Violator Spaces: Structure and Algorithms

Sharir and Welzl introduced an abstract framework for optimization problems, called LP-type problems or also generalized linear programming problems, which proved useful in algorithm design. We define a new, and as we believe, simpler and more natural framework: violator spaces, which constitute a proper generalization of LP-type problems. We show that Clarkson's randomized algorithms for low-dimensional linear programming work in the context of violator spaces. For example, in this way we obtain the fastest known algorithm for the P-matrix generalized linear complementarity problem with a constant number of blocks. We also give two new characterizations of LP-type problems: they are equivalent to acyclic violator spaces, as well as to concrete LP-type problems (informally, the constraints in a concrete LP-type problem are subsets of a linearly ordered ground set, and the value of a set of constraints is the minimum of its intersection).Comment: 28 pages, 5 figures, extended abstract was presented at ESA 2006; author spelling fixe

Large-scale evaluation of outcomes after a genetic diagnosis in children with severe developmental disorders

Purpose We sought to evaluate outcomes for clinical management after a genetic diagnosis from the Deciphering Developmental Disorders study. Methods Individuals in the Deciphering Developmental Disorders study who had a pathogenic/likely pathogenic genotype in the DECIPHER database were selected for inclusion (n = 5010). Clinical notes from regional clinical genetics services notes were reviewed to assess predefined clinical outcomes relating to interventions, prenatal choices, and information provision. Results Outcomes were recorded for 4237 diagnosed probands (85% of those eligible) from all 24 recruiting centers across the United Kingdom and Ireland. Clinical management was reported to have changed in 28% of affected individuals. Where individual-level interventions were recorded, additional diagnostic or screening tests were started in 903 (21%) probands through referral to a range of different clinical specialties, and stopped or avoided in a further 26 (0.6%). Disease-specific treatment was started in 85 (2%) probands, including seizure-control medications and dietary supplements, and contra-indicated medications were stopped or avoided in a further 20 (0.5%). The option of prenatal/preimplantation genetic testing was discussed with 1204 (28%) families, despite the relatively advanced age of the parents at the time of diagnosis. Importantly, condition-specific information or literature was given to 3214 (76%) families, and 880 (21%) were involved in family support groups. In the most common condition (KBG syndrome; 79 [2%] probands), clinical interventions only partially reflected the temporal development of phenotypes, highlighting the importance of consensus management guidelines and patient support groups. Conclusion Our results underscore the importance of achieving a clinico-molecular diagnosis to ensure timely onward referral of patients, enabling appropriate care and anticipatory surveillance, and for accessing relevant patient support groups

The Acute Retinal Necrosis Syndrome

The acute retinal necrosis syndrome is characterized by necrotizing retinitis, vitritis, and retinal vasculitis occurring in otherwise healthy patients. Experience with 11 cases and the review of 30 additional cases in the literature are presented. In this series, 50% of the affected eyes developed retinal detachments, and 64% had a final visual acuity of less than 20/200. The natural history, diagnosis, postulated etiology, and suggestions for management will be discussed