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
3-sphere homeomorphic to the one-point compactification of . In general, any topological space that is homeomorphic to the 3-sphere is called a topological 3-sphere. The homology groups of the 3-sphere are as follows: and are both infinite cyclic, while for all other indices . Any topological space with these homology groups is known as a homology 3-sphere. Initially Poincaré conjectured that all homology 3-spheres are homeomorphic to , but then he himself constructed a non-homeomorphic one, now known as the Poincaré homology sphere. Infinitely many homology spheres are now known to exist. For example, a Dehn filling with slope on any