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

A Dimension-Adaptive Multi-Index Monte Carlo Method Applied to a Model of a Heat Exchanger

We present an adaptive version of the Multi-Index Monte Carlo method, introduced by Haji-Ali, Nobile and Tempone (2016), for simulating PDEs with coefficients that are random fields. A classical technique for sampling from these random fields is the Karhunen-Lo\`eve expansion. Our adaptive algorithm is based on the adaptive algorithm used in sparse grid cubature as introduced by Gerstner and Griebel (2003), and automatically chooses the number of terms needed in this expansion, as well as the required spatial discretizations of the PDE model. We apply the method to a simplified model of a heat exchanger with random insulator material, where the stochastic characteristics are modeled as a lognormal random field, and we show consistent computational savings

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

A tri-dimensional approach for auditing brand loyalty

Over the past twenty years brand loyalty has been an important topic for both marketing practitioners and academics. While practitioners have produced proprietary brand loyalty audit models, there has been little academic research to make transparent the methodology that underpins these audits and to enable practitioners to understand, develop and conduct their own audits. In this paper, we propose a framework for a brand loyalty audit that uses a tri-dimensional approach to brand loyalty, which includes behavioural loyalty and the two components of attitudinal loyalty: emotional and cognitive loyalty. In allowing for different levels and intensity of brand loyalty, this tri-dimensional approach is important from a managerial perspective. It means that loyalty strategies that arise from a brand audit can be made more effective by targeting the market segments that demonstrate the most appropriate combination of brand loyalty components. We propose a matrix with three dimensions (emotional, cognitive and behavioural loyalty) and two levels (high and low loyalty) to facilitate a brand loyalty audit. To demonstrate this matrix, we use the example of financial services, in particular a rewards-based credit card

Vascular adaptation to exercise in humans: Role of hemodynamic stimuli

On the 400th anniversary of Harvey’s Lumleian lectures, this review focuses on “hemodynamic” forces associated with the movement of blood through arteries in humans and the functional and structural adaptations that result from repeated episodic exposure to such stimuli. The late 20th century discovery that endothelial cells modify arterial tone via paracrine transduction provoked studies exploring the direct mechanical effects of blood flow and pressure on vascular function and adaptation in vivo. In this review, we address the impact of distinct hemodynamic signals that occur in response to exercise, the interrelationships between these signals, the nature of the adaptive responses that manifest under different physiological conditions, and the implications for human health. Exercise modifies blood flow, luminal shear stress, arterial pressure, and tangential wall stress, all of which can transduce changes in arterial function, diameter, and wall thickness. There are important clinical implications of the adaptation that occurs as a consequence of repeated hemodynamic stimulation associated with exercise training in humans, including impacts on atherosclerotic risk in conduit arteries, the control of blood pressure in resistance vessels, oxygen delivery and diffusion, and microvascular health. Exercise training studies have demonstrated that direct hemodynamic impacts on the health of the artery wall contribute to the well-established decrease in cardiovascular risk attributed to physical activity. © 2017 the American Physiological Society

The role of brand loyalty and social media in e-commerce interfaces: survey results and implications for user interfaces

This paper explores the role of brand loyalty and social media in e-commerce interfaces. A survey consisting of 118 respondents was contacted to address the questions relating to online shopping and brand loyalty. Link between the frequency of access and time spent on an e-commerce user interface, and brand loyalty, gender and age profile differences, and the role of social media to branding and on-line shopping was analyzed. It was found that online loyalty differs from offline loyalty and loyalty also differed across genders, showing men were more loyal than women when shopping online. Information shared about products on social media by friends and family played an important role in purchase decision making. Website interface and ease of navigation were also key aspects for online shopping. The research concluded with recommendations to create multimodal websites which are more interactive and targeted so customer experience is enhanced and loyalty is achieved through the use of interactivity and social media

