We study Graver test sets for families of linear multi-stage stochastic integer programs with varying number of scenarios. We show that these test sets can be decomposed into finitely many “building blocks”, independent of the number of scenarios, and we give an effective procedure to compute them. The paper includes an introduction to Nash-Williams’ theory of better-quasi-orderings, which is u...

Diameter—the task of computing the length of a longest shortest path—is a fundamental graph problem. Assuming the Strong Exponential Time Hypothesis, there is no O(n)time algorithm even in sparse graphs [Roditty and Williams, 2013]. To circumvent this lower bound we aim for algorithms with running time f(k)(n+m) where k is a parameter and f is a function as small as possible. For our choices of...

The nearest integer continued fractions of Hurwitz, Minnegerode (NICF-H) and in Perron’s book Die Lehre von den Kettenbrüchen (NICF-P) are closely related. Midpoint criteria for solving Pell’s equation x2 − Dy2 = ±1 in terms of the NICF-H expansion of √ D were derived by H. C. Williams using singular continued fractions. We derive these criteria without the use of singular continued fractions. ...

An Alsynite cylinder trap and three different Williams cross-configuration traps with three adhesives were compared to determine their relative attraction to stable fly, Stomoxys calcitrans (L.), adults. Williams traps coated with Olson Sticky Stuff performed as well as Williams traps coated with Tack Trap, thus allowing fly samples collected with either adhesive to be compared. The cylinder tr...

Musical processing can be decomposed into the appreciation of global and local elements. This global/local dissociation was investigated with the processing of contour-violated and interval-violated melodies. Performance of a group of 16 children with Williams syndrome and a group of 16 control children were compared in a same-different task. Control participants were more accurate in detecting...

The relationship between age and IQ was evaluated in a cross-sectional sample of 80 individuals with Williams syndrome (17 to 52 years). The relationship between age and WAIS-R subtest scores was such that increases and decreases in raw scores occurred at a rate sufficient to maintain stability of age-corrected scaled scores, indicating a developmental trajectory similar to that of the WAIS-R n...