AACIMP 2011 Summer School. Operational Research stream. Lecture by Gerhard-Wilhelm Weber.

1. 6th International Summer School National University of Technology of the Ukraine Kiev, Ukraine, August 8-20, 2011 New Insights and Applications of Eco-Finance Networks and Collaborative Games Gerhard-Wilhelm Weber 1* SırmaZeynepAlparslanGök2, Erik Kropat3, ÖzlemDefterli4, Fatma Yelikaya-Özkurt1,Armin Fügenschuh5 1 Institute of Applied Mathematics, Middle East Technical University, Ankara, Turkey 2 Department of Mathematics, SüleymanDemirel University, Isparta, Turkey 3 Department of Computer Science, Universität der Bundeswehr München, Munich, Germany 4 Department of Mathematics and Computer Science, Cankaya University, Ankara, Turkey 5 Optimierung, Zuse Institut Berlin, Germany * Faculty of Economics, Management and Law, University of Siegen, Germany Center for Research on Optimization and Control, University of Aveiro, Portugal Universiti Teknologi Malaysia, Skudai, Malaysia

2. Outline Bio- and Financial Systems Genetic ,Gene-Environment and Eco-Finance Networks Time-Continuous and Time-Discrete Models Optimization Problems Numerical Example and Results Networks under Uncertainty Ellipsoidal Model Optimization of the Ellipsoidal Model Kyoto Game Ellipsoidal Game Theory Related Aspects from Finance Hybrid Stochastic Control Conclusion

3. Bio-Systems environment medicine food bio materials bio energy development education health care sustainability

4. Stock Markets

5. Regulatory Networks: Examples Further examples: Socio-econo-networks, stock markets, portfolio optimization, immune system, epidemiological processes …

6. Bio-Systems Medicine Environment ... Finance Health Care prediction of gene patterns based on DNA microarraychip experiments with M.U. Akhmet, H. Öktem S.W. Pickl, E. Quek Ming Poh T. Ergenç, B. Karasözen J. Gebert, N. Radde Ö. Uğur, R. Wünschiers M. Taştan, A. Tezel, P. Taylan F.B. Yilmaz, B. Akteke-Öztürk S. Özöğür, Z. Alparslan-Gök A. Soyler, B. Soyler, M. Çetin S. Özöğür-Akyüz, Ö. Defterli N. Gökgöz, E. Kropat

7. DNA experiments Ex.:yeastdata http://genome-www5.stanford.edu/

8. Analysis of DNA experiments

9. E0 : metabolic state of a cell at t0 (:=gene expression pattern),ith element of the vector E0 :=expression level of gene i,Mk := I + hkM(Ek) , Ek (k є IN0) is recursively defined as Ek+1 := MkEk. Metabolic Shift Gebert et al. (2006)

10. Modeling & Prediction data prediction, anticipation least squares – max likelihood Expression expression data matrix-valued function – metabolic reaction

11. Modeling & Prediction Ex.: Ex.: Euler, Runge-Kutta M We analyze the influence of em-parameters on the dynamics (expression-metabolic).

14. Genetic Network Ex. :

15. Genetic Network 0.4E1 gene2 gene1 0.2 E2 1 E1 gene3 gene4

16. Gene-Environment Networks if gene j regulates gene i otherwise

17. Model Class : time-autonomous form, where : d-vector of concentration levels of proteins and of certain levels of environmental factors : change in the gene-expression data in time : initial values of the gene-expression levels : experimental data vectors obtained from microarray experiments and environmental measurements : the gene-expression level (concentration rate) of the i th gene at time t denotes anyone of the first n coordinates in the d-vector of genetic and environmental states. Weber et al. (2008c), Chen et al. (1999), Gebert et al. (2004a), Gebert et al. (2006), Gebert et al. (2007), Tastan (2005), Yilmaz (2004), Yilmaz et al. (2005), Sakamoto and Iba (2001), Tastan et al. (2005) : the set of genes.

18. Model Class (i): a constant (nxn)-matrix : an (nx1)-vector of gene-expression levels represents and t the dynamical system of the n genes and their interaction alone. : : (nxn)-matrix with entries as functions of polynomials, exponential, trigonometric, splines or wavelets, containing some parameters to be optimized. (iii) Weber et al. (2008c), Tastan (2005), Tastan et al. (2006), Ugur et al. (2009), Tastan et al. (2005), Yilmaz (2004), Yilmaz et al. (2005), Weber et al. (2008b), Weber et al. (2009b) environmental effects (*) n genes , m environmental effects : (n+m)-vector and (n+m)x(n+m)-matrix, respectively.

