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

Single-Peaked Preferences over Multidimensional Binary Alternatives

Single-peaked preferences are important throughout social choice theory. In this article, we consider single-peaked preferences over multidimensional binary alternative spaces—that is, alternative spaces of the form {0, 1}n for some integer n ≥ 2. We show that preferences that are single-peaked with respect to a normalized separable base order are nonseparable except in the most trivial cases. We establish that two distinct base orders can induce the same single-peaked preference order if any only if they differ by a transposition of their two central elements. We then use this result to enumerate single-peaked binary preference orders over a separable base order

Amino acid availability acts as a metabolic rheostat to determine the magnitude of ILC2 responses

Group 2 innate lymphoid cells (ILC2) are functionally poised, tissue-resident lymphocytes that respond rapidly to damage and infection at mucosal barrier sites. ILC2 reside within complex microenvironments where they are subject to cues from both the diet and invading pathogens—including helminths. Emerging evidence suggests ILC2 are acutely sensitive not only to canonical activating signals but also perturbations in nutrient availability. In the context of helminth infection, we identify amino acid availability as a nutritional cue in regulating ILC2 responses. ILC2 are found to be uniquely preprimed to import amino acids via the large neutral amino acid transporters Slc7a5 and Slc7a8. Cell-intrinsic deletion of these transporters individually impaired ILC2 expansion, while concurrent loss of both transporters markedly impaired the proliferative and cytokine-producing capacity of ILC2. Mechanistically, amino acid uptake determined the magnitude of ILC2 responses in part via tuning of mTOR. These findings implicate essential amino acids as a metabolic requisite for optimal ILC2 responses within mucosal barrier tissues

Comparing different definitions of prediabetes with subsequent risk of diabetes: an individual participant data meta-analysis involving 76 513 individuals and 8208 cases of incident diabetes

Objective: There are currently five widely used definition of prediabetes. We compared the ability of these to predict 5-year conversion to diabetes and investigated whether there were other cut-points identifying risk of progression to diabetes that may be more useful. Research design and methods: We conducted an individual participant meta-analysis using longitudinal data included in the Obesity, Diabetes and Cardiovascular Disease Collaboration. Cox regression models were used to obtain study-specific HRs for incident diabetes associated with each prediabetes definition. Harrell's C-statistics were used to estimate how well each prediabetes definition discriminated 5-year risk of diabetes. Spline and receiver operating characteristic curve (ROC) analyses were used to identify alternative cut-points. Results: Sixteen studies, with 76 513 participants and 8208 incident diabetes cases, were available. Compared with normoglycemia, current prediabetes definitions were associated with four to eight times higher diabetes risk (HRs (95% CIs): 3.78 (3.11 to 4.60) to 8.36 (4.88 to 14.33)) and all definitions discriminated 5-year diabetes risk with good accuracy (C-statistics 0.79-0.81). Cut-points identified through spline analysis were fasting plasma glucose (FPG) 5.1 mmol/L and glycated hemoglobin (HbA1c) 5.0% (31 mmol/mol) and cut-points identified through ROC analysis were FPG 5.6 mmol/L, 2-hour postload glucose 7.0 mmol/L and HbA1c 5.6% (38 mmol/mol). Conclusions: In terms of identifying individuals at greatest risk of developing diabetes within 5 years, using prediabetes definitions that have lower values produced non-significant gain. Therefore, deciding which definition to use will ultimately depend on the goal for identifying individuals at risk of diabetes.This work was supported by the National Health and Medical Research Council of Australia (grant number 1103242). The Atherosclerosis Risk in Communities study has been funded in whole or in part with Federal funds from the National Heart, Lung, and Blood Institute, National Institutes of Health, Department of Health and Human Services, under contract nos. HHSN268201700001I, HHSN268201700002I, HHSN268201700003I, HHSN268201700005I, HHSN268201700004I. ES was supported by NIH/NIDDK grant K24DK106414. The Coronary Artery Risk Development in Young Adults Study (CARDIA) is supported by contracts HHSN2682018000031, HHSN2682018000041, HHSN2682018000051, HHSN2682018000061 and HHSN2682018000071 from the National Heart, Lung, and Blood Institute (NHLBI). The Jackson Heart Study (JHS) is supported and conducted in collaboration with Jackson State University (HHSN268201800013I), Tougaloo College (HHSN268201800014I), the Mississippi State Department of Health (HHSN268201800015I) and the University of Mississippi Medical Center (HHSN268201800010I, HHSN268201800011I and HHSN268201800012I) contracts from the National Heart, Lung, and Blood Institute (NHLBI) and the National Institute for Minority Health and Health Disparities (NIMHD). The Melbourne Collaborative Cohort Study (MCCS) recruitment was funded by VicHealth and Cancer Council Victoria. The MCCS was further augmented by Australian National Health and Medical Research Council grants 209057, 396414 and 1074383 and by infrastructure provided by Cancer Council Victoria. Cases and their vital status were ascertained through the Victorian Cancer Registry and the Australian Institute of Health and Welfare, including the National Death Index and the Australian Cancer Database. The Multi-Ethnic Study of Atherosclerosis was supported by contracts HHSN268201500003I, N01-HC-95159, N01-HC-95160, N01-HC-95161, N01-HC-95162, N01-HC-95163, N01-HC-95164, N01-HC-95165, N01-HC-95166, N01-HC-95167, N01-HC-95168 and N01-HC-95169 from the National Heart, Lung, and Blood Institute and by grants UL1-TR-000040 and UL1-TR-001079 from NCRR. The Population Study of Women in Gothenburg (PSWG) was financed in part by grants from the Swedish state under the agreement between the Swedish government and the county councils, the ALF-agreement ALFGBG-720201. VIVA Study received grants 95/0029 and 06/90270 from the Instituto de Salud Carlos III, Spain.S

