Theoretical and numerical aspects of a non-stationary preconditioned iterative method for linear discrete ill-posed problems

This work considers some theoretical and computational aspects of the recent paper (Buccini et al., 2021), whose aim was to relax the convergence conditions in a previous work by Donatelli and Hanke, and thereby make the iterative method discussed in the latter work applicable to a larger class of problems. This aim was achieved in the sense that the iterative method presented convergences for a larger class of problems. However, while the analysis presented is correct, it does not establish the superior behavior of the iterative method described. The present note describes a slight modification of the analysis that establishes the superiority of the iterative method. The new analysis allows to discuss the behavior of the algorithm when varying the involved parameters, which is also useful for their empirical estimation

Fractional graph Laplacian for image reconstruction

Image reconstruction problems, like image deblurring and computer tomography, are usually ill-posed and require regularization. A popular approach to regularization is to substitute the original problem with an optimization problem that minimizes the sum of two terms, an term and an term with . The first penalizes the distance between the measured data and the reconstructed one, the latter imposes sparsity on some features of the computed solution. In this work, we propose to use the fractional Laplacian of a properly constructed graph in the term to compute extremely accurate reconstructions of the desired images. A simple model with a fully automatic method, i.e., that does not require the tuning of any parameter, is used to construct the graph and enhanced diffusion on the graph is achieved with the use of a fractional exponent in the Laplacian operator. Since the fractional Laplacian is a global operator, i.e., its matrix representation is completely full, it cannot be formed and stored. We propose to replace it with an approximation in an appropriate Krylov subspace. We show that the algorithm is a regularization method under some reasonable assumptions. Some selected numerical examples in image deblurring and computer tomography show the performance of our proposal

A comparison of parameter choice rules for ℓp - ℓq minimization

Images that have been contaminated by various kinds of blur and noise can be restored by the minimization of an ℓp-ℓq functional. The quality of the reconstruction depends on the choice of a regularization parameter. Several approaches to determine this parameter have been described in the literature. This work presents a numerical comparison of known approaches as well as of a new one

Large-scale regression with non-convex loss and penalty

We describe a computational method for parameter estimation in linear regression, that is capable of simultaneously producing sparse estimates and dealing with outliers and heavy-tailed error distributions. The method used is based on the image restoration method proposed in Huang et al. (2017) [13]. It can be applied to problems of arbitrary size. The choice of certain parameters is discussed. Results obtained for simulated and real data are presented

Costos de la licencia de maternidad para apoyar la lactancia materna en Brasil, Ghana y México

Objective To develop a method to assess the cost of extending the duration of maternity leave for formally-employed women at the national level and apply it in Brazil, Ghana and Mexico. Methods We adapted a World Bank costing method into a five-step method to estimate the costs of extending the length of maternity leave mandates. Our method used the unit cost of maternity leave based on working women’s weekly wages; the number of additional weeks of maternity leave to be analysed for a given year; and the weighted population of women of reproductive and legal working age in a given country in that year. We weighted the population by the probability of having a baby that year among women in formal employment, according to individual characteristics. We applied nationally representative cross-sectional data from fertility, employment and population surveys to estimate the costs of maternity leave for mothers employed in the formal sector in Brazil, Ghana and Mexico for periods from 12 weeks up to 26 weeks, the WHO target for exclusive breastfeeding. Findings We estimated that 640 742 women in Brazil, 33 869 in Ghana and 288 655 in Mexico would require formal maternity leave annually. The median weekly cost of extending maternity leave for formally working women was purchasing power parity international dollars (PPP$) 195.07 per woman in Brazil, PPP$ 109.68 in Ghana and PPP$ 168.83 in Mexico. Conclusion Our costing method could facilitate evidence-based policy decisions across countries to improve maternity protection benefits and support breastfeeding

Cluster randomized trial assessing the effects of rapid ethical assessment on informed consent comprehension in a low-resource setting

Background Maximizing comprehension is a major challenge for informed consent processes in low-literacy and resource-limited settings. Application of rapid qualitative assessments to improve the informed consent process is increasingly considered useful. This study assessed the effects of Rapid Ethical Assessment (REA) on comprehension, retention and quality of the informed consent process. Methods A cluster randomized trial was conducted among participants of HPV sero-prevalence study in two districts of Northern Ethiopia, in 2013. A total of 300 study participants, 150 in the intervention and 150 in the control group, were included in the study. For the intervention group, the informed consent process was designed with further revisions based on REA findings. Informed consent comprehension levels and quality of the consent process were measured using the Modular Informed Consent Comprehension Assessment (MICCA) and Quality of Informed Consent (QuIC) process assessment tools, respectively. Result Study recruitment rates were 88.7 % and 80.7 % (p = 0.05), while study retention rates were 85.7 % and 70.3 % (p < 0.005) for the intervention and control groups respectively. Overall, the mean informed consent comprehension scores for the intervention and control groups were 73.1 % and 45.2 %, respectively, with a mean difference in comprehension score of 27.9 % (95 % CI 24.0 % - 33.4 %; p < 0.001,). Mean scores for quality of informed consent for the intervention and control groups were 89.1 % and 78.5 %, respectively, with a mean difference of 10.5 % (95 % CI 6.8 -14.2 %; p < 0.001). Conclusion Levels of informed consent comprehension, quality of the consent process, study recruitment and retention rates were significantly improved in the intervention group. We recommend REA as a potential modality to improve informed consent comprehension and quality of informed consent process in low resource settings

Effect of dietary Acrocomia aculeata kernel oil rich in medium chain fatty acids on type 2 diabetic rats.

This study evaluated the effects of dietaries formulated with kernel oil of Acrocomia aculeata (AKO), rich in medium chain fatty acids (MCFA), as partial substitute of carbohydrate calories upon blood glucose, lipid profile, insulin secretion and insulin sensitivity in diabetic rats. Overall, the dietary with any AKO dose reduced hyperglycemia, ameliorated insulin secretion, lowered insulin resistance by model HOMA-IR and HOMA-Beta and augmented pancreatic beta cells functionality, restored the number of pancreatic Beta-cell in the diabetic rats and increased it in the non-diabetic rats. In addition, AKO fed rats showed reducing triglycerides, lower density lipoprotein-cholesterol and increasing high density lipoprotein-cholesterol levels, and improved hepatic function markers. Those findings suggest AKO was effective to ameliorate the health of diabetic rats.On-line first