Let G be a finite transitive permutation group on $\Omega $. The G-invariant partitions form a sublattice of the lattice of all partitions of $\Omega $, having the further property that all its elements are uniform (that is, have all parts of the same size). If, in addition, all the equivalence relations defining the partitions commute, then the relations form an orthogonal block structure, a concept from statistics; in this case the lattice is modular. If it is distributive, then we have a poset block structure, whose automorphism group is a generalised wreath product. We examine permutation groups with these properties, which we call the OB property and PB property respectively, and in particular investigate when direct and wreath products of groups with these properties also have these properties.

A famous theorem on permutation groups asserts that a transitive imprimitive group G is embeddable in the wreath product of two factors obtained from the group (the group induced on a block by its setwise stabiliser, and the group induced on the set of blocks by G). We extend this theorem to groups with the PB property, embedding them into generalised wreath products. We show that the map from posets to generalised wreath products preserves intersections and inclusions.

We have included background and historical material on these concepts.

Background: During the COVID-19 pandemic, the rate of central line-associated bloodstream infections (CLABSI) decreased at the Veteran Affairs North Texas Health Care System. From fiscal year (FY) 2022 Quarter (Q)4 to FY2023 Q2, the CLABSI rate increased from 0 to 0.79 per 1,000 device days. Breaches in evidence-based practices for the maintenance of vascular access devices (VAD) were hypothesized to have contributed to the increase in CLABSI rate. Methods: In March 2023, a multidisciplinary workgroup was created with the primary goal of improving compliance with VAD standards of care to ≥ 95% by FY2023 Q4 and a secondary goal of decreasing CLABSI rates. A baseline assessment of 12 VAD insertion and maintenance process measures was developed using an assessment tool to record nurses’ observations and review documentation in the computerized patient record system. In addition, the facility VAD policy was updated, and nurses received competency training on VAD management. Baseline compliance data for the 12 VAD process measures was compared to data during the intervention period for acute and critical care areas. CLABSI rates (classified using the National Healthcare Safety Network surveillance criteria) were compared to the period before the creation of the workgroup, policy updates, and training. Results: Nurse observations in acute and critical care units during FY2023 were 19 (Q2), 1,284 (Q3), and 718 (Q4). From FY2023 Q2 to Q4, three of the 12 process measures met the ≥ 95% compliance goal by FY2023 Q4. The process measures that met the goal from Q2 to Q4 were clean peripheral IV catheter hub: 100% to 95.0%, unused tubing Y-sites capped with swap cap: 0% to 96.0%, and documentation of the last dressing change in CPRS: 0% to 99.0%. Notable increases were also seen for three other measures: appropriately dating of peripheral IV tubing: 78.9% to 88.0%, presence of Coban or kerlix occluding site: 0% to 46.0%, and documentation of device insertion: 0% to 89.0%. Persistent deficits were noted in the documentation of peripheral intravenous dressing dates and initials (compliance Conclusions: Enlisting a multidisciplinary team approach, including training, and updating VAD policy/procedures, led to a moderate improvement in VAD management compliance and a decline in CLABSI rates.

Next-generation X-ray satellite telescopes such as XRISM, NewAthena and Lynx will enable observations of exotic astrophysical sources at unprecedented spectral and spatial resolution. Proper interpretation of these data demands that the accuracy of the models is at least within the uncertainty of the observations. One set of quantities that might not currently meet this requirement is transition energies of various astrophysically relevant ions. Current databases are populated with many untested theoretical calculations. Accurate laboratory benchmarks are required to better understand the coming data. We obtained laboratory spectra of X-ray lines from a silicon plasma at an average spectral resolving power of $\sim$7500 with a spherically bent crystal spectrometer on the Z facility at Sandia National Laboratories. Many of the lines in the data are measured here for the first time. We report measurements of 53 transitions originating from the K-shells of He-like to B-like silicon in the energy range between $\sim$1795 and 1880 eV (6.6–6.9 Å). The lines were identified by qualitative comparison against a full synthetic spectrum calculated with ATOMIC. The average fractional uncertainty (uncertainty/energy) for all reported lines is ${\sim}5.4 \times 10^{-5}$. We compare the measured quantities against transition energies calculated with RATS and FAC as well as those reported in the NIST ASD and XSTAR’s uaDB. Average absolute differences relative to experimentally measured values are 0.20, 0.32, 0.17 and 0.38 eV, respectively. All calculations/databases show good agreement with the experimental values; NIST ASD shows the closest match overall.

The stars of the Milky Way carry the chemical history of our Galaxy in their atmospheres as they journey through its vast expanse. Like barcodes, we can extract the chemical fingerprints of stars from high-resolution spectroscopy. The fourth data release (DR4) of the Galactic Archaeology with HERMES (GALAH) Survey, based on a decade of observations, provides the chemical abundances of up to 32 elements for 917 588 stars that also have exquisite astrometric data from the Gaia satellite. For the first time, these elements include life-essential nitrogen to complement carbon, and oxygen as well as more measurements of rare-earth elements critical to modern-life electronics, offering unparalleled insights into the chemical composition of the Milky Way. For this release, we use neural networks to simultaneously fit stellar parameters and abundances across the whole wavelength range, leveraging synthetic grids computed with Spectroscopy Made Easy. These grids account for atomic line formation in non-local thermodynamic equilibrium for 14 elements. In a two-iteration process, we first fit stellar labels to all 1 085 520 spectra, then co-add repeated observations and refine these labels using astrometric data from Gaia and 2MASS photometry, improving the accuracy and precision of stellar parameters and abundances. Our validation thoroughly assesses the reliability of spectroscopic measurements and highlights key caveats. GALAH DR4 represents yet another milestone in Galactic archaeology, combining detailed chemical compositions from multiple nucleosynthetic channels with kinematic information and age estimates. The resulting dataset, covering nearly a million stars, opens new avenues for understanding not only the chemical and dynamical history of the Milky Way but also the broader questions of the origin of elements and the evolution of planets, stars, and galaxies.

This population-based cohort study examines the appropriateness of antibiotic prescribing in South Carolina via aggregated pharmacy claims data matched with diagnosis codes from medical claims. Inappropriate antibiotic prescribing decreased from 30.2% in 2012 to 22.6% in 2017 (P < 0.001) and was more common in adults >40 years old.

We examine the least squares approximation C to a symmetric matrix B, when all diagonal elements get weight w relative to all nondiagonal elements. WhenB has positivity p and C is constrained to be positive semi-definite, our main result states that, when w ≥1/2, then the rank of C is never greater than p, and when w ≤1/2 then the rank of C is at least p. For the problem of approximating a given n × n matrix with a zero diagonal by a squared-distance matrix, it is shown that the sstress criterion leads to a similar weighted least squares solution with w =(n+2)/4; the main result remains true. Other related problems and algorithmic consequences are briefly discussed.

Single crystal X-ray diffraction patterns reveal that the structure of selected anauxite crystals is the same as the structure of macroscopic kaolinite crystals. Anauxite and kaolinite crystals are intergrowths on a domain scale of units in pseudotwin orientations. Individual domains in anauxite have the triclinic geometry of kaolinite, and give X-ray reflections that compare closely in intensity with those calculated from the atomic parameters of kaolinite. Large crushed crystals of anauxite give powder patterns identical with that of kaolinite. Because it has been shown recently that the chemical composition of anauxite is also identical with that of kaolinite, it is recommended that the term “anauxite” no longer be used.