MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

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.

MSC Codes:
93A10, 94A17, 92B05
robustness, complexity, network information flow, entropy, causality

Related publications

2007 Repository Open Access
Nihat Ay and David C. Krakauer

Geometric robustness theory and biological networks

In: Theory in biosciences, 125 (2007) 2, pp. 93-121