Consistency of Markov chain quasi-Monte Carlo on continuous state spaces

The random numbers driving Markov chain Monte Carlo (MCMC) simulation are usually modeled as independent U(0,1) random variables. Tribble [Markov chain Monte Carlo algorithms using completely uniformly distributed driving sequences (2007) Stanford Univ.] reports substantial improvements when those random numbers are replaced by carefully balanced inputs from completely uniformly distributed sequences. The previous theoretical justification for using anything other than i.i.d. U(0,1) points shows consistency for estimated means, but only applies for discrete stationary distributions. We extend those results to some MCMC algorithms for continuous stationary distributions. The main motivation is the search for quasi-Monte Carlo versions of MCMC. As a side benefit, the results also establish consistency for the usual method of using pseudo-random numbers in place of random ones.Comment: Published in at http://dx.doi.org/10.1214/10-AOS831 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Application of quasi-Monte Carlo methods to PDEs with random coefficients -- an overview and tutorial

This article provides a high-level overview of some recent works on the application of quasi-Monte Carlo (QMC) methods to PDEs with random coefficients. It is based on an in-depth survey of a similar title by the same authors, with an accompanying software package which is also briefly discussed here. Embedded in this article is a step-by-step tutorial of the required analysis for the setting known as the uniform case with first order QMC rules. The aim of this article is to provide an easy entry point for QMC experts wanting to start research in this direction and for PDE analysts and practitioners wanting to tap into contemporary QMC theory and methods.Comment: arXiv admin note: text overlap with arXiv:1606.0661

A systematic review of associations between environmental exposures and development of asthma in children aged up to 9 years

Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://group.bmj.com/group/rights-licensing/permissions.Peer reviewedPublisher PD

Multigrid methods for compressible Navier-Stokes equations in low-speed flows

AbstractThe multigrid performance of pointwise, linewise and blockwise Gauss-Seidel relaxations for compressible laminar and turbulent Navier-Stokes equations is illustrated on two low-speed test problems: a flat plate and a backward facing step. The line method is an Alternating Symmetric Line Gauss-Seidel relaxation. In the block methods, the grid is subdivided into geometric blocks of n × n points with one point overlap. With in the blocks, the solution is obtained by a direct method or with an alternating modified incomplete lower-upper decomposition. The analysis is focused on flows typical for boundary layers, stagnation and recirculation regions. These are characterized by very small Mach numbers, high Reynolds numbers and high mesh aspect ratios

Ultra-low noise microwave generation with fiber-based optical frequency comb and application to atomic fountain clock

We demonstrate the use of a fiber-based femtosecond laser locked onto an ultra-stable optical cavity to generate a low-noise microwave reference signal. Comparison with both a liquid Helium cryogenic sapphire oscillator (CSO) and a Ti:Sapphire-based optical frequency comb system exhibit a stability about $3\times10^{-15}$ between 1 s and 10 s. The microwave signal from the fiber system is used to perform Ramsey spectroscopy in a state-of-the-art Cesium fountain clock. The resulting clock system is compared to the CSO and exhibits a stability of $3.5\times10^{-14}\tau^{-1/2}$. Our continuously operated fiber-based system therefore demonstrates its potential to replace the CSO for atomic clocks with high stability in both the optical and microwave domain, most particularly for operational primary frequency standards.Comment: 3 pages, 3 figure

Kinetic Characterization and X-ray Structure of a Mutant of Haloalkane Dehalogenase with Higher Catalytic Activity and Modified Substrate Range

Conversion of halogenated aliphatics by haloalkane dehalogenase proceeds via the formation of a covalent alkyl-enzyme intermediate which is subsequently hydrolyzed by water. In the wild type enzyme, the slowest step for both 1,2-dichloroethane and 1,2-dibromoethane conversion is a unimolecular enzyme isomerization preceding rapid halide dissociation. Phenylalanine 172 is located in a helix-loop-helix structure that covers the active site cavity of the enzyme, interacts with the Clβ of 1,2-dichloroethane during catalysis, and could be involved in stabilization of this helix-loop-helix region of the cap domain of the enzyme. To obtain more information about the role of this residue in dehalogenase function, we performed a mutational analysis of position 172 and studied the kinetics and X-ray structure of the Phe172Trp enzyme. The Phe172Trp mutant had a 10-fold higher kcat/Km for 1-chlorohexane and a 2-fold higher kcat for 1,2-dibromoethane than the wild-type enzyme. The X-ray structure of the Phe172Trp enzyme showed a local conformational change in the helix-loop-helix region that covers the active site. This could explain the elevated activity for 1-chlorohexane of the Phe172Trp enzyme, since it allows this large substrate to bind more easily in the active site cavity. Pre-steady-state kinetic analysis showed that the increase in kcat found for 1,2-dibromoethane conversion could be attributed to an increase in the rate of an enzyme isomerization step that preceeds halide release. The observed conformational difference between the helix-loop-helix structures of the wild-type enzyme and the faster mutant suggests that the isomerization required for halide release could be a conformational change that takes place in this region of the cap domain of the dehalogenase. It is proposed that Phe172 is involved in stabilization of the helix-loop-helix structure that covers the active site of the enzyme and creates a rigid hydrophobic cavity for small apolar halogenated alkanes.

DGP Cosmology with a Non-Minimally Coupled Scalar Field on the Brane

We construct a DGP inspired braneworld scenario where a scalar field non-minimally coupled to the induced Ricci curvature is present on the brane. First we investigate the status of gravitational potential with non-minimal coupling and observational constraints on this non-minimal model. Then we further deepen the idea of embedding of FRW cosmology in this non-minimal setup. Cosmological implications of this scenario are examined with details and the quintessence and late-time expansion of the universe within this framework are examined. Some observational constraints imposed on this non-minimal scenario are studied and relation of this model with dark radiation formalism is determined with details.Comment: 26 pages, 3 eps figure

Interrogation of caesium atoms in a fountain clock by a femtosecond laser microwave oscillator

A caesium fountain clock is operated utilizing a microwave oscillator that derives its frequency stability from a stable laser by means of a fiber-laser femtosecond frequency comb. This oscillator is based on the technology developed for optical clocks and replaces the quartz based microwave oscillator commonly used in fountain clocks. As a result, a significant decrease of the frequency instability of the fountain clock is obtained, reaching 0.74E-14 at 100 s averaging time. We could demonstrate that for a significant range of detected atom numbers the instability is limited by quantum projection noise only, and that for the current status of this fountain clock the new microwave source poses no limit on the achievable frequency instability.Comment: 4 pages, 4 figure

The Supremum Norm of the Discrepancy Function: Recent Results and Connections

A great challenge in the analysis of the discrepancy function D_N is to obtain universal lower bounds on the L-infty norm of D_N in dimensions d \geq 3. It follows from the average case bound of Klaus Roth that the L-infty norm of D_N is at least (log N) ^{(d-1)/2}. It is conjectured that the L-infty bound is significantly larger, but the only definitive result is that of Wolfgang Schmidt in dimension d=2. Partial improvements of the Roth exponent (d-1)/2 in higher dimensions have been established by the authors and Armen Vagharshakyan. We survey these results, the underlying methods, and some of their connections to other subjects in probability, approximation theory, and analysis.Comment: 15 pages, 3 Figures. Reports on talks presented by the authors at the 10th international conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, Sydney Australia, February 2011. v2: Comments of the referee are incorporate