Divergence estimates

K. H. Wolfe, M. Gouy, Y-W Yang, P. M. Sharp, and W. H. Li, Date of the monocot-dicot divergence estimated from chloroplast DNA sequence data. Proc. Nall. Acad. Sci. U.S.A. 86 6201-6205 (1989). 

Wikstrom, N., Savolainen, V. and Chase, M. W. (2003) Angiosperm divergence times Congruence and incongmence between fossils and sequence divergence estimates. In Telling the Evolutionary Time Molecular Clocks and the Fossil Record (ed. P. C. J. Donoghue and M. P. Smith). Taylor Francis, London, pp. 142-165. 

In the highly nonlinear equilibrium situations characteristic of liquid separations, the use of priori initial estimates of phase compositions that are not very close to the true compositions of these phases can lead to divergence of iterative computations or to spurious convergence upon feed composition. 

Second card FORMAT(8F10.2), control variables for the regression. This program uses a Newton-Raphson type iteration which is susceptible to convergence problems with poor initial parameter estimates. Therefore, several features are implemented which help control oscillations, prevent divergence, and determine when convergence has been achieved. These features are controlled by the parameters on this card. The default values are the result of considerable experience and are adequate for the majority of situations. However, convergence may be enhanced in some cases with user supplied values. 

Fig. 8. Casson plots of sheared and unsheared paints. The degree of divergence of the lines is used to estimate thixotropy.

In Figure 8.8, sinee the observer dynamies will never exaetly equal the system dynamies, this open-loop arrangement means that x and x will gradually diverge. If however, an output veetor y is estimated and subtraeted from the aetual output veetor y, the differenee ean be used, in a elosed-loop sense, to modify the dynamies of the observer so that the output error (y — y) is minimized. This arrangement, sometimes ealled a Luenberger observer (1964), is shown in Figure 8.9. 

Alternatively, one may attempt to estimate the integral over the derivative of the displacement field that entered in the expression for the coupling constant g= pc Jy cPr du/2. Since da is the divergence of a vector, the integral is reduced to that over a surface within the droplet s boundary ... 

The idea behind the computation of the Divergence only among adequate models in Step 2, is to base the decision for the next experiment on the models that are still competing. Models that have been found inadequate should not be included in the divergence computations. However, once the new data point becomes available it is good practice to update the parameter estimates for all models (adequate or inadequate ones). Practice has shown that under conditions of high experimental errors, as additional information becomes available some models may become adequate again ... 

If instead of precise parameter estimation, we are designing experiments for model discrimination, the best grid point of the operability region is chosen by maximizing the overall divergence, defined for dynamic systems as... 

Measurement of the diverging steady shear viscosity is an appealing experiment because of its simplicity. Even the torque on a processing machine might serve as an estimate of the diverging viscosity. It has, however, severe disadvantages that need to be considered [149] ... 

In view of the diversity of reproductive effects induced by arthropod Wolbachia, it would not be surprising if Wolbachia behaves in different ways in different filarial nematodes. The C and D Wolbachia groups are estimated to have diverged approximately 100 million years ago (see earlier). Given this fact, it is quite possible that Wolbachia in different lineages have followed different evolutionary trajectories. 

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