Quasideterminant solutions of noncommutative integrable systems

Quasideterminants are a relatively new addition to the field of integrable systems. Their simple structure disguises a wealth of interesting and useful properties, enabling solutions of noncommutative integrable equations to be expressed in a straightforward and aesthetically pleasing manner. This thesis investigates the derivation and quasideterminant solutions of two noncommutative integrable equations - the Davey-Stewartson (DS) and Sasa-Satsuma nonlinear Schrodinger (SSNLS) equations. Chapter 1 provides a brief overview of the various concepts to which we will refer during the course of the thesis. We begin by explaining the notion of an integrable system, although no concrete definition has ever been explicitly stated. We then move on to discuss Lax pairs, and also introduce the Hirota bilinear form of an integrable equation, looking at the Kadomtsev-Petviashvili (KP) equation as an example. Wronskian and Grammian determinants will play an important role in later chapters, albeit in a noncommutative setting, and, as such, we give an account of their widespread use in integrable systems. Chapter 2 provides further background information, now focusing on noncommutativity. We explain how noncommutativity can be defined and implemented, both specifically using a star product formalism, and also in a more general manner. It is this general definition to which we will allude in the remainder of the thesis. We then give the definition of a quasideterminant, introduced by Gel'fand and Retakh in 1991, and provide some examples and properties of these noncommutative determinantal analogues. We also explain how to calculate the derivative of a quasideterminant. The chapter concludes by outlining the motivation for studying our particular choice of noncommutative integrable equations and their quasideterminant solutions. We begin with the DS equations in Chapter 3, and derive a noncommutative version of this integrable system using a Lax pair approach. Quasideterminant solutions arise in a natural way by the implementation of Darboux and binary Darboux transformations, and, after describing these transformations in detail, we obtain two types of quasideterminant solution to our system of noncommutative DS equations - a quasi-Wronskian solution from the application of the ordinary Darboux transformation, and a quasi-Grammian solution by applying the binary transformation. After verification of these solutions, in Chapter 4 we select the quasi-Grammian solution to allow us to determine a particular class of solution to our noncommutative DS equations. These solutions, termed dromions, are lump-like objects decaying exponentially in all directions, and are found at the intersection of two perpendicular plane waves. We extend earlier work of Gilson and Nimmo by obtaining plots of these dromion solutions in a noncommutative setting. The work on the noncommutative DS equations and their dromion solutions constitutes our paper published in 2009. Chapter 5 describes how the well-known Darboux and binary Darboux transformations in (2+1)-dimensions discussed in the previous chapter can be dimensionally-reduced to enable their application to (1+1)-dimensional integrable equations. This reduction was discussed briefly by Gilson, Nimmo and Ohta in reference to the self-dual Yang-Mills (SDYM) equations, however we explain these results in more detail, using a reduction from the DS to the nonlinear Schrodinger (NLS) equation as a specific example. Results stated here are utilised in Chapter 6, where we consider higher-order NLS equations in (1+1)-dimension. We choose to focus on one particular equation, the SSNLS equation, and, after deriving a noncommutative version of this equation in a similar manner to the derivation of our noncommutative DS system in Chapter 3, we apply the dimensionally-reduced Darboux transformation to the noncommutative SSNLS equation. We see that this ordinary Darboux transformation does not preserve the properties of the equation and its Lax pair, and we must therefore look to the dimensionally-reduced binary Darboux transformation to obtain a quasi-Grammian solution. After calculating some essential conditions on various terms appearing in our solution, we are then able to determine and obtain plots of soliton solutions in a noncommutative setting. Chapter 7 seeks to bring together the various results obtained in earlier chapters, and also discusses some open questions arising from our work

