Abstract Algebra: An Inquiry-Based Approach, Second Edition, Supplemental Material

This text is a supplement to Abstract Algebra: An Inquiry-Based Approach, Second Edition. It includes applications of algebra to RSA encryption, check digits, the games of NIM and the 15 Puzzle, and the determination of groups of small order. In addition, reference material that could be useful for some students appears in the appendices, such as background material on functions, methods of proof (including the equivalencies of the Well-Ordering Principle and different versions of mathematical induction), and complex roots of unity. The appendices also contain a complete proof that polynomial rings are rings, a proof of the Fundamental Theorem of Algebra, and a derivation of the formula for solving any cubic equation.https://scholarworks.gvsu.edu/books/1029/thumbnail.jp

Tobacco smoking and disability progression in multiple sclerosis: United Kingdom cohort study

Tobacco smoking has been linked to an increased risk of multiple sclerosis. However, to date, results from the few studies on the impact of smoking on the progression of disability are conflicting. The aim of this study was to investigate the effects of smoking on disability progression and disease severity in a cohort of patients with clinically definite multiple sclerosis. We analysed data from 895 patients (270 male, 625 female), mean age 49 years with mean disease duration 17 years. Forty-nine per cent of the patients were regular smokers at the time of disease onset or at diagnosis (ever-smokers). Average disease severity as measured by multiple sclerosis severity score was greater in ever-smokers, by 0.68 (95% confidence interval: 0.36–1.01). The risk of reaching Expanded Disability Status Scale score milestones of 4 and 6 in ever-smokers compared to never-smokers was 1.34 (95% confidence interval: 1.12–1.60) and 1.25 (95% confidence interval: 1.02–1.51) respectively. Current smokers showed 1.64 (95% confidence interval: 1.33–2.02) and 1.49 (95% confidence interval: 1.18–1.86) times higher risk of reaching Expanded Disability Status Scale scores 4 and 6 compared with non-smokers. Ex-smokers who stopped smoking either before or after the onset of the disease had a significantly lower risk of reaching Expanded Disability Status Scale scores 4 (hazard ratio: 0.65, confidence interval: 0.50–0.83) and 6 (hazard ratio: 0.69, confidence interval: 0.53–0.90) than current smokers, and there was no significant difference between ex-smokers and non-smokers in terms of time to Expanded Disability Status Scale scores 4 or 6. Our data suggest that regular smoking is associated with more severe disease and faster disability progression. In addition, smoking cessation, whether before or after onset of the disease, is associated with a slower progression of disability

Novel Blood Pressure Locus and Gene Discovery Using Genome-Wide Association Study and Expression Data Sets From Blood and the Kidney.

Elevated blood pressure is a major risk factor for cardiovascular disease and has a substantial genetic contribution. Genetic variation influencing blood pressure has the potential to identify new pharmacological targets for the treatment of hypertension. To discover additional novel blood pressure loci, we used 1000 Genomes Project-based imputation in 150 134 European ancestry individuals and sought significant evidence for independent replication in a further 228 245 individuals. We report 6 new signals of association in or near HSPB7, TNXB, LRP12, LOC283335, SEPT9, and AKT2, and provide new replication evidence for a further 2 signals in EBF2 and NFKBIA Combining large whole-blood gene expression resources totaling 12 607 individuals, we investigated all novel and previously reported signals and identified 48 genes with evidence for involvement in blood pressure regulation that are significant in multiple resources. Three novel kidney-specific signals were also detected. These robustly implicated genes may provide new leads for therapeutic innovation

Target 2035-update on the quest for a probe for every protein

Twenty years after the publication of the first draft of the human genome, our knowledge of the human proteome is still fragmented. The challenge of translating the wealth of new knowledge from genomics into new medicines is that proteins, and not genes, are the primary executers of biological function. Therefore, much of how biology works in health and disease must be understood through the lens of protein function. Accordingly, a subset of human proteins has been at the heart of research interests of scientists over the centuries, and we have accumulated varying degrees of knowledge about approximately 65% of the human proteome. Nevertheless, a large proportion of proteins in the human proteome (∼35%) remains uncharacterized, and less than 5% of the human proteome has been successfully targeted for drug discovery. This highlights the profound disconnect between our abilities to obtain genetic information and subsequent development of effective medicines. Target 2035 is an international federation of biomedical scientists from the public and private sectors, which aims to address this gap by developing and applying new technologies to create by year 2035 chemogenomic libraries, chemical probes, and/or biological probes for the entire human proteome

Multi-ancestry GWAS of the electrocardiographic PR interval identifies 202 loci underlying cardiac conduction

