Multilevel Monte Carlo Methods for Stochastic Convection-Diffusion Eigenvalue Problems.

We develop new multilevel Monte Carlo (MLMC) methods to estimate the expectation of the smallest eigenvalue of a stochastic convection-diffusion operator with random coefficients. The MLMC method is based on a sequence of finite element (FE) discretizations of the eigenvalue problem on a hierarchy of increasingly finer meshes. For the discretized, algebraic eigenproblems we use both the Rayleigh quotient (RQ) iteration and implicitly restarted Arnoldi (IRA), providing an analysis of the cost in each case.

Rapid near-atomic resolution single-particle 3D reconstruction with SIMPLE.

Cryogenic electron microscopy (cryo-EM) and single-particle analysis enables determination of near-atomic resolution structures of biological molecules. However, large computational requirements limit throughput and rapid testing of new image processing tools. We developed PRIME, an algorithm part of the SIMPLE software suite, for determination of the relative 3D orientations of single-particle projection images.

The statistical mechanics of human weight change.

Over the past 35 years there has been a near doubling in the worldwide prevalence of obesity. Body Mass Index (BMI) distributions in high-income societies have increasingly shifted rightwards, corresponding to increases in average BMI that are due to well-studied changes in the socioeconomic environment. However, in addition to this shift, BMI distributions have also shown marked changes in their particular shape over time, exhibiting an ongoing right-skewed broadening that is not well understood.

The influence of societal individualism on a century of tobacco use: modelling the prevalence of smoking.

Background: Smoking of tobacco is estimated to have caused approximately six million deaths worldwide in 2014. Responding effectively to this epidemic requires a thorough understanding of how smoking behaviour is transmitted and modified.

Methods: We present a new mathematical model of the social dynamics that cause cigarette smoking to spread in a population, incorporating aspects of individual and social utility.

Generalized Monte Carlo loop algorithm for two-dimensional frustrated Ising models.

We introduce a generalized loop move (GLM) update for Monte Carlo simulations of frustrated Ising models on two-dimensional lattices with bond-sharing plaquettes. The GLM updates are designed to enhance Monte Carlo sampling efficiency when the system's low-energy states consist of an extensive number of degenerate or near-degenerate spin configurations, separated by large energy barriers to single spin flips. Through implementation on several frustrated Ising models, we demonstrate the effectiveness of the GLM updates in cases where both degenerate and near-degenerate sets of configurations are favored at low temperatures.

Natural and artificial RNAs occupy the same restricted region of sequence space.

Different chemical and mutational processes within genomes give rise to sequences with different compositions and perhaps different capacities for evolution. The evolution of functional RNAs may occur on a "neutral network" in which sequences with any given function can easily mutate to sequences with any other. This neutral network hypothesis is more likely if there is a particular region of composition that contains sequences that are functional in general, and if many different functions are possible within this preferred region of composition.

Monte Carlo study of degenerate ground states and residual entropy in a frustrated honeycomb lattice Ising model.

We study a classical fully frustrated honeycomb lattice Ising model using Markov-chain Monte Carlo methods and exact calculations. The Hamiltonian realizes a degenerate ground-state manifold of equal-energy states, where each hexagonal plaquette of the lattice has one and only one unsatisfied bond, with an extensive residual entropy that grows as the number of spins N. Traditional single-spin-flip Monte Carlo methods fail to sample all possible spin configurations in this ground state efficiently, due to their separation by large energy barriers.

Abundance of correctly folded RNA motifs in sequence space, calculated on computational grids.

Although functional RNA molecules are known to be biased in overall composition, the effects of background composition on the probability of finding a particular active site by chance has received little attention. The probability of finding a particular motif has important implications both for understanding the distribution of functional RNAs in ancient and modern organisms with varying genome compositions and for tuning SELEX pools to optimize the chance of finding specific functions. Here we develop a new method for calculating the probability of finding a modular motif containing base-paired regions, and use a computational grid to fold several hundred million random RNA sequences containing the core elements of the isoleucine aptamer and the hammerhead ribozyme to estimate the probability that a sequence containing these structural elements will fold correctly when isolated from background sequences of different compositions.

A hydrogen-rich early Earth atmosphere.

We show that the escape of hydrogen from early Earth's atmosphere likely occurred at rates slower by two orders of magnitude than previously thought. The balance between slow hydrogen escape and volcanic outgassing could have maintained a hydrogen mixing ratio of more than 30%. The production of prebiotic organic compounds in such an atmosphere would have been more efficient than either exogenous delivery or synthesis in hydrothermal systems.

Intermediate shocks in three-dimensional magnetohydrodynamic bow-shock flows with multiple interacting shock fronts.

Simulation results of three-dimensional (3D) stationary magnetohydrodynamic (MHD) bow-shock flows around perfectly conducting spheres are presented. For strong upstream magnetic field a new complex bow-shock flow topology arises consisting of two consecutive interacting shock fronts. It is shown that the leading shock front contains a segment of intermediate 1-3 shock type.