Modeling, inference and optimization of regulatory networks based on time series data

European Journal of Operational Research

Volumn 211, Issue 1, 2011, Pages 1-14

  Weber, Gerhard Wilhelm ^a,e,f,g   Defterli, Ozlem ^b   Alparslan Gök, Sirma Zeynep ^c   Kropat, Erik ^d  

^a MIDDLE EAST TECHNICAL UNIVERSITY   (Turkey)

^b CANKAYA UNIVERSITY   (Turkey)

^c SULEYMAN DEMIREL UNIVERSITY   (Turkey)

^d BUNDESWEHR UNIVERSITY MUNICH   (Germany)

^e UNIVERSITY OF AVEIRO   (Portugal)

^f UNIVERSITY OF SIEGEN   (Germany)

^g UNIVERSITI TEKNOLOGI MALAYSIA   (Malaysia)

Author keywords

Computational biology; Data mining; Environment; Games; Nonlinear programming; Uncertainty modeling

Indexed keywords

DATA MINING; GAME THEORY; NONLINEAR PROGRAMMING; UNCERTAINTY ANALYSIS;

COMPUTATIONAL BIOLOGY; ENVIRONMENT; FINANCIAL MATHEMATICS; GAMES; OPTIMIZATION METHOD; OPTIMIZATION TECHNIQUES; SEMI-DEFINITE PROGRAMMING; UNCERTAINTY MODELING;

INTEGER PROGRAMMING;

EID: 79551497246     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ejor.2010.06.038     Document Type: Article

References (78)

