Modeling, inference and optimization of regulatory networks based on time series data. (English) Zbl 1221.93024

Summary: In this survey paper, we present advances achieved during the last years in the development and use of OR, in particular, optimization methods in the new gene-environment and eco-finance networks, based on usually finite data series, with an emphasis on uncertainty in them and in the interactions of the model items. Indeed, our networks represent models in the form of time-continuous and time-discrete dynamics, whose unknown parameters we estimate under constraints on complexity and regularization by various kinds of optimization techniques, ranging from linear, mixed-integer, spline, semi-infinite and robust optimization to conic, e.g., semi-definite programming. We present different kinds of uncertainties and a new time-discretization technique, address aspects of data preprocessing and of stability, related aspects from game theory and financial mathematics, we work out structural frontiers and discuss chances for future research and OR application in our real world.


93A30 Mathematical modelling of systems (MSC2010)
90C30 Nonlinear programming
90C22 Semidefinite programming
Full Text: DOI


[1] Achterberg, T., 2007. Constraint Integer Programming. Ph.D. Thesis. Technische Universität Berlin, Berlin. · Zbl 1169.90414
[2] Ahuja, R.K.; Magnanti, T.L.; Orlin, J.B., Network flow: theory, algorithms and applications, (1993), Prentice Hall NJ · Zbl 1201.90001
[3] Akhmet, M.U.; Gebert, J.; Öktem, H.; Pickl, S.W.; Weber, G.-W., An improved algorithm for analytical modeling and anticipation of gene expression patterns, Journal of computational technologies, 10, 4, 3-20, (2005) · Zbl 1071.92019
[4] Alizadeh, F., Interior-point methods in semidefinite programming with applications to combinatorial optimization, SIAM journal on optimization, 5, 1, 13-51, (1995) · Zbl 0833.90087
[5] Allison, D.B.; Cui, X.; Page, G.P.; Sabripour, M., Microarray data analysis: from disarray to consolidation and consensus, Nature reviews genetics, 7, 55-65, (2006)
[6] Alparslan Gök, S.Z., 2009. Cooperative Interval Games. Ph.D. Dissertation. Middle East Technical University, Ankara, Turkey.
[7] Alparslan Gök, S.Z., Weber, G.-W., 2010. Cooperative games under ellipsoidal uncertainty. In: Proceedings of PCO 2010, 3rd Global Conference on Power Control and Optimization (ISBN 978-983-44483-1-8), February 2-4, 2010, Gold Coast, Queensland, Australia.
[8] Alparslan Gök, S.Z.; Branzei, R.; Tijs, S., Convex interval games, Journal of applied mathematics and decision sciences, 29, 14, (2009), article id 342089 · Zbl 1186.91024
[9] Alparslan Gök, S.Z.; Miquel, S.; Tijs, S., Cooperation under interval uncertainty, Mathematical methods of operations research, 69, 1, 99-109, (2009) · Zbl 1159.91310
[10] Aster, A.; Borchers, B.; Thurber, C., Parameter estimation and inverse problems, (2004), Academic Press San Diego
[11] Berthold, T., Heinz, S., Vigerske, S., 2009. Extending a CIP Framework to Solve MIQCPs. Technical Report ZIB-TR 09-23. Konrad-Zuse-Zentrum fur Informationstechnik, Berlin. · Zbl 1242.90120
[12] Brazma, A.; Hingamp, P.; Quackenbush, J.; Sherlock, G.; Spellman, P.; Stoeckert, C.; Aach, J.; Ansorge, W.; Ball, C.A.; Causton, H.C.; Gaasterland, T.; Glenisson, P.; Holstege, F.C.; Kim, I.F.; Markowitz, V.; Matese, J.C.; Parkinson, H.; Robinson, A.; Sarkans, U.; Schulze-Kremer, S.; Stewart, J.; Taylor, R.; Vilo, J.; Vingron, M., Minimum information about a microarray experiment (MIAME)-toward standards for microarray data, Nature genetics, 29, 4, 365-371, (2001)
[13] Carbayo, M.S.; Bornman, W.; Cardo, C.C., DNA microchips: technical and practical considerations, Current organic chemistry, 4, 9, 945-971, (2000)
[14] Chen, T., He, H.L., Church, G.M., 1999. Modeling gene expression with differential equations. In: Proceedings of Pacific Symposium on Biocomputing, pp. 29-40.