19. Model Class In general, in the d-dimensional extended space, with : : (dxd)-matrix, : (dx1)-vectors. Ugur and Weber (2007), Weber et al. (2008c), Weber et al. (2008b), Weber et al. (2009b)

20. Time-Discretized Model - Euler’s method, - Runge-Kutta methods, e.g., 2nd-order Heun's method 3rd-order Heun's method is introduced byDefterli et al. (2009) we rewrite it as where Ergenc and Weber (2004), Tastan (2005), Tastan et al. (2006), Tastan et al. 2005)

21. Time-Discretized Model (**) : in the extended spacedenotes the DNA microarray experimental data and the data of environmental items obtained at the time-level : approximationsobtained by the iterative formula above : initial values kthapproximation (prediction):

22. Matrix Algebra : (nxn)- and (nxm)-matrices, respectively : (n+m)x(n+m) -matrix : (n+m)-vectors Applying the 3rd-order Heun’s method to (*) gives the iterative formula (**), where

23. Matrix Algebra Final canonical block form of : = .

24. Optimization Problem mixed-integer least-squares optimization problem: Boolean variables subject to Ugur and Weber (2007), Weber et al.(2008c), Weber et al. (2008b), Weber et al. (2009b), Gebert et al. (2004a), Gebert et al. (2006), Gebert et al. (2007) , , : th : the numbers of genes regulated by gene (its outdegree), by environmental item , or by the cumulative environment, resp..

25. Mixed-Integer Problem : constant (nxn)-matrix with entries representing the effect which the expression level of gene has on the change of expression of gene genetic regulation network mixed-integer nonlinear optimization problem (MINLP): subject to : constant vectorrepresenting the lower bounds for the decrease of the transcript concentration. Binary variables :

26. Numerical Example MINLP for data: Gebert et al. (2004a) Apply 3rd-order Heun method: Take using modeling language Zimpl 3.0, we solve by SCIP 1.2 as a branch-and-cutframework, together with SOPLEX 1.4.1 as LP solver

27. Numerical Example Apply 3rd-order Heun’s time discretization :

28. ____ gene A ........ gene B _ . _ . gene C - - - - gene D Results of Euler Method for all genes:

29. ____ gene A ........ gene B _ . _ . gene C - - - - gene D Results of 3rd-order Heun Method for all genes:

30. Regulatory NetworksunderUncertainty θ2 θ1

31. Regulatory NetworksunderUncertainty θ2 θ1

32. Regulatory NetworksunderUncertainty θ2 θ1

33. Model Class under Interval Uncertainty

34. Model Class under Interval Uncertainty θ2,2 hybrid local model θ2,1 θ1,1 θ1,2

35. Model Class under Interval Uncertainty min subject to

36. Generalized Semi-Infinite Programming I, K, L finite

37. Generalized Semi-Infinite Programming Jongen, Weber, Guddat et al. homeom. asymptotic effect : structurally stable global local global

38. Generalized Semi-Infinite Programming Thm. (W. 1999/2003, 2006): Fulfilled!

39. Regulatory NetworksunderUncertainty θ2 θ1

40. Regulatory NetworksunderUncertainty θ2 θ1 Coalitions under uncertainty

41. Regulatory Networks: Interactions Determine the degree of connectivity.

42. Time-Discrete Model Clusters and Ellipsoids: Target clusters: C1,C2,…,CREnvironmental clusters: D1,D2,…,DS Target ellipsoids: X1,X2,…,XRXi = E(μi , Σi) Environmental ellipsoids: E1,E2,…,ES Ej = E(ρj ,Πj) Center Covariance matrix

43. Time-Discrete Model Time-Discrete Model: Target  Target Environment  Target ( R ) ( S ) Targetcluster TT (k) (k+1) ET (k) X ξ X A + + = E A j r r j0 j s j s r =1 s =1 ( R ) ( S ) Environmental cluster TE (k) (k+1) EE (k) X ζ E A + + = E A i r r i0 is i s r =1 s =1 Target  Environment Environment  Environment Determine system matrices and intercepts.

