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

Prenatal Bisphenol A Exposure and Early Childhood Behavior

BackgroundPrenatal exposure to bisphenol A (BPA) increases offspring aggression and diminishes differences in sexually dimorphic behaviors in rodents.ObjectiveWe examined the association between prenatal BPA exposure and behavior in 2-year-old children.MethodsWe used data from 249 mothers and their children in Cincinnati, Ohio (USA). Maternal urine was collected around 16 and 26 weeks of gestation and at birth. BPA concentrations were quantified using high-performance liquid chromatography–isotope-dilution tandem mass spectrometry. Child behavior was assessed at 2 years of age using the second edition of the Behavioral Assessment System for Children (BASC-2). The association between prenatal BPA concentrations and BASC-2 scores was analyzed using linear regression.ResultsMedian BPA concentrations were 1.8 (16 weeks), 1.7 (26 weeks), and 1.3 (birth) ng/mL. Mean (± SD) BASC-2 externalizing and internalizing scores were 47.6 ± 7.8 and 44.8 ± 7.0, respectively. After adjustment for confounders, log10-transformed mean prenatal BPA concentrations were associated with externalizing scores, but only among females [β = 6.0; 95% confidence interval (CI), 0.1–12.0]. Compared with 26-week and birth concentrations, BPA concentrations collected around 16 weeks were more strongly associated with externalizing scores among all children (β = 2.9; 95% CI, 0.2–5.7), and this association was stronger in females than in males. Among all children, measurements collected at ≤ 16 weeks showed a stronger association (β = 5.1; 95% CI, 1.5–8.6) with externalizing scores than did measurements taken at 17–21 weeks (β = 0.6; 95% CI, −2.9 to 4.1).ConclusionsThese results suggest that prenatal BPA exposure may be associated with externalizing behaviors in 2-year-old children, especially among female children

Neural field models with threshold noise

The original neural field model of Wilson and Cowan is often interpreted as the averaged behaviour of a network of switch like neural elements with a distribution of switch thresholds, giving rise to the classic sigmoidal population firing-rate function so prevalent in large scale neuronal modelling. In this paper we explore the effects of such threshold noise without recourse to averaging and show that spatial correlations can have a strong effect on the behaviour of waves and patterns in continuum models. Moreover, for a prescribed spatial covariance function we explore the differences in behaviour that can emerge when the underlying stationary distribution is changed from Gaussian to non-Gaussian. For travelling front solutions, in a system with exponentially decaying spatial interactions, we make use of an interface approach to calculate the instantaneous wave speed analytically as a series expansion in the noise strength. From this we find that, for weak noise, the spatially averaged speed depends only on the choice of covariance function and not on the shape of the stationary distribution. For a system with a Mexican-hat spatial connectivity we further find that noise can induce localised bump solutions, and using an interface stability argument show that there can be multiple stable solution branches

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

Discovering privileged topologies of molecular knots with self-assembling models

Despite the several available strategies to build complex supramolecular constructs, only a handful of different molecular knots have been synthesised so far. Here, in response to the quest for further designable topologies, we use Monte Carlo sampling and molecular dynamics simulations, informed by general principles of supramolecular assembly, as a discovery tool for thermodynamically and kinetically accessible knot types made of helical templates. By combining this approach with the exhaustive enumeration of molecular braiding patterns applicable to more general template geometries, we find that only few selected shapes have the closed, symmetric and quasi-planar character typical of synthetic knots. The corresponding collection of admissible topologies is extremely restricted. It covers all known molecular knots but it especially includes a limited set of novel complex ones that have not yet been obtained experimentally, such as 10124 and 15n41185, making them privileged targets for future self-assembling experiments

Characterization of the Autocrine/Paracrine Function of Vitamin D in Human Gingival Fibroblasts and Periodontal Ligament Cells

