Asymptotically MDS Array BP-XOR Codes

Belief propagation or message passing on binary erasure channels (BEC) is a low complexity decoding algorithm that allows the recovery of message symbols based on bipartite graph prunning process. Recently, array XOR codes have attracted attention for storage systems due to their burst error recovery performance and easy arithmetic based on Exclusive OR (XOR)-only logic operations. Array BP-XOR codes are a subclass of array XOR codes that can be decoded using BP under BEC. Requiring the capability of BP-decodability in addition to Maximum Distance Separability (MDS) constraint on the code construction process is observed to put an upper bound on the maximum achievable code block length, which leads to the code construction process to become a harder problem. In this study, we introduce asymptotically MDS array BP-XOR codes that are alternative to exact MDS array BP-XOR codes to pave the way for easier code constructions while keeping the decoding complexity low with an asymptotically vanishing coding overhead. We finally provide and analyze a simple code construction method that is based on discrete geometry to fulfill the requirements of the class of asymptotically MDS array BP-XOR codes.Comment: 8 pages, 4 figures, to be submitte

Infant weight gain and adolescent body mass index: comparison across two British cohorts born in 1946 and 2001

Objective To investigate how the relationship of infant weight gain with adolescent body mass index (BMI) differs for individuals born during compared to before the obesity epidemic era. Design Data from two British birth cohorts, the 1946 National Survey of Health and Development (NSHD, n = 4,199) and the 2001 Millennium Cohort Study (MCS, n = 9,417), were used to estimate and compare associations of infant weight gain between ages 0-3 years with adolescent outcomes. Main outcome measures BMI Z-scores and overweight/ obesity at ages 11 and 14 years. Results Infant weight gain, in Z-scores, was positively associated with adolescent BMI Z-scores in both cohorts. Non-linearity in the MCS meant that associations were only stronger than in the NSHD when infant weight gain was above -1 Z-score. Using decomposition analysis, between-cohort differences in association accounted for 20-30% of the differences (secular increases) in BMI Z-scores, although the underlying estimates were not precise with 95% confidence intervals (CI) crossing zero. Conversely, between-cohort differences in the distribution of infant weight gain accounted for approximately 9% of the differences (secular increases) in BMI Z-scores, and the underlying estimates were precise with 95% CI not crossing zero. Relative to normal weight gain (change of -0.67 to +0.67 Z-scores between ages 0-3 years), very rapid infant weight gain (> 1.34), but not rapid weight gain (+0.67 to +1.34), was associated with higher BMI Z-scores more strongly in the MCS (β = 0.790; 95% CI = 0.717, 0.862 at age 11 years) than the NSHD (0.573; 0.466, 0.681); p < 0.001 for between-cohort difference. The relationship of slow infant weight gain (< -0.67) with lower adolescent BMI was also stronger in the MCS. Very rapid or slow infant weight gain were not, however, more strongly associated with increased risk of adolescent overweight/ obesity or thinness, respectively, in the more recently born cohort. Conclusions Greater infant weight gain, at the middle/ upper-end of the distribution, was more strongly associated with higher adolescent BMI among individuals born during (compared to before) the obesity epidemic. Combined with a secular change toward greater infant weight gain, these results suggest that there are likely to be associated negative consequences for population-level health and wellbeing in the future, unless effective interventions are developed and implemented

Socioeconomic inequalities in childhood-to-adulthood BMI tracking in three British birth cohorts

Background: Body mass index (BMI) tracks from childhood to adulthood, but the extent to which this relationship varies across the distribution and according to socio-economic position (SEP) is unknown. We aimed to address this using data from three British cohort studies. Methods: We used data from: 1946 National Survey of Health and Development (NSHD, n=2,470); 1958 National Child Development Study (NCDS, n=7,747); 1970 British Cohort Study (BCS, n=5,323). BMI tracking between 11 and 42 years was estimated using quantile regression, with estimates reflecting correlation coefficients. SEP disparities in tracking were investigated using a derived SEP variable based on parental education reported in childhood. This SEP variable was then interacted with the 11-year BMI z-score. Results: In each cohort and sex, tracking was stronger at the upper end of the distribution of BMI at 42 years. For example, for men in the 1946 NSHD, the tracking estimate at the 10th quantile was 0.31 (0.20, 0.41), increasing to 0.71 (0.61, 0.82) at the 90th quantile. We observed no strong evidence of SEP inequalities in tracking in men in the 1946 and 1958 cohorts. In the 1970 cohort, however, we observed tentative evidence of stronger tracking in low SEP groups, particularly in women and at the higher end of the BMI distribution. For example, women in the 1970 cohort from low SEP backgrounds had tracking coefficients at the 50th, 70th, and 90th quantiles which were 0.05 (-0.04; 0.15), 0.19 (0.06; 0.31), and 0.22 (0.02; 0.43) units higher, respectively, than children from high SEP groups. Conclusion: Tracking was consistently stronger at the higher quantiles of the BMI distribution. We observed suggestive evidence for a pattern of greater BMI tracking in lower (compared to higher) SEP groups in the more recently born cohort, particularly in women and at the higher end of the BMI distribution

