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

Smolyak's algorithm: A powerful black box for the acceleration of scientific computations

We provide a general discussion of Smolyak's algorithm for the acceleration of scientific computations. The algorithm first appeared in Smolyak's work on multidimensional integration and interpolation. Since then, it has been generalized in multiple directions and has been associated with the keywords: sparse grids, hyperbolic cross approximation, combination technique, and multilevel methods. Variants of Smolyak's algorithm have been employed in the computation of high-dimensional integrals in finance, chemistry, and physics, in the numerical solution of partial and stochastic differential equations, and in uncertainty quantification. Motivated by this broad and ever-increasing range of applications, we describe a general framework that summarizes fundamental results and assumptions in a concise application-independent manner

Potential of Saudi natural clay as an effective adsorbent in heavy metals removal from wastewater

This study aims to examine the potential of natural clay mineral from the southern part of Saudi Arabia as an effective adsorbent material for the removal of heavy metal ions of cadmium (Cd) and nickel (Ni) from aqueous solutions. The SEM analysis showed that clay particles had mixed shapes such as elongated rod-like and rectangular shape having rough corners with larger particles of 2-8 µm in size and smaller particles in the sub-micron size range. X-ray diffraction data revealed that clay particles had a good crystalline structure and composed of a mixture of various minerals including feldspar, illite, quartz, calcite, and gypsum. The BET surface area was found to be 35 ± 1 m ² /g and the average pore size and pore volume of 6.5 ± 0.5 nm and 5.7e-02 cc/g, respectively. The X-ray fluorescence analysis of clay showed main compounds of SiO₂ (47.33%), Al₂O₃ (18.14%), Fe₂O₃ (15.89%) with many others such as CaO, MgO, TiO₂, and K₂O in minor quantities. It was found that 1.2 g of clay removed up to 99.5% of Ni and 97.5% of Cd from 40 ppm aqueous solutions. The metal removal efficiencies were increased from around 95% up to 99% by increasing the pH of aqueous solutions from 4 to 11. The adsorption of Ni and Cd ions on Saudi clay was relatively fast, and up to 97% of ions were removed from solution within 45 min. The SEM-EDX and BET analysis for recycled clays further confirmed that the metal ions were removed from water through adsorption onto the clay. The experimental data fitted well with Langmuir and Freundlich isotherms. The maximum adsorption capacity of clay for Cd and Ni from isotherms was found to be 3.3 and 2.7 mg/g respectively. The findings of this study confirm the potential role of Saudi natural clay in wastewater treatment processes as a cheap, environment-friendly and safe natural adsorbent material

Security lies in obedience - Voices of young women of a slum in Pakistan

<p>Abstract</p> <p>Background</p> <p>Existing literature shows that young people, especially women, have poor knowledge about sexuality and reproductive health. Many of the difficulties young women experience are related to beliefs and expectations in society making them more vulnerable to reproductive ill health. The objective of this study was to explore how young women living in a slum in Islamabad are prepared for marriage and how they understand and perceive their transition to marriage and the start of sexual and childbearing activity.</p> <p>Methods</p> <p>Twenty qualitative interviews and three focus group discussions were conducted with young women residing in a slum of Islamabad. Content analysis was used to explore how the participants represented and explained their situation and how decisions about their marriage were made.</p> <p>Results</p> <p>The main theme identified was <it>security lies in obedience</it>. The two sub-themes contributing to the main theme were <it>socialization into submissiveness </it>and <it>transition into adulthood in silence</it>. The theme and the sub-themes illustrate the situation of young women in a poor setting in Pakistan.</p> <p>Conclusion</p> <p>The study demonstrates how, in a culture of silence around sexuality, young women's socialization into submissiveness lays the foundation for the lack of control over the future reproductive health that they experience.</p

Significant ophthalmoarthropathy associated with ectodermal dysplasia in a child with Marshall-Stickler overlap: a case report

© 2008 Al Kaissi et al; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution Licens

Critical research gaps and translational priorities for the successful prevention and treatment of breast cancer

INTRODUCTION Breast cancer remains a significant scientific, clinical and societal challenge. This gap analysis has reviewed and critically assessed enduring issues and new challenges emerging from recent research, and proposes strategies for translating solutions into practice. METHODS More than 100 internationally recognised specialist breast cancer scientists, clinicians and healthcare professionals collaborated to address nine thematic areas: genetics, epigenetics and epidemiology; molecular pathology and cell biology; hormonal influences and endocrine therapy; imaging, detection and screening; current/novel therapies and biomarkers; drug resistance; metastasis, angiogenesis, circulating tumour cells, cancer 'stem' cells; risk and prevention; living with and managing breast cancer and its treatment. The groups developed summary papers through an iterative process which, following further appraisal from experts and patients, were melded into this summary account. RESULTS The 10 major gaps identified were: (1) understanding the functions and contextual interactions of genetic and epigenetic changes in normal breast development and during malignant transformation; (2) how to implement sustainable lifestyle changes (diet, exercise and weight) and chemopreventive strategies; (3) the need for tailored screening approaches including clinically actionable tests; (4) enhancing knowledge of molecular drivers behind breast cancer subtypes, progression and metastasis; (5) understanding the molecular mechanisms of tumour heterogeneity, dormancy, de novo or acquired resistance and how to target key nodes in these dynamic processes; (6) developing validated markers for chemosensitivity and radiosensitivity; (7) understanding the optimal duration, sequencing and rational combinations of treatment for improved personalised therapy; (8) validating multimodality imaging biomarkers for minimally invasive diagnosis and monitoring of responses in primary and metastatic disease; (9) developing interventions and support to improve the survivorship experience; (10) a continuing need for clinical material for translational research derived from normal breast, blood, primary, relapsed, metastatic and drug-resistant cancers with expert bioinformatics support to maximise its utility. The proposed infrastructural enablers include enhanced resources to support clinically relevant in vitro and in vivo tumour models; improved access to appropriate, fully annotated clinical samples; extended biomarker discovery, validation and standardisation; and facilitated cross-discipline working. CONCLUSIONS With resources to conduct further high-quality targeted research focusing on the gaps identified, increased knowledge translating into improved clinical care should be achievable within five years