The document summarizes the outline and topics of the 6th International Summer School held in Kiev, Ukraine from August 8-20, 2011. The school focused on new insights and applications of eco-finance networks and collaborative games. Topics included bio-financial systems, genetic and gene-environment networks, time-continuous and time-discrete models, optimization problems, numerical examples and results, networks under uncertainty, the ellipsoidal model, and related aspects from finance. Modeling approaches included genetic, gene regulation, and gene-environment networks as well as optimization of parameters for stability and goodness of fit.

1. 6th International Summer SchoolNational University of Technology of the UkraineKiev, Ukraine, August 8-20, 2011New Insights and Applications of Eco-Finance Networksand Collaborative GamesGerhard-Wilhelm Weber 1*SırmaZeynepAlparslanGök2, Erik Kropat3, ÖzlemDefterli4, Fatma Yelikaya-Özkurt1,Armin Fügenschuh51 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, GermanyCenter for Research on Optimization and Control, University of Aveiro, PortugalUniversiti Teknologi Malaysia, Skudai, Malaysia

2. OutlineBio- and Financial SystemsGenetic ,Gene-Environment and Eco-Finance Networks Time-Continuous and Time-Discrete ModelsOptimization ProblemsNumerical Example and ResultsNetworks under UncertaintyEllipsoidal ModelOptimization of the Ellipsoidal ModelKyoto GameEllipsoidal Game TheoryRelated Aspects from FinanceHybrid Stochastic ControlConclusion

3. Bio-Systems environmentmedicinefoodbio materialsbio energydevelopmenteducationhealth caresustainability

4. Stock Markets

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

6. Bio-Systems MedicineEnvironment... Finance Health Careprediction of gene patterns based onDNA microarraychip experimentswithM.U. Akhmet, H. Öktem S.W. Pickl, E. Quek Ming PohT. Ergenç, B. Karasözen J. Gebert, N. Radde Ö. Uğur, R. WünschiersM. Taştan, A. Tezel, P. Taylan F.B. Yilmaz, B. Akteke-ÖztürkS. Özöğür, Z. Alparslan-Gök A. Soyler, B. Soyler, M. ÇetinS. Özöğür-Akyüz, Ö. Defterli N. Gökgöz, E. Kropat

7. DNA experimentsEx.:yeastdatahttp://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 ShiftGebert et al. (2006)

10. Modeling & Predictiondataprediction, anticipation least squares – max likelihoodExpressionexpression datamatrix-valued function – metabolic reaction

11. Modeling & PredictionEx.:Ex.: Euler, Runge-KuttaMWe analyze the influence of em-parameters on the dynamics (expression-metabolic).

12. StabilityFor which parameters, i.e., for which setM(hence,dynamics), isstabilityguaranteed ?stablefeasibleMmetabolic reactionunstable unfeasiblegoodness-of-fit (model) testDef.:Mis stable :B : (complex) bounded neighbourhood ofM :

13. Stabilitycombinatorial algorithmFor which parameters, i.e., for which setM(hence,dynamics), isstabilityguaranteed ?stablefeasibleMmetabolic reactionunstable unfeasible Akhmet, Gebert, Öktem, Pickl, Weber (2005), Gebert, Laetsch, Pickl, Weber, Wünschiers (2006), Weber, Ugur, Taylan, Tezel (2009), Ugur, Pickl, Weber, Wünschiers (2009)

14. Genetic NetworkEx. :

15. Genetic Network0.4E1gene2gene10.2 E21 E1gene3gene4

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 tdenotes anyone of the first n coordinates in thed-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 levelsrepresents 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 ClassIn 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 method3rd-order Heun's method is introduced byDefterli et al. (2009)we rewrite it as whereErgenc 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 dataand the data of environmental items obtained at the time-level: approximationsobtained by the iterative formula above: initial valueskthapproximation (prediction):

