Modern mathematical methods in modeling and dynamics of regulatory systems of gene-environment networks

Download

index.pdf

Date

2011

Author

Defterli, Özlem

Metadata

Show full item record

Item Usage Stats

282
views

147
downloads

Inferring and anticipation of genetic networks based on experimental data and environmental measurements is a challenging research problem of mathematical modeling. In this thesis, we discuss gene-environment network models whose dynamics are represented by a class of time-continuous systems of ordinary differential equations containing unknown parameters to be optimized. Accordingly, time-discrete version of that model class is studied and improved by using different numerical methods. In this aspect, 3rd-order Heun’s method and 4th-order classical Runge-Kutta method are newly introduced, iteration formulas are derived and corresponding matrix algebras are newly obtained. We use nonlinear mixed-integer programming for the parameter estimation and present the solution of a constrained and regularized given mixed-integer problem. By using this solution and applying the 3rd-order Heun’s and 4th-order classical Runge-Kutta methods in the timediscretized model, we generate corresponding time-series of gene-expressions by this thesis. Two illustrative numerical examples are studied newly with an artificial data set and a realworld data set which expresses a real phenomenon. All the obtained approximate results are compared to see the goodness of the new schemes. Different step-size analysis and sensitivity tests are also investigated to obtain more accurate and stable predictions of time-series results for a better service in the real-world application areas. The presented time-continuous and time-discrete dynamical models are identified based on given data, and studied by means of an analytical theory and stability theories of rarefication, regularization and robustification.

Subject Keywords

Dynamics

URI

http://etd.lib.metu.edu.tr/upload/12613592/index.pdf
https://hdl.handle.net/11511/21201

Collections

Graduate School of Natural and Applied Sciences, Thesis

Suggestions

OpenMETU
Core

Modeling and Simulation of High Speed Railway Vehicle Dynamics Tuğçe, Yüksel; Ünlüsoy, Yavuz Samim (null; 2015-03-04) This study aims to provide mathematical model(s) for the simulation of high speed railway vehicles. The dynamic behavior of a high speed train is divided into three uncoupled motions: vertical, lateral, and longitudinal. Two models with different complexities are used to simulate vertical plane response of the vehicle to track vertical irregularities. Different wheel-rail contact formulations are utilized to simulate the lateral plane motion of the vehicle on tangent and curved tracks. For both vertical and...
Theory of impurity induced lattice distortions in the normal phase of charge density wave systems Turgut, Sadi (1994-05-01) A phenomenological Ginzburg-Laundau theory is applied to the normal phase of one-dimensional charge-density-wave systems with a finite concentration of impurities. It is found that the interaction between the impurities and the highly polarizable electron gas leads to a strong and oscillatory impurityimpurity interaction, which in turn leads to ordered impurity arrangements and to sizeable periodic lattice distortions. The effect is very strongly dependent on the charge of the impurities, their concentratio...
A Review on Data Mining and Continuous Optimization Applications in Computational Biology and Medicine Weber, Gerhard Wilhelm; Ozogur-Akyuz, Sureyya; Kropat, Erik (2009-06-01) An emerging research area in computational biology and biotechnology is devoted to mathematical modeling and prediction of gene-expression patterns; it nowadays requests mathematics to deeply understand its foundations. This article surveys data mining and machine learning methods for an analysis of complex systems in computational biology, It mathematically deepens recent advances in modeling and prediction by rigorously introducing the environment and aspects of errors and uncertainty into the genetic con...
On optimization, dynamics and uncertainty: A tutorial for gene-environment networks WEBER, G. -W.; Uğur, Ömür; Taylan, P.; TEZEL, AYSUN (2009-05-28) An emerging research area in computational biology and biotechnology is devoted to mathematical modeling and prediction of gene-expression patterns; to fully understand its foundations requires a mathematical study. This paper surveys and mathematically expands recent advances in modeling and prediction by rigorously introducing the environment and aspects of errors and uncertainty into the genetic context within the framework of matrix and interval arithmetic. Given the data from DNA microarray experiments...
Numerical simulation of scour at the rear side of a coastal revetment Şentürk, Barış Ufuk; Guler, Hasan Gokhan; Baykal, Cüneyt (2023-05-01) This paper presents the results of a numerical modeling study on the scouring of unprotected rear side material of a rubble mound coastal revetment due to the overtopping of solitary-like waves utilizing a coupled hydro-morphodynamic computational fluid dynamics (CFD) model. Three cases having various wave heights are tested with six different turbulence models together with different wall functions. The hydrodynamic results (free-surface elevations, overtopping volumes, and jet thicknesses) and morphologic...

Citation Formats

Ö. Defterli, “Modern mathematical methods in modeling and dynamics of regulatory systems of gene-environment networks,” Ph.D. - Doctoral Program, Middle East Technical University, 2011.