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
Alexander horned sphere where the need for distinction between the topological category of manifolds, and the categories of differentiable manifolds, and piecewise linear manifolds was noticed. Now consider Alexander's horned sphere as an embedding into the 3-sphere, considered as the one-point compactification of the 3-dimensional Euclidean space R. The closure of the non-simply connected domain is called the solid Alexander horned sphere. Although the solid horned sphere is not a manifold, R. H. Bing showed that its double (which is the 3-manifold obtained by gluing two copies of the horned sphere together along the corresponding points of their boundaries) is in fact the