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Regulatory Networks under Ellipsoidal Uncertainty – Data Analysis and Prediction by Optimization Theory and Dynamical Systems

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Data Mining: Foundations and Intelligent Paradigms

Part of the book series: Intelligent Systems Reference Library ((ISRL,volume 24))

Abstract

We introduce and analyze time-discrete target-environment regulatory systems (TE-systems) under ellipsoidal uncertainty. The uncertain states of clusters of target and environmental items of the regulatory system are represented in terms of ellipsoids and the interactions between the various clusters are defined by affine-linear coupling rules. The parameters of the coupling rules and the time-dependent states of clusters define the regulatory network. Explicit representations of the uncertain multivariate states of the system are determined with ellipsoidal calculus. In addition, we introduce various regression models that allow us to determine the unknown system parameters from uncertain (ellipsoidal) measurement data by applying semidefinite programming and interior point methods. Finally, we turn to rarefications of the regulatory network. We present a corresponding mixed integer regression problem and achieve a further relaxation by means of continuous optimization. We analyze the structure of the optimization problems obtained, especially, in view of their solvability, we discuss the structural frontiers and research challenges, and we conclude with an outlook.

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Authors and Affiliations

  1. Institute for Theoretical Computer Science, Mathematics and Operations Research, Universität der Bundeswehr München, Werner-Heisenberg-Weg 39, 85577, Neubiberg, Germany

    Erik Kropat

  2. Institute of Applied Mathematics, Middle East Technical University, 06531, Ankara, Turkey

    Gerhard-Wilhelm Weber

  3. Faculty of Economics, Business and Law, University of Siegen, Germany

    Gerhard-Wilhelm Weber

  4. Center for Research on Optimization and Control, University of Aveiro, Portugal

    Gerhard-Wilhelm Weber

  5. Faculty of Science, Universiti Teknologi Malaysia, Skudai, Malaysia

    Gerhard-Wilhelm Weber

  6. Bioinformatics Group, New England Biolabs Inc, 240 County Road, Ipswich, MA, 01938, USA

    Chandra Sekhar Pedamallu

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  1. Erik Kropat
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  2. Gerhard-Wilhelm Weber
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  3. Chandra Sekhar Pedamallu
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Editors and Affiliations

  1. Department of Statistics andApplied Probability, University of California , 93106, Santa Barbara, CA, USA

    Dawn E. Holmes

  2. Knowledge-Based Engineering, University of South Australia, 5095, Adelaide Mawson Lakes, SA, Australia

    Lakhmi C. Jain

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Kropat, E., Weber, GW., Pedamallu, C.S. (2012). Regulatory Networks under Ellipsoidal Uncertainty – Data Analysis and Prediction by Optimization Theory and Dynamical Systems. In: Holmes, D.E., Jain, L.C. (eds) Data Mining: Foundations and Intelligent Paradigms. Intelligent Systems Reference Library, vol 24. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23241-1_3

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