Half sphere exposure both HSEα and HSEβ based on a big dataset by using multiple-step iterative deep neural-network learning. The predicted HSEa shows a higher correlation coefficient to the stability change by residue mutants than predicted HSEβ and ASA. The results, together with its easy Ca-atom-based calculation, highlight the potential usefulness of predicted HSEa for protein structure prediction and refinement as well as function prediction. 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
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