An algorithm to analyze stability of gene-expression patterns

2006-05-01
Gebert, J
Latsch, M
Pickl, SW
Weber, Gerhard Wilhelm
Wunschiers, R
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 possible stopping. We study gene-expression data in time, mathematically model it by a time-continuous system, and time-discretize this system. By our algorithm we compute the regions of stability and instability. We give a motivating introduction from genetics, present biological and mathematical interpretations of (in)stability, point out structural frontiers and give an outlook to future research.
DISCRETE APPLIED MATHEMATICS

Suggestions

The Asian contribution to the Turkish population with respect to the Balkans: Y-chromosome perspective
Berkman, Ceren Caner; Togan, İnci Zehra (Elsevier BV, 2009-05-28)
Admixture analysis is one of the methods that can be used to calculate the contribution of migrations. There are several admixture estimation methods. In the present study, Chikhi et al.'s admixture method, which considers the effect of genetic drift, was used to estimate the male genetic contribution of Central Asia to hybrids. It was observed that the male contribution from Central Asia to Turkish population with reference to the Balkans was 13%. Comparison of the admixture estimate for Turkey with those ...
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...
Optimization of gene-environment networks in the presence of errors and uncertainty with Chebychev approximation
Weber, Gerhard Wilhelm; Taylan, P.; Alparslan-Gok, S. Z.; Oezoeguer-Akyuz, S.; Akteke-Ozturk, B. (Springer Science and Business Media LLC, 2008-12-01)
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 i...
An analysis of a linearly extrapolated BDF2 subgrid artificial viscosity method for incompressible flows
Demir, Medine (Elsevier BV, 2020-10-01)
This report extends the mathematical support of a subgrid artificial viscosity (SAV) method to simulate the incompressible Navier-Stokes equations to better performing a linearly extrapolated BDF2 (BDF2LE) time discretization. The method considers the viscous term as a combination of the vorticity and the grad-div stabilization term. SAV method introduces global stabilization by adding a term, then anti-diffuses through the extra mixed variables. We present a detailed analysis of conservation laws, includin...
A new framework of multi-objective evolutionary algorithms for feature selection and multi-label classification of video data
Karagoz, Gizem Nur; Yazıcı, Adnan; Dokeroglu, Tansel; Coşar, Ahmet (2020-06-01)
There are few studies in the literature to address the multi-objective multi-label feature selection for the classification of video data using evolutionary algorithms. Selecting the most appropriate subset of features is a significant problem while maintaining/improving the accuracy of the prediction results. This study proposes a framework of parallel multi-objective Non-dominated Sorting Genetic Algorithms (NSGA-II) for exploring a Pareto set of non-dominated solutions. The subsets of non-dominated featu...
Citation Formats
J. Gebert, M. Latsch, S. Pickl, G. W. Weber, and R. Wunschiers, “An algorithm to analyze stability of gene-expression patterns,” DISCRETE APPLIED MATHEMATICS, pp. 1140–1156, 2006, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/56601.