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1.75
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Identifiability of Delay Parameters for Nonlinear Time-delay Systems with Applications in Systems Biology
Published on Apr 04, 2007421167 Views
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 exte
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Chapter list
Identifiability of time-lag parameters for non-linear delay systems with applications in system biology00:01
Motivation00:07
Organisation00:55
The property of Identifiability01:33
Identifiability of ODE02:43
Explicit relations for the variables/parameters04:11
Simple example of a delay system, Example 104:24
Example 1 continued04:59
Input output equation06:05
Estimatig τ07:09
A plot of the output and the function ξ(τ)07:39
A delay system with unidentifiable time-lag parameter08:03
Example 2, continued08:28
Example 2, continued08:54
Identifiability of delay parameter09:24
General form for the non-linear delay systems10:12
Mathematical framework for delay systems10:38
Mathematical framework for delay systems10:49
Mathematical framework for delay systems11:18
Preliminary definitions12:04
Preliminary definitions12:18
Preliminary definitions12:33
Linear-algebraic identifiability criteria13:00
Linear-algebraic identifiability criteria, translation13:17
Linear-algebraic identifiability criteria, translation13:33
Exapmle 1, revisited13:56
Exapmle 2, revisited14:29
The JAK-STAT signalling pathway model, revisited14:51
A gene expression model for Hes115:22
A gene expression model for Hes1, continued15:49
Checking the criteria in pracise16:28
Several delays17:08
Acknowledgements17:42
A plot of the output and the function ξ(τ)18:12
Example 1 continued20:20