45. Sums of ellipsoids

46. Intersections / fusions of ellipsoidsAE + b E1 + E2 inner / outer approximations E1∩ E2 Ros et al. (2002) Parameterized family of ellipsoidal approximations Kurzhanski, Varaiya (2008)

47. Set-Theoretic Regression Problem Ellipsoidal Calculus The Regression Problem: Maximize(overlap of ellipsoids) Determine EE TT ET TE , A A , A , A matrices and is j r j s i r ,ζ vectors ξ i0 j0       measurement R S T Σ Σ Σ − − ^ (k) (k) (k)  (k) +  ^ E E X X ∩ ∩ s r r s r = 1 s = 1 k= 1 prediction

49. Sum of squares of semiaxes-> trace of covariance matrix

50. Length of largest semiaxes-> eigenvalues of covariance matrixE semidefinite programming interior point methods

51. Curse of Dimensionality Ci 1 1 0 χij 1 = Cj Tj 0

52. Curse of Dimensionality Mixed-Integer Regression Problem: R S T Σ Σ Σ − − ^ (k) (k) (k)  (k) +  ^ E E X maximize X ∩ ∩ s r r s r = 1 s = 1 k= 1 α TT ≤ deg(C )TT bounds on outdegrees such that       j j α TE ≤ deg(C )TE j j α ET ≤ deg(D )ET i i α EE ≤ deg(D )EE i i

55. Curse of Dimensionality Continuous Regression Problem: R S T Σ Σ Σ − − ^ (k) (k) (k)  (k) +  ^ E E X X ∩ maximize ∩ s r r s r = 1 s = 1 k= 1 R Σ α TT TT ≤ PTT ( TT ) such that , ξ A       j j r jr j0 r =1 R α TE Σ ≤ TE PTE ( TE ) ,ξ A j j r j0 jr r =1 R ET Σ α ET PET ( ET ≤ , ζ A ) i i s i0 is s =1 R Ex.: Robust Optimization Σ EE α EE PEE ( EE ) ≤ , ζ A i i s i0 is s =1

57. unanimity game,

58. production economy with landowners and peasants,

59. bankrupcy game, etc..There is also a cost game in environmental protection (TEM model): The aim is to reach a state which is mentioned in Kyoto Protocol by choosing control parameters such that the emissions of each player become minimized. For example, the value is taken as a control parameter.

60. Cost Games The central problem in cooperative game theory is how to allocate the gain among the individual players in a “fair” way. There are various notions of fairness and corresponding allocation rules (solution concepts). Any with is an allocation. So, a core allocation guarantees each coalition to be satisfied in the sense that it gets at least what it could get on its own.

61. TEM Model

62. TEM Model Influence of memory parameter on the emissions reduced and financial means expended

63. TEM Model

64. Games cooperative

65. IntervalGames cooperative . . . .

66. Ellipsoid Games Interval Games cooperative . . . .

67. Ellipsoid Games Interval Games cooperative . . . .

68. Ellipsoid Games Interval Games cooperative . . . .

69. Ellipsoid Games Interval Games cooperative . . . .

70. Ellipsoid Games Interval Games cooperative . . . . Robust Optimization

71. IntervalGames cooperative

72. IntervalGames cooperative Interval Glove Game

73. Ellipsoid Games cooperative

74. Ellipsoid Games cooperative Ellipsoid Glove Game

75. Ellipsoid Games cooperative Ellipsoid Kyoto Game Ellipsoid Glove Game , : (individual roles in TEM Model) : (individual role in TEM Model)

76. Ellipsoid Games cooperative Ellipsoid Malacca Police Game R

77. Ellipsoid Games cooperative re r r r r

78. Ellipsoid Games cooperative re r Farkas Lemma r r r

79. Finance Networks .

80. Finance Networks with Bubbles .

81. Finance Networks with Bubbles . hybrid

82. Financial Dynamics drift diffusion Ex.: price, wealth, interest rate, volatility processes

83. Financial Dynamics Milstein Scheme: and, based on finitely many data:

84. Financial Dynamics Identified Tikhonovregularization conic quadratic programming Interior Point Methods

85. Financial Dynamics Identified Özmen, Weber, Batmaz Important new class of (Generalized) Partial Linear Models: Important new class of (Generalized) Partial Linear Models:

