Strong convergence rates of probabilistic integrators for ordinary differential equations

Probabilistic integration of a continuous dynamical system is a way of systematically introducing model error, at scales no larger than errors introduced by standard numerical discretisation, in order to enable thorough exploration of possible responses of the system to inputs. It is thus a potentially useful approach in a number of applications such as forward uncertainty quantification, inverse problems, and data assimilation. We extend the convergence analysis of probabilistic integrators for deterministic ordinary differential equations, as proposed by Conrad et al.\ (\textit{Stat.\ Comput.}, 2017), to establish mean-square convergence in the uniform norm on discrete- or continuous-time solutions under relaxed regularity assumptions on the driving vector fields and their induced flows. Specifically, we show that randomised high-order integrators for globally Lipschitz flows and randomised Euler integrators for dissipative vector fields with polynomially-bounded local Lipschitz constants all have the same mean-square convergence rate as their deterministic counterparts, provided that the variance of the integration noise is not of higher order than the corresponding deterministic integrator. These and similar results are proven for probabilistic integrators where the random perturbations may be state-dependent, non-Gaussian, or non-centred random variables.Comment: 25 page

Pregnancy, prison and perinatal outcomes in New South Wales, Australia: a retrospective cohort study using linked health data

BACKGROUND Studies from the United States and the United Kingdom have found that imprisoned women are less likely to experience poorer maternal and perinatal outcomes than other disadvantaged women. This population-based study used both community controls and women with a history of incarceration as a control group, to investigate whether imprisoned pregnant women in New South Wales, Australia, have improved maternal and perinatal outcomes. METHODS Retrospective cohort study using probabilistic record linkage of routinely collected data from health and corrective services in New South Wales, Australia. Comparison of the maternal and perinatal outcomes of imprisoned pregnant women aged 18-44 years who gave birth between 2000-2006 with women who were (i) imprisoned at a time other than pregnancy, and (ii) community controls. OUTCOMES OF INTEREST onset of labour, method of birth, pre-term birth, low birthweight, Apgar score, resuscitation, neonatal hospital admission, perinatal death. RESULTS Babies born to women who were imprisoned during pregnancy were significantly more likely to be born pre-term, have low birthweight, and be admitted to hospital, compared with community controls. Pregnant prisoners did not have significantly better outcomes than other similarly disadvantaged women (those with a history of imprisonment who were not imprisoned during pregnancy). CONCLUSIONS In contrast to the published literature, we found no evidence that contact with prison health services during pregnancy was a "therapunitive" intervention. We found no association between imprisonment during pregnancy and improved perinatal outcomes for imprisoned women or their neonates. A history of imprisonment remained the strongest predictor of poor perinatal outcomes, reflecting the relative health disadvantage experienced by this population of women.This work was undertaken with funding from the National Health and Medical Research Council of Australia. Project Grant ID 457515

The life course consequences of single-sex and co-educational schooling

This chapter reports on a study examining whether attending single-sex rather than co-educational secondary school made a difference to the lives of a cohort of men and women born in Britain in 1958. The project aimed to assess the impact of single-sex secondary schooling, not just on short-term and narrowly academic outcomes, but also on longer-term social, psychological, and economic outcomes. In a generally gendered environment for adults, did it make any difference to have been to a gender segregated school, and in what way? This chapter provides an overview of our findings, and a discussion of the implications for policy and for future research

First records of the grasshopper \u3ci\u3eMachaerocera mexicana\u3c/i\u3e Saussure, 1859 (Orthoptera: Acrididae) from the United States and Sonora, Mexico

The grasshopper Machaerocera mexicana Saussure (Orthoptera: Acrididae) is added to the orthopteran faunas of the United States and Sonora, Mexico. Notes are presented on habitat and seasonality. El saltamontes Machaerocera mexicana Saussure (Orthoptera: Acrididae) se agrega a las faunas ortópteros de los Estados Unidos y Sonora, México. Se presenta notas sobre su hábitat y estacionalidad

First records of the grasshopper \u3ci\u3eMachaerocera mexicana\u3c/i\u3e Saussure, 1859 (Orthoptera: Acrididae) from the United States and Sonora, Mexico

The grasshopper Machaerocera mexicana Saussure (Orthoptera: Acrididae) is added to the orthopteran faunas of the United States and Sonora, Mexico. Notes are presented on habitat and seasonality. El saltamontes Machaerocera mexicana Saussure (Orthoptera: Acrididae) se agrega a las faunas ortópteros de los Estados Unidos y Sonora, México. Se presenta notas sobre su hábitat y estacionalidad

Evaluation of positive G sub Z tolerance following simulated weightlessness (bedrest)

The magnitude of physiologic changes which are known to occur in human subjects exposed to varying levels of + G sub Z acceleration following bed rest simulation of weightlessness was studied. Bed rest effects were documented by fluid and electrolyte balance studies, maximal exercise capability, 70 deg passive tilt and lower body negative pressure tests and the ability to endure randomly prescribed acceleration profiles of +2G sub Z, +3G sub Z, and +4G sub Z. Six healthy male volunteers were studied during two weeks of bed rest after adequate control observations, followed by two weeks of recovery, followed by a second two-week period of bed rest at which time an Air Force cutaway anti-G suit was used to determine its effectiveness as a countermeasure for observed cardiovascular changes during acceleration. Results showed uniform and significant changes in all measured parameters as a consequence of bed rest including a reduced ability to tolerate +G sub Z acceleration. The use of anti-G suits significantly improved subject tolerance to all G exposures and returned measured parameters such as heart rate and blood pressure towards or to pre-bed-rest (control) values in four of the six cases

The relationship between particle freeze-out distributions and HBT radius parameters

The relationship between pion and kaon space-time freeze-out distributions and the HBT radius parameters in high-energy nucleus-nucleus collisions is investigated. We show that the HBT radius parameters in general do not reflect the R.M.S. deviations of the single particle production points. Instead, the HBT radius parameters are most closely related to the curvature of the two-particle space-time relative position distribution at the origin. We support our arguments by studies with a dynamical model (RQMD 2.4).Comment: RevTex, 10 pages including 3 figures. v2: Discussion of the lambda parameter has been added. PRC, in prin