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

23. Matrix AlgebraFinal canonical block form of : = .

24. Optimization Problemmixed-integer least-squares optimization problem:Boolean variablessubject toUgur 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 genegenetic 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 ExampleMINLP for data: Gebert et al. (2004a)Apply 3rd-order Heun method:Takeusing modeling language Zimpl 3.0, we solveby SCIP 1.2 as a branch-and-cutframework, together with SOPLEX 1.4.1 as LP solver

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

28. ____ gene A........ gene B_ . _ . gene C- - - - gene DResults of Euler Method for all genes:

29. ____ gene A........ gene B_ . _ . gene C- - - - gene DResults of 3rd-order Heun Method for all genes:

30. Regulatory NetworksunderUncertaintyθ2θ1

31. Regulatory NetworksunderUncertaintyθ2θ1

32. Regulatory NetworksunderUncertaintyθ2θ1

33. Model Class under Interval Uncertainty

34. Model Class under Interval Uncertaintyθ2,2hybridlocal modelθ2,1θ1,1θ1,2

35. Model Class under Interval Uncertaintyminsubject to

36. Generalized Semi-Infinite ProgrammingI, K, L finite

37. Generalized Semi-Infinite ProgrammingJongen, Weber, Guddat et al.homeom. asymptoticeffect: structurally stableglobal local global

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

39. Regulatory NetworksunderUncertaintyθ2θ1

40. Regulatory NetworksunderUncertaintyθ2θ1Coalitions under uncertainty

41. Regulatory Networks: InteractionsDetermine the degree of connectivity.

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

43. Time-Discrete ModelTime-Discrete Model:Target  TargetEnvironment  Target(R)(S)TargetclusterTT(k)(k+1)ET(k)XξXA++=EAj r r j0j s j sr =1s =1(R)(S)Environmental clusterTE(k)(k+1)EE(k)XζEA++=EAi r r i0is i sr =1s =1Target  EnvironmentEnvironment  Environment Determine system matrices and intercepts.

44. Time-Discrete ModelEllipsoidal Calculus: Affine-linear transformations

45. Sums of ellipsoids

46. Intersections / fusions of ellipsoidsAE + bE1 + E2inner / outer approximationsE1∩ E2Ros et al. (2002)Parameterized family of ellipsoidal approximationsKurzhanski, Varaiya (2008)

47. Set-Theoretic Regression ProblemEllipsoidal CalculusThe Regression Problem:Maximize(overlap of ellipsoids) DetermineEETTETTE, AA, A, Amatricesand isj rj si r,ζvectorsξ i0 j0measurementRSTΣΣΣ−−^(k)(k)(k)(k)+^EEXX∩∩ s r r sr = 1s = 1k= 1prediction

48. Set-Theoretic Regression ProblemMeasures for the size of intersection:Volume->ellipsoid matrix determinant

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

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

51. Curse of DimensionalityCi110χij 1=CjTj0

52. Curse of DimensionalityMixed-Integer Regression Problem:RSTΣΣΣ−−^(k)(k)(k)(k)+^EEXmaximizeX∩∩ s r r sr = 1s = 1k= 1αTT≤deg(C )TT bounds on outdegreessuch thatjjαTE≤deg(C )TE jjαET≤deg(D )ET iiαEE≤deg(D )EE ii

53. Curse of DimensionalityScale free networks(metabolic networks, world wide web,…)High error tolerance

54. High attack vulnerability(removal of important nodes)Curse of DimensionalityContinuous Regression Problem:RSTΣΣΣ−−^(k)(k)(k)(k)+^EEXX∩maximize∩ s r r sr = 1s = 1k= 1RΣαTTTT≤PTT ( TT )such that, ξAjj rjrj0r =1RαTEΣ≤TEPTE ( TE ),ξAjj r j0jrr =1bounds on outdegreesRETΣαETPET ( ET ≤, ζA)ii s i0isContinuous Constraints /Probabilities s =1RΣEEαEEPEE ( EE )≤, ζAii s i0iss =1

