Central Paths and Selection of Equilibria

For two populations of players playing repeatedly a same bimatrix game, a dynamics associated with the method of analytic centers for linear programming is described. All populations' evolutions converge to static equilibria. All evolutions starting in a same connected set converge to a same equilibrium. If a starting time is sufficiently large, "almost all" evolutions end up at a single equilibrium representing all populations' pure strategy groups (phenotypes) with nonzero proportions. The dynamics is interpreted as populations' rule to learn best replying

Central Path Curvature and Iteration-Complexity for Redundant Klee—Minty Cubes

We consider a family of linear optimization problems over the n-dimensional Klee—Minty cube and show that the central path may visit all of its vertices in the same order as simplex methods do. This is achieved by carefully adding an exponential number of redundant constraints that forces the central path to take at least 2n − 2 sharp turns. This fact sug-gests that any feasible path-following interior-point method will take at least O(2n) iterations to solve this problem, whereas in practice typically only a few iterations (e.g., 50) suffices to obtain a high-quality solution. Thus, the construction potentially exhibits the worst-case iteration-complexity known to date which almost matches the theoretical iteration-complexity bound for this type of methods. In addition, this construction gives a counterexample to a conjecture that the total central path curvature is O(n)

High prevalence of oxacillinases in clinical multidrug-resistant Acinetobacter baumannii isolates from the Tshwane region, South Africa – an update

BACKGROUND : Acinetobacter baumannii is an important hospital-acquired pathogen in healthcare facilities that frequently causes bacteraemia and ventilator-associated pneumonia in intensive care units. Acinetobacter baumannii can be isolated from various sites in the hospital environment like medical equipment, bed linen, medical personnel and indwelling catheters. It is difficult to treat A. baumannii infections because of their highly resistant antimicrobial profiles. The purpose of this study was to determine the prevalence of β-lactamase genes in multidrug-resistant (MDR) clinical A. baumannii isolates using Multiplex-PCR (M-PCR) assays. METHODS : One hundred MDR A. baumannii isolates were collected from the diagnostic division of the Department of Medical Microbiology after routine analysis of the submitted specimens. All collected isolates were identified and tested for susceptibility using the VITEK 2® system (bioMérieux, France). Six isolates were excluded from this study because the isolates were incorrectly identified as A. baumannii with the VITEK 2® system (bioMérieux, France). Molecular tests, namely M-PCR assays, pulsed-field gel electrophoresis (PFGE) and multilocus sequence typing (MLST) were performed. MLST analyses were performed on representative isolates from the four major pulsotypes (≥5 isolates with 80 % similarity) and selective isolates from each minor pulsotype. RESULTS : All the A. baumannii isolates showed 100 % resistance to ampicillin, amoxicillin, cefuroxime, cefuroximine axetil, cefoxitin, cefotaxime and nitrofurantoin. Seven percent of the isolates were resistant to amikacin. Two percent of the isolates were classified as having intermediate susceptibility to tigecycline. A. baumannii isolates showed an antibiotic resistance profile of 67 % and higher to antibiotics, such as ceftazidime, cefepime, imipenem, meropenem, gentamicin, ciprofloxacin and trimethoprim/sulfamethoxazole. None of the isolates were resistant to colistin. The M-PCR assays showed that 99 % of the isolates contained the OXA-51 gene and 77 % contained the OXA-23 gene. None of the isolates contained the GES, GIM, IMP, KPC, NDM, OXA-24, OXA-58, PER, SIM, SPM, VEB and VIM genes. Representative A. baumannii isolates were grouped into five existing sequence types (ST): ST106, ST258, ST339, ST502, ST758 and ST848. Isolates belonging to the pan-European clonal lineages I and II (EUI and EUII) were identified. CONCLUSION : The high prevalence of MDR A. baumannii isolates has a severe impact on available treatment choices and this in return impacts on treatment outcomes in the studied healthcare facilities. The most dominant ST among the collected isolates was ST758, member of the EUI group. The presence of the OXA-23 gene was not restricted to a specific ST. Continuous research and surveillance is necessary to monitor the circulating β-lactamase genes in clinical settings to guide infection control policies in order to try and curb the spread of this bacterium.ML was supported by a National Research Foundation (NRF) grant. The MALDI-TOF analysis is based on research supported in part by the National Research Foundation (NRF) of South Africa (Grant specific unique reference number (UID) 74426).http://www.biomedcentral.com/bmcinfectdis/am201