CORRECTION TO "QUASI-MONTE CARLO METHODS FOR HIGH-DIMENSIONAL INTEGRATION: THE STANDARD (WEIGHTED HILBERT SPACE) SETTING AND BEYOND”

ISSN:1446-1811ISSN:1446-873

Quasi-Monte Carlo methods for high-dimensional integration: the standard (weighted Hilbert space) setting and beyond

This paper is a contemporary review of quasi-Monte Carlo (QMC) methods, that is, equal-weight rules for the approximate evaluation of high-dimensional integrals over the unit cube $[0,1]^s$. It first introduces the by-now standard setting of weighted Hilbert spaces of functions with square-integrable mixed first derivatives, and then indicates alternative settings, such as non-Hilbert spaces, that can sometimes be more suitable. Original contributions include the extension of the fast component-by-component (CBC) construction of lattice rules that achieve the optimal convergence order (a rate of almost $1/N$, where $N$ is the number of points, independently of dimension) to so-called “product and order dependent†(POD) weights, as seen in some recent applications. Although the paper has a strong focus on lattice rules, the function space settings are applicable to all QMC methods. Furthermore, the error analysis and construction of lattice rules can be adapted to polynomial lattice rules from the family of digital nets. doi:10.1017/S144618111200007

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

Two-Nucleon Scattering without partial waves using a momentum space Argonne V18 interaction

We test the operator form of the Fourier transform of the Argonne V18 potential by computing selected scattering observables and all Wolfenstein parameters for a variety of energies. These are compared to the GW-DAC database and to partial wave calculations. We represent the interaction and transition operators as expansions in a spin-momentum basis. In this representation the Lippmann-Schwinger equation becomes a six channel integral equation in two variables. Our calculations use different numbers of spin-momentum basis elements to represent the on- and off-shell transition operators. This is because different numbers of independent spin-momentum basis elements are required to expand the on- and off-shell transition operators. The choice of on and off-shell spin-momentum basis elements is made so that the coefficients of the on-shell spin-momentum basis vectors are simply related to the corresponding off-shell coefficients.Comment: 14 pages, 8 Figures, typos correcte

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

First Dark Matter Limits from a Large-Mass, Low-Background Superheated Droplet Detector

We report on the fabrication aspects and calibration of the first large active mass ($\sim15$ g) modules of SIMPLE, a search for particle dark matter using Superheated Droplet Detectors (SDDs). While still limited by the statistical uncertainty of the small data sample on hand, the first weeks of operation in the new underground laboratory of Rustrel-Pays d'Apt already provide a sensitivity to axially-coupled Weakly Interacting Massive Particles (WIMPs) competitive with leading experiments, confirming SDDs as a convenient, low-cost alternative for WIMP detection.Comment: Final version, Phys. Rev. Lett. (in press

In vitro and in vivo characterisation of Listeria monocytogenes outbreak isolates

Listeriosis is an important food-borne disease responsible for high rates of morbidity and mortality. L. monocytogenes has been the cause of several foodborne outbreaks and its ability to adapt and survive in a wide range of environmental conditions makes eradication difficult. Many L. monocytogenes strains are avirulent but have the ability to increase their virulence if exposed to environmental stresses. The aim of this study was to explain the observed increase in virulence of outbreak L. monocytogenes isolates by using phenotypic assays and whole genome sequencing. Four L. monocytogenes isolates from sweetcorn and one isolate from a raw milk (control) were sequenced and characterised using a range of phenotypic assays. The four L. monocytogenes sweetcorn isolates displayed a significant increase for in vitro adhesion and invasion of epithelial cells compared to the control isolate. They also showed a higher level of colonisation of the liver and spleen in vivo. In addition, the four L. monocytogenes isolates displayed an increased ability to form biofilms, resist heat stress and resist a combination of antimicrobials. Investigation of the genomes of the four L. monocytogenes sweet corn isolates identified Single Nucleotide Polymorphisms (SNPs) in genes, which may have a role in the observed phenotypes characteristic of these strains, particularly in response to survival properties within the environment or in terms of virulence. We highlight the importance of combining whole genomic sequencing with phenotypic characterisation as a key element in the investigation of outbreaks of foodborne pathogens

Unstaged cancer in the United States: a population-based study

<p>Abstract</p> <p>Background</p> <p>The current study examines unstaged disease for 18 cancer sites in the United States according to the influence of age, sex, race, marital status, incidence, and lethality.</p> <p>Methods</p> <p>Analyses are based on 1,040,381 male and 1,011,355 female incident cancer cases diagnosed during 2000 through 2007. Data were collected by population-based cancer registries in the National Cancer Institute's Surveillance, Epidemiology, and End Results Program.</p> <p>Results</p> <p>The level of unstaged disease was greater in more lethal cancers (e.g., liver, esophagus, and pancreas) compared with less deadly cancers (i.e., colon, urinary bladder, and female breast). Unstaged disease increased with age and is greater among non-married patients. Blacks compared with whites experienced significantly higher levels of unstaged cancers of the stomach, rectum, colon, skin (melanoma), urinary bladder, thyroid, breast, corpus, cervix, and ovaries, but lower levels of unstaged liver, lung and bronchial cancers. Males compared with females experienced significantly lower levels of unstaged cancers of the liver, pancreas, esophagus, and stomach, but significantly higher levels of unstaged lung and bronchial cancer and thyroid cancer. The percent of unstaged cancer significantly decreased over the study period for 15 of the 18 cancer sites.</p> <p>Conclusion</p> <p>Tumor staging directly affects treatment options and survival, so it is recommended that further research focus on why a decrease in unstaged disease did not occur for all of the cancer sites considered from 2000 to 2007, and why there are differential levels of staging between whites and blacks, males and females for several of the cancer sites.</p

Forward pi^0 Production and Associated Transverse Energy Flow in Deep-Inelastic Scattering at HERA

Deep-inelastic positron-proton interactions at low values of Bjorken-x down to x \approx 4.10^-5 which give rise to high transverse momentum pi^0 mesons are studied with the H1 experiment at HERA. The inclusive cross section for pi^0 mesons produced at small angles with respect to the proton remnant (the forward region) is presented as a function of the transverse momentum and energy of the pi^0 and of the four-momentum transfer Q^2 and Bjorken-x. Measurements are also presented of the transverse energy flow in events containing a forward pi^0 meson. Hadronic final state calculations based on QCD models implementing different parton evolution schemes are confronted with the data.Comment: 27 pages, 8 figures and 3 table