86. Financial Dynamics Identified Özmen, Weber, Batmaz Robust CMARS: confidence interval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . outlier outlier semi-length of confidence interval

87. Financial Dynamics Identified Özmen, Weber, Batmaz Robust CMARS: confidence interval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . outlier outlier semi-length of confidence interval

88. Portfolio Optimization Identified max utility ! or mincosts!or min risk! martingale method: Optimization Problem Representation Problem or stochastic control

89. Portfolio Optimization Identified max utility ! or mincosts!or min risk! martingale method: Optimization Problem Representation Problem or stochastic control Parameter Estimation

90. Portfolio Optimization Identified max utility ! or mincosts!or min risk! martingale method: Optimization Problem Representation Problem or stochastic control Parameter Estimation

91. Portfolio Optimization Identified max utility ! or mincosts!or min risk! martingale method: Optimization Problem Representation Problem or stochastic control Parameter Estimation

93. continuous stateSolves an SDE whose jumps are governed by the discrete state.

94. discrete stateContinuous time Markov chain.

96. Systems biology: Parameter identification.

98. Method:2ndand 3rd step hybrid Rewrite original problem as deterministic PDE optimization program: Solve PDE optimization program using adjoint method. Simple and robust…

99. References http://www3.iam.metu.edu.tr/iam/images/7/73/Willi-CV.pdf Thank you very much for your attention! gweber@metu.edu.tr

100. References Part 1 Achterberg, T., Constraint integer programming, PhD. Thesis, Technische Universitat Berlin, Berlin, 2007. Aster, A., Borchers, B., and Thurber, C., Parameter Estimation and Inverse Problems. Academic Press, San Diego; 2004. Chen, T., He, H.L., and Church, G.M., Modeling gene expression with differential equations, Proceedings of Pacific Symposium on Biocomputing 1999, 29-40. Ergenc, T,. and Weber, G.-W., Modeling and prediction of gene-expression patterns reconsidered with Runge-Kutta discretization, Journal of Computational Technologies 9, 6 (2004) 40-48. Gebert, J., Laetsch, M., Pickl, S.W., Weber, G.-W., and Wünschiers ,R., Genetic networks and anticipation of gene expression patterns, Computing Anticipatory Systems: CASYS(92)03 - Sixth International Conference,AIP Conference Proceedings 718 (2004) 474-485. Hoon, M.D., Imoto, S., Kobayashi, K., Ogasawara, N ., andMiyano, S., Inferring gene regulatory networks from time-ordered gene expression data of Bacillus subtilis using dierential equations, Proceedings of Pacific Symposium on Biocomputing (2003) 17-28. Pickl, S.W., and 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 (2001) 43-52. Sakamoto, E., and Iba, H., Inferring a system of differential equations for a gene regulatory network by using genetic programming, Proc. Congress on Evolutionary Computation 2001, 720-726. Tastan, M., Analysis and Prediction of Gene Expression Patterns by Dynamical Systems, and by a Combinatorial Algorithm, MSc Thesis, Institute of Applied Mathematics, METU, Turkey, 2005.

101. References Part 1 Tastan , M., Pickl, S.W., and Weber, G.-W., Mathematical modeling and stability analysis of gene-expression patterns in an extended space and with Runge-Kutta discretization, Proceedings of Operations Research, Bremen, 2006, 443-450. Wunderling, R., Paralleler und objektorientierter Simplex Algorithmus, PhD Thesis. Technical Report ZIB-TR 96-09. Technische Universitat Berlin, Berlin, 1996. Weber, G.-W., Alparslan -Gök, S.Z ., and Dikmen, N.. Environmental and life sciences: Gene-environment networks-optimization, games and control - a survey on recent achievements, deTombe, D. (guest ed.), special issue of Journal of Organizational Transformation and Social Change 5, 3 (2008) 197-233. Weber, G.-W., Taylan, P., Alparslan-Gök, S.Z., Özögur, S., and Akteke-Öztürk, B., Optimization of gene-environment networks in the presence of errors and uncertainty with Chebychev approximation, TOP 16, 2 (2008) 284-318. Weber, G.-W., Alparslan-Gök, S.Z ., and Söyler, B., A new mathematical approach in environmental and life sciences: gene-environment networks and their dynamics,Environmental Modeling & Assessment 14, 2 (2009) 267-288. Weber, G.-W., and Ugur, O., Optimizing gene-environment networks: generalized semi-infinite programming approach with intervals,Proceedings of International Symposium on Health Informatics and Bioinformatics Turkey '07, HIBIT, Antalya, Turkey, April 30 - May 2 (2007). Yılmaz, F.B., 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, 2004.

