Sensitivity Analysis

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.

Boolean Sensitivity

The standard definition of sensitivity at a given state of a Boolean network is defined in terms of the Hamming distance:

\[D_H(x,y) = \sum_{i} x_i \oplus y_i.\]

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

\[s_f(x) = \frac{1}{N} \sum_{i = 1}^N D_H(f(x), f(x \oplus e_i))\]

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])

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

\[s_f = \frac{1}{2^N} \sum_{x} s_f(x).\]

In Neet, just ask for it

>>> s_pombe.average_sensitivity()

For a full range of sensitivity-related features offered by Neet, see the API References.