Exactly Solvable Balanced Tenable Urns with Random Entries via the Analytic Methodology

This paper develops an analytic theory for the study of some Polya urns with random rules. The idea is to extend the isomorphism theorem in Flajolet et al. (2006), which connects deterministic balanced urns to a differential system for the generating function. The methodology is based upon adaptation of operators and use of a weighted probability generating function. Systems of differential equations are developed, and when they can be solved, they lead to characterization of the exact distributions underlying the urn evolution. We give a few illustrative examples.Comment: 23rd International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'12), Montreal : Canada (2012

The oscillatory distribution of distances in random tries

We investigate \Delta_n, the distance between randomly selected pairs of nodes among n keys in a random trie, which is a kind of digital tree. Analytical techniques, such as the Mellin transform and an excursion between poissonization and depoissonization, capture small fluctuations in the mean and variance of these random distances. The mean increases logarithmically in the number of keys, but curiously enough the variance remains O(1), as n\to\infty. It is demonstrated that the centered random variable \Delta_n^*=\Delta_n-\lfloor2\log_2n\rfloor does not have a limit distribution, but rather oscillates between two distributions.Comment: Published at http://dx.doi.org/10.1214/105051605000000106 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

The effects of Saccharomyces cerevisiae supplementation on intake, nutrient digestibility, and rumen fluid pH in Awassi female lambs

Aim: The aim of this study was to evaluate the effect of feeding low (LO)- or high (HI)-fiber diets supplemented with Saccharomyces cerevisiae (SC) on nutrient intake, digestibility, nitrogen balance, rumen fluid pH, and serum concentrations of glucose and urea nitrogen in Awassi female lambs in a 2×2 factorial arrangement of treatments. Materials and Methods: Experimental diets were as follows: (1) LO-fiber diet with no SC supplementation (-LO), (2) LO-fiber diet supplemented with SC (+LO), (3) HI-fiber diet with no SC supplementation (-HI), or (4) HI-fiber diet supplemented with SC (+HI). Eight female lambs were used in a replicated 4×4 Latin square design with 15-day experimental periods (10-day adaptation period and 5-day collection period). Results: A fiber×SC interaction (p≤0.05) was detected for dry matter (DM) and crude protein (CP) intake among diets showing greater DM and CP intake for +LO diet compared to +HI group supplemented with SC, whereas -LO and -HI were intermediate. A fiber×SC interaction (p=0.05) was also detected for the neutral detergent fiber (NDF) intake among diets. Intake of NDF was greater for the -HI diet compared with +LO and -LO diets. Similarly, NDF intake was greater for +HI diet than -LO diet. A tendency (p=0.07) for a fiber×SC interaction was detected for acid detergent fiber (ADF) intake among diets as well. ADF intake tended to be greater for HI-fiber diets. No difference was observed in the rumen fluid pH for lambs fed with the different diets. No fiber×SC interactions were detected for the digestibility of DM, CP, NDF, and ADF among dietary treatments. Digestibility of DM was greater (72.9 g/100 g vs. 67.1 g/100 g; p=0.0002) for LO versus HI fiber. However, NDF and ADF digestibilities were greater (60.8 and 61.9 g/100 g vs. 55.8 and 52.7 g/100 g for NDF and ADF digestibility, respectively; p≤0.01) for the HI-fiber than the LO-fiber diets. Conclusion: Results obtained in the current study indicate that SC supplementation has a minimal effect on the performance of Awassi female lambs fed with varying fiber levels

Decline in subarachnoid haemorrhage volumes associated with the first wave of the COVID-19 pandemic

BACKGROUND: During the COVID-19 pandemic, decreased volumes of stroke admissions and mechanical thrombectomy were reported. The study\u27s objective was to examine whether subarachnoid haemorrhage (SAH) hospitalisations and ruptured aneurysm coiling interventions demonstrated similar declines. METHODS: We conducted a cross-sectional, retrospective, observational study across 6 continents, 37 countries and 140 comprehensive stroke centres. Patients with the diagnosis of SAH, aneurysmal SAH, ruptured aneurysm coiling interventions and COVID-19 were identified by prospective aneurysm databases or by International Classification of Diseases, 10th Revision, codes. The 3-month cumulative volume, monthly volumes for SAH hospitalisations and ruptured aneurysm coiling procedures were compared for the period before (1 year and immediately before) and during the pandemic, defined as 1 March-31 May 2020. The prior 1-year control period (1 March-31 May 2019) was obtained to account for seasonal variation. FINDINGS: There was a significant decline in SAH hospitalisations, with 2044 admissions in the 3 months immediately before and 1585 admissions during the pandemic, representing a relative decline of 22.5% (95% CI -24.3% to -20.7%, p\u3c0.0001). Embolisation of ruptured aneurysms declined with 1170-1035 procedures, respectively, representing an 11.5% (95%CI -13.5% to -9.8%, p=0.002) relative drop. Subgroup analysis was noted for aneurysmal SAH hospitalisation decline from 834 to 626 hospitalisations, a 24.9% relative decline (95% CI -28.0% to -22.1%, p\u3c0.0001). A relative increase in ruptured aneurysm coiling was noted in low coiling volume hospitals of 41.1% (95% CI 32.3% to 50.6%, p=0.008) despite a decrease in SAH admissions in this tertile. INTERPRETATION: There was a relative decrease in the volume of SAH hospitalisations, aneurysmal SAH hospitalisations and ruptured aneurysm embolisations during the COVID-19 pandemic. These findings in SAH are consistent with a decrease in other emergencies, such as stroke and myocardial infarction

Reducing the environmental impact of surgery on a global scale: systematic review and co-prioritization with healthcare workers in 132 countries

Abstract Background Healthcare cannot achieve net-zero carbon without addressing operating theatres. The aim of this study was to prioritize feasible interventions to reduce the environmental impact of operating theatres. Methods This study adopted a four-phase Delphi consensus co-prioritization methodology. In phase 1, a systematic review of published interventions and global consultation of perioperative healthcare professionals were used to longlist interventions. In phase 2, iterative thematic analysis consolidated comparable interventions into a shortlist. In phase 3, the shortlist was co-prioritized based on patient and clinician views on acceptability, feasibility, and safety. In phase 4, ranked lists of interventions were presented by their relevance to high-income countries and low–middle-income countries. Results In phase 1, 43 interventions were identified, which had low uptake in practice according to 3042 professionals globally. In phase 2, a shortlist of 15 intervention domains was generated. In phase 3, interventions were deemed acceptable for more than 90 per cent of patients except for reducing general anaesthesia (84 per cent) and re-sterilization of ‘single-use’ consumables (86 per cent). In phase 4, the top three shortlisted interventions for high-income countries were: introducing recycling; reducing use of anaesthetic gases; and appropriate clinical waste processing. In phase 4, the top three shortlisted interventions for low–middle-income countries were: introducing reusable surgical devices; reducing use of consumables; and reducing the use of general anaesthesia. Conclusion This is a step toward environmentally sustainable operating environments with actionable interventions applicable to both high– and low–middle–income countries