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.
ABSTRACTThe Children Future Education and the Development Accounts (CFEDAs) are the first anti-poverty policy in Taiwan developed to provide incentives for the poor to accumulate assets for their future. Using CFEDAs as an example, this article analyses the process of developing and implementing an asset-based policy. It begins with an introduction to the policy structure. It then reviews the history of how the innovative idea of building assets for the poor became a policy proposal before presenting the convergence of three policy streams driving the prioritisation of CFEDAs in Taiwan’s policy agenda. It concludes with challenges facing the policy implementation. 相似文献
Economic theory establishes that pension privatization weakens the link between old and young and so reduces the incentive to invest in public education in an economy with lower return rate of capital than growth rate of wage. However, empirical studies of the link change are few. In this paper, we investigate the effects of pension privatization and the central government’s subsidy to individual accounts on public education spending in a three-period overlapping generation model. And then, we take contemporary pension reforms in a number of Chinese provinces as offering natural experiment conditions. Using a difference-in-difference framework and 282 municipal districts panel data over years 1998–2009, we test the pension-education theoretical link change. Both our theoretical and empirical results confirm that pension privatization is adversely associated with local public spending on education in China. Private pension subsidies, moreover, magnify this effect. Our study supports the theoretical assertion and selective empirical findings of a negative intergenerational effect of pension privatization. 相似文献
This paper investigates the impact of pension income on living arrangements of the elderly. Taking advantage of a unique opportunity due to the recent establishment and expansion of the New Rural Pension Scheme in China, we explicitly address the endogeneity of pension status and pension income through a fixed-effect model with instrumental variable approach by exploiting exogenous time variation in the program implementation at county level. We find an overall positive effect of pension income on independent living as well as considerable heterogeneity. The positive income effects of the NRPS are concentrated among the elderly with adult children living nearby, of higher socio-economic status, and with better health at baseline; for other groups, the effects are insignificant. We also find that more generous programs exhibit larger effects. Our results highlight that living arrangement is multidimensional in rural China. 相似文献
We propose a new typology of paternalistic leadership styles based on how leaders demonstrate authoritarianism and benevolence, the two essential components of this type of leadership. Benevolence-dominant paternalistic leadership refers to leaders' sole dependence on the use of benevolence without their strong assertion of authority, whereas authoritarianism-dominant paternalistic leadership is based mainly on authoritarianism itself; classical paternalistic leadership, which best fits early observations of paternalistic leaders, refers to the salient combination of both leadership components. We used two distinct samples and methods to test this typology and the association with subordinate performance. Across the two studies, a field investigation with Taiwanese military supervisor-subordinate dyads and a hypothetical scenario experiment with U.S. working adults, we found a positive relationship between classical paternalistic leadership and subordinate performance as strong as that between benevolence-dominant paternalistic leadership and performance. Our findings echo the phenomenon that paternalistic leaders tend to combine benevolence with authoritarianism to affect subordinate performance. 相似文献
For a simple graph G on n vertices with adjacency matrix A, Motzkin and Strauss established a remarkable connection between the clique number and the global maximum value of the quadratic programm: \(\textit{max}\{ \mathbf {x}^T A \mathbf {x}\}\) on the standard simplex: \(\{\sum _{i=1}^{n} x_i =1, x_i \ge 0 \}\). In Gibbons et al. (Math Oper Res 122:754–768, 1997), an extension of the Motzkin–Straus formulation was provided for the vertex-weighted clique number of a graph. In this paper, we provide a continuous characterization of the maximum vertex-weighted clique problem for vertex-weighted uniform hypergraphs. 相似文献