Difference between fragments and n-mers?

There is a lot of terminology pertaining to the subsystems, i.e. monomers, fragments, overlaps, \(n\)-mers, etc. At the same time, there is also the realization that all of the methods boil down to running a series of computations and then combining those results to approximate the results of the target system. Natural questions then are: “Do we even need to discern among these terms?”, “Can we just ignore the origin of the subystems and treat them in a unified manner?”

The Hypothesis

TODO: citations

Given a set of subsystems, we can use the inclusion-exclusion principle to determine the additional overlaps, and the weights of those overlaps, needed to approximate the supersystem property. Notably, it does not matter if the provided subsystems are:

• disjoint fragments,

• non-disjoint fragments,

• \(n\)-mers formed from disjoint fragments,

• \(n\)-mers formed from non-disjoint fragments,

• a mix of non-disjoint fragments and their overlaps,

• a mix of \(n\)-mers formed from disjoint fragments and the overlaps of those \(n\)-mers, or

• a mix of \(n\)-mers formed from non-disjoint fragments and the overlaps of those \(n\)-mers.

Practical Distincitions

• Atoms in fragments are usually spatially close together

• n-mers may have spatially distant atoms