### Table 10: Multi-level hierarchy: Example 2. #Iterations #Q-levels

### Table 11: Multi-level hierarchy: Example 3. Example 3: Now we consider the three-level hierarchy of gure 4. Let fij be the input-output map of the jth agent in the ith level of the hierarchy. In the present example, we choose: f31(x31) = 2 sin(5 (x31 ? :5))

### Table 9: Multi-level hierarchy: Example 1. except for two di erences: rstly, the agent A not only quantizes his environment x, but also evaluates his input-output map g( ) on the environment x and sends the quantized outcome to the supervisor; and secondly, S, in addition to receiving messages from A, observes his own local environment y. The desired-outcome function is f(x; y). Here we take:

### Table 2. Statistics of the multi-level preconditioner

"... In PAGE 5: ... In the table, the 5th and 6th columns indicate the total number of Newton iterations and Krylov iterations used in the Newton loop and by the GMRES solver, respectively, before the simulation convergence is reached. The performance of the proposed multi-level preconditioner is summarized in Table2 on the same set of designs, where the total number of Krylov iterations corresponds to that is used by the top- level FGMRES solver. Different from the previous experiments, we have adopted a multi-level structure where the largest sub- problem size on the next level is approximately one fourth of that on the current level.... ..."

### Table 4. Multi-Level Threshold Results

"... In PAGE 7: ... Multi-Level Threshold Results Threshold Level 4 3 2 1 Value #28in Meters#29 30 18 8 2 Table 5. Multi-Level Threshold Values Table4 shows the number of PDUs generated and the average error in AOI and SR when our multi- level threshold dead reckoning algorithm is used. The threshold values used in di#0Berent levels are listed in Table 5.... In PAGE 7: ... The threshold values used in di#0Berent levels are listed in Table 5. It can be seen from Table4 that there is a great reduction in the average error in SR, compared to the average error in AOI. In our algorithm, if entity A is in entity B apos;s SR, a minimum threshold will be used in the dead reckoning so that B will receive A apos;s update packets most frequently.... ..."

### Table 5: MULTI-LEVEL MODELS

1998

"... In PAGE 28: ...xist with more time periods. To date, they are far from being solved. Computation on Multi-Level Instances Results for the ML-G instances are presented in Table 5. The results in Table5 show that at least on these simple academic models bc ? prod typically dominates bc ? opt and mp ? opt. This is due to the automatic conversion to an echelon stock formulation in combination with the path inequalities.... ..."

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### Table 2. Statistics of multi-level preconditioner

"... In PAGE 5: ... In the table, the 5th and 6th columns indicate the total number of Krylov iterations used in the Newton loop and by the GMRES solver, respectively, before the convergence is reached. The performance of the proposed multi-level preconditioner is summarized in Table2 . on the same set of designs, where the total number of Krylov iterations corresponds to that is used by the top- level FGMRES solver.... ..."

### Table 2. Number of objects retrieved by our top-down algorithm for the DB amp;LP Web source

1999

"... In PAGE 7: ... To demonstrate the efficiency of the top- down algorithm in dealing with multi-level hierarchies, we use it to extract complex objects representing journal vol- umes and papers from these pages. The results are sum- marized in Table2 . The algorithm was able to identify and... ..."

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