Parameter Graphs
This tutorial showcases how one can generate parameter sets, i.e., $f_1 \times f_2 \times \ldots \times f_n$ supporting each steady state.
Then we plots the corresponding parameter graphs, i.e., 2D projections of $f_a \times f_b$ combinations. The figures won't look the same or be as beautiful as the one in the manuscript as it has been done manually in TikZ.
Toggle Switch
We can get a compact form of the parameter set for each node. The MBMs supporting these states can be arrived by taking combinations for each element in the set.
Otherwise, one can get the longer form where each parameter combination is present.
state A B
0 00 0 0
1 01 0 ID
2 01 0 1
3 01 ID ID
4 01 ID 1
5 10 ID 0
6 10 ID ID
7 10 1 0
8 10 1 ID
9 11 1 1
This allows for subsetting, and counting the exact number of models supporting each state.
We can then plot this as a parameter graph. The color of the heatmap gives the multistability it supports and the individual states are mentioned in the annotation, seperated by linebreak.
One can also get the parameter sets that support multistability between different states.
Toggle Switch with Self-Activation
Similar exercise can be done for networks with more inputs, but the visualization becomes tricky to interpret from the discontinuity due to partial order.
topo = '../../Inputs/Topo/TSSA.topo'
adjmat = mn.utils.topo_to_adj(topo)
ps = mn.tl.param_set(adjmat)
mn.pl.PG(ps,'A','B', (2,2))
states = pd.DataFrame([[1,0],[0,1],[0,0]], columns=adjmat.columns)
mn.tl.multistable(adjmat, states)
2 Team network with 3 nodes
For networks with more than 2 nodes, 2D parameter graph visualization becomes challenging. The approach is to iterate over parameter values for the additional nodes, creating separate 2D projections where other node functions are held constant.
ps = mn.tl.param_set(adjmat)
for funC in ps.loc[:,'C'].unique():
pssub = ps[ps.loc[:,'C'] == funC]
mn.pl.PG(pssub,'A','B', (2,2))