The electrocardiographic PR interval reflects atrioventricular conduction, and is associated with conduction abnormalities, pacemaker implantation, atrial fibrillation (AF), and cardiovascular mortality. Here we report a multi-ancestry (N=293,051) genome-wide association meta-analysis for the PR interval, discovering 202 loci of which 141 have not previously been reported. Variants at identified loci increase the percentage of heritability explained, from 33.5% to 62.6%. We observe enrichment for cardiac muscle developmental/contractile and cytoskeletal genes, highlighting key regulation processes for atrioventricular conduction. Additionally, 8 loci not previously reported harbor genes underlying inherited arrhythmic syndromes and/or cardiomyopathies suggesting a role for these genes in cardiovascular pathology in the general population. We show that polygenic predisposition to PR interval duration is an endophenotype for cardiovascular disease, including distal conduction disease, AF, and atrioventricular pre-excitation. These findings advance our understanding of the polygenic basis of cardiac conduction, and the genetic relationship between PR interval duration and cardiovascular disease. On the electrocardiogram, the PR interval reflects conduction from the atria to ventricles and also serves as risk indicator of cardiovascular morbidity and mortality. Here, the authors perform genome-wide meta-analyses for PR interval in multiple ancestries and identify 141 previously unreported genetic loci.Peer reviewe

Software for the frontiers of quantum chemistry:An overview of developments in the Q-Chem 5 package

This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange–correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear–electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an “open teamware” model and an increasingly modular design

Worldwide trends in blood pressure from 1975 to 2015: a pooled analysis of 1479 population-based measurement studies with 19.1 million participants

AbstractBackground: Raised blood pressure is an important risk factor for cardiovascular diseases and chronic kidney disease. We estimated worldwide trends in mean systolic and mean diastolic blood pressure, and the prevalence of, and number of people with, raised blood pressure, defined as systolic blood pressure of 140 mm Hg or higher or diastolic blood pressure of 90 mm Hg or higher.Methods: For this analysis, we pooled national, subnational, or community population-based studies that had measured blood pressure in adults aged 18 years and older. We used a Bayesian hierarchical model to estimate trends from 1975 to 2015 in mean systolic and mean diastolic blood pressure, and the prevalence of raised blood pressure for 200 countries. We calculated the contributions of changes in prevalence versus population growth and ageing to the increase in the number of adults with raised blood pressure.Findings: We pooled 1479 studies that had measured the blood pressures of 19.1 million adults. Global age-standardised mean systolic blood pressure in 2015 was 127.0 mm Hg (95% credible interval 125.7–128.3) in men and 122.3 mm Hg (121.0–123.6) in women; age-standardised mean diastolic blood pressure was 78.7 mm Hg (77.9–79.5) for men and 76.7 mm Hg (75.9–77.6) for women. Global age-standardised prevalence of raised blood pressure was 24.1% (21.4–27.1) in men and 20.1% (17.8–22.5) in women in 2015. Mean systolic and mean diastolic blood pressure decreased substantially from 1975 to 2015 in high-income western and Asia Pacific countries, moving these countries from having some of the highest worldwide blood pressure in 1975 to the lowest in 2015. Mean blood pressure also decreased in women in central and eastern Europe, Latin America and the Caribbean, and, more recently, central Asia, Middle East, and north Africa, but the estimated trends in these super-regions had larger uncertainty than in high-income super-regions. By contrast, mean blood pressure might have increased in east and southeast Asia, south Asia, Oceania, and sub-Saharan Africa. In 2015, central and eastern Europe, sub-Saharan Africa, and south Asia had the highest blood pressure levels. Prevalence of raised blood pressure decreased in high-income and some middle-income countries; it remained unchanged elsewhere. The number of adults with raised blood pressure increased from 594 million in 1975 to 1.13 billion in 2015, with the increase largely in low-income and middle-income countries. The global increase in the number of adults with raised blood pressure is a net effect of increase due to population growth and ageing, and decrease due to declining age-specific prevalence.Interpretation: During the past four decades, the highest worldwide blood pressure levels have shifted from high-income countries to low-income countries in south Asia and sub-Saharan Africa due to opposite trends, while blood pressure has been persistently high in central and eastern Europe.Abstract Background: Raised blood pressure is an important risk factor for cardiovascular diseases and chronic kidney disease. We estimated worldwide trends in mean systolic and mean diastolic blood pressure, and the prevalence of, and number of people with, raised blood pressure, defined as systolic blood pressure of 140 mm Hg or higher or diastolic blood pressure of 90 mm Hg or higher. Methods: For this analysis, we pooled national, subnational, or community population-based studies that had measured blood pressure in adults aged 18 years and older. We used a Bayesian hierarchical model to estimate trends from 1975 to 2015 in mean systolic and mean diastolic blood pressure, and the prevalence of raised blood pressure for 200 countries. We calculated the contributions of changes in prevalence versus population growth and ageing to the increase in the number of adults with raised blood pressure. Findings: We pooled 1479 studies that had measured the blood pressures of 19.1 million adults. Global age-standardised mean systolic blood pressure in 2015 was 127.0 mm Hg (95% credible interval 125.7–128.3) in men and 122.3 mm Hg (121.0–123.6) in women; age-standardised mean diastolic blood pressure was 78.7 mm Hg (77.9–79.5) for men and 76.7 mm Hg (75.9–77.6) for women. Global age-standardised prevalence of raised blood pressure was 24.1% (21.4–27.1) in men and 20.1% (17.8–22.5) in women in 2015. Mean systolic and mean diastolic blood pressure decreased substantially from 1975 to 2015 in high-income western and Asia Pacific countries, moving these countries from having some of the highest worldwide blood pressure in 1975 to the lowest in 2015. Mean blood pressure also decreased in women in central and eastern Europe, Latin America and the Caribbean, and, more recently, central Asia, Middle East, and north Africa, but the estimated trends in these super-regions had larger uncertainty than in high-income super-regions. By contrast, mean blood pressure might have increased in east and southeast Asia, south Asia, Oceania, and sub-Saharan Africa. In 2015, central and eastern Europe, sub-Saharan Africa, and south Asia had the highest blood pressure levels. Prevalence of raised blood pressure decreased in high-income and some middle-income countries; it remained unchanged elsewhere. The number of adults with raised blood pressure increased from 594 million in 1975 to 1.13 billion in 2015, with the increase largely in low-income and middle-income countries. The global increase in the number of adults with raised blood pressure is a net effect of increase due to population growth and ageing, and decrease due to declining age-specific prevalence. Interpretation: During the past four decades, the highest worldwide blood pressure levels have shifted from high-income countries to low-income countries in south Asia and sub-Saharan Africa due to opposite trends, while blood pressure has been persistently high in central and eastern Europe

