Kustaanheimo-Stiefel Regularization and the Quadrupolar Conjugacy

In this note, we present the Kustaanheimo-Stiefel regularization in a symplectic and quaternionic fashion. The bilinear relation is associated with the moment map of the $S^{1}$- action of the Kustaanheimo-Stiefel transformation, which yields a concise proof of the symplecticity of the Kustaanheimo-Stiefel transformation symplectically reduced by this circle action. The relation between the Kustaanheimo-Stiefel regularization and the Levi-Civita regularization is established via the investigation of the Levi-Civita planes. A set of Darboux coordinates (which we call Chenciner-F\'ejoz coordinates) is generalized from the planar case to the spatial case. Finally, we obtain a conjugacy relation between the integrable approximating dynamics of the lunar spatial three-body problem and its regularized counterpart, similar to the conjugacy relation between the extended averaged system and the averaged regularized system in the planar case.Comment: 19 pages, corrected versio

Piecewise Linear Models for the Quasiperiodic Transition to Chaos

We formulate and study analytically and computationally two families of piecewise linear degree one circle maps. These families offer the rare advantage of being non-trivial but essentially solvable models for the phenomenon of mode-locking and the quasi-periodic transition to chaos. For instance, for these families, we obtain complete solutions to several questions still largely unanswered for families of smooth circle maps. Our main results describe (1) the sets of maps in these families having some prescribed rotation interval; (2) the boundaries between zero and positive topological entropy and between zero length and non-zero length rotation interval; and (3) the structure and bifurcations of the attractors in one of these families. We discuss the interpretation of these maps as low-order spline approximations to the classic ``sine-circle'' map and examine more generally the implications of our results for the case of smooth circle maps. We also mention a possible connection to recent experiments on models of a driven Josephson junction.Comment: 75 pages, plain TeX, 47 figures (available on request

Prognostic model to predict postoperative acute kidney injury in patients undergoing major gastrointestinal surgery based on a national prospective observational cohort study.

Background: Acute illness, existing co-morbidities and surgical stress response can all contribute to postoperative acute kidney injury (AKI) in patients undergoing major gastrointestinal surgery. The aim of this study was prospectively to develop a pragmatic prognostic model to stratify patients according to risk of developing AKI after major gastrointestinal surgery. Methods: This prospective multicentre cohort study included consecutive adults undergoing elective or emergency gastrointestinal resection, liver resection or stoma reversal in 2-week blocks over a continuous 3-month period. The primary outcome was the rate of AKI within 7 days of surgery. Bootstrap stability was used to select clinically plausible risk factors into the model. Internal model validation was carried out by bootstrap validation. Results: A total of 4544 patients were included across 173 centres in the UK and Ireland. The overall rate of AKI was 14·2 per cent (646 of 4544) and the 30-day mortality rate was 1·8 per cent (84 of 4544). Stage 1 AKI was significantly associated with 30-day mortality (unadjusted odds ratio 7·61, 95 per cent c.i. 4·49 to 12·90; P < 0·001), with increasing odds of death with each AKI stage. Six variables were selected for inclusion in the prognostic model: age, sex, ASA grade, preoperative estimated glomerular filtration rate, planned open surgery and preoperative use of either an angiotensin-converting enzyme inhibitor or an angiotensin receptor blocker. Internal validation demonstrated good model discrimination (c-statistic 0·65). Discussion: Following major gastrointestinal surgery, AKI occurred in one in seven patients. This preoperative prognostic model identified patients at high risk of postoperative AKI. Validation in an independent data set is required to ensure generalizability

The socioeconomic impact of tuberculosis on children and adolescents : a scoping review and conceptual framework

