Optimization of gene-environment networks in the presence of errors and uncertainty with Chebychev approximation

Date

2008-12-01

Author

Weber, Gerhard Wilhelm
Taylan, P.
Alparslan-Gok, S. Z.
Oezoeguer-Akyuz, S.
Akteke-Ozturk, B.

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

41
views

0
downloads

This mathematical contribution is addressed towards the wide interface of life and human sciences that exists between biological and environmental information. Like very few other disciplines only, the modeling and prediction of genetical data is requesting mathematics nowadays to deeply understand its foundations. This need is even forced by the rapid changes in a world of globalization. Such a study has to include aspects of stability and tractability; the still existing limitations of modern technology in terms of measurement errors and uncertainty have to be taken into account. In this paper, the important role played by the environment is rigorously introduced into the biological context and connected with employing the theories of optimization and dynamical systems. Especially, a matrix-vector and interval concept and algebra are used; some special attention is paid to splines. From data got by DNA microarray experiments and environmental measurements we extract nonlinear ordinary differential equations. This is done by Chebychev approximation and semi-infinite optimization. Then, time-discretized dynamical systems are studied. By a combinatorial algorithm which constructs and follows polyhedra sequences, the region of parametric stability is detected. This is used for testing and maybe improving the goodness of the achieved model. We analyze the topological landscape of gene-environment networks in terms of structural stability which we characterize. This pioneering practically motivated and theoretically elaborated work is devoted to a contribution to better health care, progress in medicine, better education, and to recommending more healthy living conditions. The present paper mainly bases on the authors’ and their coauthors’ contributions of the last few years, it critically discusses structural frontiers and future challenges, while respecting related research contributions, giving access and referring to alternative concepts that exist in the literature.

Subject Keywords

Statistics and Probability, Discrete Mathematics and Combinatorics

URI

https://hdl.handle.net/11511/52094

Journal

TOP

DOI

https://doi.org/10.1007/s11750-008-0052-5

Collections

Graduate School of Applied Mathematics, Article

Suggestions

OpenMETU
Core

A new outlier detection method based on convex optimization: application to diagnosis of Parkinson's disease TAYLAN, PAKİZE; Yerlikaya-Ozkurt, Fatma; Bilgic Ucak, Burcu; Weber, Gerhard Wilhelm (Informa UK Limited, 2020-12-01) Neuroscience is a combination of different scientific disciplines which investigate the nervous system for understanding of the biological basis. Recently, applications to the diagnosis of neurodegenerative diseases like Parkinson's disease have become very promising by considering different statistical regression models. However, well-known statistical regression models may give misleading results for the diagnosis of the neurodegenerative diseases when experimental data contain outlier observations that l...
An algorithm to analyze stability of gene-expression patterns Gebert, J; Latsch, M; Pickl, SW; Weber, Gerhard Wilhelm; Wunschiers, R (Elsevier BV, 2006-05-01) Many problems in the field of computational biology consist of the analysis of so-called gene-expression data. The successful application of approximation and optimization techniques, dynamical systems, algorithms and the utilization of the underlying combinatorial structures lead to a better understanding in that field. For the concrete example of gene-expression data we extend an algorithm, which exploits discrete information. This is lying in extremal points of polyhedra, which grow step by step, up to a...
Integration of topological measures for eliminating non-specific interactions in protein interaction networks BAYIR, Murat Ali; GUNEY, Tacettin Dogacan; Can, Tolga (Elsevier BV, 2009-05-28) High-throughput protein interaction assays aim to provide a comprehensive list of interactions that govern the biological processes in a cell. These large-scale sets of interactions, represented as protein-protein interaction networks, are often analyzed by computational methods for detailed biological interpretation. However, as a result of the tradeoff between speed and accuracy, the interactions reported by high-throughput techniques occasionally include non-specific (i.e., false-positive) interactions. ...
Long-tailed graphical model and frequentist inference of the model parameters for biological networks AĞRAZ, MELİH; Purutçuoğlu Gazi, Vilda (Informa UK Limited, 2020-03-12) The biological organism is a complex structure regulated by interactions of genes and proteins. Various linear and nonlinear models can define activations of these interactions. In this study, we have aimed to improve the Gaussian graphical model (GGM), which is one of the well-known probabilistic and parametric models describing steady-state activations of biological systems, and its inference based on the graphical lasso, shortly Glasso, method. Because, GGM with Glasso can have low accuracy when the syst...
Evaluation of the genetic algorithm parameters on the optimization performance: a case study on pump-and-treat remediation design Gungor-Demirci, Gamze; Aksoy, Ayşegül (Springer Science and Business Media LLC, 2010-12-01) In this study, the impacts of different crossover and encoding schemes on the performance of a genetic algorithm (GA) in finding optimal pump-and-treat (P&T) remediation designs are investigated. For this purpose, binary and Gray encodings of the decision variables are tested. Uniform and two-point crossover schemes are evaluated for two different crossover probabilities. Analysis is performed for two P&T system optimization scenarios. Results show that uniform crossover operator with Gray encoding outperfo...

Citation Formats

G. W. Weber, P. Taylan, S. Z. Alparslan-Gok, S. Oezoeguer-Akyuz, and B. Akteke-Ozturk, “Optimization of gene-environment networks in the presence of errors and uncertainty with Chebychev approximation,” TOP, pp. 284–318, 2008, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/52094.