关于Menger概率赋范空间上线性算子的共鸣定理

提出 Menger 概率赋范线性空间上集合有界性的简化定义,利用 Menger概率赋范空间的线性拓扑性质,在较弱的 t-模条件下,建立了概率有界、概率半有界、非概率无界意义下线性算子的共鸣定理。     

Discrete Probability Distributions for Probabilistic Fracture Mechanics

Recently, discrete probability distributions (DPDs) have been suggested for use in risk analysis calculations to simplify the numerical computations which must be performed to determine failure probabilities. Specifically, DPDs have been developed to investigate probabilistic functions, that is, functions whose exact form is uncertain. The analysis of defect growth in materials by probabilistic fracture mechanics (PFM) models provides an example in which probabilistic functions play an important role. This paper compares and contrasts Monte Carlo simulation and DPDs as tools for calculating material failure due to fatigue crack growth. For the problem studied, the DPD method takes approximately one third the computation time of the Monte Carlo approach for comparable accuracy. It is concluded that the DPD method has considerable promise in low-failure-probability calculations of importance in risk assessment. In contrast to Monte Carlo, the computation time for the DPD approach is relatively insensitive to the magnitude of the probability being estimated.     

Incomplete Contracts: Where do We Stand?

The paper takes stock of the advances and directions for research on the incomplete contracting front. It first illustrates some of the main ideas of the incomplete contract literature through an example. It then offers methodological insights on the standard approach to modeling incomplete contracts; in particular it discusses a tension between two assumptions made in the literature, namely rationality and the existence of transaction costs. Last, it argues that, contrary to what is commonly argued, the complete contract methodology need not be unable to account for standard institutions such as authority and ownership; and it concludes with a discussion of the research agenda.     

Effects of differential reinforcement and rules with feedback on preference for choice and verbal reports

We evaluated the effects of differential reinforcement and accurate verbal rules with feedback on the preference for choice and the verbal reports of 6 adults. Participants earned points on a probabilistic schedule by completing the terminal links of a concurrent-chains arrangement in a computer-based game of chance. In free-choice terminal links, participants selected 3 numbers from an 8-number array; in restricted-choice terminal links participants selected the order of 3 numbers preselected by a computer program. A pop-up box then informed the participants if the numbers they selected or ordered matched or did not match numbers generated by the computer but not displayed; matching in a trial resulted in one point earned. In baseline sessions, schedules of reinforcement were equal across free- and restricted-choice arrangements and a running tally of points earned was shown each trial. The effects of differentially reinforcing restricted-choice selections were evaluated using a reversal design. For 4 participants, the effects of providing a running tally of points won by arrangement and verbal rules regarding the schedule of reinforcement were also evaluated using a nonconcurrent multiple-baseline-across-participants design. Results varied across participants but generally demonstrated that (a) preference for choice corresponded more closely to verbal reports of the odds of winning than to reinforcement schedules, (b) rules and feedback were correlated with more accurate verbal reports, and (c) preference for choice corresponded more highly to the relative number of reinforcements obtained across free- and restricted-choice arrangements in a session than to the obtained probability of reinforcement or to verbal reports of the odds of winning.     

概率度量理论在分析概率论中的应用

把文献[1]中的引理推广为分析概率论中有用的极限定理，改进了文献[1]的主要结果及简化了其证明过程，并获得了一个在概率微分方程理论中有重要应用的实用概率度量空间；给出了随机线性泛函延拓定理的应用；建立了概率微分方程解的局部存在性定理．     

A Probabilistic Arsenic Exposure Assessment for Children Who Contact CCA-Treated Playsets and Decks, Part 1: Model Methodology, Variability Results, and Model Evaluation

Concerns have been raised regarding the safety of young children who may contact arsenic residues while playing on and around chromated copper arsenate (CCA)-treated wood playsets and decks. Although CCA registrants voluntarily canceled the production of treated wood for residential use in 2003, the potential for exposure from existing structures and surrounding soil still poses concerns. The EPA's Office of Research and Development developed and applied the probabilistic Stochastic Human Exposure and Dose Simulation model for wood preservatives (SHEDS-Wood) to estimate children's absorbed dose of arsenic from CCA. Skin contact with, and nondietary ingestion of, arsenic in soil and wood residues were considered for the population of children in the United States who frequently contact CCA-treated wood playsets and decks. Model analyses were conducted to assess the range in population estimates and the impact of potential mitigation strategies such as the use of sealants and hand washing after play events. The results show predicted central values for lifetime annual average daily dose values for arsenic ranging from 10(-6) to 10(-5) mg/kg/day, with predicted 95th percentiles on the order of 10(-5) mg/kg/day. There were several orders of magnitude between lower and upper percentiles. Residue ingestion via hand-to-mouth contact was determined to be the most significant exposure route for most scenarios. Results of several alternative scenarios were similar to baseline results, except for the scenario with greatly reduced residue concentrations through hypothetical wood sealant applications; in this scenario, exposures were lower, and the soil ingestion route dominated. SHEDS-Wood estimates are typically consistent with, or within the range of, other CCA exposure models.     

Variability and Uncertainty Meet Risk Management and Risk Communication

In the past decade, the use of probabilistic risk analysis techniques to quantitatively address variability and uncertainty in risks increased in popularity as recommended by the 1994 National Research Council that wrote Science and Judgment in Risk Assessment. Under the 1996 Food Quality Protection Act, for example, the U.S. EPA supported the development of tools that produce distributions of risk demonstrating the variability and/or uncertainty in the results. This paradigm shift away from the use of point estimates creates new challenges for risk managers, who now struggle with decisions about how to use distributions in decision making. The challenges for risk communication, however, have only been minimally explored. This presentation uses the case studies of variability in the risks of dying on the ground from a crashing airplane and from the deployment of motor vehicle airbags to demonstrate how better characterization of variability and uncertainty in the risk assessment lead to better risk communication. Analogies to food safety and environmental risks are also discussed. This presentation demonstrates that probabilistic risk assessment has an impact on both risk management and risk communication, and highlights remaining research issues associated with using improved sensitivity and uncertainty analyses in risk assessment.     

Methods for Uncertainty Analysis: A Comparative Survey

This paper presents a survey and comparative evaluation of methods which have been developed for the determination of uncertainties in accident consequences and probabilities, for use in probabilistic risk assessment. The methods considered are: analytic techniques, Monte Carlo simulation, response surface approaches, differential sensitivity techniques, and evaluation of classical statistical confidence bounds. It is concluded that only the response surface and differential sensitivity approaches are sufficiently general and flexible for use as overall methods of uncertainty analysis in probabilistic risk assessment. The other methods considered, however, are very useful in particular problems.     

A Probabilistic Feasibility and Value Analysis of the Generalized Assignment Problem

We study the generalized assignment problem, under a probabilistic model for its cost and requirement parameters. First we address the issue of feasibility by deriving a tight condition on the probabilistic model that ensures that the corresponding problem instances are feasible with probability one as the number of jobs goes to infinity. Then, under an additional condition on the parameters, we show that the optimal solution value, normalized by dividing by the number of jobs, converges with probability one to a constant, again as the number of jobs goes to infinity. Finally, we discuss various examples.