The integral fractional Laplacian of order $s \in (0,1)$ is a nonlocal operator. It known that solutions to the Dirichlet problem involving such an operator exhibit algebraic boundary singularity regardless domain regularity. This, in turn, deteriorates global regularity and as result convergence rate numerical solutions. For finite element discretizations, we derive local error estimates $H^s$...

Scales in RNA, based on geometrical considerations, can be exploited for the analysis and prediction of RNA structures. By using spectral decomposition, geometric information that relates to a given RNA fold can be reduced to a single positive scalar number, the second eigenvalue of the Laplacian matrix corresponding to the tree-graph representation of the RNA secondary structure. Along with th...

Docking-i.e., interaction of a small molecule (ligand) with a proteic structure (receptor)-represents the ground of drug action mechanism of the vast majority of bioactive chemicals. Ligand and receptor accommodate their geometry and energy, within this interaction, in the benefit of receptor-ligand complex. In an induced fit docking, the structure of ligand is most susceptible to changes in to...