Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
Analysis and prediction of gene expression patterns by dynamical systems, and by a combinatorial algorithm
Download
index.pdf
Date
2005
Author
Taştan, Mesut
Metadata
Show full item record
Item Usage Stats
64
views
36
downloads
Cite This
Modeling and prediction of gene-expression patterns has an important place in computational biology and bioinformatics. The measure of gene expression is determined from the genomic analysis at the mRNA level by means of microarray technologies. Thus, mRNA analysis informs us not only about genetic viewpoints of an organism but also about the dynamic changes in environment of that organism. Different mathematical methods have been developed for analyzing experimental data. In this study, we discuss the modeling approaches and the reasons why we concentrate on models derived from differential equations and improve the pioneering works in this field by including affine terms on the right-hand side of the nonlinear differential equations and by using Runge- Kutta instead of Euler discretization, especially, with Heun̕s method. Herewith, for stability analysis we apply modified Brayton and Tong algorithm to time-discrete dynamics in an extended space.
Subject Keywords
Differential equations.
URI
http://etd.lib.metu.edu.tr/upload/12606672/index.pdf
https://hdl.handle.net/11511/15402
Collections
Graduate School of Applied Mathematics, Thesis
Suggestions
OpenMETU
Core
Oscillation of second order matrix equations on time scales
Selçuk, Aysun; Ağacık, Zafer; Department of Mathematics (2004)
The theory of time scales is introduced by Stefan Hilger in his PhD thesis in 1998 in order to unify continuous and discrete analysis. In our thesis, by making use of the time scale calculus we study the oscillation of nonlinear matrix differential equations of second order. the first chapter is introductory in nature and contains some basic definitions and tools of the time scales calculus, while certain well-known results have been presented with regard to oscillation of the solutions of second order matr...
Boundary value problems for higher order linear impulsive differential equations
Uğur, Ömür; Akhmet, Marat; Taşeli, Hasan; Department of Mathematics (2003)
The theory of impulsive di®erential equations has become an important area of research in recent years. Linear equations, meanwhile, are fundamental in most branches of applied mathematics, science, and technology. The theory of higher order linear impulsive equations, however, has not been studied as much as the cor- responding theory of ordinary di®erential equations. In this work, higher order linear impulsive equations at xed moments of impulses together with certain boundary conditions are investigated...
On principles of b-smooth discontinuous flows
Akalın, Ebru Çiğdem; Akhmet, Marat; Department of Mathematics (2004)
Discontinuous dynamical system defined by impulsive autonomous differential equation is a field that has actually been considered rarely. Also, the properties of such systems have not been discussed thoroughly in the course of mathematical researches so far. This thesis comprises two parts, elaborated with a number of examples. In the first part, some results of the previous studies on the classical dynamical system are exposed. In the second part, the definition of discontinuous dynamical system defined by...
Inverse problems for parabolic equations
Baysal, Arzu; Çelebi, Okay; Department of Mathematics (2004)
In this thesis, we study inverse problems of restoration of the unknown function in a boundary condition, where on the boundary of the domain there is a convective heat exchange with the environment. Besides the temperature of the domain, we seek either the temperature of the environment in Problem I and II, or the coefficient of external boundary heat emission in Problem III and IV. An additional information is given, which is the overdetermination condition, either on the boundary of the domain (in Proble...
Mathematical modelling of enzymatic reactions, simulation and parameter estimation
Özöğür, Süreyya; Karasözen, Bülent; Department of Scientific Computing (2005)
A deep and analytical understanding of the human metabolism grabbed attention of scientists from biology, medicine and pharmacy. Mathematical models of metabolic pathways offer several advances for this deep and analytical understanding due to their incompensable potential in predicting metabolic processes and anticipating appropriate interventions when required. This thesis concerns mathematical modeling analysis and simulation of metabolic pathways. These pathways include intracellular and extracellular c...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
M. Taştan, “Analysis and prediction of gene expression patterns by dynamical systems, and by a combinatorial algorithm,” M.S. - Master of Science, Middle East Technical University, 2005.