[15] Collins, W.D., Hu, C. Fuzzily determined interval matrix games. <http://www-bisc.cs.berkeley.edu/BISCSE2005/Abstracts_Proceeding/Friday/FM3/Chenyi_Hu.pdf>.
[16] Córdoba Bueno, M., Fundamentals and practice of financial mathematics, (2006), Dykinson S.L. Madrid, Spain
[17] Defterli, O., Fügenschuh, A., Weber, G.-W., 2010. New discretization and optimization techniques with results in the dynamics of gene-environment networks. In: Proceedings of PCO 2010, 3rd Global Conference on Power Control and Optimization (ISBN 978-983-444483-1-8), February 2-4, 2010, Gold Coast, Queensland, Australia.
[18] DeRisi, J.; Iyer, V.; Brown, P., Exploring the metabolic and genetic control of gene expression on a genomic scale, Science, 278, 680-686, (1997)
[19] Dress, A., Karasözen, B., Stadler, P.F., Weber G.-W., (Guest Eds.) 2009. Special issue: networks in computational biology, Discrete Applied Mathematics 157, 10.
[20] Dubois, D.M.; Kalisz, E., Precision and stability of Euler, runge – kutta and incursive algorithm for the harmonic oscillator, International journal of computing anticipatory systems, 14, 21-36, (2004)
[21] Ergenç, T.; Weber, G.-W., Modeling and prediction of gene-expression patterns reconsidered with Runge-Kutta discretization. special issue at the occasion of 70th birthday of prof. Dr. karl roesner, TU Darmstadt, Journal of computational technologies, 9, 6, 40-48, (2004) · Zbl 1060.92045
[22] Fiedler, M.; Nedoma, J.; Ramik, J.; Rohn, J.; Zimmermann, K., Linear optimization problems with inexact data, (2006), Springer Verlag Berlin · Zbl 1106.90051
[23] Gebert, J.; Lätsch, M.; Pickl, S.W.; Weber, G.-W.; Wünschiers, R., Genetic networks and anticipation of gene expression patterns, Computing Anticipatory Systems: CASYS(92)03 - Sixth International Conference, AIP conference Proceedings, 718, 474-485, (2004)
[24] Gebert, J.; Lätsch, M.; Quek, E.M.P.; Weber, G.-W., Analyzing and optimizing genetic network structure via path-finding, Journal of computational technologies, 9, 3, 3-12, (2004) · Zbl 1057.92030
[25] Gebert, J.; Öktem, H.; Pickl, S.W.; Radde, N.; Weber, G.-W.; Yılmaz, F.B., Inference of gene expression patterns by using a hybrid system formulation – an algorithmic approach to local state transition matrices, (), 63-66
[26] Gebert, J., Lätsch, M., Pickl, S.W., Weber, G.-W., Wünschiers, R., 2006. An algorithm to analyze stability of gene-expression pattern. In: Anthony, M., Boros, E., Hammer, P.L., Kogan, A. (Guest Eds.), (special issue) Discrete Mathematics and Data Mining II. Discrete Applied Mathematics 154(7), 1140-1156.