Socioeconomic inequalities in childhood and adolescent body-mass index, weight, and height from 1953 to 2015: an analysis of four longitudinal, observational, British birth cohort studies

Background Socioeconomic inequalities in childhood body mass index (BMI) have been repeatedly documented in high income countries, yet there is uncertainty regarding how they have changed across time, how inequalities in the composite parts of BMI have changed (weight and height), and whether inequalities differ in magnitude across the outcome distributions. We investigated socioeconomic inequalities in childhood/adolescent weight, height, and BMI from 1953 to 2015 using British birth cohorts born in 1946, 1958, 1970, and 2001. Methods Associations between childhood social class and anthropometric outcomes at age 7, 10/11 and 14/16 years were examined to assess socioeconomic inequalities in each cohort using gender-adjusted linear regression models. Multilevel models were used to examine if these inequalities widened or narrowed from childhood to adolescence; quantile regression was used to examine whether the magnitude of inequalities differed across the outcome distribution. Findings Lower social class was associated with lower childhood/adolescent weight in earlier-born cohorts (1946-1970), yet with higher weight in the 2001 cohort. Lower social class was associated with shorter height in all cohorts, yet the absolute magnitude of this difference narrowed across generations. There was little inequality in childhood BMI in the 1946–1970 cohorts, yet inequalities were present in the 2001 cohort, and in all cohorts at 14/16 years (p<0.05 age x social class interactions). BMI and weight inequalities were larger in the 2001 cohort and systematically larger at higher quantiles—eg, in the 2001 cohort at 11 years there was a 0.98kg/m2 difference (0.63, 1.33) in median BMI (lowest to highest social class), yet 2.54kg/m2 (1.85, 3.22) difference at the 90th BMI percentile. Interpretation In the later 20th and early 21st centuries, socioeconomic inequalities in weight reversed, those in height narrowed, while inequalities in BMI and obesity emerged and widened. These drastic changes highlight the powerful impact of societal changes on child-adolescent growth and the insufficiency of previous policies in preventing obesity and its socioeconomic inequality. New and effective policies are required to reduce BMI inequalities in current and future children and adolescents. Without effective interventions, it is anticipated these inequalities will widen further throughout adulthood

The InterLACE study: design, data harmonization and characteristics across 20 studies on women's health

The International Collaboration for a Life Course Approach to Reproductive Health and Chronic Disease Events (InterLACE) project is a global research collaboration that aims to advance understanding of women's reproductive health in relation to chronic disease risk by pooling individual participant data from several cohort and cross-sectional studies. The aim of this paper is to describe the characteristics of contributing studies and to present the distribution of demographic and reproductive factors and chronic disease outcomes in InterLACE

Linear regression analysis of associations between trunk length and mid-life cognitive function.

<p>Linear regression analysis of associations between trunk length and mid-life cognitive function.</p

Linear regression analysis of associations between leg length and mid-life cognitive function.

<p>Linear regression analysis of associations between leg length and mid-life cognitive function.</p

The 98^th, 91^st, and 50^th adulthood BMI centiles from sex- and study-stratified LMS models plotted against the normal cut-offs.

<p>BMI: Body Mass Index, LMS: Lambda-Mu-Sigma, NSHD: Medical Research Council National Survey of Health and Development, NCDS National Child Development Study, BCS: British Cohort Study.</p

Trajectories of the probability of overweight or obesity (versus normal weight) from sex- and study-stratified multilevel logistic regression models.

<p>NSHD: Medical Research Council National Survey of Health and Development, NCDS National Child Development Study, BCS: British Cohort Study, ALSPAC: Avon Longitudinal Study of Parents and Children, MCS: Millennium Cohort Study.</p

Study-stratified box plots for height, weight, and BMI Z-scores according to the UK-WHO chart at 10 or 11 years of age.

<p>BMI: Body Mass Index, UK-WHO: United Kingdom-World Health Organisation, NSHD: Medical Research Council National Survey of Health and Development, NCDS National Child Development Study, BCS: British Cohort Study, ALSPAC: Avon Longitudinal Study of Parents and Children, MCS: Millennium Cohort Study.</p