Some properties and generating functions of generalized harmonic numbers

In this paper, we introduce higher-order harmonic numbers and derive their relevant properties and generating functions by using an umbral-type method. We discuss the link with recent works on the subject, and show that the combinations of umbral and other techniques (such as the Laplace and other types of integral transforms) yield a very efficient tool to explore the properties of these numbers

Systematic review and meta-analysis of reduction in all-cause mortality from walking and cycling and shape of dose response relationship

BACKGROUND AND OBJECTIVE: Walking and cycling have shown beneficial effects on population risk of all-cause mortality (ACM). This paper aims to review the evidence and quantify these effects, adjusted for other physical activity (PA). DATA SOURCES: We conducted a systematic review to identify relevant studies. Searches were conducted in November 2013 using the following health databases of publications: Embase (OvidSP); Medline (OvidSP); Web of Knowledge; CINAHL; SCOPUS; SPORTDiscus. We also searched reference lists of relevant texts and reviews. STUDY ELIGIBILITY CRITERIA AND PARTICIPANTS: Eligible studies were prospective cohort design and reporting walking or cycling exposure and mortality as an outcome. Only cohorts of individuals healthy at baseline were considered eligible. STUDY APPRAISAL AND SYNTHESIS METHODS: Extracted data included study population and location, sample size, population characteristics (age and sex), follow-up in years, walking or cycling exposure, mortality outcome, and adjustment for other co-variables. We used random-effects meta-analyses to investigate the beneficial effects of regular walking and cycling. RESULTS: Walking (18 results from 14 studies) and cycling (8 results from 7 studies) were shown to reduce the risk of all-cause mortality, adjusted for other PA. For a standardised dose of 11.25 MET.hours per week (or 675 MET.minutes per week), the reduction in risk for ACM was 11% (95% CI = 4 to 17%) for walking and 10% (95% CI = 6 to 13%) for cycling. The estimates for walking are based on 280,000 participants and 2.6 million person-years and for cycling they are based on 187,000 individuals and 2.1 million person-years. The shape of the dose-response relationship was modelled through meta-analysis of pooled relative risks within three exposure intervals. The dose-response analysis showed that walking or cycling had the greatest effect on risk for ACM in the first (lowest) exposure interval. CONCLUSIONS AND IMPLICATIONS: The analysis shows that walking and cycling have population-level health benefits even after adjustment for other PA. Public health approaches would have the biggest impact if they are able to increase walking and cycling levels in the groups that have the lowest levels of these activities. REVIEW REGISTRATION: The review protocol was registered with PROSPERO (International database of prospectively registered systematic reviews in health and social care) PROSPERO 2013: CRD42013004266

GRANADA consensus on analytical approaches to assess associations with accelerometer-determined physical behaviours (physical activity, sedentary behaviour and sleep) in epidemiological studies

The inter-relationship between physical activity, sedentary behaviour and sleep (collectively defined as physical behaviours) is of interest to researchers from different fields. Each of these physical behaviours has been investigated in epidemiological studies, yet their codependency and interactions need to be further explored and accounted for in data analysis. Modern accelerometers capture continuous movement through the day, which presents the challenge of how to best use the richness of these data. In recent years, analytical approaches first applied in other scientific fields have been applied to physical behaviour epidemiology (eg, isotemporal substitution models, compositional data analysis, multivariate pattern analysis, functional data analysis and machine learning). A comprehensive description, discussion, and consensus on the strengths and limitations of these analytical approaches will help researchers decide which approach to use in different situations. In this context, a scientific workshop and meeting were held in Granada to discuss: (1) analytical approaches currently used in the scientific literature on physical behaviour, highlighting strengths and limitations, providing practical recommendations on their use and including a decision tree for assisting researchers’ decision-making; and (2) current gaps and future research directions around the analysis and use of accelerometer data. Advances in analytical approaches to accelerometer-determined physical behaviours in epidemiological studies are expected to influence the interpretation of current and future evidence, and ultimately impact on future physical behaviour guidelines

Fruit, vegetable intake and blood pressure trajectories in older age

Diet rich in fruits and vegetables (F&V) is an established protective factor for hypertension, but the available evidence regarding the impact of F&V consumption on age-related blood pressure change is limited. We examined whether systolic (SBP) and diastolic (DBP) blood pressure trajectories are influenced by F&V intakes in an ageing Russian cohort. Dietary data was available for 8997 men and women in the Health, Alcohol and Psychosocial Factors in Eastern Europe prospective cohort study. Blood pressure measurements were taken at three time-points over 12 years of follow-up, during which time the mean age of the sample changed from 58 to 69 years. The relationships between F&V intake and SBP and DBP were assessed using mixed-effect multilevel models. In the multivariable adjusted models, fruit intake was inversely related to both systolic and diastolic blood pressure at baseline (mean SBP and DBP was 3.5 mmHg and 1.4 mm Hg lower in the highest compared to the lowest intake tertiles, respectively (both p values < 0.001)). However, it was not associated with blood pressure change over time (difference in annual SBP and DBP change was 0.11 mmHg (p value = 0.138) and 0.01 mmHg (p value = 0.894), respectively). We found no significant link between vegetable intake and blood pressure, neither cross-sectionally nor longitudinally. In addition to the association with diet, we observed increasing SBP and mostly steady DBP over age, with deceleration and downward turn after the ages of 55-59 years. On the whole, this analysis found no consistent association between F&V intake and trajectories of blood pressure in older age

How can entrepreneurial interventions in a university context impact the entrepreneurial intention of their students?

