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A survey on OR and mathematical methods applied on gene-environment networks

Author

Listed:
  • Gerhard-Wilhelm Weber
  • Erik Kropat
  • Basak Akteke-Öztürk
  • Zafer-Korcan Görgülü

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. Copyright Springer-Verlag 2009

Suggested Citation

  • Gerhard-Wilhelm Weber & Erik Kropat & Basak Akteke-Öztürk & Zafer-Korcan Görgülü, 2009. "A survey on OR and mathematical methods applied on gene-environment networks," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 17(3), pages 315-341, September.
    • Handle: RePEc:spr:cejnor:v:17:y:2009:i:3:p:315-341
    DOI: 10.1007/s10100-009-0092-4
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    References listed on IDEAS

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    1. Carlo Carraro & Vito Fragnelli (ed.), 2004. "Game Practice and the Environment," Books, Edward Elgar Publishing, number 3344.
    2. Dinko Dimitrov & Stef Tijs & Rodica Branzei, 2003. "Shapley-like values for interval bankruptcy games," Economics Bulletin, AccessEcon, vol. 3(9), pages 1-8.
    3. repec:ebl:ecbull:v:3:y:2003:i:9:p:1-8 is not listed on IDEAS
    4. Gerhard-Wilhelm Weber & Aysun Tezel, 2007. "On generalized semi-infinite optimization of genetic networks," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(1), pages 65-77, July.
    5. G.-W. Weber & P. Taylan & S. Alparslan-Gök & S. Özöğür-Akyüz & B. Akteke-Öztürk, 2008. "Optimization of gene-environment networks in the presence of errors and uncertainty with Chebychev approximation," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(2), pages 284-318, December.
    6. Tijs, S.H. & Brânzei, R., 2004. "Cost sharing in a joint project," Other publications TiSEM 38dc89bd-b4ec-43a6-bdef-a, Tilburg University, School of Economics and Management.
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    Cited by:

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    3. Chandra Pedamallu & Linet Ozdamar & Erik Kropat & Gerhard-Wilhelm Weber, 2012. "A system dynamics model for intentional transmission of HIV/AIDS using cross impact analysis," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 20(2), pages 319-336, June.
    4. Immanuel Bomze & Karl F. Dörner & Richard F. Hartl & Ulrike Leopold-Wildburger & Georg Pflug & Marion Rauner & Christian Stummer & Gernot Tragler & Tina Wakolbinger, 2018. "Emerging and innovative OR applications: a special issue in honor of Walter J. Gutjahr," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 26(2), pages 259-263, June.
    5. Chen, Jianxin & Zheng, Junhao & Zhang, Tonghua & Hou, Rui & Zhou, Yong-wu, 2022. "Dynamical complexity of pricing and green level for a dyadic supply chain with capital constraint," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 195(C), pages 1-21.

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