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
Simplicial sphere "i"-faces of any simplicial "d"-sphere with "f" = "n" vertices. This conjecture was proved for polytopal spheres by Peter McMullen in 1970 and by Richard Stanley for general simplicial spheres in 1975. The g"-conjecture, formulated by McMullen in 1970, asks for a complete characterization of "f"-vectors of simplicial "d"-spheres. In other words, what are the possible sequences of numbers of faces of each dimension for a simplicial "d"-sphere? In the case of polytopal spheres, the answer is given by the g"-theorem, proved in 1979 by Billera and Lee (existence) and Stanley (necessity). It has been conjectured that the same conditions