Genetic risk prediction of atrial fibrillation

Background—Atrial fibrillation (AF) has a substantial genetic basis. Identification of individuals at greatest AF risk could minimize the incidence of cardioembolic stroke. Methods—To determine whether genetic data can stratify risk for development of AF, we examined associations between AF genetic risk scores and incident AF in five prospective studies comprising 18,919 individuals of European ancestry. We examined associations between AF genetic risk scores and ischemic stroke in a separate study of 509 ischemic stroke cases (202 cardioembolic [40%]) and 3,028 referents. Scores were based on 11 to 719 common variants (≥5%) associated with AF at P-values ranging from <1x10-3 to <1x10-8 in a prior independent genetic association study. Results—Incident AF occurred in 1,032 (5.5%) individuals. AF genetic risk scores were associated with new-onset AF after adjusting for clinical risk factors. The pooled hazard ratio for incident AF for the highest versus lowest quartile of genetic risk scores ranged from 1.28 (719 variants; 95%CI, 1.13-1.46; P=1.5x10-4) to 1.67 (25 variants; 95%CI, 1.47-1.90; P=9.3x10-15). Discrimination of combined clinical and genetic risk scores varied across studies and scores (maximum C statistic, 0.629-0.811; maximum ΔC statistic from clinical score alone, 0.009-0.017). AF genetic risk was associated with stroke in age- and sex-adjusted models. For example, individuals in the highest versus lowest quartile of a 127-variant score had a 2.49-fold increased odds of cardioembolic stroke (95%CI, 1.39-4.58; P=2.7x10-3). The effect persisted after excluding individuals (n=70) with known AF (odds ratio, 2.25; 95%CI, 1.20-4.40; P=0.01). Conclusions—Comprehensive AF genetic risk scores were associated with incident AF beyond associations for clinical AF risk factors, though offered small improvements in discrimination. AF genetic risk was also associated with cardioembolic stroke in age- and sex-adjusted analyses. Efforts are warranted to determine whether AF genetic risk may improve identification of subclinical AF or help distinguish between stroke mechanisms

Effect of anion type in the performance of ionic liquid/poly(vinylidene fluoride) electromechanical actuators

Low voltage actuators based on poly(vinylidene fluoride)(PVDF)with 10, 25 and 40 % 1-hexyl-3-methylimidazolium chloride ([C6mim][Cl])and 1-hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([C6mim][NTf2]) are prepared by solvent casting in order to evaluate the effect of anion size in the bending properties. Independently of the ionic liquid type and content, its presence leads to the crystallization of PVDF in the -phase. The addition of ionic liquid into the polymer matrix decreases significantly its degree of crystallinity and the elastic modulus. It is also confirmed the good miscibility between PVDF and IL,determinedby the interaction of the CF2groups from the PVDF chains with the imidazolium ring in the ionic liquid (IL). The AC conductivity of the composites depends both on the amount of ionic liquid content and anion size. The bending movement of the IL/PVDF composites is correlated to theirdegree of crystallinity, mechanical properties and ionic conductivity value and the best value of bending response (0.53 %) being found for IL/PVDF composite with40 wt% of [C6mim][Cl] at an applied voltage of 10 volts square signal.The authors thank the FCT-Fundação para a Ciência e Tecnologia-for financial support in the framework of the Strategic Funding UID/FIS/04650/2013, projects PTDC/EEI-SII/5582/2014 and PTDC/CTM-ENE/5387/2014,and grants SFRH/BD/90215/2012 (J.C.D.), SFRH/BPD/112547/2015 (C.M.C.). The authors thank Solvay for kindly supplying the high quality materials. Financial support from the Basque Government Industry Department under the ELKARTEK Program is also acknowledged.The authorsexpress their gratitude to the Ministry of the Higher Education and Scientific Research of Tunisiafor a research fellowship

Genetic association study of QT interval highlights role for calcium signaling pathways in myocardial repolarization.

The QT interval, an electrocardiographic measure reflecting myocardial repolarization, is a heritable trait. QT prolongation is a risk factor for ventricular arrhythmias and sudden cardiac death (SCD) and could indicate the presence of the potentially lethal mendelian long-QT syndrome (LQTS). Using a genome-wide association and replication study in up to 100,000 individuals, we identified 35 common variant loci associated with QT interval that collectively explain ∼8-10% of QT-interval variation and highlight the importance of calcium regulation in myocardial repolarization. Rare variant analysis of 6 new QT interval-associated loci in 298 unrelated probands with LQTS identified coding variants not found in controls but of uncertain causality and therefore requiring validation. Several newly identified loci encode proteins that physically interact with other recognized repolarization proteins. Our integration of common variant association, expression and orthogonal protein-protein interaction screens provides new insights into cardiac electrophysiology and identifies new candidate genes for ventricular arrhythmias, LQTS and SCD

