A survey on OR and mathematical methods applied on gene-environment networks |
| |
Authors: | Gerhard-Wilhelm Weber Erik Kropat Basak Akteke-Öztürk Zafer-Korcan Görgülü |
| |
Institution: | 1. Institute of Applied Mathematics, Middle East Technical University, 06531, Ankara, Turkey 2. Faculty of Economics, Business and Law, University of Siegen, 57068, Siegen, Germany 3. Department of Mathematics, University Erlangen-Nuremberg, 91058, Erlangen, Germany 4. Universit?t der Bundeswehr München, 85577, Neubiberg, Germany
|
| |
Abstract: | In this paper, we survey the recent advances and mathematical foundations of gene-environment networks. We explain their interdisciplinary
implications with special regard to human and life sciences as well as financial sciences. Special attention is paid to applications
in Operational Research and environmental protection. Originally developed in the context of modeling and prediction of gene-expression
patterns, gene-environment networks have proved to provide a conceptual framework for the modeling of dynamical systems with
respect to errors and uncertainty as well as the influence of certain environmental items. Given the noise-prone measurement
data we extract nonlinear differential equations to describe and analyze the interactions and regulating effects between the
data items of interest and the environmental items. In particular, these equations reflect data uncertainty by the use of
interval arithmetics and comprise unknown parameters resulting in a wide variety of the model. For an identification of these
parameters Chebychev approximation and generalized semi-infinite optimization are applied. In addition, the time-discrete
counterparts of the nonlinear equations are introduced and their parametrical stability is investigated by a combinatorial
algorithm which detects the region of parameter stability. Finally, we analyze the topological landscape of the gene-environment
networks in terms of structural stability. We conclude with an application of our analysis and introduce the eco-finance networks. |
| |
Keywords: | Gene-environment networks Operational research Financial mathematics Environmental protection Generalized semi-infinite programming Dynamical systems Computational statistics Uncertainty Identification Structural stability Computational biology |
本文献已被 SpringerLink 等数据库收录! |
|