The idea is brilliant, even if a bit unclear. The authors are interested in adaptation, and how an organism adapts to environmental change. To do this (theoretically), they create a mathematical model of several known signaling pathways. These pathways are then "perturbed" using a series of input transformations, and evaluated using a series of outputs. This has been done by Uri Alon before to look at the phenomenon of "switching" in biological systems.
The main premise is that the fold-change of inputs, and not the change in their absolute value per se, provide a signal to the organism about its environment. The organism adapts to this response, either through accommodation (learning to incorporate the signal into its behavioral repertoire) or through a robustness mechanism (learning to respond to the signal without disturbance). Models of signaling pathways were used to illustrate how adaptation proceeds given different types of network organization (feedforward vs. feedback).
The most interesting contribution of this paper involves their interpretation of adaptation as being a form of disturbance rejection. Disturbance rejection is a form of control in which certain parts of a signal are rejected as noise. Thus, one of the hypotheses presented here is that adaptation is a form of noise reduction. This may or may not be true, considering that adaptation can be a very general process. Noise might be minimized as a result of adaptation, but noise may also play a role in allowing further adaptation. As you read the paper, keep in mind that the results are meant to represent bacteria, and not necessarily plants or animals.