1. Achterberg, T.; 2007. Constraint Integer Programming. Ph.D. Thesis. Technische Universität Berlin, Berlin.
2. R.K. Ahuja, T.L. Magnanti, and J.B. Orlin Network Flow: Theory, Algorithms and Applications 1993 Prentice Hall NJ
3. M.U. Akhmet, J. Gebert, H. Öktem, S.W. Pickl, and G.-W. Weber An improved algorithm for analytical modeling and anticipation of gene expression patterns Journal of Computational Technologies 10 4 2005 3 20
4. F. Alizadeh Interior-point methods in semidefinite programming with applications to combinatorial optimization SIAM Journal on Optimization 5 1 1995 13 51
5. D.B. Allison, X. Cui, G.P. Page, and M. Sabripour Microarray data analysis: from disarray to consolidation and consensus Nature Reviews Genetics 7 2006 55 65
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. S.Z. Alparslan Gök, R. Branzei, and S. Tijs Convex interval games Journal of Applied Mathematics and Decision Sciences 29 2009 14 10.1115/2009/342089 article id 342089
9. S.Z. Alparslan Gök, S. Miquel, and S. Tijs Cooperation under interval uncertainty Mathematical Methods of Operations Research 69 1 2009 99 109
10. A. Aster, B. Borchers, and C. Thurber 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.
12. A. Brazma, P. Hingamp, J. Quackenbush, G. Sherlock, P. Spellman, C. Stoeckert, J. Aach, W. Ansorge, C.A. Ball, H.C. Causton, T. Gaasterland, P. Glenisson, F.C. Holstege, I.F. Kim, V. Markowitz, J.C. Matese, H. Parkinson, A. Robinson, U. Sarkans, S. Schulze-Kremer, J. Stewart, R. Taylor, J. Vilo, and M. Vingron Minimum information about a microarray experiment (MIAME)-toward standards for microarray data Nature Genetics 29 4 2001 365 371
13. M.S. Carbayo, W. Bornman, and C.C. Cardo DNA Microchips: technical and practical considerations Current Organic Chemistry 4 9 2000 945 971
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. M. Córdoba Bueno 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. J. DeRisi, V. Iyer, and P. Brown Exploring the metabolic and genetic control of gene expression on a genomic scale Science 278 1997 680 686
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. D.M. Dubois, and E. Kalisz Precision and stability of Euler, Runge-Kutta and incursive algorithm for the harmonic oscillator International Journal of Computing Anticipatory Systems 14 2004 21 36
21. T. Ergen, and G.-W. Weber 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 2004 40 48
22. M. Fiedler, J. Nedoma, J. Ramik, J. Rohn, and K. Zimmermann Linear Optimization Problems with Inexact Data 2006 Springer Verlag Berlin
23. J. Gebert, M. Lätsch, S.W. Pickl, G.-W. Weber, and R. Wünschiers Genetic networks and anticipation of gene expression patterns Computing Anticipatory Systems: CASYS(92)03 - Sixth International Conference AIP Conference Proceedings 718 2004 474 485
24. J. Gebert, M. Lätsch, E.M.P. Quek, and G.-W. Weber Analyzing and optimizing genetic network structure via path-finding Journal of Computational Technologies 9 3 2004 3 12
25. J. Gebert, H. Öktem, S.W. Pickl, N. Radde, G.-W. Weber, and F.B. Yilmaz Inference of gene expression patterns by using a hybrid system formulation - an algorithmic approach to local state transition matrices G.E. Lasker, D.M. Dubois, Anticipative and Predictive Models in Systems Science I 2004 IIAS (International Institute for Advanced Studies) in Windsor Ontario 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.
28. A. Gökmen, S. Kayaligil, G.-W. Weber, I. Gökmen, M. Ecevit, A. Sürmeli, T. Bali, Y. Ecevit, H. Gökmen, and D.J. DeTombe Balaban Valley project: Improving the quality of life in rural area in Turkey International Scientific Journal of Methods and Models of Complexity 7 2004 1 http://www.fss.uu.nl/ms/cvd/isj/index7-1.htm
29. J. Guckenheimer, and P. Holmes 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.
31. M. Heath 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.
33. S. Huang Gene expression profiling, genetic networks and cellular states: an integrating concept for tumorigenesis and drug discovery Journal of Molecular Medicine 77 1999 469 480
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. E. Kropat, G.-W. Weber, and J.J. Rückmann Regression analysis for clusters in gene-environment networks based on ellipsoidal calculus and optimization Dynamics of Continuous, Discrete and Impulsive System 17 5 2010
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.
38. A.B. Kurzhanski, and I. Vályi Ellipsoidal Calculus for Estimation and Control 1997 Birkhäuser
39. A.A. Kurzhanski, and P. Varaiya 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. Y.F. Li, S. Venkatesh, and D. Li Modeling global emissions and residues of pesticided Environmental Modeling and Assessment 9 2004 237 243
44. D. Lozovanu, S. Pickl, and G.-W. Weber 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 2004 351 361
45. Özcan, S.; Yildirim, 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. Özöür, S.; Sadiolu Celep, A.G.; Karasözen, B.; Yildirim, 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.
49. S. Pickl Convex games and feasible sets in control theory Mathematical Methods of Operations Research 53 1 2001 51 66
50. S. Pickl 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 2002 196 205
51. S.W. Pickl, and G.-W. Weber Optimization of a time-discrete nonlinear dynamical system from a problem of ecology - an analytical and numerical approach Journal of Computational Technologies 6 1 2001 43 52
52. S.W. Pickl, and G.-W. Weber Optimal control of heating processes with special emphasis on earth warming P. Chamoni, R. Leisten, A. Martin, J. Minnemann, H. Stadler, Operations Research Proceedings 2001 2002 Springer Verlag Heidelberg, New York 247 254
53. L. Ros, A. Sabater, and F. Thomas An ellipsoidal calculus based on propagation and fusion IEEE Transactions on Systems, Man and Cybernetics, Part B: Cybernetics 32 4 2002 430 442
54. J.J. Rückmann, and J.A. Gómez On generalized semi-infinite programming (invited paper) TOP 14 1 2006 57 59
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. O. Stein Bi-level Strategies in Semi-infinite Programming 2003 Kluwer Academic Publishers Boston
57. Stojaković, M.; 2009. Imprecise probability and application in finance. In: 14th International Congress on Computational and Applied Mathematics (ICCAM 2009), Antalya, Turkey.
58. Tatan, 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. Tatan, M.; Ergen, 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. Tatan, 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.
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.
62. Ö. Uur, and G.-W. Weber 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 2007 357 379
63. Ö. Uur, S.W. Pickl, G.-W. Weber, and R. Wünschiers An algorithmic approach to analyze genetic networks and biological energy production: an introduction and contribution where OR meets biology Optimization 58 1 2009 1 22
64. L. Vandenberghe, and S. Boyd Semidefinite programming SIAM Review 38 1 1996 49 95
65. G.-W. Weber Charakterisierung struktureller Stabilität in der nichtlinearen Optimierung H.H. Bock, H.T. Jongen, W. Plesken, Aachener Beiträge zur Mathematik vol. 5 1992 Augustinus Publishing House (now: Mainz Publishing House) Aachen
66. G.-W. Weber Generalized semi-infinite optimization and related topics K.H. Hofmannn, R. Wille, Research and Exposition in Mathematics vol. 29 2003 Heldermann Publishing House Lemgo
67. G.-W. Weber, and A. Tezel On generalized semi-infinite optimization of genetic networks TOP, The Operational Research Journal of SEIO (Spanish Statistics and Operations Research Society) 15 1 2007 65 77
68. Weber, G.-W.; Uur, 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. G.-W. Weber, P. Taylan, S.Z. Alparslan Gök, S. Özöür, and B. Akteke Öztürk Optimization of gene-environment networks in the presence of errors and uncertainty with Chebychev approximation TOP 16 2 2008 284 318
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.
72. G.-W. Weber, S.Z. Alparslan Gök, and B. Söyler A new mathematical approach in environmental and life sciences: gene-environment networks and their dynamics Environmental Modeling & Assessment 14 2 2009 267 288
73. G.-W. Weber, E. Kropat, B. Akteke-Öztürk, and Z.K. Görgülü A survey on OR and mathematical methods applied on gene-environment networks Central European Journal of Operations Research 17 3 2009 315 341 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
74. G.-W. Weber, Ö. Uur, P. Taylan, and A. Tezel On optimization, dynamics and uncertainty: a tutorial for gene-environment networks (special issue) Networks in Computational Biology Discrete Applied Mathematics 157 10 2009 2494 2513
75. H. Wolkowicz, R. Saigal, and L. Vandenberghe 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.
77. Yilmaz, 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. Yilmaz, 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.