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An update rule and a convergence result for a penalty function method
Optimization and dynamics of geneenvironment networks with intervals
1.  Institute of Applied Mathematics, Middle East Technical University, 06531 Ankara, Turkey, Turkey 
Based on data from DNA microarray experiments, nonlinear ordinary differential equations are extracted by leastsquares and, then, timediscretized dynamical systems are derived. Using a combinatorial algorithm which constructs and observes polyhedra sequences, the region of parametric stability is detected. This supports the testing of the quality of data fitting. For the parameter estimation we apply a GSIP problem; we characterize its structural stability.
Hopefully, this pioneering study will serve and lead to a more realistic understanding and forecast in biomedicine, food engineering, and biotechnology. The inclusion of error and imprecision intervals may lead to a more careful evaluation of the experimental data in the forthcoming years, especially, when the microarray technology becomes more and more refined.
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