Background: Tuberculosis (TB) has been repeatedly shown to have socioeconomic impacts in both individual-level and ecological studies; however, much less is known about this effect among children and adolescents and the extent to which being affected by TB during childhood and adolescence can have life-course implications. This paper describes the results of the development of a conceptual framework and scoping review to review the evidence on the short- and long-term socioeconomic impact of tuberculosis on children and adolescents. Objectives: To increase knowledge of the socioeconomic impact of TB on children and adolescents. Methods: We developed a conceptual framework of the socioeconomic impact of TB on children and adolescents, and used scoping review methods to search for evidence supporting or disproving it. We searched four academic databases from 1 January 1990 to 6 April 2021 and conducted targeted searches of grey literature. We extracted data using a standard form and analysed data thematically. Results: Thirty-six studies (29 qualitative, five quantitative and two mixed methods studies) were included in the review. Overall, the evidence supported the conceptual framework, suggesting a severe socioeconomic impact of TB on children and adolescents through all the postulated pathways. Effects ranged from impoverishment, stigma, and family separation, to effects on nutrition and missed education opportunities. TB did not seem to exert a different socioeconomic impact when directly or indirectly affecting children/adolescents, suggesting that TB can affect this group even when they are not affected by the disease. No study provided sufficient follow-up to observe the long-term socioeconomic effect of TB in this age group. Conclusion: The evidence gathered in this review reinforces our understanding of the impact of TB on children and adolescents and highlights the importance of considering effects during the entire life course. Both ad-hoc and sustainable social protection measures and strategies are essential to mitigate the socioeconomic consequences of TB among children and adolescents.publishedVersionPeer reviewe

The effects of social determinants of health on acquired immune deficiency syndrome in a low-income population of Brazil: a retrospective cohort study of 28.3 million individuals.

BACKGROUND: Social determinants of health (SDH) include factors such as income, education, and race, that could significantly affect the human immunodeficiency virus and acquired immunodeficiency syndrome (HIV/AIDS). Studies on the effects of SDH on HIV/AIDS are limited, and do not yet provide a systematic understanding of how the various SDH act on important indicators of HIV/AIDS progression. We aimed to evaluate the effects of SDH on AIDS morbidity and mortality. METHODS: A retrospective cohort of 28.3 million individuals was evaluated over a 9-year period (from 2007 to 2015). Multivariable Poisson regression, with a hierarchical approach, was used to estimate the effects of SDH-at the individual and familial level-on AIDS incidence, mortality, and case-fatality rates. FINDINGS: A total of 28,318,532 individuals, representing the low-income Brazilian population, were assessed, who had a mean age of 36.18 (SD: 16.96) years, 52.69% (14,920,049) were female, 57.52% (15,360,569) were pardos, 34.13% (9,113,222) were white/Asian, 7.77% (2,075,977) were black, and 0.58% (154,146) were indigenous. Specific socioeconomic, household, and geographic factors were significantly associated with AIDS-related outcomes. Less wealth was strongly associated with a higher AIDS incidence (rate ratios-RR: 1.55; 95% confidence interval-CI: 1.43-1.68) and mortality (RR: 1.99; 95% CI: 1.70-2.34). Lower educational attainment was also greatly associated with higher AIDS incidence (RR: 1.46; 95% CI: 1.26-1.68), mortality (RR: 2.76; 95% CI: 1.99-3.82) and case-fatality rates (RR: 2.30; 95% CI: 1.31-4.01). Being black was associated with a higher AIDS incidence (RR: 1.53; 95% CI: 1.45-1.61), mortality (RR: 1.69; 95% CI: 1.57-1.83) and case-fatality rates (RR: 1.16; 95% CI: 1.03-1.32). Overall, also considering the other SDH, individuals experiencing greater levels of socioeconomic deprivation were, by far, more likely to acquire AIDS, and to die from it. INTERPRETATION: In the population studied, SDH related to poverty and social vulnerability are strongly associated with a higher burden of HIV/AIDS, most notably less wealth, illiteracy, and being black. In the absence of relevant social protection policies, the current worldwide increase in poverty and inequalities-due to the consequences of the COVID-19 pandemic, and the effects of war in the Ukraine-could reverse progress made in the fight against HIV/AIDS in low- and middle-income countries (LMIC). FUNDING: National Institute of Allergy and Infectious Diseases (NAIDS), National Institutes of Health (NIH), US Grant Number: 1R01AI152938