id: 06004538
dt: a
an: 06004538
au: Kropat, Erik; Weber, Gerhard-Wilhelm; Pedamallu, Chandra Sekhar
ti: Regulatory networks under ellipsoidal uncertainty ‒ data analysis and
    prediction by optimization theory and dynamical systems.
so: Holmes, Dawn E. (ed.) et al., Data mining: foundations and intelligent
    paradigms. Volume 2: Statistical, Bayesian, time series and other
    theoretical aspects. Berlin: Springer (ISBN 978-3-642-23240-4/hbk;
    978-3-642-23241-1/ebook). Intelligent Systems Reference Library 24,
    27-56 (2012).
py: 2012
pu: Berlin: Springer
la: EN
cc: 
ut: regulatory systems; continuous optimization; mixed integer programming;
    mathematical modeling; uncertainty; networks; operations research;
    parameter estimation; dynamical systems; gene-environment networks;
    eco-finance networks
ci: 
li: doi:10.1007/978-3-642-23241-1_3
ab: Summary: 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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