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Öğe Dynamical gene-environment networks under ellipsoidal uncertainty: set-theoretic regression analysis based on ellipsoidal or(Sprınger-Verlag Berlın, 2011) Kropat, Erik; Weber, Gerhard-Wilhelm; Belen, Selma; Peixoto, MM; Pinto, AA; Rand, DAWe consider dynamical gene-environment networks under ellipsoidal uncertainty and discuss the corresponding set-theoretic regression models. Clustering techniques are applied for an identification of functionally related groups of genes and environmental factors. Clusters can partially overlap as single genes possibly regulate multiple groups of data items. The uncertain states of cluster elements are represented in terms of ellipsoids referring to stochastic dependencies between the multivariate data variables. The time-dependent behaviour of the system variables and clusters is determined by a regulatory system with (affine-) linear coupling rules. Explicit representations of the uncertain multivariate future states of the system are calculated by ellipsoidal calculus. Various set-theoretic regression models are introduced in order to estimate the unknown system parameters. Hereby, we extend our Ellipsoidal Operations Research previously introduced for gene-environment networks of strictly disjoint clusters to possibly overlapping clusters. We analyze the corresponding optimization problems, in particular in view of their solvability by interior point methods and semidefinite programming and we conclude with a discussion of structural frontiers and future research challenges.Öğe On the classical Maki-Thompson rumour model in continuous time(SPRINGER, 2011) Belen, Selma; Kropat, Erik; Weber, Gerhard-WilhelmIn this paper, the Maki-Thompson model is slightly refined in continuous time, and a new general solution is obtained for each dynamics of spreading of a rumour. It is derived an equation for the size of a stochastic rumour process in terms of transitions. We give new lower and upper bounds for the proportion of total ignorants who never learned a rumour and the proportion of total stiflers who either forget the rumour or cease to spread the rumour when the rumour process stops, under general initial conditions. Simulation results are presented for the analytical solutions. The model and these numerical results are capable to explain the behaviour of the dynamics of any other dynamical system having interactions similar to the ones in the stochastic rumour process and requiring numerical interpretations to understand the real phenomena better. The numerical process in the differential equations of the model is investigated by using error-estimates. The estimated error is calculated by the Runge-Kutta method and found either negligible or zero for a relatively small size of the population. This pioneering paper introduces a new mathematical method into Operations research, motivated by various areas of scientific, social and daily life, it presents numerical computations, discusses structural frontiers and invites the interested readers to future research.Öğe OPTIMIZATION APPLIED ON REGULATORY AND ECO-FINANCE NETWORKS - SURVEY AND NEW DEVELOPMENTS -(Yokohama Publ, 2010) Weber, Gerhard-Wilhelm; Kropat, Erik; Tezel, Aysun; Belen, SelmaIn this paper we survey recent advances and mathematical foundations of regulatory networks. We explain their interdisciplinary implications with special regard to Operational Research and financial sciences and introduce the so-called eco-finance networks. These networks, originally developed in the context of modeling and prediction of gene-expression patterns, 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 investigate 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. We analyze the structural stability of the regulatory networks, we discuss a modeling by stochastic differential equations and explain how spline regression applied in an additive model could be integrated into our analysis. We conclude with two examples for eco-finance networks in the fields of CO2-emissions-control and portfolio Optimization for natural gas transportation systems.Öğe Optimization applied on regulatory and eco-finance networks -survey and new developments(2010) Weber, Gerhard-Wilhelm; Kropat, Erik; Tezel, Aysun; Belen, SelmaIn this paper we survey recent advances and mathematical foundations of regulatory networks. We explain their interdisciplinary implications with special regard to Operational Research and financial sciences and introduce the so-called eco-finance networks. These networks, originally developed in the context of modeling and prediction of gene-expression patterns, 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 investigate 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. We analyze the structural stability of the regulatory networks, we discuss a modeling by stochastic differential equations and explain how spline regression applied in an additive model could be integrated into our analysis. We conclude with two examples for eco-finance networks in the fields of CO2-emissions-control and portfolio optimization for natural gas transportation systems. © 2010 Yokohama Publishers.
