Efficient calculation of the worst-case error and (fast) component-by-component construction of higher order polynomial lattice rules

We show how to obtain a fast component-by-component construction algorithm for higher order polynomial lattice rules. Such rules are useful for multivariate quadrature of high-dimensional smooth functions over the unit cube as they achieve the near optimal order of convergence. The main problem addressed in this paper is to find an efficient way of computing the worst-case error. A general algorithm is presented and explicit expressions for base~2 are given. To obtain an efficient component-by-component construction algorithm we exploit the structure of the underlying cyclic group. We compare our new higher order multivariate quadrature rules to existing quadrature rules based on higher order digital nets by computing their worst-case error. These numerical results show that the higher order polynomial lattice rules improve upon the known constructions of quasi-Monte Carlo rules based on higher order digital nets

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

The effects of read length, quality and quantity on microsatellite discovery and primer development: from Illumina to PacBio

The advent of next-generation sequencing (NGS) technologies has transformed the way microsatellites are isolated for ecological and evolutionary investigations. Recent attempts to employ NGS for microsatellite discovery have used the 454, Illumina, and Ion Torrent platforms, but other methods including single-molecule real-time DNA sequencing (Pacific Biosciences or PacBio) remain viable alternatives. We outline a workflow from sequence quality control to microsatellite marker validation in three plant species using PacBio circular consensus sequencing (CCS). We then evaluate the performance of PacBio CCS in comparison with other NGS platforms for microsatellite isolation, through simulations that focus on variations in read length, read quantity and sequencing error rate. Although quality control of CCS reads reduced microsatellite yield by around 50%, hundreds of microsatellite loci that are expected to have improved conversion efficiency to functional markers were retrieved for each species. The simulations quantitatively validate the advantages of long reads and emphasize the detrimental effects of sequencing errors on NGS-enabled microsatellite development. In view of the continuing improvement in read length on NGS platforms, sequence quality and the corresponding strategies of quality control will become the primary factors to consider for effective microsatellite isolation. Among current options, PacBio CCS may be optimal for rapid, smallscale microsatellite development due to its flexibility in scaling sequencing effort, while platforms such as Illumina MiSeq will provide cost-efficient solutions for multispecies microsatellite projects.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/108219/1/Na2014.pdf85Description of Na2014.pdf : main articl

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

Laser frequency stabilization to a single ion

A fundamental limit to the stability of a single-ion optical frequency standard is set by quantum noise in the measurement of the internal state of the ion. We discuss how the interrogation sequence and the processing of the atomic resonance signal can be optimized in order to obtain the highest possible stability under realistic experimental conditions. A servo algorithm is presented that stabilizes a laser frequency to the single-ion signal and that eliminates errors due to laser frequency drift. Numerical simulations of the servo characteristics are compared to experimental data from a frequency comparison of two single-ion standards based on a transition at 688 THz in 171Yb+. Experimentally, an instability sigma_y(100 s)=9*10^{-16} is obtained in the frequency difference between both standards.Comment: 15 pages, 5 figures, submitted to J. Phys.

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.

Versatile compact atomic source for high resolution dual atom interferometry

We present a compact $^{87}$Rb atomic source for high precision dual atom interferometers. The source is based on a double-stage magneto-optical trap (MOT) design, consisting of a 2-dimensional (2D)-MOT for efficient loading of a 3D-MOT. The accumulated atoms are precisely launched in a horizontal moving molasses. Our setup generates a high atomic flux ($>10^{10}$ atoms/s) with precise and flexibly tunable atomic trajectories as required for high resolution Sagnac atom interferometry. We characterize the performance of the source with respect to the relevant parameters of the launched atoms, i.e. temperature, absolute velocity and pointing, by utilizing time-of-flight techniques and velocity selective Raman transitions.Comment: uses revtex4, 9 pages, 12 figures, submitted to Phys. Rev.

Hot new directions for quasi-Monte Carlo research in step with applications

This article provides an overview of some interfaces between the theory of quasi-Monte Carlo (QMC) methods and applications. We summarize three QMC theoretical settings: first order QMC methods in the unit cube $[0,1]^s$ and in $\mathbb{R}^s$, and higher order QMC methods in the unit cube. One important feature is that their error bounds can be independent of the dimension $s$ under appropriate conditions on the function spaces. Another important feature is that good parameters for these QMC methods can be obtained by fast efficient algorithms even when $s$ is large. We outline three different applications and explain how they can tap into the different QMC theory. We also discuss three cost saving strategies that can be combined with QMC in these applications. Many of these recent QMC theory and methods are developed not in isolation, but in close connection with applications