Trends in adult body-mass index in 200 countries from 1975 to 2014: a pooled analysis of 1698 population-based measurement studies with 19.2 million participants

Background Underweight and severe and morbid obesity are associated with highly elevated risks of adverse health outcomes. We estimated trends in mean body-mass index (BMI), which characterises its population distribution, and in the prevalences of a complete set of BMI categories for adults in all countries. Methods We analysed, with use of a consistent protocol, population-based studies that had measured height and weight in adults aged 18 years and older. We applied a Bayesian hierarchical model to these data to estimate trends from 1975 to 2014 in mean BMI and in the prevalences of BMI categories (<18.5 kg/m(2) [underweight], 18.5 kg/m(2) to <20 kg/m(2), 20 kg/m(2) to <25 kg/m(2), 25 kg/m(2) to <30 kg/m(2), 30 kg/m(2) to <35 kg/m(2), 35 kg/m(2) to <40 kg/m(2), = 40 kg/m(2) [morbid obesity]), by sex in 200 countries and territories, organised in 21 regions. We calculated the posterior probability of meeting the target of halting by 2025 the rise in obesity at its 2010 levels, if post-2000 trends continue. Findings We used 1698 population-based data sources, with more than 19.2 million adult participants (9.9 million men and 9.3 million women) in 186 of 200 countries for which estimates were made. Global age-standardised mean BMI increased from 21.7 kg/m(2) (95% credible interval 21.3-22.1) in 1975 to 24.2 kg/m(2) (24.0-24.4) in 2014 in men, and from 22.1 kg/m(2) (21.7-22.5) in 1975 to 24.4 kg/m(2) (24.2-24.6) in 2014 in women. Regional mean BMIs in 2014 for men ranged from 21.4 kg/m(2) in central Africa and south Asia to 29.2 kg/m(2) (28.6-29.8) in Polynesia and Micronesia; for women the range was from 21.8 kg/m(2) (21.4-22.3) in south Asia to 32.2 kg/m(2) (31.5-32.8) in Polynesia and Micronesia. Over these four decades, age-standardised global prevalence of underweight decreased from 13.8% (10.5-17.4) to 8.8% (7.4-10.3) in men and from 14.6% (11.6-17.9) to 9.7% (8.3-11.1) in women. South Asia had the highest prevalence of underweight in 2014, 23.4% (17.8-29.2) in men and 24.0% (18.9-29.3) in women. Age-standardised prevalence of obesity increased from 3.2% (2.4-4.1) in 1975 to 10.8% (9.7-12.0) in 2014 in men, and from 6.4% (5.1-7.8) to 14.9% (13.6-16.1) in women. 2.3% (2.0-2.7) of the world's men and 5.0% (4.4-5.6) of women were severely obese (ie, have BMI = 35 kg/m(2)). Globally, prevalence of morbid obesity was 0.64% (0.46-0.86) in men and 1.6% (1.3-1.9) in women. Interpretation If post-2000 trends continue, the probability of meeting the global obesity target is virtually zero. Rather, if these trends continue, by 2025, global obesity prevalence will reach 18% in men and surpass 21% in women; severe obesity will surpass 6% in men and 9% in women. Nonetheless, underweight remains prevalent in the world's poorest regions, especially in south Asia.Wellcome Trust, Grand Challenges Canada