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A Review on Data Mining and Continuous Optimization Applications in Computational Biology and Medicine

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Executive Summary

An emerging research area in computational biology and biotechnology is devoted to mathematical modeling and prediction of gene-expression patterns; it nowadays requests mathematics to deeply understand its foundations. This paper surveys data mining and machine learning methods for an analysis of complex systems in computational biology. It mathematically deepens recent advances in modeling and prediction by rigorously introducing the environment and aspects of errors and uncertainty into the genetic context within the framework of matrix and interval arithmetics. Given the data from DNA microarray experiments and environmental measurements one extracts nonlinear ordinary differential equations which contain parameters that are to be determined. This is done by a generalized Chebychev approximation and generalized semi-infinite optimization. Then, time-discretized dynamical systems are studied.

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