Random Walks on Thompson\u27s Group F

In this paper we consider the statistical properties of random walks on Thompson’s group F . We use two-way forest diagrams to represent elements of F . First we describe the random walk of F by relating the steps of the walk to the possible interactions between two-way forest diagrams and the elements of {x0,x1}, the finite generating set of F, and their inverses. We then determine the long-term probabilistic and recurrence properties of the walk

Impact of the COVID-19 pandemic on patients with paediatric cancer in low-income, middle-income and high-income countries: a multicentre, international, observational cohort study

OBJECTIVES: Paediatric cancer is a leading cause of death for children. Children in low-income and middle-income countries (LMICs) were four times more likely to die than children in high-income countries (HICs). This study aimed to test the hypothesis that the COVID-19 pandemic had affected the delivery of healthcare services worldwide, and exacerbated the disparity in paediatric cancer outcomes between LMICs and HICs. DESIGN: A multicentre, international, collaborative cohort study. SETTING: 91 hospitals and cancer centres in 39 countries providing cancer treatment to paediatric patients between March and December 2020. PARTICIPANTS: Patients were included if they were under the age of 18 years, and newly diagnosed with or undergoing active cancer treatment for Acute lymphoblastic leukaemia, non-Hodgkin's lymphoma, Hodgkin lymphoma, Wilms' tumour, sarcoma, retinoblastoma, gliomas, medulloblastomas or neuroblastomas, in keeping with the WHO Global Initiative for Childhood Cancer. MAIN OUTCOME MEASURE: All-cause mortality at 30 days and 90 days. RESULTS: 1660 patients were recruited. 219 children had changes to their treatment due to the pandemic. Patients in LMICs were primarily affected (n=182/219, 83.1%). Relative to patients with paediatric cancer in HICs, patients with paediatric cancer in LMICs had 12.1 (95% CI 2.93 to 50.3) and 7.9 (95% CI 3.2 to 19.7) times the odds of death at 30 days and 90 days, respectively, after presentation during the COVID-19 pandemic (p<0.001). After adjusting for confounders, patients with paediatric cancer in LMICs had 15.6 (95% CI 3.7 to 65.8) times the odds of death at 30 days (p<0.001). CONCLUSIONS: The COVID-19 pandemic has affected paediatric oncology service provision. It has disproportionately affected patients in LMICs, highlighting and compounding existing disparities in healthcare systems globally that need addressing urgently. However, many patients with paediatric cancer continued to receive their normal standard of care. This speaks to the adaptability and resilience of healthcare systems and healthcare workers globally

Twelve-month observational study of children with cancer in 41 countries during the COVID-19 pandemic

Childhood cancer is a leading cause of death. It is unclear whether the COVID-19 pandemic has impacted childhood cancer mortality. In this study, we aimed to establish all-cause mortality rates for childhood cancers during the COVID-19 pandemic and determine the factors associated with mortality