Half sphere exposure Half sphere exposure Half Sphere Exposure (HSE) is a protein solvent exposure measure that was first introduced by . Like all solvent exposure measures it measures how buried amino acid residues are in a protein. It is found by counting the number of amino acid neighbors within two half spheres of chosen radius around the amino acid. The calculation of HSE is found by dividing a contact number (CN) sphere in two halves by the plane perpendicular to the Cβ-Cα vector. This simple division of the CN sphere results in two strikingly different measures, HSE-up and HSE-down. HSE-up is defined
Exotic sphere Similar manifolds are called Brieskorn spheres. Given an (orientation-preserving) diffeomorphism , gluing the boundaries of two copies of the standard disk "D" together by "f" yields a manifold called a "twisted sphere" (with "twist" "f"). It is homotopy equivalent to the standard "n"-sphere because the gluing map is homotopic to the identity (being an orientation-preserving diffeomorphism, hence degree 1), but not in general diffeomorphic to the standard sphere. Setting formula_25 to be the group of twisted "n"-spheres (under connect sum), one obtains the exact sequence For , every exotic "n"-sphere is diffeomorphic to a twisted sphere, a result proven by