BSDE, Path-dependent PDE and Nonlinear Feynman-Kac Formula

In this paper, we introduce a type of path-dependent quasilinear (parabolic) partial differential equations in which the (continuous) paths on an interval [0,t] becomes the basic variables in the place of classical variables (t,x). This new type of PDE are formulated through a classical backward stochastic differential equation (BSDEs, for short) in which the terminal values and the generators are allowed to be general functions of Brownian paths. In this way we have established a new type of nonlinear Feynman-Kac formula for a general non-Markovian BSDE. Some main properties of regularities for this new PDE was obtained

Interfacial Bond Adhesion Enhancement Mechanism Analysis of Self Stressing Alkali Activated Slag Concrete-Filled Round Steel Tube

To investigate the interfacial adhesion behaviour and its enhancement mechanism of self-stressing alkali activated slag concrete-filled round steel tube, push-out samples, expansion performance test specimens, and SEM, XRD micro-test specimens were made with different dosage of calcium sulphoaluminate and calcium oxide expansive agent. The results show that the maximum interfacial adhesion stress is at 70-80 mm from the free end of the samples, and increases with the increase of the expansive agent dosage. The expansive agent such as calcium sulphoaluminate and calcium oxide can effectively reduce the drying shrinkage performance of the core concrete, and then improve the interaction between steel tube and core concrete. Micro-test analysis results show that the main expansive source providing expansive power in the AASC system is Ca(OH)

Aging, the urban-rural gap and disability trends: 19 years of experience in China - 1987 to 2006

As the age of a population increases, so too does the rate of disability. In addition, disability is likely to be more common in rural compared with urban areas. The present study aimed to examine the influence of rapid population changes in terms of age and rural/urban residence on the prevalence of disability. Data from the 1987 and 2006 China Sampling Surveys on Disability were used to estimate the impacts of rapid ageing and the widening urban-rural gap on the prevalence of disability. Stratum specific rates of disability were estimated by 5-year age-group and type of residence. The decomposition of rates method was used to calculate the rate difference for each stratum between the two surveys. The crude disability rate increased from 4.89% in 1987 to 6.39% in 2006, a 1.5% increase over the 19 year period. However, after the compositional effects from the overall rates of changing age-structure in 1987 and 2006 were eliminated by standardization, the disability rate in 1987 was 6.13%, which is higher than that in 2006 (5.91%). While in 1987 the excess due to rural residence compared with urban was ,1.0%, this difference increased to .1.5% by 2006, suggesting a widening disparity by type of residence. When rates were decomposed, the bulk of the disability could be attributed to ageing, and very little to rural residence. However, a wider gap in prevalence between rural and urban areas could be observed in some age groups by 2006. The increasing number of elderly disabled persons in China and the widening discrepancy of disability prevalence between urban and rural areas may indicate that the most important priorities for disability prevention in China are to reinforce health promotion in older adults and improve health services in rural communities

An Efficient Fault Recovery Algorithm in Multiprocessor Mixed-Criticality Systems

Recent years, there is an increasing interest of integrating mixed-criticality functionalities onto a shared computing platform in automotive, avionics and the control industry. The benefits of such an integration include reduced hardware cost and high computational performance. Also, new challenges appear as a result of the integration since interferences across tasks with different criticalities are introduced and these interferences could potentially lead to catastrophic results. Failures are likely to be more frequent due to the interferences. Hence, it is becoming increasingly important to deal with faults in mixed-criticality systems. Although several approaches have been proposed to handle failures in mixed-criticality systems, they come either with a high cost due to a hardware replication (spatial redundancy) or with a poor utilization due to reexecution (time redundancy). In this paper, we study a scheme that provides fault recovery through task reallocations in response to permanent faults in multiprocessor mixed-criticality systems. We present an algorithm to minimize the number of task reallocations while retaining the promise that the most critical applications continue to meet their deadlines. The performance evaluation of the proposed algorithm is carried out by comparing it with two baseline algorithms. In order to evaluate the performance of algorithms from the perspective of mixed-criticality systems, we choose the state of art metric called ductility to formally measure the effects of deadline misses for tasks with different criticality levels. Under this metric, a high-criticality task is considered more important than all low-criticality tasks combined. The simulation results confirm the effectiveness of our proposed algorithm in both minimizing the number of task reallocations and retaining the promised performance of highcriticality tasks