A conceptual and mathematical basis for experimental perturbations is necessary not only for the design of experiments for system identification but also for the foundation of a theory of network robustness. We use an approach to robustness of a functional network against knockouts that is based on conditional independence (CI) statements, building on the robustness theory proposed by Nihat Ay and David Krakauer.

Algebraic statistics provides methods from commutative algebra and algebraic geometry in order to study such collections of CI statements. In particular, primary decomposition of CI ideals can be used to determine the solution set of these statements. We aim at further studying such varieties in order to derive design principles for robust systems.

This project is part of the VW project Evolution of Networks: Modelling the complexity and robustness of evolving biochemical networks , and it is also supported by the Santa Fe Institute .

Katja Müller
Further Information:
Supported by the Volkswagen Stiftung
Related Group Publications:
Ay, N.: Ingredients for robustness. Theory in biosciences, 139 (2020) 4, p. 309-318 Bibtex [DOI]

Ay, N. ; Krakauer, D. C. and J. C. Flack: Robustness, causal networks, and experimental design. Princeton University Press, 2018 Bibtex

Rauh, J.: The polytope of \(k\)-star densities. The electronic journal of combinatorics, 24 (2017) 1, P1.4 Bibtex [DOI]

Rauh, J. and N. Ay: Robustness, canalyzing functions and systems design. Theory in biosciences, 133 (2014) 2, p. 63-78 Bibtex MIS-Preprint: 66/2012 [DOI] [ARXIV]

Rauh, J.: Generalized binomial edge ideals. Advances in applied mathematics, 50 (2013) 3, p. 409-414 Bibtex [DOI] [ARXIV]

Rauh, J. and N. Ay: Robustness and conditional independence ideals. Bibtex MIS-Preprint: 63/2011 [ARXIV]

Herzog, J. ; Hibi, T. ; Hreinsdottir, F. ; Kahle, T. and J. Rauh: Binomial edge ideals and conditional independence statements. Advances in applied mathematics, 45 (2010) 3, p. 317-333 Bibtex [DOI] [ARXIV]

Krakauer, D. C. ; Flack, J. C. and N. Ay: Probabilistic design principles for robust multimodal communication networks. Modelling perception with artificial neural networks / C. R. Tosh... (eds.). Cambridge University Press, 2010. - P. 255-268 Bibtex [DOI]

Ay, N. ; Flack, J. C. and D. C. Krakauer: Robustness and complexity co-constructed in multimodal signalling networks. Philosophical transactions of the Royal Society of London / B, 362 (2007) 1479, p. 441-447 Bibtex [DOI]

Ay, N. and D. C. Krakauer: Geometric robustness theory and biological networks. Theory in biosciences, 125 (2007) 2, p. 93-121 Bibtex MIS-Preprint: 14/2006 [DOI]