On generalized semi-infinite optimization of genetic networks

2007-07-01
Weber, Gerhard Wilhelm
Tezel, Aysun
Since some years, the emerging area of computational biology is looking for its mathematical foundations. Based on modem contributions given to this area, our paper approaches modeling and prediction of gene-expression patterns by optimization theory, with a special emphasis on generalized semi-infinite optimization. Based on experimental data, nonlinear ordinary differential equations are obtained by the optimization of least-squares errors. The genetic process can be investigated by a time-discretization and a utilization of a combinatorial algorithm to detect the stability regions. We represent the dynamical systems by means of matrices which allow biological-medical interpretations, and by genetic or new gene-environment networks. For evaluating these networks we optimize them under constraints imposed. For controlling the connectedness structure of the network, we introduce GSIP into this modem application field which can lead to important services in medicine and biotechnology, including energy production and material science.

Suggestions

On optimization, dynamics and uncertainty: A tutorial for gene-environment networks
WEBER, G. -W.; Uğur, Ömür; Taylan, P.; TEZEL, AYSUN (2009-05-28)
An emerging research area in computational biology and biotechnology is devoted to mathematical modeling and prediction of gene-expression patterns; to fully understand its foundations requires a mathematical study. This paper surveys and mathematically expands 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 arithmetic. Given the data from DNA microarray experiments...
An algorithmic approach to analyse genetic networks and biological energy production: an introduction and contribution where OR meets biology
Uğur, Ömür; WEBER, G. -W.; WUENSCHIERS, R. (2009-01-01)
An emerging research area in computational biology and biotechnology is devoted to modelling and prediction of gene-expression patterns. In this article, after a short review of recent achievements we deepen and extend them, especially, by emphasizing and analysing the elegant means of matrix algebra. Based on experimental data, ordinary differential equations with nonlinearities on the right-hand side and a generalized treatment of the absolute shift term, representing the environmental effects, are invest...
A Review on Data Mining and Continuous Optimization Applications in Computational Biology and Medicine
Weber, Gerhard Wilhelm; Ozogur-Akyuz, Sureyya; Kropat, Erik (2009-06-01)
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 article 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 con...
Optimization and dynamics of gene-environment networks with intervals
Uğur, Ömür (2007-05-01)
There are a few areas of science and technology which are only as challenging, emerging and promising as computational biology. This area is looking for its mathematical foundations, for methods of prediction while guaranteeing robustness, and it is of a rigorous interdisciplinary nature. In this paper, we deepen and extend the approach of learning gene-expression patterns in the framework of gene-environment networks by optimization, especially, generalized semi-infinite optimization (GSIP). With respect t...
Mathematical contributions to dynamics and optimization of gene-environment networks
Weber, Gerhard Wilhelm; Tezel, Aysun; TAYLAN, PAKİZE; Soyler, Alper; Cetin, Mehmet (Informa UK Limited, 2008-01-01)
This article contributes to a further introduction of continuous optimization in the field of computational biology which is one of the most challenging and emerging areas of science, in addition to foundations presented and the state-of-the-art displayed in [C.A. Floudas and P.M. Pardalos, eds., Optimization in Computational Chemistry and Molecular Biology: Local and Global Approaches, Kluwer Academic Publishers, Boston, 2000]. Based on a summary of earlier works by the coauthors and their colleagues, it r...
Citation Formats
G. W. Weber and A. Tezel, “On generalized semi-infinite optimization of genetic networks,” TOP, pp. 65–77, 2007, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/56732.