"... In PAGE 5: ...We have provided an experimental validation of this result and an extension of the formula in the case where q lt;1. The regression model behaves well on our simulations and we provide a synthesis of experimental results in Table1 and Figures 1, 2. Other examples Our machinery has also been tested on other families (see [10] for further examples).... ..."

"... In PAGE 5: ... We have provided an experimental validation of this result and an extension of the formula in the case where q lt; 1. The regression model behaves well on our simulations and we provide a synthesis of experimental results in Table1 and Figures 1, 2. Other examples Our machinery has also been tested on other families (see [10] for further examples).... ..."

"... In PAGE 5: ... We have provided an experimental validation of this result and an extension of the formula in the case where q lt; 1. The regression model behaves well on our simulations and we provide a synthesis of experimental results in Table1 and Figures 1, 2. Other examples Our machinery has also been tested on other families (see [10] for further examples).... ..."

"... In PAGE 4: ... Equation (14) can be used to de- termine the range of values over which the elements of c can be varied without changing the optimal bfs, x . The method in Table1 calculates the values for each optimal bfs x . The corresponding vectors x B( )... In PAGE 4: ... What we are really interested in, is the sensitivity of on the decisions made by the sensory perception controller. For example, if the initial SDP state is 0 = 0:5 and the discount factor changes from 0:9 to 0:7, will this cause the SPC to consult another monitor rst? To answer these kinds of questions, the method in Table1 must be executed on all possible permutations. The optimal permutation z is given by the optimal value function.... In PAGE 4: ... For all values of , let x B( ) be the basic components of the optimal bfs and cB( ) be the basic components of the modi ed reward vector. Then, we have VNm( 0; z; ) = cB( )Tx B( ) (16) The modi ed reward vector cB( ) is calculated from the stored values of c0 B and in Table1 and the func- tion f, ie. cB( ) = c0 B( ) f( ... In PAGE 5: ... Figures 4 and 5 show the sensitivity of the decisions made by the SPC as a function of the discount factor . The method in Table1 was used to nd the optimal bfs x for all the permutations and equations (16) and (17) were used to nd the optimal permutation z . All the process monitors are available to the SPC.... ..."

"... In PAGE 17: ...Two Range Anisotropic Models With both the constant mean model and the quadratic trend model, we use the general range anisotropic form in (17) for the correlation structure. Table1 gives posterior means, standard deviations and 95% interval estimates for the constant mean model parameters. The posterior mean for 1 is 1.... In PAGE 17: ... The posterior mean and intervals for the range as a function of angle are presented in Figure 6 with the maximum range (strongest correlation) roughly parallel to the coastline ( 50 ? 60 ). Posterior means, standard deviations and interval estimates for the quadratic trend model apos;s variance components are also presented in Table1 and the trend surface pa- rameters associated with (21) in Table 2. As with the constant mean model, the range anisotropic covariance structure is far from isotropy or geometric anisotropy.... ..."

"... In PAGE 19: ... Table 1 contains results for the baseline models. Table4 refers to the models with drift and leverage. The bootstrap methods rely on 999 bootstrap replications for each of the 10,000 Monte Carlo replications.... ..."