Inference of piecewise linear systems with an improved method employing jump detection

Selçuk, Ahmet Melih
Inference of regulatory relations in dynamical systems is a promising active research area. Recently, most of the investigations in this field have been stimulated by the researches in functional genomics. In this thesis, the inferential modeling problem for switching hybrid systems is studied. The hybrid systems refers to dynamical systems in which discrete and continuous variables regulate each other, in other words the jumps and flows are interrelated. In this study, piecewise linear approximations are used for modeling purposes and it is shown that piecewise linear models are capable of displaying the evolutionary characteristics of switching hybrid systems approxi- mately. For the mentioned systems, detection of switching instances and inference of locally linear parameters from empirical data provides a solid understanding about the system dynamics. Thus, the inference methodology is based on these issues. The primary difference of the inference algorithm is the idea of transforming the switch- ing detection problem into a jump detection problem by derivative estimation from discrete data. The jump detection problem has been studied extensively in signal processing literature. So, related techniques in the literature has been analyzed care- fully and suitable ones adopted in this thesis. The primary advantage of proposed method would be its robustness in switching detection and derivative estimation. The theoretical background of this robustness claim and the importance of robustness for real world applications are explained in detail.


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...
Development of tools for modeling hybrid systems with memory
Gökgöz, Nurgul; Öktem, Hakan; Department of Scientific Computing (2008)
Regulatory processes and history dependent behavior appear in many dynamical systems in nature and technology. For modeling regulatory processes, hybrid systems offer several advances. From this point of view, to observe the capability of hybrid systems in a history dependent system is a strong motivation. In this thesis, we developed functional hybrid systems which exhibit memory dependent behavior such that the dynamics of the system is determined by both the location of the state vector and the memory. T...
Derivation of Transcriptional Regulatory Relationships by Partial Least Squares Regression
Tan, Mehmet; Polat, Faruk; Alhajj, Reda (2009-11-04)
As the number of genes in a transcriptional regulatory network is large and the number of samples in biological data types is usually small, there is a need for integrating multiple data types for reverse engineering these networks. In this paper, we propose a method to integrate microarray gene expression, ChIP-chip and transcription factor binding motif data sets in a partial least squares regression model to derive transcription factors (TFs) gene interactions. Both single and synergistic effects of TFs ...
Kropat, Erik; Ozmen, Ayse; Weber, Gerhard Wilhelm; Meyer-Nieberg, Silja; DEFTERLİ, ÖZLEM (2016-04-01)
Target-environment networks provide a conceptual framework for the analysis and prediction of complex regulatory systems such as genetic networks, eco-finance networks or sensor-target assignments. These evolving networks consist of two major groups of entities that are interacting by unknown relationships. The structure and dynamics of the hidden regulatory system have to be revealed from uncertain measurement data. In this paper, the concept of fuzzy target-environment networks is introduced and various f...
Chaotic behavior of triatomic clusters
Yurtsever, E; Elmaci, N (1997-01-01)
The dynamics of triatomic clusters is investigated employing two-body Lennard-Jones and three-body Axilrod-Teller potential functions. Lyapunov exponents are calculated for the total energy range of -2.70 epsilon <E< -0.72 epsilon. The effects of the initial geometry of the cluster, its angular momentum, and the magnitude of three-body interactions are analyzed. It has been found that the dominating factor for the extent of chaotic behavior is the energy assigned to vibrational modes. The introduction of th...
Citation Formats
A. M. Selçuk, “Inference of piecewise linear systems with an improved method employing jump detection,” M.S. - Master of Science, Middle East Technical University, 2007.