We investigate the groups of units of one-relator and special inverse monoids. These are inverse monoids which are defined by presentations, where all the defining relations are of the form $r=1$. We develop new approaches for finding presentations for the group of units of a special inverse monoid, and apply these methods to give conditions under which the group admits a presentation with the same number of defining relations as the monoid. In particular, our results give sufficient conditions for the group of units of a one-relator inverse monoid to be a one-relator group. When these conditions are satisfied, these results give inverse semigroup theoretic analogues of classical results of Adjan for one-relator monoids, and Makanin for special monoids. In contrast, we show that in general these classical results do not hold for one-relator and special inverse monoids. In particular, we show that there exists a one-relator special inverse monoid whose group of units is not a one-relator group (with respect to any generating set), and we show that there exists a finitely presented special inverse monoid whose group of units is not finitely presented.

A prefix monoid is a finitely generated submonoid of a finitely presented group generated by the prefixes of its defining relators. Important results of Guba (1997), and of Ivanov, Margolis and Meakin (2001), show how the word problem for certain one-relator monoids, and inverse monoids, can be reduced to solving the membership problem in prefix monoids of certain one-relator groups. Motivated by this, in this paper, we study the class of prefix monoids of finitely presented groups. We obtain a complete description of this class of monoids. All monoids in this family are finitely generated, recursively presented and group-embeddable. Our results show that not every finitely generated recursively presented group-embeddable monoid is a prefix monoid, but for every such monoid, if we take a free product with a suitably chosen free monoid of finite rank, then we do obtain a prefix monoid. Conversely, we prove that every prefix monoid arises in this way. Also, we show that the groups that arise as groups of units of prefix monoids are precisely the finitely generated recursively presented groups, whereas the groups that arise as Schützenberger groups of prefix monoids are exactly the recursively enumerable subgroups of finitely presented groups. We obtain an analogous result classifying the Schützenberger groups of monoids of right units of special inverse monoids. We also give some examples of right cancellative monoids arising as monoids of right units of finitely presented special inverse monoids, and we show that not all right cancellative recursively presented monoids belong to this class.

Our recent review demonstrates that “purity” is a messy construct with at least nine popular scientific understandings. Cultural beliefs about self-control help unify some of these understandings, but much messiness remains. The harm-centric theory of dyadic morality suggests that purity violations can be comprehensively understood as abstract harms, acts perceived by some people (and not others) to indirectly cause suffering.

Background: Aeromonas is a gram-negative rod known to be present in water, sewage and soil which may cause infections especially in immunocompromised hosts. Cases of Aeromonas gastroenteritis have been associated with warmer weather. In total, 3 patients with extensively drug resistant (XDR) Aeromonas were identified at our facility between August and September 2022 on 2 intensive care units (ICUs). Our infection prevention, microbiology, and facility teams investigated these cases to determine whether a common source could be the mode of transmission. Methods: To first determine whether patients’ Aeromonas specimens were related, whole-genome sequencing (WGS) of the clinical isolates from 3 patients was performed using the Illumina DNA Prep Kit and Illumina MiSeq. Sequencing analysis was performed using CLC Genomics Workbench for de novo assembly, single-nucleotide polymorphisms (SNP) calling, and tree generation, Geneious Prime for reference-based assembly, annotation, and quality assessment, KmerFinder for reference identification, and the Comprehensive Antibiotic Resistance Database for resistance gene detection via protein homology. Chart review revealed that patients occupied multiple rooms between 2 ICUs (Fig. 1). Because water is a known source of Aeromonas, facility records were reviewed for water intrusion events. This analysis identified several cases in the affected patient and surrounding rooms. Sinks and faucets from 10 rooms were swabbed followed by direct plating on blood, MacConkey agar, and Aeromonas-selective cefsulodin-Irgasan-novobiocin (CIN) agar plates. Lastly, the city temperatures before and after positive cases were reviewed to identify whether any correlation could be shown between temperature and timing of infection. Results: WGS analysis revealed that the 3 Aeromonas isolates (all identified as A. hydrophila) were not directly related (minimum distance, 934 SNPs) and harbored between 4 and 19 unique antimicrobial resistance genes, including co-occurring carbapenemases VIM-2 and KPC-3 in 1 isolate and OXA-232 in another. Of the 20 environmental samples, few gram-negative nonfermenting bacteria and no Aeromonas isolates were detected (Fig. 1). Elevated city did loosely proceed patient cases of Aeromonas, suggesting a possible role of higher temperature, which may have promoted the growth of Aeromonas during the periods of the 3 cases and thus may contribute to the nosocomial infections (Fig. 2). Conclusions: Although our investigation did not reveal a definitive cause for the Aeromonas cases, it did show the importance prompt identification and investigation can have on mitigating the spread of a cluster. Our facility has not identified any additional nosocomial cases. Monitoring water intrusion events and plans for remediation continue to be a priority.

Disclosures: None

Background: Reflexive urine culturing, a strategy wherein urine cultures are only performed on samples with pyuria, is increasingly being used to reduce unnecessary urine cultures, healthcare costs, and inappropriate antibiotics. To support implementation of a reflexive urine-culture order for pediatric patients aged <18 years, we assessed the proportion of urine cultures that would be avoided with reflexive urine culturing, and we calculated the sensitivity and negative predictive value (NPV) of the ≥10 white blood cells (WBC) per high-powered field (HPF) threshold for diagnosing urinary tract infections (UTI) in patients aged <18 years who presented to the pediatric emergency department (ED). Methods: A retrospective review of patients <18 years with a urine culture performed from January to May 2022 in an urban, tertiary-care, pediatric ED was performed. A positive urine culture was defined as ≥50,000 CFU/mL for catheterized specimens and ≥100,000 CFU/mL for clean-catch or unspecified specimens. Pyuria was defined as ≥10 WBC/HPF. ‘True UTI’ was defined as a positive urine culture with a consistent clinical presentation (eg, fever or dysuria). Sensitivity, specificity, and NPV were calculated using the pyuria threshold of ≥10WBC/HPF compared to the gold standard of a ‘true UTI.’ Results: During the study period, 658 patients aged <18 years had urine cultures sent, of which 46 (7%) were positive. In all, 407 urine cultures (61.9%) were obtained by clean catch, 233 (35.4%) were obtained by urethral catheterization, 2 (0.3%) were obtained by Foley catheter, and 16 (2.4%) were unspecified. Among the 46 positive cultures, 32 (69.6%) had ≥10 WBC/HPF, and 55 (9.0%) of 612 negative cultures had ≥10 WBC/HPF. Of the 14 patients with positive urine cultures without pyuria, 8 had a contaminated sample or asymptomatic bacteriuria, 3 had urologic abnormalities, and 3 were infants aged <3 months. Of the 14 patients, 3 (21.4%) had a consistent clinical presentation for UTI and were treated with antibiotics: 2 were infants aged <3 months and 1 had urologic abnormalities. Using the ≥10 WBC/HPF threshold compared to ‘true UTI,’ sensitivity was 91.4%, specificity was 91.5%, positive predictive value was 36%, and NPV was 99.5%. Sensitivity and NPV increased to 100% when infants aged <3 months and urologic patients with positive urine culture were excluded. We estimated a cost saving of ~$200,000 had reflexive testing been in place. Conclusions: A reflexive urine culture for specimens with ≥10 WBC/HPF would have reduced the number of urine cultures substantially because 571 (86.8%) of 658 urine cultures would not have been performed. To prevent missed diagnoses of UTI, infants aged <3 months and children with urologic abnormalities should be excluded from this diagnostic stewardship intervention.

Disclosures: None