Polytopes associated to Dihedral Groups

In this note we investigate the convex hull of those $n \times n$-permutation matrices that correspond to symmetries of a regular $n$-gon. We give the complete facet description. As an application, we show that this yields a Gorenstein polytope, and we determine the Ehrhart $h^*$-vector

Permutation Polytopes of Cyclic Groups

We investigate the combinatorics and geometry of permutation polytopes associated to cyclic permutation groups, i.e., the convex hulls of cyclic groups of permutation matrices. We give formulas for their dimension and vertex degree. In the situation that the generator of the group consists of at most two orbits, we can give a complete combinatorial description of the associated permutation polytope. In the case of three orbits the facet structure is already quite complex. For a large class of examples we show that there exist exponentially many facets.Comment: 15 page

Permutation Polytopes of Cyclic Groups

We investigate the combinatorics and geometry of permutation polytopes associated to cyclic permutation groups, i.e., the convex hulls of cyclic groups of permutation matrices. In the situation that the generator of the group consists of at most two orbits, we can give a complete combinatorial description of the associated permutation polytope. In the case of three orbits the facet structure is already quite complex. For a large class of examples we show that there exist exponentially many facets

Protocol-Driven Initiation and Weaning of High-Flow Nasal Cannula for Patients With Bronchiolitis: A Quality Improvement Initiative*

ObjectivesBronchiolitis is the most common cause for nonelective infant hospitalization in the United States with increasing utilization of high-flow nasal cannula (HFNC). We standardized initiation and weaning of HFNC for bronchiolitis and quantified the impact on outcomes. Our specific aim was to reduce hospital and ICU length of stay (LOS) by 10% between two bronchiolitis seasons after implementation.DesignA quality improvement (QI) project using statistical process control methodology.SettingTertiary-care children's hospital with 24 PICU and 48 acute care pediatric beds.PatientsChildren less than 24 months old with bronchiolitis without other respiratory diagnoses or underlying cardiac, respiratory, or neuromuscular disorders between December 2017 and November 2018 (baseline), and December 2018 and February 2020 (postintervention).InterventionsInterventions included development of an HFNC protocol with initiation and weaning guidelines, modification of protocol and respiratory assessment classification, education, and QI rounds with a focus on efficient HFNC weaning, transfer, and/or discharge.Measurements and main resultsA total of 223 children were included (96 baseline and 127 postintervention). The primary outcome metric, average LOS per patient, decreased from 4.0 to 2.8 days, and the average ICU LOS per patient decreased from 2.8 to 1.9 days. The secondary outcome metric, average HFNC treatment hours per patient, decreased from 44.0 to 36.3 hours. The primary and secondary outcomes met criteria for special cause variation. Balancing measures included ICU readmission rates, 30-day readmission rates, and adverse events, which were not different between the two periods.ConclusionsA standardized protocol for HFNC management for patients with bronchiolitis was associated with decreased hospital and ICU LOS, less time on HFNC, and no difference in readmissions or adverse events