A mathematical modeling and approximation of gene expression patterns by linear and quadratic regulatory relations and analysis of gene networks

Download

index.pdf

Date

2004

Author

Yılmaz, Fatma Bilge

Metadata

Show full item record

Item Usage Stats

317
views

99
downloads

This thesis mainly 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 di erential 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-continuous model. We analyze the approximating model under the aspect of stability. Finally, from the considered models we derive gene regulatory networks, discuss their qualitative features of the networks and provide a basis for analyzing networks with nonlinear connections.

Subject Keywords

General.

URI

http://etd.lib.metu.edu.tr/upload/12605382/index.pdf
https://hdl.handle.net/11511/14585

Collections

Graduate School of Applied Mathematics, Thesis

Suggestions

OpenMETU
Core

Inference of switching networks by using a piecewise linear formulation Akçay, Didem; Öktem, Hakan; Department of Scientific Computing (2005) Inference of regulatory networks has received attention of researchers from many fields. The challenge offered by this problem is its being a typical modeling problem under insufficient information about the process. Hence, we need to derive the apriori unavailable information from the empirical observations. Modeling by inference consists of selecting or defining the most appropriate model structure and inferring the parameters. An appropriate model structure should have the following properties. The model...
A computational procedure for estimating residual stresses and secondary plastic flow limits in nonlinearly strain hardening rotating shafts Eraslan, Ahmet Nedim (Springer Science and Business Media LLC, 2005-03-01) A computational procedure to estimate the residual stress distributions and the limit angular speeds for avoiding secondary plastic deformation in nonlinearly strain hardening rotating elastic-plastic shafts is given. The model is based on von Mises yield condition, J(2) deformation theory and a Swift-type hardening law. The boundary value problem for the governing nonlinear differential equation is solved by a shooting method using Newton iterations with numerically approximated tangent. Solid as well as h...
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...
A unifying grid approach for solving potential flows applicable to structured and unstructured grid configurations Cete, A. Ruhsen; Yuekselen, M. Adil; Kaynak, Uenver (Elsevier BV, 2008-01-01) In this study, an efficient numerical method is proposed for unifying the structured and unstructured grid approaches for solving the potential flows. The new method, named as the "alternating cell directions implicit - ACDI", solves for the structured and unstructured grid configurations equally well. The new method in effect applies a line implicit method similar to the Line Gauss Seidel scheme for complex unstructured grids including mixed type quadrilateral and triangle cells. To this end, designated al...
Exponential stability of periodic solutions of recurrent neural networks with functional dependence on piecewise constant argument Akhmet, Marat; Cengiz, Nur (The Scientific and Technological Research Council of Turkey, 2018-01-01) In this study, we develop a model of recurrent neural networks with functional dependence on piecewise constant argument of generalized type. Using the theoretical results obtained for functional differential equations with piecewise constant argument, we investigate conditions for existence and uniqueness of solutions, bounded solutions, and exponential stability of periodic solutions. We provide conditions based on the parameters of the model.

Citation Formats

F. B. Yılmaz, “A mathematical modeling and approximation of gene expression patterns by linear and quadratic regulatory relations and analysis of gene networks,” M.S. - Master of Science, Middle East Technical University, 2004.