RESUMEN
In this article, we prove optimal convergence rates results for regularization methods for solving linear ill-posed operator equations in Hilbert spaces. The results generalizes existing convergence rates results on optimality to general source conditions, such as logarithmic source conditions. Moreover, we also provide optimality results under variational source conditions and show the connection to approximative source conditions.
RESUMEN
We propose a parsimonious, yet effective, susceptible-exposed-infected-removed-type model that incorporates the time change in the transmission and death rates. The model is calibrated by Tikhonov-type regularization from official reports from New York City (NYC), Chicago, the State of São Paulo, in Brazil and British Columbia, in Canada. To forecast, we propose different ways to extend the transmission parameter, considering its estimated values. The forecast accuracy is then evaluated using real data from the above referred places. All the techniques accurately provided forecast scenarios for periods 15 days long. One of the models effectively predicted the magnitude of the four waves of infections in NYC, including the one caused by the Omicron variant for periods of 45 days using out-of-sample data.
RESUMEN
BACKGROUND: High early postnatal weight gain has been associated with childhood adiposity; however, the mechanism remains unknown. DNA methylation is a hypothesised mechanism linking early life exposures and subsequent disease. However, epigenetic changes associated with high early weight gain have not previously been investigated. Our aim was to investigate the associations between early weight gain, peripheral blood DNA methylation, and subsequent overweight/obese. Data from the UK Avon Longitudinal study of Parents and Children (ALSPAC) cohort were used to estimate associations between early postnatal weight gain and epigenome-wide DNA CpG site methylation (Illumina 450 K Methylation Beadchip) in blood in childhood (n = 125) and late adolescence (n = 96). High weight gain in the first year (a change in weight z-scores > 0.67), both unconditional (rapid weight gain) and conditional on birthweight (rapid thrive), was related to individual CpG site methylation and across regions using the meffil pipeline, with and without adjustment for cell type proportions, and with 5% false discovery rate correction. Variation in methylation at high weight gain-associated CpG sites was then examined with regard to body composition measures in childhood and adolescence. Replication of the differentially methylated CpG sites was sought using whole-blood DNA samples from 104 children from the UK Southampton Women's Survey. RESULTS: Rapid infant weight gain was associated with small (+ 1% change) increases in childhood methylation (age 7) for two distinct CpG sites (cg01379158 (NT5M) and cg11531579 (CHFR)). Childhood methylation at one of these CpGs (cg11531579) was also higher in those who experienced rapid weight gain and were subsequently overweight/obese in adolescence (age 17). Rapid weight gain was not associated with differential DNA methylation in adolescence. Childhood methylation at the cg11531579 site was also suggestively associated with rapid weight gain in the replication cohort. CONCLUSIONS: This study identified associations between rapid weight gain in infancy and small increases in childhood methylation at two CpG sites, one of which was replicated and was also associated with subsequent overweight/obese. It will be important to determine whether loci are markers of early rapid weight gain across different, larger populations. The mechanistic relevance of these differentially methylated sites requires further investigation.