Automatic Quotients of Free Groups

Automatic groups admitting prefix closed automatic structures with uniqueness are characterized as the quotients of free groups by normal subgroups possessing sets of free generators satisfying certain language-theoretic conditions.Comment: 14 pages, no figures. Minor corrections. Statements of theorems and lemmas are unchange

Groups whose word problems are not semilinear

Suppose that G is a finitely generated group and W is the formal language of words defining the identity in G. We prove that if G is a nilpotent group, the fundamental group of a finite volume hyperbolic three-manifold, or a right-angled Artin group whose graph lies in a certain infinite class, then W is not a multiple context free language

Comparison of sputum collection methods for tuberculosis diagnosis: a systematic review and pairwise and network meta-analysis

Background The performance of laboratory tests to diagnose pulmonary tuberculosis is dependent on the quality of the sputum sample tested. The relative merits of sputum collection methods to improve tuberculosis diagnosis are poorly characterised. We therefore aimed to investigate the effects of sputum collection methods on tuberculosis diagnosis. Methods We did a systematic review and meta-analysis to investigate whether non-invasive sputum collection methods in people aged at least 12 years improve the diagnostic performance of laboratory testing for pulmonary tuberculosis. We searched PubMed, Google Scholar, ProQuest, Web of Science, CINAHL, and Embase up to April 14, 2017, to identify relevant experimental, case-control, or cohort studies. We analysed data by pairwise meta-analyses with a random-effects model and by network meta-analysis. All diagnostic performance data were calculated at the sputum-sample level, except where authors only reported data at the individual patient-level. Heterogeneity was assessed, with potential causes identified by logistic meta-regression. Findings We identified 23 eligible studies published between 1959 and 2017, involving 8967 participants who provided 19 252 sputum samples. Brief, on-demand spot sputum collection was the main reference standard. Pooled sputum collection increased tuberculosis diagnosis by microscopy (odds ratio [OR] 1·6, 95% CI 1·3–1·9, p<0·0001) or culture (1·7, 1·2–2·4, p=0·01). Providing instructions to the patient before sputum collection, during observed collection, or together with physiotherapy assistance increased diagnostic performance by microscopy (OR 1·6, 95% CI 1·3–2·0, p<0·0001). Collecting early morning sputum did not significantly increase diagnostic performance of microscopy (OR 1·5, 95% CI 0·9–2·6, p=0·2) or culture (1·4, 0·9–2·4, p=0·2). Network meta-analysis confirmed these findings, and revealed that both pooled and instructed spot sputum collections were similarly effective techniques for increasing the diagnostic performance of microscopy. Interpretation Tuberculosis diagnoses were substantially increased by either pooled collection or by providing instruction on how to produce a sputum sample taken at any time of the day. Both interventions had a similar effect to that reported for the introduction of new, expensive laboratory tests, and therefore warrant further exploration in the drive to end the global tuberculosis epidemic