Algorithmic Randomness and Capacity of Closed Sets

We investigate the connection between measure, capacity and algorithmic randomness for the space of closed sets. For any computable measure m, a computable capacity T may be defined by letting T(Q) be the measure of the family of closed sets K which have nonempty intersection with Q. We prove an effective version of Choquet's capacity theorem by showing that every computable capacity may be obtained from a computable measure in this way. We establish conditions on the measure m that characterize when the capacity of an m-random closed set equals zero. This includes new results in classical probability theory as well as results for algorithmic randomness. For certain computable measures, we construct effectively closed sets with positive capacity and with Lebesgue measure zero. We show that for computable measures, a real q is upper semi-computable if and only if there is an effectively closed set with capacity q

Inhibitor clinical burden of disease: a comparative analysis of the CHESS data.

From Europe PMC via Jisc Publications Router.Publication status: PublishedBACKGROUND:Patients with hemophilia and inhibitors generally face greater disease burden compared to patients without inhibitors. While raising awareness of relative burden may improve the standard of care for patients with inhibitors, comparative data are sparse. Analyzing data drawn from the Cost of Haemophilia across Europe - a Socioeconomic Survey (CHESS) study, the aim of this study was to compare the clinical burden of disease in patients with severe hemophilia with and without inhibitors. Hemophilia specialists (N = 139) across five European countries completed an online survey between January-April 2015, providing demographic, clinical and 12-month ambulatory/secondary care activity data for 1285 patients. Patients with hemophilia who currently presented with inhibitors and those who never had inhibitors were matched on baseline characteristics via propensity score matching. Outcomes were compared between the two cohorts using a paired t-test or Wilcoxon signed-rank or McNemar's test. RESULTS:The proportion of patients who currently presented with inhibitors was 4.5% (58/1285). Compared to PS-matched patients without inhibitors, patients with inhibitors experienced more than twice the mean annual number of bleeds (mean ± standard deviation, 8.29 ± 9.18 vs 3.72 ± 3.95; p < .0001) and joint bleeds (2.17 ± 1.90 vs 0.98 ± 1.15; p < .0001), and required more hemophilia-related (mean ± standard deviation, 1.79 ± 1.83 vs 0.64 ± 1.13) and bleed-related hospitalizations (1.86 ± 1.88 vs 0.81 ± 1.26), hemophilia-related consultations (9.30 ± 4.99 vs 6.77 ± 4.47), and outpatient visits (22.09 ± 17.77 vs 11.48 ± 16.00) (all, p < .001). More than one-half (53.5%) experienced moderate/severe pain necessitating medication compared to one-third (32.8%) of patients without inhibitors (p = .01). CONCLUSIONS:Patients with hemophilia and inhibitors exhibited greater clinical burden and higher resource utilization compared to their peers without inhibitors. Strategies for improving the standard of care may alleviate burden in this population