Energy applications of ionic liquids

Ionic liquids offer a unique suite of properties that make them important candidates for a number of energy related applications. Cation–anion combinations that exhibit low volatility coupled with high electrochemical and thermal stability, as well as ionic conductivity, create the possibility of designing ideal electrolytes for batteries, super-capacitors, actuators, dye sensitised solar cells and thermoelectrochemical cells. In the field of water splitting to produce hydrogen they have been used to synthesize some of the best performing water oxidation catalysts and some members of the protic ionic liquid family co-catalyse an unusual, very high energy efficiency water oxidation process. As fuel cell electrolytes, the high proton conductivity of some of the protic ionic liquid family offers the potential of fuel cells operating in the optimum temperature region above 100 °C. Beyond electrochemical applications, the low vapour pressure of these liquids, along with their ability to offer tuneable functionality, also makes them ideal as CO2 absorbents for post-combustion CO2 capture. Similarly, the tuneable phase properties of the many members of this large family of salts are also allowing the creation of phase-change thermal energy storage materials having melting points tuned to the application. This perspective article provides an overview of these developing energy related applications of ionic liquids and offers some thoughts on the emerging challenges and opportunities

Validity of the international physical activity questionnaire and the Singapore prospective study program physical activity questionnaire in a multiethnic urban Asian population

<p>Abstract</p> <p>Background</p> <p>Physical activity patterns of a population remain mostly assessed by the questionnaires. However, few physical activity questionnaires have been validated in Asian populations. We previously utilized a combination of different questionnaires to assess leisure time, transportation, occupational and household physical activity in the Singapore Prospective Study Program (SP2). The International Physical Activity Questionnaire (IPAQ) has been developed for a similar purpose. In this study, we compared estimates from these two questionnaires with an objective measure of physical activity in a multi-ethnic Asian population.</p> <p>Methods</p> <p>Physical activity was measured in 152 Chinese, Malay and Asian Indian adults using an accelerometer over five consecutive days, including a weekend. Participants completed both the physical activity questionnaire in SP2 (SP2PAQ) and IPAQ long form. 43subjects underwent a second set of measurements on average 6 months later to assess reproducibility of the questionnaires and the accelerometer measurements. Spearman correlations were used to evaluate validity and reproducibility and correlations for validity were corrected for within-person variation of accelerometer measurements. Agreement between the questionnaires and the accelerometer measurements was also evaluated using Bland Altman plots.</p> <p>Results</p> <p>The corrected correlation with accelerometer estimates of energy expenditure from physical activity was better for the SP2PAQ (vigorous activity: r = 0.73; moderate activity: r = 0.27) than for the IPAQ (vigorous activity: r = 0.31; moderate activity: r = 0.15). For moderate activity, the corrected correlation between SP2PAQ and the accelerometer was higher for Chinese (r = 0.38) and Malays (r = 0.57) than for Indians (r = -0.09). Both questionnaires overestimated energy expenditure from physical activity to a greater extent at higher levels of physical activity than at lower levels of physical activity. The reproducibility for moderate activity (accelerometer: r = 0.68; IPAQ: r = 0.58; SP2PAQ: r = 0.55) and vigorous activity (accelerometer: 0.52; IPAQ: r = 0.38; SP2PAQ: r = 0.75) was moderate to high for all instruments.</p> <p>Conclusion</p> <p>The agreement between IPAQ and accelerometer measurements of energy expenditure from physical activity was poor in our Asian study population. The SP2PAQ showed good validity and reproducibility for vigorous activity, but performed less well for moderate activity particularly in Indians. Further effort is needed to develop questionnaires that better capture moderate activity in Asian populations.</p

Estimated prevalence of exposure to occupational carcinogens in Australia (2011-2012)

Background and objectives: Although past studies of workplace exposures have contributed greatly to our understanding of carcinogens, significant knowledge gaps still exist with regard to the actual extent of exposure among current workers, with no routinely collected population-based data being available in most countries. This study, the Australian Work Exposures Study (AWES), aimed to investigate the current prevalence of occupational exposure to carcinogens. Methods: A random sample of men and women aged between 18 and 65, who were currently in paid employment, were invited to participate in a telephone interview collecting information about their current job and various demographic factors. Interviews were conducted using a web-based application (OccIDEAS). OccIDEAS uses the expert exposure method in which participants are asked about their job tasks and predefined algorithms are used to automatically assign exposures. Responses were obtained from 5023 eligible Australian residents, resulting in an overall response rate of 53%. Results: 1879 respondents (37.6%) were assessed as being exposed to at least one occupational carcinogen in their current job. Extrapolation of these figures to the Australian working population suggested 3.6 million (40.3%) current workers could be exposed to carcinogens in their workplace. Exposure prevalence was highest among farmers, drivers, miners and transport workers, as well as men and those residing in regional areas. Conclusions: This study demonstrates a practical, web-based approach to collecting population information on occupational exposure to carcinogens and documents the high prevalence of current exposure to occupational carcinogens in the general population

