The Radius of Metric Subregularity

There is a basic paradigm, called here the radius of well-posedness, which quantifies the "distance" from a given well-posed problem to the set of ill-posed problems of the same kind. In variational analysis, well-posedness is often understood as a regularity property, which is usually employed to measure the effect of perturbations and approximations of a problem on its solutions. In this paper we focus on evaluating the radius of the property of metric subregularity which, in contrast to its siblings, metric regularity, strong regularity and strong subregularity, exhibits a more complicated behavior under various perturbations. We consider three kinds of perturbations: by Lipschitz continuous functions, by semismooth functions, and by smooth functions, obtaining different expressions/bounds for the radius of subregularity, which involve generalized derivatives of set-valued mappings. We also obtain different expressions when using either Frobenius or Euclidean norm to measure the radius. As an application, we evaluate the radius of subregularity of a general constraint system. Examples illustrate the theoretical findings.Comment: 20 page

Evaluation of nutritional status in children with refractory epilepsy

BACKGROUND: children affected by refractory epilepsy could be at risk of malnutrition because of feeding difficulties (anorexia, chewing, swallowing difficulties or vomiting) and chronic use of anticonvulsants, which may affect food intake and energy metabolism. Moreover, their energy requirement may be changed as their disabilities would impede normal daily activities. The aim of the present study was to evaluate nutritional status, energy metabolism and food intake in children with refractory epilepsy. METHODS: 17 children with refractory epilepsy (13 boys and 4 girls; mean age 9 ± 3,2 years; Body Mass Index 15,7 ± 3,6) underwent an anthropometric assessment, body composition evaluation by dual-energy X-ray absorptiometry, detailed dietetic survey and measurement of resting energy expenditure by indirect calorimetry. Weight-for-age, height-for-age (stunting) and weight-for-height (wasting) were estimated compared to those of a reference population of the same age. RESULTS: 40% of children were malnourished and 24% were wasted. The nutritional status was worse in the more disabled children. Dietary intake resulted unbalanced (18%, 39%, 43% of total daily energy intake derived respectively from protein, lipid and carbohydrate). Adequacy index [nutrient daily intake/recommended allowance (RDA) × 100] was < 60% for calcium iron and zinc. CONCLUSION: many children with refractory epilepsy would benefit from individual nutritional assessment and management as part of their overall care

Chronic kidney disease after liver, cardiac, lung, heart–lung, and hematopoietic stem cell transplant

Patient survival after cardiac, liver, and hematopoietic stem cell transplant (HSCT) is improving; however, this survival is limited by substantial pretransplant and treatment-related toxicities. A major cause of morbidity and mortality after transplant is chronic kidney disease (CKD). Although the majority of CKD after transplant is attributed to the use of calcineurin inhibitors, various other conditions such as thrombotic microangiopathy, nephrotic syndrome, and focal segmental glomerulosclerosis have been described. Though the immunosuppression used for each of the transplant types, cardiac, liver and HSCT is similar, the risk factors for developing CKD and the CKD severity described in patients after transplant vary. As the indications for transplant and the long-term survival improves for these children, so will the burden of CKD. Nephrologists should be involved early in the pretransplant workup of these patients. Transplant physicians and nephrologists will need to work together to identify those patients at risk of developing CKD early to prevent its development and progression to end-stage renal disease