Probabilistic integration of a continuous dynamical system is a way of systematically introducing discretisation 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. (Stat Comput 27(4):1065–1082, 2017. https://doi.org/10.1007/s11222-016-9671-0), 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.
The role of voluntary and community sector organizations in the delivery of public services is increasing and these changes
bring new responsibilities and benefits to organizations that have the capacity to participate. There are concerns within
the sector about the implications for citizenship and participation. The sector is highly dependent on volunteers yet little
is known about how organizational change in response to new relationships with the statutory sector impact upon the commitment
and well-being of people who volunteer. This paper addresses that gap in knowledge for older volunteers. Drawing upon collaborative
research with a voluntary organization in the north of England, the authors explore the meanings and aspirations of volunteering
for older people, and explain how and why changes associated with closer engagement with public service delivery and less
grant dependency can be disempowering for them.
Activity and species-specific responses of insectivorous bats in different urban-forest conditions provides a general perspective on the adaptability and vulnerability of bat species towards urbanization intensity. Here we evaluated species richness and activity patterns of aerial insectivorous bats across an urbanized landscape in the highlands of Chiapas, in Mexico. Acoustic monitoring of echolocation calls was conducted for 27 nights over a period of four months. Species richness and relative activity of insectivorous bats were estimated in a landscape with different conditions of urbanization intensity: urban areas, non-urban and forest areas. We identified a total of 14 bat species and three phonotypes. Bat species richness and relative activity was similar (X2 = 0.568, gl = 2, p > 0.05), but species composition differed among conditions. We observed a significant higher occurrence of Bauerus dubiaquercus, Eptesicus brasiliensis and Myotis californicus in forest sites. Urban sites presented higher occurrence of Molossus rufus and phonotype Molossidae 2, while non-urban sites presented a higher occurrence of Eptesicus furinalis and phonotype Molossidae 2. We were able to identify bat species according to their relative activity in relation todifferent landscape conditions. Species of the Molossidae family presented the highest activity in urban sites, which was positively affected by the number of streetlights, while species of the Vespertilionidae presented the highest activity in forest sites, which was positively related totree density. While urbanization tends to diminish native biodiversity and alter faunal communities, our results show a similar richness and relative activity of aerial insectivorous bats along the urban ecosystem. The effect of urbanization intensity becomes more apparent in species-specific bat activity; the response of species towards particular habitat conditions depends on local habitat quality and characteristics (i.e., presence of streetlights, vegetation cover and tree density). 相似文献
This article addresses the question of whether the Caribbean is particularly attractive or unattractive to foreign investors, and if it has specific characteristics that attract or deter FDI. An econometric analysis of data from 135 countries for 1980‐2002 shows that the Caribbean does not suffer from low inflows of FDI; on the contrary, Caribbean countries receive more FDI than comparable countries in other regions. This reflects two contradictory effects. On the one hand, FDI inflows may be particularly sensitive to political instability in the region; on the other hand, the absence of regulation appears to have been a particularly beneficial factor in attracting FDI to the Caribbean. 相似文献