Multi-center feasibility study evaluating recruitment, variability in risk factors and biomarkers for a diet and cancer cohort in India

<p>Abstract</p> <p>Background</p> <p>India's population exhibits diverse dietary habits and chronic disease patterns. Nutritional epidemiologic studies in India are primarily of cross-sectional or case-control design and subject to biases, including differential recall of past diet. The aim of this feasibility study was to evaluate whether a diet-focused cohort study of cancer could be established in India, providing insight into potentially unique diet and lifestyle exposures.</p> <p>Methods</p> <p>Field staff contacted 7,064 households within three regions of India (New Delhi, Mumbai, and Trivandrum) and found 4,671 eligible adults aged 35-69 years. Participants completed interviewer-administered questionnaires (demographic, diet history, physical activity, medical/reproductive history, tobacco/alcohol use, and occupational history), and staff collected biological samples (blood, urine, and toenail clippings), anthropometric measurements (weight, standing and sitting height; waist, hip, and thigh circumference; triceps, sub-scapula and supra-patella skin fold), and blood pressure measurements.</p> <p>Results</p> <p>Eighty-eight percent of eligible subjects completed all questionnaires and 67% provided biological samples. Unique protein sources by region were fish in Trivandrum, dairy in New Delhi, and pulses (legumes) in Mumbai. Consumption of meat, alcohol, fast food, and soft drinks was scarce in all three regions. A large percentage of the participants were centrally obese and had elevated blood glucose levels. New Delhi participants were also the least physically active and had elevated lipids levels, suggesting a high prevalence of metabolic syndrome.</p> <p>Conclusions</p> <p>A high percentage of participants complied with study procedures including biological sample collection. Epidemiologic expertise and sufficient infrastructure exists at these three sites in India to successfully carry out a modest sized population-based study; however, we identified some potential problems in conducting a cohort study, such as limited number of facilities to handle biological samples.</p

A cross-sectional investigation of regional patterns of diet and cardio-metabolic risk in India

<p>Abstract</p> <p>Background</p> <p>The role of diet in India's rapidly progressing chronic disease epidemic is unclear; moreover, diet may vary considerably across North-South regions.</p> <p>Methods</p> <p>The India Health Study was a multicenter study of men and women aged 35-69, who provided diet, lifestyle, and medical histories, as well as blood pressure, fasting blood, urine, and anthropometric measurements. In each region (Delhi, n = 824; Mumbai, n = 743; Trivandrum, n = 2,247), we identified two dietary patterns with factor analysis. In multiple logistic regression models adjusted for age, gender, education, income, marital status, religion, physical activity, tobacco, alcohol, and total energy intake, we investigated associations between regional dietary patterns and abdominal adiposity, hypertension, diabetes, and dyslipidemia.</p> <p>Results</p> <p>Across the regions, more than 80% of the participants met the criteria for abdominal adiposity and 10 to 28% of participants were considered diabetic. In Delhi, the "fruit and dairy" dietary pattern was positively associated with abdominal adiposity [highest versus lowest tertile, multivariate-adjusted OR and 95% CI: 2.32 (1.03-5.23); P_trend= 0.008] and hypertension [2.20 (1.47-3.31); P_trend< 0.0001]. In Trivandrum, the "pulses and rice" pattern was inversely related to diabetes [0.70 (0.51-0.95); P_trend= 0.03] and the "snacks and sweets" pattern was positively associated with abdominal adiposity [2.05 (1.34-3.14); P_trend= 0.03]. In Mumbai, the "fruit and vegetable" pattern was inversely associated with hypertension [0.63 (0.40-0.99); P_trend= 0.05] and the "snack and meat" pattern appeared to be positively associated with abdominal adiposity.</p> <p>Conclusions</p> <p>Cardio-metabolic risk factors were highly prevalent in this population. Across all regions, we found little evidence of a Westernized diet; however, dietary patterns characterized by animal products, fried snacks, or sweets appeared to be positively associated with abdominal adiposity. Conversely, more traditional diets in the Southern regions were inversely related to diabetes and hypertension. Continued investigation of diet, as well as other environmental and biological factors, will be needed to better understand the risk profile in this population and potential means of prevention.</p