Simplicial Homology of Random Configurations

Given a Poisson process on a d-dimensional torus, its random geometric simplicial complex is the complex whose vertices are the points of the Poisson process and simplices are given by the C̆ech complex associated to the coverage of each point. By means of Malliavin calculus, we compute explicitly the three first-order moments of the number of k-simplices, and provide a way to compute higher-order moments. Then we derive the mean and the variance of the Euler characteristic. Using the Stein method, we estimate the speed of convergence of the number of occurrences of any connected subcomplex as it converges towards the Gaussian law when the intensity of the Poisson point process tends to infinity. We use a concentration inequality for Poisson processes to find bounds for the tail distribution of the Betti number of first order and the Euler characteristic in such simplicial complexes.

In vitro antimicrobial susceptibility of Helcococcus kunzii and molecular analysis of macrolide and tetracycline resistance

Thanks to the recent advent of matrix-assisted laser desorption/ionisation time-of-flight (MALDI-TOF) technology, Helcococcus kunzii is now easily identifiable and considered as an opportunistic pathogen. However, data about antimicrobial susceptibilities remain very limited. The aim of the study was, then, to assess its in vitro susceptibility to 18 antimicrobial agents and to investigate the genetic basis of macrolide and tetracycline resistance. Thirty-nine human clinical isolates of H. kunzii collected from 2008 to 2013 were studied, as well as the type strain ATCC 51366(T). Minimum inhibitory concentrations (MICs) of penicillin G, amoxicillin, cefotaxime, imipenem, gentamicin, erythromycin, clindamycin, quinupristin-dalfopristin, ciprofloxacin, levofloxacin, tetracycline, tigecycline, vancomycin, teicoplanin, linezolid, daptomycin, cotrimoxazole and rifampin were determined by the microdilution method. Screening for macrolide [erm(A) including erm(TR), erm(B), erm(C), erm(F), erm(T), erm(X), msr(A) and mef(A)] and tetracycline [tet(L), tet(M) and tet(O)] resistance genes was performed, as well as the detection of mutations in 23S rRNA. Except for one strain resistant to cefotaxime, all strains were categorised as susceptible to β-lactams, glycopeptides, linezolid, daptomycin and tigecycline. Whereas ciprofloxacin and gentamicin exhibited limited activity, 95% of strains were categorised as susceptible to levofloxacin. Concerning erythromycin, a bimodal distribution was observed, with 29 'wild-type' strains (MICs from 0.25 to 2 mg/L) and 11 'resistant' strains (MICs ≥ 256 mg/L), including ten harbouring erm(TR). Two isolates exhibited acquired tetracycline resistance (MICs of 16 mg/L) by the production of tet(M). This large study on the in vitro antimicrobial susceptibility of H. kunzii suggests that β-lactams (especially penicillins) should be preferred for the treatment.