102. References Part 2 Aster, A., Borchers, B., and Thurber, C., Parameter Estimation and Inverse Problems, Academic Press, 2004. Boyd, S., and Vandenberghe, L., Convex Optimization, Cambridge University Press, 2004. Buja, A., Hastie, T., and Tibshirani, R., Linear smoothers and additive models, The Ann. Stat. 17,2(1989) 453-510. Fox, J., Nonparametric regression, Appendix to an R and S-Plus Companion to Applied Regression, Sage Publications, 2002. Friedman, J.H., Multivariate adaptive regression splines, Annals of Statistics 19, 1 (1991) 1-141. Hastie, T., and Tibshirani, R., Generalized additive models, Statist. Science 1, 3 (1986) 297-310. Hastie, T., and Tibshirani, R., Generalized additive models: some applications, J. Amer. Statist. Assoc. 82, 398 (1987) 371-386. Hastie, T., Tibshirani, R., and Friedman, J.H., The Element of Statistical Learning, Springer, 2001. Hastie, T.J., and Tibshirani, R.J., Generalized Additive Models, New York, Chapman and Hall, 1990. Kloeden, P.E, Platen, E., and Schurz, H., Numerical Solution of SDE ThroughComputer Experiments, Springer, 1994. Korn, R., and Korn, E., Options Pricing and Portfolio Optimization: Modern Methods ofFinancial Mathematics, Oxford University Press, 2001. Nash, G., and Sofer, A., Linear and Nonlinear Programming, McGraw-Hill, New York, 1996. Nemirovski, A., Lectures on modern convex optimization, Israel Institute of Technology (2002).

103. References Part 2 Nemirovski, A., Modern Convex Optimization, lecture notes, Israel Institute of Technology (2005). Nesterov, Y.E , and Nemirovskii,A.S., Interior Point Methods in Convex Programming, SIAM, 1993. Önalan, Ö., Martingale measures for NIG Lévyprocesses with applications to mathematicalfinance, presentation at Advanced Mathematical Methods for Finance, Side, Antalya, Turkey, April 26-29, 2006. Taylan, P., Weber, G.-W.,and Kropat, E.,Approximation of stochastic differential equationsby additive modelsusing splines and conic programming, International Journal of Computing Anticipatory Systems 21(2008) 341-352. Taylan, P., Weber, G.-W., and Beck, A.,New approaches to regression by generalized additive modelsand continuous optimization for modernapplications in finance, science and techology, Optimization 56, 5-6 (2007) 1-24. Taylan, P., Weber, G.-W.,andYerlikaya, F., A new approach to multivariate adaptive regression splineby using Tikhonov regularization and continuous optimization, TOP 18, 2 (December 2010) 377-395. Seydel, R., Tools for ComputationalFinance, Springer, Universitext, 2004. Weber, G.-W., Taylan, P., Akteke-Öztürk, B., and Uğur, Ö., Mathematical and datamining contributions dynamics and optimization of gene-environment networks,inthe special issue Organization in Matter fromQuarks to Proteins of Electronic Journalof Theoretical Physics. Weber, G.-W.,Taylan, P., Yıldırak, K.,and Görgülü, Z.K., Financial regression and organization, DCDIS-B (Dynamics of Continuous, Discrete andImpulsive Systems (Series B)) 17, 1b (2010) 149-174.

104. Appendix DNA experiments Control Material Test Material Laser Scan of the Array mRNA -Isolation Sequence Data (cDNA, Genome, cDNA -Synthesis Genbank, etc.) and Labeling Selection or Design and Synthesis of the Probes Hybridization Picture Analysis Array Production Array Preparation Sample Preparation Data Analysis

106. On the other hand, GLM with CMARS (GPLM) performs better than both Tikhonov regularization and CMARS with respect to all the measures for both data sets.