Advanced mathematical and statistical tools in the dynamic modelling and simulation of gene-environment networks

In this study, some methodologies and a review of the recently obtained new results are presented for the problem of modeling, anticipation and forecasting of genetic regulatory systems, as complex systems. In this respect, such kind of complex systems are modeled in the dynamical sense into the two different ways, namely, by a system of ordinary differential equations (ODEs) and Gaussian graphical methods (GGM). An artificial time-course microarray dataset of a gene-network is modeled as an example by using both ODE method and GGM. In this analysis, since the actual interactions of the nodes, i.e., genes, are assumed to be unknown, the discrete time measurements are initially used for the inference of the system’s interactions, i.e., the edges between nodes, by the underlying two methods. Then, the results of inference from ordinary differential equation based model are applied to a class of previously developed new numerical schemes for the generation of further states of the system. In this simulation, we present the recent results of a set of explicit Runge-Kutta methods that are implemented.


Modern tools for the time-discrete dynamics and optimization of gene-environment networks
DEFTERLİ, ÖZLEM; Fuegenschuh, Armin; Weber, Gerhard Wilhelm (Elsevier BV, 2011-12-01)
In this study, we discuss the models of genetic regulatory systems, so-called gene-environment networks. The dynamics of such kind of systems are described by a class of time-continuous ordinary differential equations having a general form (E) over dot = M(E)E, where E is a vector of gene-expression levels and environmental factors and M(E) is the matrix having functional entries containing unknown parameters to be optimized. Accordingly, time-discrete versions of that model class are studied and improved b...
Application of nonlinear unit root tests and threshold autoregressive models
Uysal, Ela; Yıldırım Kasap, Dilem; Department of Economics (2012)
Popularity of nonlinear threshold models and unit root tests has increased after the recent empirical studies concerning the effects of business cycles on macroeconomic data. These studies have shown that an economic variable may react differently in response to downturns and recoveries in a business cycle. Inspiring from empirical results, this thesis investigates dynamics of Turkish key macroeconomic data, namely capacity utilization rate, growth of import and export volume indices, growth of gross domest...
Mathematical Modeling and Approximation of Gene Expression Patterns
Yılmaz, Fatih; Öktem, Hüseyin Avni (2004-09-03)
This study concerns modeling, approximation and inference of gene regulatory dynamics on the basis of gene expression patterns. The dynamical behavior of gene expressions is represented by a system of ordinary differential equations. We introduce a gene-interaction matrix with some nonlinear entries, in particular, quadratic polynomials of the expression levels to keep the system solvable. The model parameters are determined by using optimization. Then, we provide the time-discrete approximation of our time...
Development of test structures and methods for characterization of MEMS materials
Yıldırım, Ender; Arıkan, Mehmet Ali Sahir; Department of Mechanical Engineering (2005)
This study concerns with the testing methods for mechanical characterization at micron scale. The need for the study arises from the fact that the mechanical properties of materials at micron scale differ compared to their bulk counterparts, depending on the microfabrication method involved. Various test structures are designed according to the criteria specified in this thesis, and tested for this purpose in micron scale. Static and fatigue properties of the materials are aimed to be extracted through the ...
A philosophical analysis of computational modeling in cognitive science
Ürgen, Burcu Ayşen; Bağçe, Samet; Department of Cognitive Sciences (2007)
This study analyses the methodology of computational cognitive modeling as one of the ways of conducting research in cognitive science. The aim of the study is to provide an understanding of the place of computational cognitive models in understanding human cognition. Considering the vast number of computational cognitive models which have been just given to account for some cognitive phenomenon by solely simulating some experimental study and fitting to empirical data, a practice-oriented approach is adopt...
Citation Formats
V. Purutçuoğlu Gazi, Advanced mathematical and statistical tools in the dynamic modelling and simulation of gene-environment networks. 2014, p. 257.