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
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