This paper explores the link between the entrepreneurial intention of students in higher education and the entrepreneurial interventions an institution can provide to support them. The study uses data collected from 679 undergraduate students from Chinese and UK Universities. The instrument for data collection was a paper-based questionnaire. This study uses the integrated model of entrepreneurial intentions as the theoretical underpinning for this approach. The initial findings highlight the perceived need for a range of entrepreneurship interventions, with business training programmes being the highest priority, followed by mentoring, specialist business advice, low-cost finance, business networking events and enterprise clubs. It also shows that those with different Intention Horizons do request a different portfolio of interventions. The paper provides an evidence-based approach to entrepreneurship education design and the development of interventions to support a range of students with and without entrepreneurial intention. This work suggests a previously under-articulated relationship between the nascent entrepreneur’s Intention Horizon, university interventions, and entrepreneurial action. There are numerous calls for further contextualisation of entrepreneurship education which this paper fulfils (Baron and Shane in Psychol Entrepreneurship 19-39, 2007; Byrne et al. in Edward Elgar Publishing, 2014). It further develops the narrative around both contextualisation, the previous experience of the students and the range and importance of these interventions to support the creation of a new venture

Satellite and in situ sampling mismatches: Consequences for the estimation of satellite sea surface salinity uncertainties

Validation of satellite sea surface salinity (SSS) products is typically based on comparisons with in-situ measurements at a few meters’ depth, which are mostly done at a single location and time. The difference in term of spatio-temporal resolution between the in-situ near-surface salinity and the two-dimensional satellite SSS results in a sampling mismatch uncertainty. The Climate Change Initiative (CCI) project has merged SSS from three satellite missions. Using an optimal interpolation, weekly and monthly SSS and their uncertainties are estimated at a 50 km spatial resolution over the global ocean. Over the 2016–2018 period, the mean uncertainty on weekly CCI SSS is 0.13, whereas the standard deviation of weekly CCI minus in-situ Argo salinities is 0.24. Using SSS from a high-resolution model reanalysis, we estimate the expected uncertainty due to the CCI versus Argo sampling mismatch. Most of the largest spatial variability of the satellite minus Argo salinity is observed in regions with large estimated sampling mismatch. A quantitative validation is performed by considering the statistical distribution of the CCI minus Argo salinity normalized by the sampling and retrieval uncertainties. This quantity should follow a Gaussian distribution with a standard deviation of 1, if all uncertainty contributions are properly taken into account. We find that (1) the observed differences between Argo and CCI data in dynamical regions (river plumes, fronts) are mainly due to the sampling mismatch; (2) overall, the uncertainties are well estimated in CCI version 3, much improved compared to CCI version 2. There are a few dynamical regions where discrepancies remain and where the satellite SSS, their associated uncertainties and the sampling mismatch estimates should be further validated

Age and the association between apolipoprotein E genotype and Alzheimer disease: A cerebrospinal fluid biomarker-based case-control study

Background: The ε4 allele of apolipoprotein E (APOE) gene and increasing age are two of the most important known risk factors for developing Alzheimer disease (AD). The diagnosis of AD based on clinical symptoms alone is known to have poor specificity; recently developed diagnostic criteria based on biomarkers that reflect underlying AD neuropathology allow better assessment of the strength of the associations of risk factors with AD. Accordingly, we examined the global and age-specific association between APOE genotype and AD by using the A/T/N classification, relying on the cerebrospinal fluid (CSF) levels of β-amyloid peptide (A, β-amyloid deposition), phosphorylated tau (T, pathologic tau), and total tau (N, neurodegeneration) to identify patients with AD. Methods and findings: This case–control study included 1,593 white AD cases (55.4% women; mean age 72.8 [range = 44–96] years) with abnormal values of CSF biomarkers from nine European memory clinics and the American Alzheimer’s Disease Neuroimaging Initiative (ADNI) study. A total of 11,723 dementia-free controls (47.1% women; mean age 65.6 [range = 44–94] years) were drawn from two longitudinal cohort studies (Whitehall II and Three-City), in which incident cases of dementia over the follow-up were excluded from the control population. Odds ratio (OR) and population attributable fraction (PAF) for AD associated with APOE genotypes were determined, overall and by 5-year age categories. In total, 63.4% of patients with AD and 22.6% of population controls carried at least one APOE ε4 allele. Compared with non-ε4 carriers, heterozygous ε4 carriers had a 4.6 (95% confidence interval 4.1–5.2; p < 0.001) and ε4/ε4 homozygotes a 25.4 (20.4–31.2; p < 0.001) higher OR of AD in unadjusted analysis. This association was modified by age (p for interaction < 0.001). The PAF associated with carrying at least one ε4 allele was greatest in the 65–70 age group (69.7%) and weaker before 55 years (14.2%) and after 85 years (22.6%). The protective effect of APOE ε2 allele for AD was unaffected by age. Main study limitations are that analyses were based on white individuals and AD cases were drawn from memory centers, which may not be representative of the general population of patients with AD. Conclusions: In this study, we found that AD diagnosis based on biomarkers was associated with APOE ε4 carrier status, with a higher OR than previously reported from studies based on only clinical AD criteria. This association differs according to age, with the strongest effect at 65–70 years. These findings highlight the need for early interventions for dementia prevention to mitigate the effect of APOE ε4 at the population level

