Convergence and Perturbation Resilience of Dynamic String-Averaging Projection Methods

We consider the convex feasibility problem (CFP) in Hilbert space and concentrate on the study of string-averaging projection (SAP) methods for the CFP, analyzing their convergence and their perturbation resilience. In the past, SAP methods were formulated with a single predetermined set of strings and a single predetermined set of weights. Here we extend the scope of the family of SAP methods to allow iteration-index-dependent variable strings and weights and term such methods dynamic string-averaging projection (DSAP) methods. The bounded perturbation resilience of DSAP methods is relevant and important for their possible use in the framework of the recently developed superiorization heuristic methodology for constrained minimization problems.Comment: Computational Optimization and Applications, accepted for publicatio

Gyermekkori Langerhans-sejtes histiocytosissal szerzett magyarországi tapasztalataink

BACKGROUND: Langerhans cell histiocytosis (LCH) in children is relatively rare, and the long-term analysis of therapy results has not been done yet in Hungary. PURPOSE: In this review we summarise the incidence, clinical features, prognostic risk factors and treatment results of children's LCH in Hungary, using data from the National Childhood Cancer Registry in Hungary in a 20-year period between 1981 and 2000. RESULTS: From January 1981 to December 2000, 111 children under 18 years of age were newly diagnosed with LCH in Hungary. The male-female ratio was 1.36:1, the mean age: 4 years 11 months. The minimal and median follow-up time was 3.48 years and 10.98 years respectively. 38 children had single-system disease, while in 73 cases we found systemic dissemination already at the time of diagnosis. Twenty-two patients were treated only by local surgery, 7 by surgery with local irradiation and 5 children received only local irradiation. In two cases remission was obtained with local steroid administration. 75 patient received chemotherapy. During the twenty years 14 children died, 9 due to the progression of the disease. Sixteen of the 111 patients had relapse with a mean of 2.16+/-1.29 years after the first diagnosis. Three patients with relapse got chemotherapy generally used in lymphoma and remission was achieved. The overall survival of all patients (n=111) was 88.3+/-3.1% at 5 years and 87.3+/-3.2% at 10 and 20 years. CONCLUSION: Childhood LCH is a well treatable disease and the survival rate is high. Even disseminated diseases have a quite good prognosis in childhood