Linearly-Used Continuations in the Enriched Effect Calculus

Under non-commutative Stone duality, there is a correspondence between second countable Hausdorff \'etale groupoids which have a Cantor space of identities and what we call Tarski inverse monoids: that is, countable Boolean inverse $\wedge$-monoids with semilattices of idempotents which are countable and atomless. Tarski inverse monoids are therefore the algebraic counterparts of the \'etale groupoids studied by Matui and provide a natural setting for many of his calculations. Under this duality, we prove that natural properties of the \'etale groupoid correspond to natural algebraic properties of the Tarski inverse monoid: effective groupoids correspond to fundamental Tarski inverse monoids and minimal groupoids correspond to $0$-simplifying Tarski inverse monoids. Particularly interesting are the principal groupoids which correspond to Tarski inverse monoids where every element is a finite join of infinitesimals and idempotents. Here an infinitesimal is simply a non-zero element with square zero. Such inverse monoids are natural infinite generalizations of finite symmetric inverse monoids. The groups of units of fundamental Tarski inverse monoids generalize the finite symmetric groups and include amongst their number the Thompson groups $G_{n,1}$ as well as the groups of units of what we term AF inverse monoids, Krieger's ample groups being examples. We characterize such groups as subgroups of particular kinds of the group of homeomorphisms of the Cantor space.Comment: arXiv admin note: substantial text overlap with arXiv:1407.147

Linear-use CPS translations in the enriched effect calculus

Vol. 8(4:2)2012, pp. 1–27 www.lmcs-online.or

The enriched effect calculus: syntax and semantics

This paper introduces the enriched effect calculus, which extends established type theories for computational effects with primitives from linear logic. The new calculus provides a formalism for expressing linear aspects of computational effects; for example, the linear usage of imperative features such as state and/or continuations. The enriched effect calculus is implemented as an extension of a basic effect calculus without linear primitives, which is closely related to Moggi’s computational metalanguage, Filinski’s effect PCF and Levy’s call-by-push-value. We present syntactic results showing: the fidelity of the behaviour of the linear connectives of the enriched effect calculus; the conservativity of the enriched effect calculus over its non-linear core (the effect calculus); and the non-conservativity of intuitionistic linear logic when considered as an extension of the enriched effect calculus. The second half of the paper investigates models for the enriched effect calculus, based on enriched category theory. We give several examples of such models, relating them to models of standard effect calculi (such as those based on monads), and to models of intuitionistic linear logic. We also prove soundness and completeness.

The 2021 WHO catalogue of Mycobacterium tuberculosis complex mutations associated with drug resistance: a genotypic analysis.

Background: Molecular diagnostics are considered the most promising route to achievement of rapid, universal drug susceptibility testing for Mycobacterium tuberculosis complex (MTBC). We aimed to generate a WHO-endorsed catalogue of mutations to serve as a global standard for interpreting molecular information for drug resistance prediction. Methods: In this systematic analysis, we used a candidate gene approach to identify mutations associated with resistance or consistent with susceptibility for 13 WHO-endorsed antituberculosis drugs. We collected existing worldwide MTBC whole-genome sequencing data and phenotypic data from academic groups and consortia, reference laboratories, public health organisations, and published literature. We categorised phenotypes as follows: methods and critical concentrations currently endorsed by WHO (category 1); critical concentrations previously endorsed by WHO for those methods (category 2); methods or critical concentrations not currently endorsed by WHO (category 3). For each mutation, we used a contingency table of binary phenotypes and presence or absence of the mutation to compute positive predictive value, and we used Fisher's exact tests to generate odds ratios and Benjamini-Hochberg corrected p values. Mutations were graded as associated with resistance if present in at least five isolates, if the odds ratio was more than 1 with a statistically significant corrected p value, and if the lower bound of the 95% CI on the positive predictive value for phenotypic resistance was greater than 25%. A series of expert rules were applied for final confidence grading of each mutation. Findings: We analysed 41 137 MTBC isolates with phenotypic and whole-genome sequencing data from 45 countries. 38 215 MTBC isolates passed quality control steps and were included in the final analysis. 15 667 associations were computed for 13 211 unique mutations linked to one or more drugs. 1149 (7·3%) of 15 667 mutations were classified as associated with phenotypic resistance and 107 (0·7%) were deemed consistent with susceptibility. For rifampicin, isoniazid, ethambutol, fluoroquinolones, and streptomycin, the mutations' pooled sensitivity was more than 80%. Specificity was over 95% for all drugs except ethionamide (91·4%), moxifloxacin (91·6%) and ethambutol (93·3%). Only two resistance mutations were identified for bedaquiline, delamanid, clofazimine, and linezolid as prevalence of phenotypic resistance was low for these drugs. Interpretation: We present the first WHO-endorsed catalogue of molecular targets for MTBC drug susceptibility testing, which is intended to provide a global standard for resistance interpretation. The existence of this catalogue should encourage the implementation of molecular diagnostics by national tuberculosis programmes. Funding: Unitaid, Wellcome Trust, UK Medical Research Council, and Bill and Melinda Gates Foundation