Neet provides an API for computing various measures of sensitivity on Networks via the
SensitivityMixin. Sensitivity, in its simplest form, is a measure of how small
perturbations of the network’s state change under the dynamics. In the sensitivity parlance, a
network is called, sub-critical, critical, or chaotic if the perturbation tends to shrink,
stay the same, or grow over time.
As of the v1.0.0 release, only the
neet.boolean module provides implementations of the
sensitivity interface. A subsequent release will generalize this mixin to support a wider range
of network models.
The standard definition of sensitivity at a given state of a Boolean network is defined in terms of the Hamming distance:
That is, the number of bits differing between two binary states, \(x\) and \(y\). A Hamming neighbor of a state \(x\) is a state that differs from it by exactly \(1\) bit. We can write \(x \oplus e_i\) to represent the Hamming neighbor of \(x\) which differs in the \(i\)-th bit. The sensitivity of the state \(x\) is then defined as
where \(f\) is the network’s update function, and \(N\) is the number of nodes in the network.
Neet makes computing sensitivity at a given network state as straightforward as possible:
>>> s_pombe.sensitivity([0, 0, 0, 0, 0, 0, 0, 0 ,0]) 1.5555555555555556
More often than not, though, you’ll want to compute the average of the sensitivity over all of the states of the network. That is
In Neet, just ask for it
>>> s_pombe.average_sensitivity() 0.9513888888888888
For a full range of sensitivity-related features offered by Neet, see the API References.