kyuhyongpark
commented
1 year ago As I mentioned in #72, I need the full SDs calculated and stored for the in-depth analysis. Right now I have rough results on the 'easy-to-calculate' networks.
Here's a simple visualization of SD size and SD depth, with the available data. I'll try to keep update it. https://docs.google.com/spreadsheets/d/1NVDuxSWYEbrHx2vo7j4lsZI8IT-9DL1uhQr3SfIHUSA/edit?usp=sharing
jcrozum
Here are some thoughts on what we want to look at when we construct SDs and find the attractors.
Not complete / Not univocal / Not faithful minimal trapspaces
Not complete
This means that there is a motif avoidant attractor So far we have not found a single motif avoidant attractor.
Not univocal
This means there are more than 2 attractors in a single minimal trapspace. So far we found none, as number of attractors always matched the number of minimal trapspaces.
Not faithful
This means that the attractor does not span the whole minimal trapspace. I think there will be many such cases, but I don't know how to find and count them.
Correlations between parameters
NOTE: even for the full expansion, source nodes are treated separately. This may make it difficult to compare random models with empirical models, because the source nodes are already fixed in empirical models.
[x] We found that empirical models do not show significant correlation between N and size/depth/n_att, at least in the range of N = 10~300.
[x] We found that the size and n_att scale exponentially with depth. i.e. d ~ log(size) and d ~ log(n_att). Depth tend to be larger than log2(n_att) in both the empirical models and the random models. This means that the models' decisions tend to be inefficient compared to a binary search.
[ ] We need size, depth, n_att for larger random NK models and random NCF models, to build better figure for the succession diagram scaling. This should be done with full expansion.
[ ] We need n_att and depth for larger random NK models, to reproduce n_att vs N graph made with pystablemotifs. Also we can look for correlations between depth and N for the random NK model. Since there is correlation between #att and N for random NK models (n_att ~ N0.12), we can expect d ~ 0.12 log(N). We can use source SCC expansion for this.
Other properties
We are almost certain that the succession diagram can come in any shape. Hence the properties of the SD should be coming from the properties of the ensembles.
Decision points Suppose we do a breath first search from each attractor. For each pair of attractors, the lowest trapspace where they meet could be called the decision point of the pair. What's the portion of the nodes that are decision points? For example, the simplified SD of the cell cycle model
The green nodes are the decision points.
If the system is monostable, there will be no decision points.
If the system only consists of sources (and if we don't fix sources when we construct the SD), every node in the SD will be decision points.
Reducing nodes with out-degree 1 These nodes will not be decision points. Maybe reducing them will reveal more?