We introduce 'formal methods' of mechanized reasoning from computer science to address two problems in auction design and practice: is a given auction design soundly specified, possessing its intended properties; and, is the design faithfully implemented when actually run? Failure on either...

Several family-based approaches for testing genetic association with traits obtained from longitudinal or repeated measurement studies have been previously proposed. These approaches utilize the multivariate data more efficiently by using estimated optimal weights to combine univariate tests. We...