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

Busulphan-Cyclophosphamide Cause Endothelial Injury, Remodeling of Resistance Arteries and Enhanced Expression of Endothelial Nitric Oxide Synthase

Stem cell transplantation (SCT) is a curative treatment for malignant and non malignant diseases. However, transplantation-related complications including cardiovascular disease deteriorate the clinical outcome and quality of life. We have investigated the acute effects of conditioning regimen on the pharmacology, physiology and structure of large elastic arteries and small resistance-sized arteries in a SCT mouse model. Mesenteric resistance arteries and aorta were dissected from Balb/c mice conditioned with busulphan (Bu) and cyclophosphamide (Cy). In vitro isometric force development and pharmacology, in combination with RT-PCR, Western blotting and electron microscopy were used to study vascular properties. Compared with controls, mesenteric resistance arteries from the Bu-Cy group had larger internal circumference, showed enhanced endothelium mediated relaxation and increased expression of endothelial nitric oxide synthase (eNOS). Bu-Cy treated animals had lower mean blood pressure and signs of endothelial injury. Aortas of treated animals had a higher reactivity to noradrenaline. We conclude that short-term consequences of Bu-Cy treatment divergently affect large and small arteries of the cardiovascular system. The increased noradrenaline reactivity of large elastic arteries was not associated with increased blood pressure at rest. Instead, Bu-Cy treatment lowered blood pressure via augmented microvascular endothelial dependent relaxation, increased expression of vascular eNOS and remodeling toward a larger lumen. The changes in the properties of resistance arteries can be associated with direct effects of the compounds on vascular wall or possibly indirectly induced via altered translational activity associated with the reduced hematocrit and shear stress. This study contributes to understanding the mechanisms that underlie the early effects of conditioning regimen on resistance arteries and may help in designing further investigations to understand the late effects on vascular system

Treatment of childhood acute lymphoblastic leukemia after the first relapse: curative strategies.

Treatment of recurrent childhood acute lymphoblastic leukemia (ALL) has been controversial in the last decade. Conventional intensive chemotherapy (CHEMO) can cure up to 30% of children who have relapsed after ALL: similar results have been obtained with autologous bone marrow transplantation (ABMT), but allogeneic bone marrow transplantation (AlloBMT) seems to be the best therapeutic option. In this review the authors point out the contribution of current strategy in the setting of children with ALL who experience a first relapse and should be offered optimal treatment in order to obtain the best disease-free survival (DFS). The principal objective of this issue is to reach a possible consensus on the more controversial points regarding factors considered strong predictors of the outcome of the relapsed patients, second-line chemotherapy, optimal timing and type of transplantation. Data published in the literature over the last decade concerning early and late relapse in childhood ALL suggest that improvements in cure rates may be achieved by intensification of the relapse treatment both with chemotherapy and with different types of transplantation. An accurate search for Medline data has been performed in order to understand the risk-benefit ratio of aggressive therapy adopted in this setting. Modern first-line treatment protocols for childhood ALL have contributed to curing an ever larger number of patients but this strategy could be responsible for creating a more resistant leukemic clone at the time of systemic or extramedullary relapse. This hypothesis emerges from a number of single or multicenter experiences; thus clinical and biological features in relapsed patients are being studied carefully in order to understand which risk-directed second-line therapy should be best adopted. The BFM group classified ALL relapses as "very early", "early", or "late" according to the time from diagnosis to first relapse (i.e. 18 and < 30 or more than 30 months) and has shown that about 2/3 of the small fraction of children with late extramedullary relapses or late non T-marrow relapses or early combined non T-relapses can be rescued by chemotherapy; in contrast ALL early relapses or T-immunophenotype ALL relapses can be rescue only by AlloBMT. Since 1990 the AIEOP group adopted BFM-like first-line treatment and experienced similar situations for relapsed patients so that, even in absence of a real common relapse protocol, they went in the same direction as the BFM group as far as hematopoietic stem cell transplantation (HSCT) procedures and decision were concerned. A recent AIEOP study on the destiny of 192 consecutive patients with ALL in 2nd complete remission and not having an HLA suitable sibling donor is presented in this issue. The value of different HSCT procedures is addressed and the protection against a new relapse seems to be real, although, of course, the risk-benefit ratio should always be evaluated. Very few prospective studies on the treatment of childhood ALL relapse have been set up in the last decade because of many difficulties regarding common second-line therapies, some reluctance versus HSCT in consideration of the transplant-related mortality and the so-called late effects. Additional modifications of allogeneic family and unrelated donor HSCT strategies and the promising results both of cord HSCT and auto-grafting methods including in vitro purging or post-transplant immunotherapy, are making transplantation procedures for ALL relapsed patients more appropriate and increasing confidence in their use. The possibility of performing common prospective international studies should be encouraged over the next years in order to elucidate an area of great research as is that of the treatment of childhood ALL relapse