Supporting 'persistent safety-windows' #1
Description
Similar to the concept of persistent homology in topological data analysis, a next idea to look at with emerald can be persistent safety-windows: keeping alpha constant, increasing Δ from Δ = 0 until all safety windows vanished, and store the safety information for every Delta value. We then have the additional information on how robust certain intervals in the sequences are, that is, how long do they stay safe, as they continuously start to split and shrink throughout the process.
This is already possible by calling EMERALD for every Δ parameter, but this is computationally very expensive. I expect to be able to update the alignment space and the safety-windows in an amortized fashion.