where s is a Sachs graph (as defined in 3 ) , Sn is the set of all Sachs graphs with n vertices, c(s) is the number of components3 and r(s) is the number of cycles 3, in S. N is the number of vertices in G. This formula may be applied to the graphs associated with conjugated hydrocarbons in a straightforward way, as described by Graovac et al.3. There have been several other (ostensibly differe...

Posterior dislocations of the shoulder joint can result in an impression fracture over the anteromedial humeral head, termed the reverse Hill-Sachs lesion, the presence of which can contribute to recurrent dislocations. Methods described to repair this defect include using allografts, iliac crest and coracoid process autografts, and bone graft substitutes. We describe a novel technique using th...

The constraints on the asymptotic behavior of the conformal factor and conformal extrinsic curvature imposed by the initial value equations of general relativity on constant mean extrinsic curvature (CMC) hypersurfaces are analyzed in detail. We derive explicit formulas for the Bondi-Sachs energy and momentum in terms of coefficients of asymptotic expansions on CMC hypersurfaces near future nul...

Carrier screening programs have historically been focused within a particular group---e.g., Tay-Sachs among Ashkenazic Jews and sickle cell anemia among African Americans. With cystic fibrosis (CF), the potential target population is larger and less defined, which may introduce both technical and organizational complexity not present in past carrier screening. This appendix describes past carri...