[27] Gebert, J., Radde, N., Weber, G.-W., 2007. Modelling gene regulatory networks with piecewise linear differential equations. In: special issue (feature cluster) Challenges of Continuous Optimization in Theory and Applications. European Journal of Operational Research 181(3), 1148-1165. · Zbl 1124.92008
[28] Gökmen, A.; Kayaligil, S.; Weber, G.-W.; Gökmen, I.; Ecevit, M.; Sürmeli, A.; Bali, T.; Ecevit, Y.; Gökmen, H.; DeTombe, D.J., Balaban valley project: improving the quality of life in rural area in Turkey, International scientific journal of methods and models of complexity, 7, 1, (2004)
[29] Guckenheimer, J.; Holmes, P., Nonlinear oscillations, dynamical systems, and bifurcations of vector fields, (1997), Springer Berlin
[30] Hastie, T., Tibshirani, R., Friedman, J., 2001. The Elements of Statistical Learning - Data Mining, Inference and Prediction, Springer Series in Statistics, New York. · Zbl 0973.62007
[31] Heath, M., Scientific computing: an introductory survey, (2002), McGraw-Hill New York
[32] Hoon, M.D., Imoto, S., Kobayashi, K., Ogasawara, N., Miyano, S., 2003. Inferring gene regulatory networks from time-ordered gene expression data of Bacillus subtilis using differential equations. In: Proceedings of Pacific Symposium on Biocomputing, pp. 17-28. · Zbl 1219.92032
[33] Huang, S., Gene expression profiling, genetic networks and cellular states: an integrating concept for tumorigenesis and drug discovery, Journal of molecular medicine, 77, 469-480, (1999)
[34] Koch, T., 2004. Rapid Mathematical Programming. Ph.D. Thesis. Technical Report ZIB-TR 04-58. Technische Universität Berlin, Berlin.
[35] Kropat, E., Weber, G.-W., Akteke Öztürk, B., 2008. Eco-finance networks under uncertainty. In: Herskovits, J., Canelas, A., Cortes, H., Aroztegui, M. (Eds), Proceedings of the International Conference on Engineering Optimization (CD), EngOpt 2008. Rio de Janeiro, Brazil. ISBN 978857650156-5.
[36] Kropat, E.; Weber, G.-W.; Rückmann, J.J., Regression analysis for clusters in gene-environment networks based on ellipsoidal calculus and optimization, Dynamics of continuous, discrete and impulsive system, 17, 5, (2010) · Zbl 1206.93009
[37] Kropat, E., Weber, G.-W., Pedamallu, C.S., 2010b. Regulatory networks under ellipsoidal uncertainty – optimization theory and dynamical systems. Preprint No. 138. Institute of Applied Mathematics, METU, Ankara. · Zbl 1231.68208
[38] Kurzhanski, A.B.; Vályi, I., Ellipsoidal calculus for estimation and control, (1997), Birkhäuser · Zbl 0865.93001
[39] Kurzhanski, A.A.; Varaiya, P., Ellipsoidal toolbox manual, (2008), EECS Department, University of California Berkeley
[40] Kyoto, 1997a. Kyoto Contract. <http://www.unfccc.org/resource/convkp.html>.
[41] Kyoto, 1997b. Kyoto Protocol. <http://en.wikipedia.org/wiki/Kyoto-Protocol> (state: 22.09.07).
[42] Kyoto, 1997c. Kyoto Protocol. <http://vitalgraphics.grida.no/kyoto>.
[43] Li, Y.F.; Venkatesh, S.; Li, D., Modeling global emissions and residues of pesticided, Environmental modeling and assessment, 9, 237-243, (2004)
[44] Lozovanu, D.; Pickl, S.; Weber, G.-W., Optimization, monotonicity and the determination of Nash equilibria – an algorithmic analysis, (Invited paper) Computing Anticipatory Systems: CASYS’03 - Sixth International Conference, AIP conference Proceedings, 718, 351-361, (2004)
[45] Özcan, S., Yıldırım, V., Kaya, L., Becher, D., Hecker, M., Özcengiz, G., 2005. Phanerochaete chrysoporium proteome and a large scale study of heavy metal response. In: HIBIT - Proceedings of International Symposium on Health Informatics and Bioinformatics, Turkey’05. Antalya, Turkey, 2005, pp. 108-114.
[46] Özceylan, E., Paksoy, T., del Rosario, E., Kropat, E., Weber, G.-W., 2010. A review on the state of the energy sector of Turkey from the perspective of Operational Research – an invitation by OR. In: Proceedings of PCO 2010, 3rd Global Conference on Power Control and Optimization (ISBN: 978-983-44483-1-8), February 2-4, 2010, Gold Coast, Queensland, Australia.
