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Geometric robustness theory and biological networks
Nihat Ay and David C. Krakauer
We provide a geometric framework for investigating the robustness of biological networks. We use information measures to quantify the impact of knockout perturbations to simple networks. Robustness has two components, a measure of the causal contribution of a node or nodes, and a measure of the change or exclusion dependence, of the network following node removal. Causality is measured as statistical contribution of a node to network function, whereas exclusion dependence measures the difference between the distribution of unperturbed network functions and the reconfigured network function. We explore the role that redundancy plays in increasing robustness, and how redundacy can be exploited by an error correcting code implemented by a network. We provide examples of the robustness measure when applied to familiar boolean functions such as the AND, OR amd XOR functions. We discuss the relationship between robustness measures and related measures of complexity.