Mathematical and data mining contributions to dynamics and optimization of gene-environment networks

Date

2007-01-01

Author

Weber, Gerhard-Wilhelm
Taylan, Pakize
Öztürk, Başak
Uğur, Ömür

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This paper further introduces continuous optimization into the fields of computational biologyandenvironmental protection which belong to the most challengingandemerging areas of science. It refines earlier ones of our models on gene-environment patterns by the use of optimization theory. We emphasize that it bases onandpresents work done in [61, 66]. Furthermore, our paper tries to detectandovercome some structural frontiers of our methods applied to the recently introduced gene-environment networks. Based on the experimental data, we investigate the ordinary differential equations having nonlinearities on the right-handsideanda generalized treatment of the absolute shift term which represents the environmental effects. The genetic process is studied by a time-discretization, in particular, Runge-Kutta type discretization. The possibility of detecting stabilityandinstability regions is being shown by a utilization of the combinatorial algorithm of BraytonandTong which is based on the orbits of polyhedra. The time-continuousanddiscrete systems can be represented by means of matrices allowing biological implications, they encodeandare motivated by our gene-environment networks. A specific contribution of this paper consists in a careful but rigorous integration of the environment into modelinganddynamics,andin further new sights. Relations to parameter estimation within modeling, especially, by using optimization, are indicated,andfuture research is addressed, especially towards the use of stochastic differential equations. This practically motivatedandtheoretically elaborated work is devoted for a contribution to better health care, progress in medicine, a better educationandmore healthy living conditions recommended.Keywords: computational biology, generalized semi-infinite programming,mathematicalmodeling, dynamical systems, gene-expression data, environment, stability, structural stability, structural frontiers, continuous, discrete, hybrid, spline, inverse problem, penalization, regularization, stochastic differential equationsPrevious article: Computer SimulationandOptimization of Stirrer Hydrodynamics at High Reynolds NumbersPrevNext article: Derivative Free Optimization of Stirrer ConfigurationsNext

URI

https://hdl.handle.net/11511/104598

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Department of Industrial Engineering, Article