous assessment of convergence, and we developed two novel statistics, delta and epsilon, for this purpose. Although likelihood values invariably stabilized quickly, adequate sampling of the posterior distribution of tree topologies took considerably longer. Our results suggest that multimodality is common for data sets with 30 or more taxa and that this results in slow convergence and mixing. However, we also found that the pragmatic approach of combining data from several short, replicated runs into a metachain to estimate bipartition posterior probabilities provided good approximations, and that such estimates were no worse in approximating a reference posterior distribution than those obtained using a single long run of the same length as the metachain. Precision appears to be best when heated Markov chains have low temperatures, whereas chains with high temperatures appear to sample trees with high posterior probabilities only rarely. [Bayesian phylogenetic inference; heating parameter; Markov chain Monte Carlo; replicated chains.]

Gaussian quantum Monte Carlo methods for fermions and bosons

We introduce a new class of quantum Monte Carlo methods, based on a Gaussian quantum operator representation of fermionic states. The methods enable first-principles dynamical or equilibrium calculations in many-body Fermi systems, and, combined with the existing Gaussian representation for bosons, provide a unified method of simulating Bose-Fermi systems. As an application relevant to the Fermi sign problem, we calculate finite-temperature properties of the two dimensional Hubbard model and the dynamics in a simple model of coherent molecular dissociation.

Grand canonical Monte Carlo simulation study of methane adsorption at an open graphite surface and in slitlike carbon pores at 273 K

Grand canonical Monte Carlo (GCMC) simulation was used for the systematic investigation of the supercritical methane adsorption at 273 K on an open graphite surface and in slitlike micropores of different sizes. For both considered adsorption systems the calculated excess adsorption isotherms exhibit a maximum. The effect of the pore size on the maximum surface excess and isosteric enthalpy of adsorption for methane storage at 273 K is discussed. The microscopic detailed picture of methane densification near the homogeneous graphite wall and in slitlike pores at 273 K is presented with selected local density profiles and snapshots. Finally, the reliable pore size distributions, obtained in the range of the microporosity, for two pitch-based microporous activated carbon fibers are calculated from the local excess adsorption isotherms obtained via the GCMC simulation. The current systematic study of supercritical methane adsorption both on an open graphite surface and in slitlike micropores performed by the GCMC summarizes recent investigations performed at slightly different temperatures and usually a lower pressure range by advanced methods based on the statistical thermodynamics.

A Mixture model with random-effects components for clustering correlated gene-expression profiles

Motivation: The clustering of gene profiles across some experimental conditions of interest contributes significantly to the elucidation of unknown gene function, the validation of gene discoveries and the interpretation of biological processes. However, this clustering problem is not straightforward as the profiles of the genes are not all independently distributed and the expression levels may have been obtained from an experimental design involving replicated arrays. Ignoring the dependence between the gene profiles and the structure of the replicated data can result in important sources of variability in the experiments being overlooked in the analysis, with the consequent possibility of misleading inferences being made. We propose a random-effects model that provides a unified approach to the clustering of genes with correlated expression levels measured in a wide variety of experimental situations. Our model is an extension of the normal mixture model to account for the correlations between the gene profiles and to enable covariate information to be incorporated into the clustering process. Hence the model is applicable to longitudinal studies with or without replication, for example, time-course experiments by using time as a covariate, and to cross-sectional experiments by using categorical covariates to represent the different experimental classes. Results: We show that our random-effects model can be fitted by maximum likelihood via the EM algorithm for which the E(expectation) and M(maximization) steps can be implemented in closed form. Hence our model can be fitted deterministically without the need for time-consuming Monte Carlo approximations. The effectiveness of our model-based procedure for the clustering of correlated gene profiles is demonstrated on three real datasets, representing typical microarray experimental designs, covering time-course, repeated-measurement and cross-sectional data. In these examples, relevant clusters of the genes are obtained, which are supported by existing gene-function annotation. A synthetic dataset is considered too.

Structure of saccharose-based carbon and transport of confined fluids: hybrid reverse Monte Carlo reconstruction and simulation studies

We present results of the reconstruction of a saccharose-based activated carbon (CS1000a) using hybrid reverse Monte Carlo (HRMC) simulation, recently proposed by Opletal et al. [1]. Interaction between carbon atoms in the simulation is modeled by an environment dependent interaction potential (EDIP) [2,3]. The reconstructed structure shows predominance of sp(2) over sp bonding, while a significant proportion of sp(3) hybrid bonding is also observed. We also calculated a ring distribution and geometrical pore size distribution of the model developed. The latter is compared with that obtained from argon adsorption at 87 K using our recently proposed characterization procedure [4], the finite wall thickness (FWT) model. Further, we determine self-diffusivities of argon and nitrogen in the constructed carbon as functions of loading. It is found that while there is a maximum in the diffusivity with respect to loading, as previously observed by Pikunic et al. [5], diffusivities in the present work are 10 times larger than those obtained in the prior work, consistent with the larger pore size as well as higher porosity of the activated saccharose carbon studied here.

Application of Monte Carlo simulations to identify an appropriate dosage strategy for patients receiving a continuous intravenous infusion of enoxaparin

Aim: To identify an appropriate dosage strategy for patients receiving enoxaparin by continuous intravenous infusion (CII). Methods: Monte Carlo simulations were performed in NONMEM, (200 replicates of 1000 patients) to predict steady state anti-Xa concentrations (Css) for patients receiving a CII of enoxaparin. The covariate distribution model was simulated based on covariate demographics in the CII study population. The impact of patient weight, renal function (creatinine clearance (CrCL)) and patient location (intensive care unit (ICU)) were evaluated. A population pharmacokinetic model was used as the input-output model (1-compartment first order output model with mixed residual error structure). Success of a dosing regimen was based on the percent of Css that is between the therapeutic range of 0.5 IU/ml to 1.2 IU/ml. Results: The best dose for patients in the ICU was 4.2IU/kg/h (success mean 64.8% and 90% prediction interval (PI): 60.1–69.8%) if CrCL60ml/min, the best dose was 8.3IU/kg/h (success mean 65.4%, 90% PI: 58.5–73.2%). Simulations suggest that there was a 50% improvement in the success of the CII if the dose rate for ICU patients with CrCL

Adsorption of Supercritical fluids on graphitised thermal carbon black: Molecular layer structure theory versus grand canonical Monte Carlo simulation

This paper presents a detailed analysis of adsorption of supercritical fluids on nonporous graphitized thermal carbon black. Two methods are employed in the analysis. One is the molecular layer structure theory (MLST), proposed recently by our group, and the other is the grand canonical Monte Carlo (GCMC) simulation. They were applied to describe the adsorption of argon, krypton, methane, ethylene, and sulfur hexafluoride on graphitized thermal carbon black. It was found that the MLST describes all the experimental data at various temperatures well. Results from GCMC simulations describe well the data at low pressure but show some deviations at higher pressures for all the adsorbates tested. The question of negative surface excess is also discussed in this paper.

Testing multiple mapping conditioning mixing for Monte Carlo probability density function simulations

Mitarai [Phys. Fluids 17, 047101 (2005)] compared turbulent combustion models against homogeneous direct numerical simulations with extinction/recognition phenomena. The recently suggested multiple mapping conditioning (MMC) was not considered and is simulated here for the same case with favorable results. Implementation issues crucial for successful MMC simulations are also discussed.