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

Exercise-Induced Changes in Exhaled NO Differentiates Asthma With or Without Fixed Airway Obstruction From COPD With Dynamic Hyperinflation.

Asthmatic patients with fixed airway obstruction (FAO) and patients with chronic obstructive pulmonary disease (COPD) share similarities in terms of irreversible pulmonary function impairment. Exhaled nitric oxide (eNO) has been documented as a marker of airway inflammation in asthma, but not in COPD. To examine whether the basal eNO level and the change after exercise may differentiate asthmatics with FAO from COPD, 27 normal subjects, 60 stable asthmatics, and 62 stable COPD patients were studied. Asthmatics with FAO (n = 29) were defined as showing a postbronchodilator FEV(1)/forced vital capacity (FVC) ≤70% and FEV(1) less than 80% predicted after inhaled salbutamol (400 μg). COPD with dynamic hyperinflation (n = 31) was defined as a decrease in inspiratory capacity (ΔIC%) after a 6 minute walk test (6MWT). Basal levels of eNO were significantly higher in asthmatics and COPD patients compared to normal subjects. The changes in eNO after 6MWT were negatively correlated with the percent change in IC (r = −0.380, n = 29, P = 0.042) in asthmatics with FAO. Their levels of basal eNO correlated with the maximum mid-expiratory flow (MMEF % predicted) before and after 6MWT. In COPD patients with air-trapping, the percent change of eNO was positively correlated to ΔIC% (rs = 0.404, n = 31, P = 0.024). We conclude that asthma with FAO may represent residual inflammation in the airways, while dynamic hyperinflation in COPD may retain NO in the distal airspace. eNO changes after 6MWT may differentiate the subgroups of asthma or COPD patients and will help toward delivery of individualized therapy for airflow obstruction

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

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

Constraints on Three-Neutrino Mixing from Atmospheric and Reactor Data

Observations of atmospheric neutrinos are usually analyzed using the simplifying approximation that either $\nu_\mu \leftrightarrow \nu_\tau$ or $\nu_e \leftrightarrow \nu_\mu$ two-flavor mixing is relevant. Here we instead consider the data using the simplifying approximation that only one neutrino mass scale is relevant. This approximation is the minimal three-flavor notation that includes the two relevant two-flavor approximations. The constraints in the parameter space orthogonal to the usual, two-flavor analyses are studied.Comment: 15 pages, preprint IUHET-26

Structure of a seeded palladium nanoparticle and its dynamics during the hydride phase transformation

Palladium absorbs large volumetric quantities of hydrogen at room temperature and ambient pressure, making the palladium hydride system a promising candidate for hydrogen storage. Here, we use Bragg coherent diffraction imaging to map the strain associated with defects in three dimensions before and during the hydride phase transformation of an individual octahedral palladium nanoparticle, synthesized using a seed-mediated approach. The displacement distribution imaging unveils the location of the seed nanoparticle in the final nanocrystal. By comparing our experimental results with a finite-element model, we verify that the seed nanoparticle causes a characteristic displacement distribution of the larger nanocrystal. During the hydrogen exposure, the hydride phase is predominantly formed on one tip of the octahedra, where there is a high number of lower coordinated Pd atoms. Our experimental and theoretical results provide an unambiguous method for future structure optimization of seed-mediated nanoparticle growth and in the design of palladium-based hydrogen storage systems

Data Visualization on Global Trends on Cancer Incidence An Application of IBM Watson Analytics

Visual analytics is widely used to explore data patterns and trends. This work leverages cancer data collected by World Health Organization (WHO) across over a hundred of cancer registries worldwide. In this study, we present a visual analytics platform, IBM Watson Analytics, to explore the patterns of global cancer incidence. We included 26 cancers from different geographic regions. An interactive interface was applied to plot a choropleth map to show global cancer distribution, and line charts to demonstrate historical cancer trends over 29 years. Subgroup analyses were conducted for different age groups. With real-time interactive features, we can easily explore the data with a selection of any cancer type, gender, age group, or geographical region. This platform is running on the cloud, so it can handle data in huge volumes, and is assessable by any computer connected to the Internet

Efficient simulation of the spatial transmission dynamics of influenza

Early data from the 2009 H1N1 pandemic (H1N1pdm) suggest that previous studies over-estimated the within-country rate of spatial spread of pandemic influenza. As large spatially resolved data sets are constructed, the need for efficient simulation code with which to investigate the spatial patterns of the pandemic becomes clear. Here, we present a significant improvement to the efficiency of an individual based stochastic disease simulation framework commonly used in multiple previous studies. We quantify the efficiency of the revised algorithm and present an alternative parameterization of the model in terms of the basic reproductive number. We apply the model to the population of Taiwan and demonstrate how the location of the initial seed can influence spatial incidence profiles and the overall spread of the epidemic. Differences in incidence are driven by the relative connectivity of alternate seed locations. The ability to perform efficient simulation allows us to run a batch of simulations and take account of their average in real time. The averaged data are stable and can be used to differentiate spreading patterns that are not readily seen by only conducting a few runs. © 2010 Tsai et al.published_or_final_versio