Recent works at the interface of algebraic combinatorics, algebraic geometry, number theory and topology have provided new integer-valued invariants on integer partitions. It is natural to consider the distribution of partitions when sorted by these invariants in congruence classes. We consider the prominent situations that arise from extensions of the Nekrasov–Okounkov hook product formula and from Betti numbers of various Hilbert schemes of n points on ${\mathbb {C}}^2$ . For the Hilbert schemes, we prove that homology is equidistributed as $n\to \infty $ . For t-hooks, we prove distributions that are often not equidistributed. The cases where $t\in \{2, 3\}$ stand out, as there are congruence classes where such counts are zero. To obtain these distributions, we obtain analytic results of independent interest. We determine the asymptotics, near roots of unity, of the ubiquitous infinite products

$$ \begin{align*}F_1(\xi; q):=\prod_{n=1}^{\infty}\left(1-\xi q^n\right), \ \ \ F_2(\xi; q):=\prod_{n=1}^{\infty}\left(1-(\xi q)^n\right) \ \ \ {\mathrm{and}}\ \ \ F_3(\xi; q):=\prod_{n=1}^{\infty}\left(1-\xi^{-1}(\xi q)^n\right). \end{align*} $$

Background: Nursing home (NH) residents and staff were at high risk for COVID-19 early in the pandemic; several studies estimated seroprevalence of infection in NH staff to be 3-fold higher among CNAs and nurses compared to other staff. Risk mitigation added in Fall 2020 included systematic testing of residents and staff (and furlough if positive) to reduce transmission risk. We estimated risks for SARS-CoV-2 infection among NH staff during the first winter surge before widespread vaccination. Methods: Between February and May 2021, voluntary serologic testing was performed on NH staff who were seronegative for SARS-CoV-2 in late Fall 2020 (during a previous serology study at 14 Georgia NHs). An exposure assessment at the second time point covered prior 3 months of job activities, community exposures, and self-reported COVID-19 vaccination, including very recent vaccination (≤4 weeks). Risk factors for seroconversion were estimated by job type using multivariable logistic regression, accounting for interval community-incidence and interval change in resident infections per bed. Results: Among 203 eligible staff, 72 (35.5%) had evidence of interval seroconversion (Fig. 1). Among 80 unvaccinated staff, interval infection was significantly higher among CNAs and nurses (aOR, 4.9; 95% CI, 1.4–20.7) than other staff, after adjusting for race and interval community incidence and facility infections. This risk persisted but was attenuated when utilizing the full study cohort including those with very recent vaccination (aOR, 1.8; 95% CI, 0.9–3.7). Conclusions: Midway through the first year of the pandemic, NH staff with close or common resident contact continued to be at increased risk for infection despite enhanced infection prevention efforts. Mitigation strategies, prior to vaccination, did not eliminate occupational risk for infection. Vaccine utilization is critical to eliminate occupational risk among frontline healthcare providers.

Funding: None

Disclosures: None

The impact of influenza and pneumonia on individuals in clinical risk groups in England has not previously been well characterized. Using nationally representative linked databases (Clinical Practice Research Database (CPRD), Hospital Episode Statistics (HES) and Office for National Statistics (ONS)), we conducted a retrospective cohort study among adults (≥ 18 years) during the 2010/2011–2019/2020 influenza seasons to estimate the incidence of influenza- and pneumonia-diagnosed medical events (general practitioner (GP) diagnoses, hospitalisations and deaths), stratified by age and risk conditions. The study population included a seasonal average of 7.2 million individuals; approximately 32% had ≥1 risk condition, 42% of whom received seasonal influenza vaccines. Medical event incidence rates increased with age, with ~1% of adults aged ≥75 years hospitalized for influenza/pneumonia annually. Among individuals with vs. without risk conditions, GP diagnoses occurred 2–5-fold more frequently and hospitalisations were 7–10-fold more common. Among those with obesity, respiratory, kidney or cardiovascular disorders, hospitalisation were 5–40-fold more common than in individuals with no risk conditions. Though these findings likely underestimate the full burden of influenza, they emphasize the concentration of disease burden in specific age and risk groups and support existing recommendations for influenza vaccination.