[47] Özöğür, S., Sağdıçoğlu Celep, A.G., Karasözen, B., Yıldırım, N., Weber, G.-W., 2005. Dynamical modelling of enzymatic reactions, simulation and parameter estimation with genetic algorithms. In: HIBIT - Proceedings of International Symposium on Health Informatics and Bioinformatics, Turkey’05. Antalya, Turkey, pp. 78-84.
[48] Pickl, S., 1998. Der τ-value als Kontrollparameter - Modellierung und Analyse eines Joint-Implementation Programmes mithilfe der dynamischen kooperativen Spieltheorie und der diskreten Optimierung. Doctoral Thesis. Department of Mathematics, Darmstadt University of Technology. · Zbl 0997.90512
[49] Pickl, S., Convex games and feasible sets in control theory, Mathematical methods of operations research, 53, 1, 51-66, (2001) · Zbl 1030.91046
[50] Pickl, S., An iterative solution to the nonlinear time-discrete TEM model – the occurence of chaos and a control theoretic algorithmic approach, AIP conference Proceedings, 627, 1, 196-205, (2002)
[51] Pickl, S.W.; Weber, G.-W., Optimization of a time-discrete nonlinear dynamical system from a problem of ecology - an analytical and numerical approach, Journal of computational technologies, 6, 1, 43-52, (2001) · Zbl 1016.91014
[52] Pickl, S.W.; Weber, G.-W., Optimal control of heating processes with special emphasis on Earth warming, (), 247-254
[53] Ros, L.; Sabater, A.; Thomas, F., An ellipsoidal calculus based on propagation and fusion, IEEE transactions on systems, man and cybernetics, part B: cybernetics, 32, 4, 430-442, (2002)
[54] Rückmann, J.J.; Gómez, J.A., On generalized semi-infinite programming (invited paper), Top, 14, 1, 57-59, (2006)
[55] Sakamoto, E., Iba, H., 2001. Inferring a system of differential equations for a gene regulatory network by using genetic programming. In: Proceedings of the Congress on Evolutionary Computation, pp. 720-726.
[56] Stein, O., Bi-level strategies in semi-infinite programming, (2003), Kluwer Academic Publishers Boston · Zbl 1103.90094
[57] Stojaković, M., 2009. Imprecise probability and application in finance. In: 14th International Congress on Computational and Applied Mathematics (ICCAM 2009), Antalya, Turkey.
[58] Taştan, M., 2005. Analysis and Prediction of Gene Expression Patterns by Dynamical Systems, and by a Combinatorial Algorithm. MSc Thesis. Institute of Applied Mathematics, METU, Turkey.
[59] Taştan, M., Ergenç, T., Pickl, S.W., Weber, G.-W., 2005. Stability analysis of gene expression patterns by dynamical systems and a combinatorial algorithm. In: HIBIT - Proceedings of International Symposium on Health Informatics and Bioinformatics, Turkey ’05. Antalya, Turkey; 2005, pp. 67-75.
[60] Taştan, M., Pickl, S.W., Weber, G.-W., 2006. Mathematical modeling and stability analysis of gene-expression patterns in an extended space and with Runge-Kutta discretization. In: Proceedings of Operations Research, Bremen, pp. 443-450. · Zbl 1114.90469
[61] Taylan, P., Weber, G.-W., Beck, A., 2007. New approaches to regression by generalized additive models and continuous optimization for modern applications in finance, science and technology. In: (special issue – in honour of Prof. Dr. Alexander Rubinov), Burachik, B., Yang, X. (Guest Eds.), Optimization 56(5-6), 1-24. · Zbl 1123.62055
[62] Uğur, Ö.; Weber, G.-W., Optimization and dynamics of gene-environment networks with intervals (special issue – in honour of prof. Dr. Alexander rubinov), Journal of industrial management and optimization (IJOR), 3, 2, 357-379, (2007) · Zbl 1131.92027
[63] Uğur, Ö.; Pickl, S.W.; Weber, G.-W.; Wünschiers, R., An algorithmic approach to analyze genetic networks and biological energy production: an introduction and contribution where OR meets biology, Optimization, 58, 1, 1-22, (2009) · Zbl 1158.92312
[64] Vandenberghe, L.; Boyd, S., Semidefinite programming, SIAM review, 38, 1, 49-95, (1996) · Zbl 0845.65023
[65] Weber, G.-W., Charakterisierung struktureller stabilität in der nichtlinearen optimierung, () · Zbl 0796.90066
[66] Weber, G.-W., Generalized semi-infinite optimization and related topics, () · Zbl 1056.90134
[67] Weber, G.-W.; Tezel, A., On generalized semi-infinite optimization of genetic networks, TOP, the operational research journal of SEIO (Spanish statistics and operations research society), 15, 1, 65-77, (2007) · Zbl 1123.93018
[68] Weber, G.-W., Uğur, Ö., 2007. Optimizing gene-environment networks: generalized semi-infinite programming approach with intervals. In: Proceedings of International Symposium on Health Informatics and Bioinformatics Turkey ’07, HIBIT, Antalya, Turkey, April 30-May 2, 2007. <http://hibit.ii.metu.edu.tr/07/index.html>.