Strongly exchange-coupled triplet pairs in an organic semiconductor

From biological complexes to devices based on organic semiconductors, spin interactions play a key role in the function of molecular systems. For instance, triplet-pair reactions impact operation of organic light-emitting diodes as well as photovoltaic devices. Conventional models for triplet pairs assume they interact only weakly. Here, using electron spin resonance, we observe long-lived, strongly-interacting triplet pairs in an organic semiconductor, generated via singlet fission. Using coherent spin-manipulation of these two-triplet states, we identify exchange-coupled (spin-2) quintet complexes co-existing with weakly coupled (spin-1) triplets. We measure strongly coupled pairs with a lifetime approaching 3 µs and a spin coherence time approaching 1 µs, at 10 K. Our results pave the way for the utilization of high-spin systems in organic semiconductors.Gates-Cambridge Trust, Winton Programme for the Physics of Sustainability, Freie Universität Berlin within the Excellence Initiative of the German Research Foundation, Engineering and Physical Sciences Research Council (Grant ID: EP/G060738/1)This is the author accepted manuscript. The final version is available from Nature Publishing Group at http://dx.doi.org/10.1038/nphys3908

f(R) theories

Over the past decade, f(R) theories have been extensively studied as one of the simplest modifications to General Relativity. In this article we review various applications of f(R) theories to cosmology and gravity - such as inflation, dark energy, local gravity constraints, cosmological perturbations, and spherically symmetric solutions in weak and strong gravitational backgrounds. We present a number of ways to distinguish those theories from General Relativity observationally and experimentally. We also discuss the extension to other modified gravity theories such as Brans-Dicke theory and Gauss-Bonnet gravity, and address models that can satisfy both cosmological and local gravity constraints.Comment: 156 pages, 14 figures, Invited review article in Living Reviews in Relativity, Published version, Comments are welcom

A review on substances and processes relevant for optical remote sensing of extremely turbid marine areas, with a focus on the Wadden Sea

The interpretation of optical remote sensing data of estuaries and tidal flat areas is hampered by optical complexity and often extreme turbidity. Extremely high concentrations of suspended matter, chlorophyll and dissolved organic matter, local differences, seasonal and tidal variations and resuspension are important factors influencing the optical properties in such areas. This review gives an overview of the processes in estuaries and tidal flat areas and the implications of these for remote sensing in such areas, using the Wadden Sea as a case study area. Results show that remote sensing research in extremely turbid estuaries and tidal areas is possible. However, this requires sensors with a large ground resolution, algorithms tuned for high concentrations of various substances and the local specific optical properties of these substances, a simultaneous detection of water colour and land-water boundaries, a very short time lag between acquisition of remote sensing and in situ data used for validation and sufficient geophysical and ecological knowledge of the area. © 2010 The Author(s)

Protein kinase C and cardiac dysfunction: a review

Heart failure (HF) is a physiological state in which cardiac output is insufficient to meet the needs of the body. It is a clinical syndrome characterized by impaired ability of the left ventricle to either fill or eject blood efficiently. HF is a disease of multiple aetiologies leading to progressive cardiac dysfunction and it is the leading cause of deaths in both developed and developing countries. HF is responsible for about 73,000 deaths in the UK each year. In the USA, HF affects 5.8 million people and 550,000 new cases are diagnosed annually. Cardiac remodelling (CD), which plays an important role in pathogenesis of HF, is viewed as stress response to an index event such as myocardial ischaemia or imposition of mechanical load leading to a series of structural and functional changes in the viable myocardium. Protein kinase C (PKC) isozymes are a family of serine/threonine kinases. PKC is a central enzyme in the regulation of growth, hypertrophy, and mediators of signal transduction pathways. In response to circulating hormones, activation of PKC triggers a multitude of intracellular events influencing multiple physiological processes in the heart, including heart rate, contraction, and relaxation. Recent research implicates PKC activation in the pathophysiology of a number of cardiovascular disease states. Few reports are available that examine PKC in normal and diseased human hearts. This review describes the structure, functions, and distribution of PKCs in the healthy and diseased heart with emphasis on the human heart and, also importantly, their regulation in heart failure