55. Curse of DimensionalityContinuous Regression Problem:RSTΣΣΣ−−^(k)(k)(k)(k)+^EEXX∩maximize∩ s r r sr = 1s = 1k= 1RΣαTTTT≤PTT ( TT )such that, ξAjj rjrj0r =1RαTEΣ≤TEPTE ( TE ),ξAjj r j0jrr =1RETΣαETPET ( ET ≤, ζA)ii s i0iss =1REx.:Robust OptimizationΣEEαEEPEE ( EE )≤, ζAii s i0iss =1

56. Cost GamesCost games are very important in the practice of OR.Ex.: airport game,

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 GamesThe 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. Gamescooperative

65. IntervalGamescooperative....

66. Ellipsoid Games Interval Gamescooperative....

67. Ellipsoid Games Interval Gamescooperative....

68. Ellipsoid Games Interval Gamescooperative....

69. Ellipsoid Games Interval Gamescooperative....

70. Ellipsoid Games Interval Gamescooperative....Robust Optimization

71. IntervalGamescooperative

72. IntervalGamescooperativeInterval Glove Game

73. Ellipsoid Games cooperative

74. Ellipsoid Games cooperativeEllipsoid Glove Game

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

76. Ellipsoid Games cooperativeEllipsoid Malacca Police GameR

77. Ellipsoid Games cooperativererrrr

78. Ellipsoid Games cooperativererFarkas Lemmarrr

79. Finance Networks.

80. Finance Networks with Bubbles.

81. Finance Networks with Bubbles.hybrid

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

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

84. Financial Dynamics IdentifiedTikhonovregularizationconic quadratic programmingInterior Point Methods

85. Financial Dynamics IdentifiedÖzmen, Weber, BatmazImportant new class of (Generalized) Partial Linear Models: Important new class of (Generalized) Partial Linear Models:

86. Financial Dynamics IdentifiedÖzmen, Weber, BatmazRobust CMARS: confidence interval..... ....................... . . . ..outlieroutliersemi-length of confidence interval

87. Financial Dynamics IdentifiedÖzmen, Weber, BatmazRobust CMARS: confidence interval..... ....................... . . . ..outlieroutliersemi-length of confidence interval

88. Portfolio Optimization Identified max utility ! ormincosts!ormin risk!martingale method: Optimization Problem Representation Problemor stochastic control

89. Portfolio Optimization Identified max utility ! ormincosts!ormin risk!martingale method: Optimization ProblemRepresentation Problemor stochastic controlParameter Estimation

90. Portfolio Optimization Identified max utility ! ormincosts!ormin risk! martingale method: Optimization Problem Representation Problemor stochastic controlParameter Estimation

91. Portfolio Optimization Identified max utility ! ormincosts!ormin risk! martingale method: Optimization ProblemRepresentation Problemor stochastic controlParameter Estimation

92. HybridStochastic ControlControl of Stochastic Hybrid Systems, R.Raffardstandard Brownian motion

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

94. discrete stateContinuous time Markov chain.

95. controlApplicationshybridEngineering:Maintain dynamical system in safe domain for maximum time.

96. Systems biology: Parameter identification.

97. Finance: Optimal portfolio selection.Method:1st stephybridDerive a PDE satisfied by the objective function in terms of the generator:Example 1: If thenExample 2: If then

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

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

100. References Part 1Achterberg, 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 1Tastan , 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 2Aster, 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 2Nemirovski, 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 contributionsdynamics and optimization of gene-environment networks,inthe special issue Organization in MatterfromQuarks 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. AppendixDNA experimentsControl MaterialTest MaterialLaser Scan of the ArraymRNA-IsolationSequence Data(cDNA, Genome,cDNA-SynthesisGenbank, etc.)and LabelingSelection or Design andSynthesis of the ProbesHybridizationPicture AnalysisArray ProductionArray PreparationSample PreparationData Analysis

105. Identifying Stochastic Differential EquationsAppendixApplicationF. Yerlikaya Özkurt, G.-W. Weber, P. Taylan Evaluation of the models based on performance values:CMARS performs better than Tikhonov regularization with respect to all themeasures for both data sets.

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.