Random Graph-Homomorphisms and Logarithmic Degree

A graph homomorphism between two graphs is a map from the vertex set of one graph to the vertex set of the other graph, that maps edges to edges. In this note we study the range of a uniformly chosen homomorphism from a graph G to the infinite line Z. It is shown that if the maximal degree of G is `sub-logarithmic', then the range of such a homomorphism is super-constant. Furthermore, some examples are provided, suggesting that perhaps for graphs with super-logarithmic degree, the range of a typical homomorphism is bounded. In particular, a sharp transition is shown for a specific family of graphs C_{n,k} (which is the tensor product of the n-cycle and a complete graph, with self-loops, of size k). That is, given any function psi(n) tending to infinity, the range of a typical homomorphism of C_{n,k} is super-constant for k = 2 log(n) - psi(n), and is 3 for k = 2 log(n) + psi(n)

The Association Between Empirical Antibiotic Treatment and Mortality in Severe Infections Caused by Carbapenem-resistant Gram-negative Bacteria: A prospective study

Background. Empirical colistin should be avoided. We aimed to evaluate the association between covering empirical antibiotics (EAT) and mortality for infections caused by carbapenem-resistant gram-negative bacteria (CRGNB). Methods. This was a secondary analysis of a randomized controlled trial, including adults with bloodstream infections, pneumonia, or urosepsis caused by CRGNB. All patients received EAT followed by covering targeted therapy. The exposure variable was covering EAT in the first 48 hours. The outcome was 28-day mortality. We adjusted the analyses by multivariable regression analysis and propensity score matching. Results. The study included 406 inpatients with severe CRGNB infections, mostly Acinetobacter baumannii (312/406 [77%]). Covering EAT was given to 209 (51.5%) patients, mostly colistin (n = 200). Patients receiving noncovering EAT were older, more frequently unconscious and dependent, carrying catheters, and mechanically ventilated with pneumonia. Mortality was 84 of 197 (42.6%) with noncovering vs 96 of 209 (45.9%) with covering EAT (P = .504). Covering EAT was not associated with survival in the adjusted analysis; rather, there was a weak association with mortality (odds ratio [OR], 1.37; 95% confidence interval [CI], 1.02-1.84). Results were similar for colistin monotherapy and colistin-carbapenem combination EAT. In the propensity score-matched cohort (n = 338) covering antibiotics were not significantly associated with mortality (OR, 1.42; 95% CI, .91-2.22). Similar results were obtained in an analysis of 14-day mortality. Conclusions. Empirical use of colistin before pathogen identification, with or without a carbapenem, was not associated with survival following severe infections caused by CRGNBs, mainly A. baumannii. © The Author(s) 2018. Published by Oxford University Press for the Infectious Diseases Society of America. All rights reserved. For permissions, e-mail: [email protected]

Colistin resistance development following colistin-meropenem combination therapy versus colistin monotherapy in patients with infections caused by carbapenem-resistant organisms

Background. We evaluated whether carbapenem-colistin combination therapy reduces the emergence of colistin resistance, compared to colistin monotherapy, when given to patients with infections due to carbapenem-resistant Gram-negative organisms. Methods. This is a pre-planned analysis of a secondary outcome from a randomized, controlled trial comparing colistin monotherapy with colistin-meropenem combination for the treatment of severe infections caused by carbapenem-resistant, colistin-susceptible Gram-negative bacteria. We evaluated rectal swabs taken on Day 7 or later for the presence of new colistin-resistant (ColR) isolates. We evaluated the emergence of any ColR isolate and the emergence of ColR Enterobacteriaceae (ColR-E). Results. Data were available for 214 patients for the primary analysis; emergent ColR organisms were detected in 22 (10.3%). No difference was observed between patients randomized to treatment with colistin monotherapy (10/106, 9.4%) versus patients randomized to colistin-meropenem combination therapy (12/108, 11.1%; P = .669). ColR-E organisms were detected in 18/249 (7.2%) patients available for analysis. No difference was observed between the 2 treatment arms (colistin monotherapy 6/128 [4.7%] vs combination therapy 12/121 [9.9%]; P = .111). Enterobacteriaceae, as the index isolate, was found to be associated with development of ColR-E (hazard ratio, 3.875; 95% confidence interval, 1.475–10.184; P = .006). Conclusions. Carbapenem-colistin combination therapy did not reduce the incidence of colistin resistance emergence in patients with infections due to carbapenem-resistant organisms. Further studies are necessary to elucidate the development of colistin resistance and methods for its prevention. © The Author(s) 2019

