Assessing the effect of unknown widespread perturbations in complex systems using the ν-gap

Pinpointing the exact locations of perturbations can help to detect and correct faults in large-scale systems, such as power grids (lost of transmission lines), internet (loss of servers) and biological systems (diseases). This paper outlines a mathematical framework to study the effect of perturbations on large-scale systems, with particular emphasis to biological applications. In particular, it focuses on wide-spread perturbations that target unknown components of the system. These problems are usually studied with genome-wide assays, which are becoming increasingly popular and accessible. However, analysis of the data sets produced by this technology remains challenging: genome-wide experiments are often inherently noisy, with a small number of measurements, and a low sampling rate. The paper first develops a simple yet powerful network inference tool based on LTIs. We compare this tool with the current state of the art. Then, as its major contribution, the paper develops a method for network differentiation, where it detects the effects of perturbations in large scale-systems. The method is based on the ν-gap, a control engineering tool that measures the distance between linear models. A major difference between this work and others, is that we look at changes in dynamics in links, as opposed to the standard differential expression analysis that focuses on changes in node concentrations. Through an illustrative model, the paper shows how perturbations impact certain links in the network, which can then be captured by differences between LTIs with the ν-gap.