As is illustrated in Figure 4, these tissue time-activity curves represent the measured activity concentration averaged across the VOI - which implies that, in the ensemble of volume elements (voxels) comprising a VOI, all voxels share the same parameters of the underlying physiological and biochemical processes, and only differ as they are different realisations of the same random process.
In this Appendix we analyse the difference between the data associated with different realisations of such competitive dynamics and the adjustments to real data in terms of stochastic models such as (m_{2} k)), (m_{3} k)), and (m_{4} k)) given by Eq. (2).
Subsequent comparison of different realisations of the same imaging method revealed differences in the performance of specific imaging platforms for different applications, and in some cases differences between different realisations of the same method for the same application 38– 40.
A number of different realisations of the TCD exist: several of these express the critical distance as a function of material fatigue limit (Δσ0) and crack propagation threshold (ΔKth).
In this paper we used the intermediate-complexity multi-species model TreeMig to examine whether different realisations of future climate influences with the same temporal mean and the same interannual variability cause fundamental differences in simulated migration.
This study presents an ensemble of 50 model chains considering five different realisations of the A1B ECHand and HadCM3 climate projections, two different averaging methods to transfer the climate variables to the system scale and five different hydrological models that represent reasonable conceptualizations of the karst system.
Monte Carlo Simulation are conducted on different realisations of the random fields; the predicted responses are compared to previously published measurements and to reference FE simulations, in which the material strength is taken as uniform and equal to the measured average.
These three solutions correspond to three different realisations of (h(x)).
Top: (L^{2}) norm of stable steady states of (3) for a Gaussian threshold distribution, with many different initial conditions, different realisations of (h(x)), and various (h_{0}).
This process was replicated 99 times to create a total of 99 simulated point patterns with different realisations of the non-stationary process.