Treatment Outcomes of Colistin- And Carbapenem-resistant Acinetobacter baumannii Infections: An Exploratory Subgroup Analysis of a Randomized Clinical Trial

Background: We evaluated the association between mortality and colistin resistance in Acinetobacter baumannii infections and the interaction with antibiotic therapy. Methods: This is a secondary analysis of a randomized controlled trial of patients with carbapenem-resistant gram-negative bacterial infections treated with colistin or colistin-meropenem combination. We evaluated patients with infection caused by carbapenem-resistant A. baumannii (CRAB) identified as colistin susceptible (CoS) at the time of treatment and compared patients in which the isolate was confirmed as CoS with those whose isolates were retrospectively identified as colistin resistant (CoR) when tested by broth microdilution (BMD). The primary outcome was 28-day mortality. Results: Data were available for 266 patients (214 CoS and 52 CoR isolates). Patients with CoR isolates had higher baseline functional capacity and lower rates of mechanical ventilation than patients with CoS isolates. All-cause 28-day mortality was 42.3% (22/52) among patients with CoR strains and 52.8% (113/214) among patients with CoS isolates (P =. 174). After adjusting for variables associated with mortality, the mortality rate was lower among patients with CoR isolates (odds ratio [OR], 0.285 [95% confidence interval {CI},. 118-.686]). This difference was associated with treatment arm: Mortality rates among patients with CoR isolates were higher in those randomized to colistin-meropenem combination therapy compared to colistin monotherapy (OR, 3.065 [95% CI, 1.021-9.202]). Conclusions: Colistin resistance determined by BMD was associated with lower mortality among patients with severe CRAB infections. Among patients with CoR isolates, colistin monotherapy was associated with a better outcome compared to colistin-meropenem combination therapy. Clinical Trials Registration: NCT01732250. © 2018 The Author(s) 2018

Colistin plus meropenem for carbapenem-resistant Gram-negative infections: in vitro synergism is not associated with better clinical outcomes

Objectives: In vitro models showing synergism between polymyxins and carbapenems support combination treatment for carbapenem-resistant Gram-negative (CRGN) infections. We tested the association between the presence of in vitro synergism and clinical outcomes in patients treated with colistin plus meropenem. Methods: This was a secondary analysis of AIDA, a randomized controlled trial comparing colistin with colistin–meropenem for severe CRGN infections. We tested in vitro synergism using a checkerboard assay. Based on the fractional inhibitory concentration (ΣFIC) index for each colistin–meropenem combination, we categorized results as synergistic, antagonistic or additive/indifferent. The primary outcome was clinical failure at 14 days. Secondary outcomes were 14- and 28-day mortality and microbiological failure. Results: The sample included 171 patients with infections caused by carbapenem-resistant Acinetobacter baumannii (n = 131), Enterobacteriaceae (n = 37) and Pseudomonas aeuruginosa (n = 3). In vitro testing showed synergism for 73 isolates, antagonism for 20 and additivism/indifference for 78. In patients who received any colistin plus meropenem, clinical failure at 14 days was 59/78 (75.6%) in the additivism/indifference group (reference category), 54/73 (74.0%) in the synergism group (adjusted odds ratio (aOR) 0.76, 95% CI 0.31–1.83), and 11/20 (55%) in the antagonism group (aOR 0.77, 95% CI 0.22–2.73). There was no significant difference between groups for any secondary outcome. Comparing the synergism group to patients treated with colistin monotherapy, synergism was not protective against 14-day clinical failure (aOR 0.52, 95% CI 0.26–1.04) or 14-day mortality (aOR1.09, 95% CI 0.60–1.96). Discussion: In vitro synergism between colistin and meropenem via checkerboard method did not translate into clinical benefit. © 2020 European Society of Clinical Microbiology and Infectious Disease