***4. Version 2024-09-16**: This is the version included at the root folder of this repository. The difference with the previous version is that we modified the c++ script to compute the linking number between minimum loops **ComputeLinking.c++**.
***4. Version 2024-09-16**: The difference with the previous version is that we modified the c++ script to compute the linking number between minimum loops **ComputeLinking.c++**.
> *LinkingMap* change from a 2D vector to an integer. This saves a lot of memory ram, particularly when dealing with several loops.
>
> The mn-elements of the linking matrix are now printed only when the linking between loops m and n is different from zero. This saves storage space.
>
> We don't perform the loop to reconstruct the second minimum loops starting from a different bead. Instead, we work-out a set of translations that allows us to compute linking only once between every pair of minimum loops. This saves computational time.
***5. Version 2024-12-19**: This is the version included at the root folder of this repository:
> First, we modified the Mathematica script (**MinLoops.m**) to compute the minimum loops: in the previous version we used to find all loops passing through a vertex ($r_{1}$) and formed by at the most $l_{max}=20$ DNAns. Then, we selected the smallest of these loops. This is not efficient and therefore, this time we compute first all the loops formed by $l=l_{min}=4$ DNAns. If no loops are found, we continue our search (through the same vertex $r_{1}$) of loops made by l=5 DNAns. This process is repeated until we find at least one loop of any length $l\in[l_{min},l_{max}]$.
>
> We also modified **fractalD_ring_v2.cpp**. In the previous version we used to impose a constraint in the radius of gyration of nanostars ($R_{g, min} < 0.3L$, where L is the size of the cubic box). This was necessary to exclude fake rings (linear chains linked through the PBC) in our analysis. Howevever, if we use a more general form of the Minimum Image Criteria (MIC) to reconstruct loops, then we can remove this condition and only ask that the end-to-end distance of reconstructed loops is smaller than the distance between consecutive beads in the arms of a DNAns.
>
> The same general form of the MIC is implemented in **ComputeLinking.c++**.
