Identifiability of Delay Parameters for Nonlinear Time-delay Systems with Applications in Systems Biology
published: April 4, 2007, recorded: March 2007, views: 421135
Report a problem or upload filesIf you have found a problem with this lecture or would like to send us extra material, articles, exercises, etc., please use our ticket system to describe your request and upload the data.
Enter your e-mail into the 'Cc' field, and we will keep you updated with your request's status.
The concept of parameter identifiability will be introduced briefly, followed by a short description of how this property can be tested for ODE-systems in general by rank calculations. Then, the extension of this analysis to delay systems, recently developed by Xia et al.  and Zhang et al.  will be reviewed. In these works, the authors use the framework of modules over non-commutative rings to formulate an analogous rank test for parameter identifiability of delay systems with known time-delays. Our ongoing work will then be motivated by a model of cellular signal transduction by Timmer et al. , where the sojourn time of STAT-5 in the nucleus is modelled by an unknown time delay which is estimated numerically by Timmer et al.. We will show how the identifiability of the time delay parameter is determined by the form of the external input-output representation of the system. Working in the mathematical framework of  and , we formulate explicit criteria based on rank calculations for the space spanned by the gradients of the output derivatives. Finally, several examples of biological systems from the literature will be discussed.
Joint work with Bernt Wennberg.
Link this pageWould you like to put a link to this lecture on your homepage?
Go ahead! Copy the HTML snippet !