[69] Weber, G.-W., Alparslan Gök, S.Z., Dikmen, N., 2008. Environmental and life sciences: Gene-environment networks-optimization, games and control – a survey on recent achievements. In: DeTombe, D., (Guest Ed.), special issue of Journal of Organizational Transformation and Social Change 5(3), 197-233.
[70] Weber, G.-W.; Taylan, P.; Alparslan Gök, S.Z.; Özöğür, S.; Akteke Öztürk, B., Optimization of gene-environment networks in the presence of errors and uncertainty with Chebychev approximation, Top, 16, 2, 284-318, (2008) · Zbl 1155.93012
[71] Weber, G.-W., Tezel, A., Taylan, P., Soyler, A., Çetin, M., 2008. Mathematical contributions to dynamics and optimization of gene-environment networks. In: Pallaschke, D., Stein, O. (Eds.), special issue (in Celebration of Prof. Dr. Hubertus Th. Jongen’s 60th Birthday). Optimization 57(2), 353-377. · Zbl 1139.93002
[72] Weber, G.-W.; Alparslan Gök, S.Z.; Söyler, B., A new mathematical approach in environmental and life sciences: gene-environment networks and their dynamics, Environmental modeling & assessment, 14, 2, 267-288, (2009)
[73] Weber, G.-W.; Kropat, E.; Akteke-Öztürk, B.; Görgülü, Z.K., A survey on OR and mathematical methods applied on gene-environment networks, Central European journal of operations research, 17, 3, 315-341, (2009), Special Issue on “Innovative Approaches for Decision Analysis in Energy, Health, and Life Sciences” at the occasion of EURO XXII 2007 (Prague, Czech Republic, July 8-11, 2007), Dlouhy, M., Pickl, S., Rauner, M., Leopold-Wildburger, U., (Guest Eds.), doi:10.1007/s10100-009-0092-4 · Zbl 1204.90001
[74] Weber, G.-W.; Uğur, Ö.; Taylan, P.; Tezel, A., On optimization, dynamics and uncertainty: a tutorial for gene-environment networks, (special issue) Networks in Computational Biology, Discrete applied mathematics, 157, 10, 2494-2513, (2009) · Zbl 1172.92015
[75] Wolkowicz, H.; Saigal, R.; Vandenberghe, L., Handbook of semidefinite programming: theory, algorithms, and applications, International series in operations research and management science, vol. 27, (2000), Kluwer Academic Publishers Dordrecht, The Netherlands
[76] Wunderling, R., 1996. Paralleler und objektorientierter Simplex-Algorithmus. Ph.D. Thesis. Technical Report ZIB-TR 96-09. Technische Universitat Berlin, Berlin. · Zbl 0871.65048
[77] Yılmaz, F.B., 2004. A Mathematical Modeling and Approximation of Gene Expression Patterns by Linear and Quadratic Regulatory Relations and Analysis of Gene Networks. MSc Thesis. Institute of Applied Mathematics, METU, Turkey.
[78] Yılmaz, F.B., Öktem, H., Weber, G.-W., 2005. Mathematical modeling and approximation of gene expression patterns and gene networks. In: Fleuren, F., den Hertog, D., Kort, P. (Eds.), Operations Research Proceedings, pp. 280-287.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.