Background: We previously demonstrated that 25-hydroxyvitamin D-3, the precursor of 1 alpha,25-dihydroxyvitamin D-3, is abundant around periodontal soft tissues. Here we investigate whether 25-hydroxyvitamin D-3 is converted to 1 alpha,25-dihydroxyvitamin D-3 in periodontal soft tissue cells and explore the possibility of an autocrine/paracrine function of 1 alpha,25-dihydroxyvitamin D-3 in periodontal soft tissue cells. Methodology/Principal Findings: We established primary cultures of human gingival fibroblasts and human periodontal ligament cells from 5 individual donors. We demonstrated that 1 alpha-hydroxylase was expressed in human gingival fibroblasts and periodontal ligament cells, as was cubilin. After incubation with the 1 alpha-hydroxylase substrate 25-hydroxyvitamin D-3, human gingival fibroblasts and periodontal ligament cells generated detectable 1 alpha,25-dihydroxyvitamin D-3 that resulted in an up-regulation of CYP24A1 and RANKL mRNA. A specific knockdown of 1 alpha-hydroxylase in human gingival fibroblasts and periodontal ligament cells using siRNA resulted in a significant reduction in both 1 alpha, 25-dihydroxyvitamin D-3 production and mRNA expression of CYP24A1 and RANKL. The classical renal regulators of 1 alpha-hydroxylase (parathyroid hormone, calcium and 1 alpha,25-dihydroxyvitamin D-3) and Porphyromonas gingivalis lipopolysaccharide did not influence 1 alpha-hydroxylase expression significantly, however, interleukin-1 beta and sodium butyrate strongly induced 1 alpha-hydroxylase expression in human gingival fibroblasts and periodontal ligament cells. Conclusions/Significance: In this study, the expression, activity and functionality of 1 alpha-hydroxylase were detected in human gingival fibroblasts and periodontal ligament cells, raising the possibility that vitamin D acts in an autocrine/paracrine manner in these cells.http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000305781700070&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701Multidisciplinary SciencesSCI(E)PubMed13ARTICLE6e39878

Predictors of colorectal cancer screening in diverse primary care practices

BACKGROUND: To explain why rates of colorectal cancer (CRC) screening including fecal occult blood testing (FOBT), flexible sigmoidoscopy (FS), colonoscopy (CS), and barium enema (BE), are low, this study assessed determinants of CRC screening from medical records. METHODS: Data were abstracted from patients aged ≥64 years selected from each clinician from 30 diverse primary care practices (n = 981). Measurements included the rates of annual FOBT, ever receiving FOBT, ever receiving FS/CS/BE under a combination variable, endoscopy/barium enema (EBE). RESULTS: Over five years, 8% had received annual FOBT, 53% had ever received FOBT and 22% had ever received EBE. Annual FOBT was negatively associated with female gender, odds ratio (OR) = .23; 95% confidence interval = .12–.44 and positively associated with routinely receiving influenza vaccine, OR = 2.55 (1.45–4.47); and more office visits: 3 to <5 visits/year, OR = 2.78 (1.41–5.51), and ≥5 visits/year, OR = 3.35 (1.52-7.42). Ever receiving EBE was negatively associated with age ≥75 years, OR = .66 (.46–.95); being widowed, OR = .59 (.38–.92); and positively associated with more office visits: 3 to <5 visits/year, OR = 1.83 (1.18–2.82) and ≥5 visits/year, OR = 2.01 (1.14–3.55). CONCLUSION: Overall CRC screening rates were low, but were related to the number of primary care office visits. FOBT was related to immunization status, suggesting the possible benefit of linking these preventive services

Formative evaluation of the telecare fall prevention project for older veterans

<p>Abstract</p> <p>Background</p> <p>Fall prevention interventions for community-dwelling older adults have been found to reduce falls in some research studies. However, wider implementation of fall prevention activities in routine care has yielded mixed results. We implemented a theory-driven program to improve care for falls at our Veterans Affairs healthcare facility. The first project arising from this program used a nurse advice telephone line to identify patients' risk factors for falls and to triage patients to appropriate services. Here we report the formative evaluation of this project.</p> <p>Methods</p> <p>To evaluate the intervention we: 1) interviewed patient and employee stakeholders, 2) reviewed participating patients' electronic health record data and 3) abstracted information from meeting minutes. We describe the implementation process, including whether the project was implemented according to plan; identify barriers and facilitators to implementation; and assess the incremental benefit to the quality of health care for fall prevention received by patients in the project. We also estimate the cost of developing the pilot project.</p> <p>Results</p> <p>The project underwent multiple changes over its life span, including the addition of an option to mail patients educational materials about falls. During the project's lifespan, 113 patients were considered for inclusion and 35 participated. Patient and employee interviews suggested support for the project, but revealed that transportation to medical care was a major barrier in following up on fall risks identified by nurse telephone triage. Medical record review showed that the project enhanced usual medical care with respect to home safety counseling. We discontinued the program after 18 months due to staffing limitations and competing priorities. We estimated a cost of $9194 for meeting time to develop the project.</p> <p>Conclusions</p> <p>The project appeared feasible at its outset but could not be sustained past the first cycle of evaluation due to insufficient resources and a waning of local leadership support due to competing national priorities. Future projects will need both front-level staff commitment and prolonged high-level leadership involvement to thrive.</p