As practitioners of a historical science, paleontologists and geoscientists are well versed in the idea that the ability to understand and to anticipate the future relies upon our collective knowledge of the past. Despite this understanding, the fundamental role that the history of paleontology and the geosciences plays in shaping the structure and culture of our disciplines is seldom recognized and therefore not acted upon sufficiently. Here, we present a brief review of the history of paleontology and geology in Western countries, with a particular focus on North America since the 1800s. Western paleontology and geology are intertwined with systematic practices of exclusion, oppression, and erasure that arose from their direct participation in the extraction of geological and biological resources at the expense of Black, Indigenous, and People of Color (BIPOC). Our collective failure to acknowledge this history hinders our ability to address these issues meaningfully and systemically in present-day educational, academic, and professional settings. By discussing these issues and suggesting some ways forward, we intend to promote a deeper reflection upon our collective history and a broader conversation surrounding racism, colonialism, and exclusion within our scientific communities. Ultimately, it is necessary to listen to members of the communities most impacted by these issues to create actionable steps forward while holding ourselves accountable for the past.

Ethnohistoric accounts indicate that the people of Australia's Channel Country engaged in activities rarely recorded elsewhere on the continent, including food storage, aquaculture and possible cultivation, yet there has been little archaeological fieldwork to verify these accounts. Here, the authors report on a collaborative research project initiated by the Mithaka people addressing this lack of archaeological investigation. The results show that Mithaka Country has a substantial and diverse archaeological record, including numerous large stone quarries, multiple ritual structures and substantial dwellings. Our archaeological research revealed unknown aspects, such as the scale of Mithaka quarrying, which could stimulate re-evaluation of Aboriginal socio-economic systems in parts of ancient Australia.

Greenland's future contribution to sea-level rise is strongly dependent on the extent to which dynamic perturbations, originating at the margin, can drive increased ice flow within the ice-sheet interior. However, reported observations of ice dynamical change at distances >~50 km from the margin have a very low spatial and temporal resolution. Consequently, the likely response of the ice-sheet's interior to future oceanic and atmospheric warming is poorly constrained. Through combining GPS and satellite-image-derived ice velocity measurements, we measure multi-decadal (1993–1997 to 2014–2018) velocity change at 45 inland sites, encompassing all regions of the ice sheet. We observe an almost ubiquitous acceleration inland of tidewater glaciers in west Greenland, consistent with acceleration and retreat at glacier termini, suggesting that terminus perturbations have propagated considerable distances (>100 km) inland. In contrast, outside of Kangerlussuaq, we observe no acceleration inland of tidewater glaciers in east Greenland despite terminus retreat and near-terminus acceleration, and suggest propagation may be limited by the influence of basal topography and ice geometry. This pattern of inland dynamical change indicates that Greenland's future contribution to sea-level will be spatially complex and will depend on the capacity for dynamic changes at individual outlet glacier termini to propagate inland.

Loeys–Dietz syndrome is a connective tissue disorder known to cause aggressive aortopathy in paediatric patients, but it is extremely rare for cardiovascular events to present during infancy. We report the first successful aortic repair in a neonate with LDS presenting in extremis with an early onset, massive aortic aneurysm.

Philosophers, archeologists, and other heritage professionals often take a rather negative view of heritage reconstruction, holding that it is inappropriate or even impermissible. In this essay, we argue that taking such hardline attitudes toward the reconstruction of heritage is unjustified. To the contrary, we believe that the reconstruction of heritage can be both permissible and beneficial, all things considered. In other words, sometimes we have good reasons, on balance, to pursue reconstructions, and doing so can be morally acceptable. In defending this claim, we discern a number of arguments made against heritage reconstruction and demonstrate that these arguments are either exaggerated or lack support.

We report electronic medical record interventions to reduce Clostridioides difficile testing risk ‘alert fatigue.’ We used a behavioral approach to diagnostic stewardship and observed a decrease in the number of tests ordered of ~4.5 per month (P < .0001). Although the number of inappropriate tests decreased during the study period, delayed testing increased.

On 30 September 2017, an Air France Airbus A380-800 suffered a failure of its fourth engine while over Greenland. This failure resulted in the loss of the engine fan hub, fan blades and surrounding structure. An initial search recovered 30 pieces of light debris, but the primary part of interest, a ~220 kg titanium fan hub, was not recovered because it had a different fall trajectory than the light debris, impacted into the ice-sheet's snow surface, and was quickly covered by drifting snow. Here we describe the methods used for the detection of the fan hub and details of the field campaigns. The search area included two crevasse fields of at least 50 snow-covered crevasses 1 to ~30 m wide with similar snow bridge thicknesses. After 21 months and six campaigns, using airborne synthetic aperture radar, ground-penetrating radar, transient electromagnetics and an autonomous vehicle to survey the crevasse fields, the fan hub was found within ~1 m of a crevasse at a depth of ~3.3 to 4 m and was excavated with shovels, chain saws, an electric winch, sleds and a gasoline heater, by workers using fall-arrest systems.