A New Mathematical Approach in Environmental and Life Sciences: Gene–Environment Networks and Their Dynamics |
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Authors: | G-W Weber S Z Alparslan-Gök B Söyler |
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Institution: | (1) Institute of Applied Mathematics, METU, 06531 Ankara, Turkey;(2) Faculty of Arts and Sciences, Department of Mathematics, Süleyman Demirel University, 32 260 Isparta, Turkey;(3) Department of Food Engineering, METU, 06531 Ankara, Turkey |
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Abstract: | An important research area in life sciences is devoted to modeling, prediction, and dynamics of gene-expression patterns.
As clearly understood in these days, this enterprise cannot become satisfactory without acknowledging the role of the environment.
To a representation of past, present, and most likely future states, we also encounter measurement errors and uncertainties.
This paper surveys and improves recent advances in understanding the foundations and interdisciplinary implications of the
newly introduced gene–environment networks, and it integrates the important theme of carbon dioxide emission reduction into
the networks and dynamics. We also introduce some operational and managerial issues of practical working and decision making,
expressed in terms of sliding windows, quadrants (modules) of parametric effects, and navigating (controlling) between such effects and directing them. Given data from DNA microarray experiments and environmental records, we extract
nonlinear ordinary differential equations that contain parameters that have to be determined. For this, we employ modern (Chebychevian)
approximation and (generalized semi-infinite) optimization. After this is provided, time- discretized dynamical systems are
studied. A combinatorial algorithm with polyhedra sequences allows to detect the region of parametric stability. Finally,
we analyze the topological landscape of gene–environment networks with its structural (in)stability. By embedding as a module
and investigating CO2 emission control and figuring out game theoretical aspects, we conclude. This pioneering work is theoretically elaborated,
practically devoted to health care, medicine, education, living conditions, and environmental protection, and it invites the
readers to future research.
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Keywords: | Environment Computational biology Errors Uncertainty Modeling Dynamics Intervals Matrices Stability Approximation GSIP Games Topology Conic programming |
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