Pressure and pain In Systemic sclerosis/Scleroderma - an evaluation of a simple intervention (PISCES): randomised controlled trial protocol

Background: foot problems associated with Systemic Sclerosis (SSc)/Scleroderma have been reported to be both common and disabling. There are only limited data describing specifically, the mechanical changes occurring in the foot in SSc. A pilot project conducted in preparation for this trial confirmed the previous reports of foot related impairment and reduced foot function in people with SSc and demonstrated a link to mechanical etiologies. To-date there have been no formal studies of interventions directed at the foot problems experienced by people with Systemic Sclerosis. The primary aim of this trial is to evaluate whether foot pain and foot-related health status in people with Systemic Sclerosis can be improved through the provision of a simple pressure-relieving insole. Methods: the proposed trial is a pragmatic, multicenter, randomised controlled clinical trial following a completed pilot study. In four participating centres, 140 consenting patients with SSc and plantar foot pain will be randomised to receive either a commercially available pressure relieving and thermally insulating insole, or a sham insole with no cushioning or thermal properties. The primary end point is a reduction in pain measured using the Foot Function Index Pain subscale, 12 weeks after the start of intervention. Participants will complete the primary outcome measure (Foot Function Index pain sub-scale) prior to randomisation and at 12 weeks post randomisation. Secondary outcomes include participant reported pain and disability as derived from the Manchester Foot Pain and Disability Questionnaire and plantar pressures with and without the insoles in situ. Discussion: this trial protocol proposes a rigorous and potentially significant evaluation of a simple and readily provided therapeutic approach which, if effective, could be of a great benefit for this group of patients

High rates of albuminuria but not of low eGFR in Urban Indigenous Australians: the DRUID Study

