The increasing availability of maps of dense polymorphic markers makes use of haplotype data in family-based association analyses an attractive alternative to single marker association tests. We describe a novel class of statistics designed to test for an association between marker haplotypes and a qualitative trait using the parent-parent-affected-offspring trio design. Our haplotype runs test...

In a Diamond and Dybvig (1983) environment, Green and Lin (2003) take a mechanism design approach and show that a bank run equilibrium cannot exist. Peck and Shell (2003) generalize their economic environment and show that it can. The bank run, however, does not emerge because of modifications to the economic environment but rather because the mechanism that implements allocations is not an opt...

In [2], a short and elegant proof was presented showing that a binary word of length n contains at most n − 3 runs. Here we show, using the same technique and a computer search, that the number of runs in a binary word of length n is at most 22 23 n < 0.957n.