We suggest a simple method to assess how many normal modes are needed to map a conformational change. By projecting the conformational change onto a subspace of the normal-mode vectors and using root mean square deviation as a test of accuracy, we find that the first 20 modes only contribute 50% or less of the total conformational change in four test cases (myosin, calmodulin, NtrC, and hemoglo...

are integral forms arising from norms on number fields. We prove that the natural density of the set of integers represented by a norm form is zero, while the relative natural density of the set of prime numbers represented by a norm form exists and is positive. These results require tools from class field theory, including the Artin-Chebotarev density theorem and the Hilbert class field. We in...

We report a Scottish child with inv dup (15) and compare the clinical features with those of previously reported cases. Since the first report by Parker and Alfi in 1972, there have been 44 reports of patients with confirmed or suspected inv dup (15). The extra chromosomal material has been variously described, but in all cases there appears to be an additional G group sized chromosome in which...