<p>Abstract</p> <p>Background</p> <p>Indigenous Australians have an incidence of end stage kidney disease 8-10 times higher than non-Indigenous Australians. The majority of research studies concerning Indigenous Australians have been performed in rural or remote regions, whilst the majority of Indigenous Australians actually live in urban settings. We studied prevalence and factors associated with markers of kidney disease in an urban Indigenous Australian cohort, and compared results with those for the general Australian population.</p> <p>Methods</p> <p>860 Indigenous adult participants of the Darwin Region Urban Indigenous Diabetes (DRUID) Study were assessed for albuminuria (urine albumin-creatinine ratio≥2.5 mg/mmol males, ≥3.5 mg/mmol females) and low eGFR (estimated glomular filtration rate < 60 mls/min/1.73 m²). Associations between risk factors and kidney disease markers were explored. Comparison was made with the AusDiab cohort (n = 8,936 aged 25-64 years), representative of the general Australian adult population.</p> <p>Results</p> <p>A high prevalence of albuminuria (14.8%) was found in DRUID, whilst prevalence of low eGFR was 2.4%. Older age, higher HbA1c, hypertension, higher C-reactive protein and current smoking were independently associated with albuminuria on multiple regression. Low eGFR was independently associated with older age, hypertension, albuminuria and higher triglycerides. Compared to AusDiab participants, DRUID participants had a 3-fold higher adjusted risk of albuminuria but not of low eGFR.</p> <p>Conclusions</p> <p>Given the significant excess of ESKD observed in Indigenous versus non-Indigenous Australians, these findings could suggest either: albuminuria may be a better prognostic marker of kidney disease than low eGFR; that eGFR equations may be inaccurate in the Indigenous population; a less marked differential between Indigenous and non-Indigenous Australians for ESKD rates in urban compared to remote regions; or that differences in the pathophysiology of chronic kidney disease exist between Indigenous and non-Indigenous populations.</p

Living Well with Diabetes: a randomized controlled trial of a telephone-delivered intervention for maintenance of weight loss, physical activity and glycaemic control in adults with type 2 diabetes

Background By 2025, it is estimated that approximately 1.8 million Australian adults (approximately 8.4% of the adult population) will have diabetes, with the majority having type 2 diabetes. Weight management via improved physical activity and diet is the cornerstone of type 2 diabetes management. However, the majority of weight loss trials in diabetes have evaluated short-term, intensive clinic-based interventions that, while producing short-term outcomes, have failed to address issues of maintenance and broad population reach. Telephone-delivered interventions have the potential to address these gaps. Methods/Design Using a two-arm randomised controlled design, this study will evaluate an 18-month, telephone-delivered, behavioural weight loss intervention focussing on physical activity, diet and behavioural therapy, versus usual care, with follow-up at 24 months. Three-hundred adult participants, aged 20-75 years, with type 2 diabetes, will be recruited from 10 general practices via electronic medical records search. The Social-Cognitive Theory driven intervention involves a six-month intensive phase (4 weekly calls and 11 fortnightly calls) and a 12-month maintenance phase (one call per month). Primary outcomes, assessed at 6, 18 and 24 months, are: weight loss, physical activity, and glycaemic control (HbA1c), with weight loss and physical activity also measured at 12 months. Incremental cost-effectiveness will also be examined. Study recruitment began in February 2009, with final data collection expected by February 2013. Discussion This is the first study to evaluate the telephone as the primary method of delivering a behavioural weight loss intervention in type 2 diabetes. The evaluation of maintenance outcomes (6 months following the end of intervention), the use of accelerometers to objectively measure physical activity, and the inclusion of a cost-effectiveness analysis will advance the science of broad reach approaches to weight control and health behaviour change, and will build the evidence base needed to advocate for the translation of this work into population health practice

A Multisite Preregistered Paradigmatic Test of the Ego-Depletion Effect

We conducted a preregistered multilaboratory project (k = 36; N = 3,531) to assess the size and robustness of ego-depletion effects using a novel replication method, termed the paradigmatic replication approach. Each laboratory implemented one of two procedures that was intended to manipulate self-control and tested performance on a subsequent measure of self-control. Confirmatory tests found a nonsignificant result (d = 0.06). Confirmatory Bayesian meta-analyses using an informed-prior hypothesis (δ = 0.30, SD = 0.15) found that the data were 4 times more likely under the null than the alternative hypothesis. Hence, preregistered analyses did not find evidence for a depletion effect. Exploratory analyses on the full sample (i.e., ignoring exclusion criteria) found a statistically significant effect (d = 0.08); Bayesian analyses showed that the data were about equally likely under the null and informed-prior hypotheses. Exploratory moderator tests suggested that the depletion effect was larger for participants who reported more fatigue but was not moderated by trait self-control, willpower beliefs, or action orientation.</p

Global wealth disparities drive adherence to COVID-safe pathways in head and neck cancer surgery

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