Kinetic parameter distribution identifiability

Here n(square matrix formed from the kinetic parameters p, k, and c. The nature of O may be recognized by expressing Eq. (2) in matrix form and identifying the resulting square matrix with O. O is called here the Smith Ewart coupling matrix because its elements in Eq. (5) describe bow latex particles change state as a consequence of the Smith-Ewart mechanisms (entry, exit, and bimolecular termination). 

The aforementioned example is characteristic of a situation in which the steady-state (macroscopic) reaction rate is constant, but the reacting adsorbed species are nevertheless not uniformly distributed over the surface. Most common in this respect are spiral waves that are characteristic of excitable media, where the excitation not necessarily requires an external perturbation, but may often be identified with an inherent local variation of kinetic parameters such as a defect zone on the surface. The core of the spiral may then be formed by a local defect to which the spiral is... 

For each class of PIE it may be sufficient to analyse only a limited number of bounding initiating events that can then represent a bounding response for a group of events. The basis for these selected bounding events should be described in this section. Those plant parameters important to the outcome of the safety analysis should be identified. These would typically include reactor power and its distribution core temperature cladding oxidation and/or deformation pressures in the primary and secondary system containment parameters temperatures and flows reactivity coefficients reactor kinetics parameters and the worth of reactivity devices. 

Numerical identifiability also becomes a problem with a poorly or inadequately designed experiment. For example, a drug may exhibit multi-exponential kinetics but due to analytical assay limitations or a sampling schedule that stops sampling too early, one or more later phases may not be identifiable. Alternatively, if sampling is started too late, a rapid distribution phase may be missed after bolus administration. In these cases, the model is identifiable but the data are such that all the model components cannot be estimated. Attempting to fit the more complex model to data that do not support such a model may result in optimization problems that either do not truly optimize or result in parameter estimates that are unstable and highly variable. 

Unfortunately, there has been minimal work on identifiability issues with respect to population kinetic analysis. The current work on identifiability of kinetic models (Jacquez, 1985 belli and DiStefano, 1980 Cobelli and Saccomani, 1990) focuses on estimation for an individual experiment. With regard to population analysis and Bayesian estimation of parameters for an individual from the population, it is the population analysis step for which identifiability issues need to be considered. Once a prior distribution... 

The possibility of using alternative kinetic schemes to rationalise the same fitting parameters, and the fact that in general a distribution of lifetimes can be fitted successfully by a sum of discrete exponential terms are the main reasons against the multi-exponential approach [86]. However, this difficulty can be overcome when narrow and well-separated time distributions can be identified, and... 

Thus, the effect that a Co(II)-based CCTA has on the course of the polymerization, and on the product properties of an emulsion polymerization, is governed by the intrinsic activity and the partitioning behavior of the catalyst. Radical desorption from the particle phase to the aqueous phase preceded by chain transfer is the main kinetic event controlling the course of the polymerization. The product properties in terms of the partide size distribution and the aqueous phase solubility of the CCTA are the key parameters controlling the course of the polymerization and the partide size distribution. Two limiting scenarios have been identified in cases of fast CCTA entry and exit, mono-modal MWDs can be obtained and with slow CCTA entry and exit, bimodal MWDs can be obtained one peak can be attributed to the generation by bimolecular termination prodna produced in polymer partides devoid of CCTA, while a transfer-derived peak can be attribnted to polymer partides containing one or more CCTA molecules. ... 

Knowledge of the g values and the detailed hyper-fine interactions (A values) allow us to help identify radical species, and these parameters contain information about the electron distribution within the molecule. Radicals are often present as intermediates during a reaction consequently their identification will give information concerning the reaction mechanism and measurement of how their concentration changes with time will give kinetic data. 

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