Healthy obesity and risk of accelerated functional decline and disability

BACKGROUND/OBJECTIVES: Some obese adults have a normal metabolic profile and are considered 'healthy', but whether they experience faster ageing than healthy normal-weight adults is unknown. We compared decline in physical function, worsening of bodily pain, and likelihood of future mobility limitation and disability between these groups. SUBJECTS/METHODS: This was a population-based observational study using repeated measures over 2 decades (Whitehall II cohort data). Normal-weight (body mass index (BMI) 18.5-24.9 kg/m(2)), overweight (25.0-29.9 kg/m(2)), and obese (⩾30.0 kg/m(2)) adults were considered metabolically healthy if they had 0 or 1 of 5 risk factors (hypertension, low high-density lipoprotein cholesterol, high triacylglycerol, high blood glucose, and insulin resistance) in 1991/94. Decline in physical function and worsening of bodily pain based on change in Short Form Health Survey items using 8 repeated measures over 18.8 years (1991/94-2012/13) was compared between metabolic-BMI groups using linear mixed models. Odds of mobility limitation based on objective walking speed (slowest tertile) and of disability based on limitations in ⩾1 of 6 basic activities of daily living, each using 3 repeated measures over 8.3 years (2002/04-2012/13), were compared using logistic mixed models. RESULTS: In multivariable-adjusted mixed models on up to 6635 adults (initial mean age 50 years; 70% male), healthy normal-weight adults experienced a decline in physical function of -3.68 (95% CI=-4.19, -3.16) score units per decade; healthy obese adults showed an additional -3.48 (-4.88, -2.08) units decline. Healthy normal-weight adults experienced a -0.49 (-0.12, 1.11) score unit worsening of bodily pain per decade; healthy obese adults had an additional -2.23 (-0.69, -3.78) units worsening. Healthy obesity versus healthy normal-weight conferred 3.39 (2.29, 5.02) times higher odds of mobility limitation and 3.75 (1.94, 7.24) times higher odds of disability. CONCLUSIONS: Our results suggest that obesity, even if metabolically healthy, accelerates age-related declines in functional ability and poses a threat to independence in older age.International Journal of Obesity accepted article preview online, 21 February 2017. doi:10.1038/ijo.2017.51

Adiposity in early, middle and later adult life and cardiometabolic risk markers in later life; findings from the British regional heart study.

OBJECTIVES: This research investigates the associations between body mass index (BMI) at 21, 40-59, 60-79 years of age on cardiometabolic risk markers at 60-79 years. METHODS: A prospective study of 3464 British men with BMI measured at 40-59 and 60-79 years, when cardiometabolic risk was assessed. BMI at 21 years was ascertained from military records, or recalled from middle-age (adjusted for reporting bias); associations between BMI at different ages and later cardiometabolic risk markers were examined using linear regression. Sensitive period, accumulation and mobility life course models were devised for high BMI (defined as BMI≥75th centile) and compared with a saturated BMI trajectory model. RESULTS: At ages 21, 40-59 and 60-79 years, prevalences of overweight (BMI≥25 kg/m2) were 12%, 53%, 70%, and obesity (≥30 kg/m2) 1.6%, 6.6%, and 17.6%, respectively. BMI at 21 years was positively associated with serum insulin, blood glucose, and HbA1c at 60-79 years, with increases of 1.5% (95%CI 0.8,2.3%), 0.4% (0.1,0.6%), 0.3% (0.1,0.4%) per 1 kg/m2, respectively, but showed no associations with blood pressure or blood cholesterol. However, these associations were modest compared to those between BMI at 60-79 years and serum insulin, blood glucose and HbA1c at 60-79 years, with increases of 8.6% (8.0,9.2%), 0.7% (0.5,0.9%), and 0.5% (0.4,0.7%) per 1 kg/m2, respectively. BMI at 60-79 years was also associated with total cholesterol and blood pressure. Associations for BMI at 40-59 years were mainly consistent with those of BMI at 60-79 years. None of the life course models fitted the data as well as the saturated model for serum insulin. A sensitive period at 50 years for glucose and HbA1c and sensitive period at 70 years for blood pressure were identified. CONCLUSIONS: In this cohort of men who were thin compared to more contemporary cohorts, BMI in later life was the dominant influence on cardiovascular and diabetes risk. BMI in early adult life may have a small long-term effect on diabetes risk