Expander graphs are known to facilitate effective routing and most real-world networks have expansion properties. At the other extreme, it has been shown that in some special graphs, removing certain edges can lead to more efficient routing. This phenomenon is known as Braess’s paradox and is usually regarded as a rare event. In contrast to what one might expect, we show that Braess’s paradox i...

The consistency of the estimator is obtained by a direct application of the the Law of Large Numbers (LLN) as ξ is bounded. The total probability

Copulas are a useful tool for understanding relationships among multivariate variables, and are important tools for describing the dependence structure between random variables, with different copulas representing different dependencies. Since the study of dependence is critically important in Statistics in order to carry out reliable analyses, understanding and applying results from copulas ca...

This paper is based on Wald Lectures given at the annual meeting of the IMS in Minneapolis during August 2005. It is a survey of the theory of large deviations. 1. Large deviations for sums. The role of " large deviations " is best understood through an example.

The Customer is the only non-developer role in eXtreme Programming (XP). Initial XP literature [1, 2] provided little guidance concerning this role; however Beck & Fowler did acknowledge the risk associated with the Customer role: All the best talent and technology and process in the world will fail when the customer isn’t up to scratch [1, p.17] Our research [4] is beginning to explore the pra...

Extreme Value Analysis can be used to extrapolate sample inspection data into uninspected regions of a component. These methods can be used in conjunction with structural reliability software to predict the probability of future failure of the component. This information can help both operators and regulators make risk-based decisions on the future operation of the plant. This paper illustrates...