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

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

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

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

Magnesium administration provokes motor unit survival, after sciatic nerve injury in neonatal rats

BACKGROUND: We examined the time course of the functional alterations in two types of muscles following sciatic nerve crush in neonatal rats and the neuroprotective effect of Mg(2+). METHODS: The nerve crush was performed on the 2(nd )postnatal day. MgSO(4)*7H(2)O was administered daily for two weeks. Animals were examined for the contractile properties and for the number of motor units of extensor digitorum longus and soleus muscles at three postnatal stages and adulthood. Four experimental groups were included in this study: i) controls, ii) axotomized rats, iii) magnesium treated controls and iv) axotomized and Mg(2+)-treated rats. RESULTS: Axotomy resulted in 20% MU survival in EDL and 50% in soleus. In contrast, magnesium treatment resulted in a significant motor unit survival (40% survival in EDL and 80% in soleus). The neuroprotective effects of Mg(2+ )were evident immediately after the Mg(2+)-treatment. Immature EDL and soleus muscles were slow and fatigueable. Soleus gradually became fatigue resistant, whereas, after axotomy, soleus remained fatigueable up to adulthood. EDL gradually became fastcontracting. Tetanic contraction in axotomized EDL was just 3,3% of the control side, compared to 15,2% in Mg(2+)-treated adult rats. The same parameter for axotomized soleus was 12% compared to 97% in Mg(2+)-treated adult rats. CONCLUSIONS: These results demonstrate that motoneuron death occurs mostly within two weeks of axotomy. Magnesium administration rescues motoneurons and increases the number of motor units surviving into adulthood. Fast and slow muscles respond differently to axotomy and to subsequent Mg(2+ )treatment in vivo

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

A systems biology approach towards understanding and treating non-neovascular age-related macular degeneration

Age-related macular degeneration (AMD) is the most common cause of blindness among the elderly in the developed world. While treatment is effective for the neovascular or "wet" form of AMD, no therapy is successful for the non-neovascular or "dry" form. Here we discuss the current knowledge on dry AMD pathobiology and propose future research directions that would expedite the development of new treatments. In our view, these should emphasize system biology approaches that integrate omic, pharmacological, and clinical data into mathematical models that can predict disease onset and progression, identify biomarkers, establish disease causing mechanisms, and monitor response to therapy

From bulletins to bullets to blogs and beyond: The Karen’s ongoing communication war

Geff Green focuses on the communication approaches taken by the Karen communities displaced from Burma and who live in diaspora. Apparent control and empowerment provided by new technologies may be illusive. When using media for warfare or perhaps for more innocuous public relations purposes, activists may actually create ‘ammunition’ for opponents. Targeted attacks on specific communities or ‘audiences’ have a high impact by reifying discourse in a devastating way by connecting to lived experience in the victim

Reduced Transmissibility of East African Indian Strains of Mycobacterium tuberculosis

BACKGROUND: Mycobacterium tuberculosis (MTB) has been classified into 4 main lineages. Some reports have associated certain lineages with particular clinical phenotypes, but there is still insufficient information regarding the clinical and epidemiologic implications of MTB lineage variation. METHODS: Using large sequence polymorphisms we classified MTB isolates from a population-based study in Montreal, Canada into the 4 major lineages, and identified the associated clinical and epidemiologic features. In addition, IS6110-RFLP and spoligotyping were used as indicators of recent TB transmission. The study population was divided into a derivation cohort, diagnosed between 2001 and 2007, and a separate validation cohort, diagnosed between 1996 and 2000. RESULTS: In the derivation cohort, when compared to the other MTB lineages, the East African-Indian (EAI) lineage was associated with lower rates of TB transmission, as measured by: positive TST among close contacts of pulmonary TB cases (adjusted odds ratio 0.6: [95% confidence interval 0.4-0.9]), and clustered TB cases (0.3: [<0.001-0.6]). Severe forms of TB were also less likely among the EAI group (0.4: [<0.001-0.8]). There were no significant differences when comparing patients with the other MTB lineages. In the validation cohort, the EAI lineage was associated with lower rates of positive TST among contacts (0.5: [0.3-0.9]) and a trend towards less clustered TB cases (0.5: [0.1-1.8]) when compared to the other lineages. Disease severity among the different groups was not significantly different in the validation cohort. CONCLUSIONS: We conclude that in Montreal, EAI strains were associated with reduced transmission compared to other MTB lineages