Hopf algebras and Markov chains: Two examples and a theory

The operation of squaring (coproduct followed by product) in a combinatorial Hopf algebra is shown to induce a Markov chain in natural bases. Chains constructed in this way include widely studied methods of card shuffling, a natural "rock-breaking" process, and Markov chains on simplicial complexes. Many of these chains can be explictly diagonalized using the primitive elements of the algebra and the combinatorics of the free Lie algebra. For card shuffling, this gives an explicit description of the eigenvectors. For rock-breaking, an explicit description of the quasi-stationary distribution and sharp rates to absorption follow.Comment: 51 pages, 17 figures. (Typographical errors corrected. Further fixes will only appear on the version on Amy Pang's website, the arXiv version will not be updated.

Detector Description and Performance for the First Coincidence Observations between LIGO and GEO

For 17 days in August and September 2002, the LIGO and GEO interferometer gravitational wave detectors were operated in coincidence to produce their first data for scientific analysis. Although the detectors were still far from their design sensitivity levels, the data can be used to place better upper limits on the flux of gravitational waves incident on the earth than previous direct measurements. This paper describes the instruments and the data in some detail, as a companion to analysis papers based on the first data.Comment: 41 pages, 9 figures 17 Sept 03: author list amended, minor editorial change

A 62-minute orbital period black widow binary in a wide hierarchical triple

Over a dozen millisecond pulsars are ablating low-mass companions in close binary systems. In the original ‘black widow’, the eight-hour orbital period eclipsing pulsar PSR J1959+2048 (PSR B1957+20)1, high-energy emission originating from the pulsar2 is irradiating and may eventually destroy3 a low-mass companion. These systems are not only physical laboratories that reveal the interesting results of exposing a close companion star to the relativistic energy output of a pulsar, but are also believed to harbour some of the most massive neutron stars4, allowing for robust tests of the neutron star equation of state. Here we report observations of ZTF J1406+1222, a wide hierarchical triple hosting a 62-minute orbital period black widow candidate, the optical flux of which varies by a factor of more than ten. ZTF J1406+1222 pushes the boundaries of evolutionary models5, falling below the 80-minute minimum orbital period of hydrogen-rich systems. The wide tertiary companion is a rare low-metallicity cool subdwarf star, and the system has a Galactic halo orbit consistent with passing near the Galactic Centre, making it a probe of formation channels, neutron star kick physics6 and binary evolution

An Evaluation of the COVID-19 Pandemic and Perceived Social Distancing Policies in Relation to Planning, Selecting, and Preparing Healthy Meals: An Observational Study in 38 Countries Worldwide

Objectives: To examine changes in planning, selecting, and preparing healthy foods in relation to personal factors (time, money, stress) and social distancing policies during the COVID-19 crisis. Methods: Using cross-sectional online surveys collected in 38 countries worldwide in April-June 2020 (N = 37,207, Mage 36.7 SD 14.8, 77% women), we compared changes in food literacy behaviors to changes in personal factors and social distancing policies, using hierarchical multiple regression analyses controlling for sociodemographic variables. Results: Increases in planning (4.7 SD 1.3, 4.9 SD 1.3), selecting (3.6 SD 1.7, 3.7 SD 1.7), and preparing (4.6 SD 1.2, 4.7 SD 1.3) healthy foods were found for women and men, and positively related to perceived time availability and stay-at-home policies. Psychological distress was a barrier for women, and an enabler for men. Financial stress was a barrier and enabler depending on various sociodemographic variables (all p < 0.01). Conclusion: Stay-at-home policies and feelings of having more time during COVID-19 seem to have improved food literacy. Stress and other social distancing policies relate to food literacy in more complex ways, highlighting the necessity of a health equity lens. Copyright 2021 De Backer, Teunissen, Cuykx, Decorte, Pabian, Gerritsen, Matthys, Al Sabbah, Van Royen and the Corona Cooking Survey Study Group.This research was funded by the Research Foundation Flanders (G047518N) and Flanders Innovation and Entrepreneurship (HBC.2018.0397). These funding sources had no role in the design of the study, the analysis and interpretation of the data or the writing of, nor the decision to publish the manuscript.Scopu

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

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