Ten restarts from other random initial conditions converged to very similar distributions, so the first one was retained.
Given a condition, we calculated the percentage of the 10,000 randomly sampled initial states converged to the cell cycle or sporulation attractor with and without a perturbation.
Under either condition, a significant portion of initial states converged to the "other" attractor (neither cell cycle nor sporulation), which illustrates the stochasticity in the network.
When either cell cycle or sporulation signal is turned on, as expected, the cell prefers the corresponding attractor: under growth condition, 70%and16%6% of initial states converged to cell cycle and sporulation attractors, respectively; under sporulation condition, these percentages were <0.1%and50%0%.
Numerically simulating (13) from different initial points chosen from a grid in the hypercube [0,1]3, we counted the number of initial points converging to a given NEP so as to estimate the volume of its region of attraction.
The designed controllers guarantee that a given linear functions of the state vector, starting from any initial condition, converges exponentially to its prescribed zones.
The results show that a minimum of 90% (usually around 95%) of the initial values converge to the global minimum giving the true optimal weighting factors.
More than half of the twenty best simulations started from random initial conditions converge to the folding funnel of the native conformation, but several competing low-energy metastable conformations were observed.
According to the physical experiments in the Ordos Basin, sandstone porosity decreases with increasing overburden load, and the porosity-decrease trends of two similar samples with different initial porosities converge gradually.
The essence of this method consists in construction of an initial approximation of the feedback matrix such that a numerical sequence, which generated by arbitrary iterative method and beginning from this initial approximation, converges to an exact solution of the feedback design problem.
