A quasi-tree is a geodesic metric space quasi-isometric to a tree. We give a general construction of many actions of groups on quasitrees. The groups we can handle include non-elementary (relatively) hyperbolic groups, CAT (0) groups with rank 1 elements, mapping class groups and Out(F n ). As an application, we show that mapping class groups act on finite products of δ-hyperbolic spaces so that orbit maps are quasi-isometric embeddings. We prove that mapping class groups have finite asymptotic dimension.
The density conjecture of Bers, Sullivan and Thurston predicts that each complete hyperbolic 3-manifold M with finitely generated fundamental group is an algebraic limit of geometrically finite hyperbolic 3-manifolds. We prove that the conjecture obtains for each complete hyperbolic 3manifold with no cusps and incompressible ends.
An accurate system of identifying and classifying suspected measles cases is critical for the measles surveillance system in the United States. To examine the performance of the clinical case definition in predicting laboratory confirmation of suspected cases of measles, we reviewed 4 studies conducted between 1981 and 1994. A clinical case definition was examined that included a generalized maculopapular rash, fever (>or=38.3 degrees C, if measured), and either a cough, coryza, or conjunctivitis. Serological confirmation of measles was done either by hemagglutination inhibition assay, complement fixation assay, or enzyme immunoassays. The positive predictive value of the clinical case definition decreased from 74% to 1% as incidence decreased from 171 cases/100000 population to 1.3 cases/100000 population. Sensitivity was high, and for the larger studies with the most precise estimates, sensitivity was 76%-88%. The low positive predictive value of the clinical case definition in settings of low incidence demonstrates that serological confirmation is essential to ensure an accurate diagnosis of measles when measles is rare.
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