"... In PAGE 4: ... Table1 shows the 4 most likely trajectories returned by BFTE for the scenario in Figure 5, with their source state, target state, a priori state trajectory probability, and percent error when compared to the true a priori probabilities. It is important to notice that since BFTE splits the two trajecto- ries leading to st+1 1... ..."

"... In PAGE 4: ... Table1 shows the 4 most likely trajectories returned by BFTE for the scenario in Figure 5, with their source state, target state, a priori state trajectory probability, and percent error when compared to the true a priori probabilities. It is... In PAGE 5: ... 4.2 Best-First Belief State Enumeration Using BFBSE to generate estimates for the IMU/PS scenario would entirely remove the problem exhibited in Table1 . In- stead of approximating the belief state by searching over most likely trajectories, BFBSE uses the HMM belief state propa- gation equation directly as its utility function.... ..."

"... In PAGE 5: ... 15 Figure 5: Demonstrated trajectories. As described in the previous section, 5 state left-to- right HMM is assigned to each trajectory and the calculated approximation log posterior probabilities corresponding to the number of the clusters ranging from 1 to 6 is shown in Table4 . The value increases monotonously as in the previous case, and a signifi- cant curvature appears around the number 2 in this case.... ..."

"... In PAGE 9: ... For both versions of the 15-state usage model in Fig. 2, Table8 gives the matrix of trajectory entropies as defined by Ekroot and Cover [2]. For the model with uniform transition probabilities, H(T{Inv, Term}) 19.... In PAGE 9: ...erm}) 11.144. The second version has fewer typical paths from invocation to termination than the first. The entries in Table8 provide a measure of the uncertainty in selection of a path between two states where that path occurs within a long-run chain of states generated by the usage model. Table 9 gives the matrix of test trajectory entropies where C S: Blank cells in the matrices indicate that there are no paths in the corresponding trajectory.... In PAGE 9: ... The entries in this table provide a measure of the uncertainty in selection of a path between two states where that path occurs within a single test case. Note that, except for the last two rows, the right hand column of each matrix corresponds to those of Table8 . The value for each element of a given row of Table 9 is less than or equal to the value of the right-hand column element of the correspond- ing row.... ..."

"... In PAGE 19: ... Ip = mpr2 p 2 = 7:168 10?6kg m2. Table 2 shows the measured pre-impact and post-impact velocities for nine sample trajectories from Table1 . By substituting the pre-impact velocities into the no sliding condition (48), we predict that sliding will not terminate in trajectories 4,5, and 9 and will terminate in the other trajectories.... ..."

"... In PAGE 19: ... I p = m p r 2 p 2 =7:168 10 ;6 kg m 2 . Table 2 shows the measured pre-impact and post-impact velocities for nine sample trajectories from Table1 . By substituting the pre-impact velocities into the no sliding condition (48), we predict that sliding will not terminate in trajectories 4,5, and 9 and will terminate in the other trajectories.... ..."

"... In PAGE 3: ... Qualitative Measures In addition to geographical data analysis, we developed qualitative measures to address our hypothesis that there might be some structure to the movements we observed. Qualitative measures in this study comprise 38 characteristic variables in representing specific patterns of trajectories ( Table1 ). Each variable was deduced from the trajectories drawn by participants.... In PAGE 3: ...86 indicating strong agreement among researchers and an acceptable qualitative coding approach. Pooled statistics ( Table1 ) of each qualitative measure reveal that in the line configurations with and without obstacles as well as the circular configuration, participants tended to initially move away in reference to target locations. Corresponding patterns of trajectories to each column in Table 1 are shown in Figure 2.... In PAGE 3: ... Pooled statistics (Table 1) of each qualitative measure reveal that in the line configurations with and without obstacles as well as the circular configuration, participants tended to initially move away in reference to target locations. Corresponding patterns of trajectories to each column in Table1 are shown in Figure 2. Additionally, the top two variables that were highly consistent in each configuration are summarized in Table 2.... In PAGE 5: ... As a result, a total of 34 qualitative variables were analyzed using the SOM technique. Table1 details a full description of each variable. Subplots in Figure 7 illustrate characteristics of the 34 variables, relative to all other variables.... ..."