### Table 2. Multi-step approximation error

1998

"... In PAGE 10: ....2. Results of experiments. Results of experiments for the one-step and multi- step approximation errors are shown in Table 1 and Table2 respectively. For all cases, the errors induced by the LL method are much smaller than the errors induced by the Euler method.... ..."

Cited by 6

### Table 2: Multi-step forecasting example (T = 2)

"... In PAGE 13: ... The main tuning parameter is the forecast horizon, T , which dictates how far in the future to forecast. To flnd the maximum likelihood measurement sequence, the algorithm must try all possible combinations of future measurement sequences (see the case for the forecast horizon T = 2 in Table2 ), and flnd the measurement sequence that maximizes the likelihood. Recall that q indicates all the times that a target is detected, and r denotes the times that it is not detected.... ..."

### Table 4: General form of multi-step algorithms. x : non-zero coe cient

"... In PAGE 11: ... Appendix A: Multi-step scheme coe cients In this study, three families of schemes are used for the multi-step particle path integration algorithms: Adams-Bashforth, Adams-Moulton, and backwards di erentiation. The general forms for the coe cients are shown in Table4 and the speci c coe cients for the schemes are presented in Tables 5-7. Appendix B: Non-constant timestep algorithms Most of the algorithms which we have discussed for constant timesteps can easily be extended to non- constant timesteps.... ..."

### Table 4. Comparison of Multi-Step Linear Connections between Groups on Post-Interview

in Using Domino and Relational Causality to Analyze Ecosystems: Realizing What Goes Around Comes Around

"... In PAGE 18: ... 16 Multi-Step Linear Connections: The complexity level of the connections made by students on the post-interview shows a clear impact of intervention condition. Table4 shows a comparison of the multi-step linear connections made between groups from the pre- to post-interviews. While the AO group had the highest gain in two-step linear connections (AO = 17; CM = 7; CON = 3), the CM group gained the most in three-step (AO = 2; CM = 7; CON = 1) and four-step (AO = 1; CM = 2; CON = 0) connections.... ..."

### Table 4: General form of multi-step algorithms. x : non-zero coe cient

"... In PAGE 13: ... Appendix A: Multi-step scheme coe cients In this study, three families of schemes are used for the multi-step particle path integration algorithms: Adams-Bashforth, Adams-Moulton, and backwards di erentiation. The general forms for the coe cients are shown in Table4 and the speci c coe cients for the schemes are presented in Tables 5-7. Appendix B: Non-constant timestep algorithms Most of the algorithms which we have discussed for constant timesteps can easily be extended to non- constant timesteps.... ..."

### Table 6: One step RBF algorithm compared to multi-step MSA. (Based on reduced- parameter set.)

1998

"... In PAGE 16: ... Table6 shows the performance of the algorithms for a given SIL misclassi cation cost. For comparison purposes, the results of the 2-step RBF ensemble algorithms are also pro- vided.... ..."

Cited by 7

### Table 6: One step RBF algorithm compared to multi-step MSA. (Based on reduced-parameter set.)

1998

"... In PAGE 15: ... Table6 shows the performance of the algorithms for a given SIL misclassification cost. For comparison purposes, the results of the 2-step RBF ensemble algorithms are also provided.... ..."

Cited by 7

### Table 5.1 SSP multi-step methods #282.14#29

2001

Cited by 1

### Table 1: Notation for the multi-step RESTART/LRE and result variables

"... In PAGE 18: ... A STEP-BY-STEP RESTART/LRE In this section, the results for the optimal parameter settings for the minimal number of trials of the step-by-step strategy are given. The notation given in Table1 is used for splitting the complementary distribution function BZB4DCB5 into D1 B7BDintervals.... In PAGE 20: ...BZ BU BP C8CUAB AL BUCV BP C8CUAB AL BUCYAB AL C1 D1A0BD CVC8CUAB AL C1 D1A0BD CYAB AL C1 D1A0BE CV A1A1A1C8CUAB AL C1 BD CYAB AL C1 BC CVC8CUAB AL C1 BC CV BM (7) For this method, the number of trials in each step D2 CX can be calculated by the LRE formula, see Table1 and [47]. Taking the sum over all steps and then successively using the necessary condition for a minimum, the optimal levels C0 A3 CX and the minimal number of trials D2 min can be determined as functions of the loss probability C0 D1 BP BZ BU : C0 A3 CX B4C0 D1 B5BP AW C9 CX CYBPBC AD D1A0CX CY C9 D1 CYBPCXB7BD AD CXB7BD CY C0 CXB7BD D1 AX BD D1B7BD BN (8) D2 minB4C0 D1 B5BP D1 B7BD CS BE CB AW D1 CH CXBPBC AD CX AX BD D1B7BD AI BD C0 D1 AJ BD D1B7BD BM (9) The error in D1 steps (D1 B7BDintervals) is: CS BE BU BPB4CS BE CB B7BDB5 D1B7BD A0 BD AX CS BE CB BPB4CS BE BU B7BDB5 BD D1B7BD A0 BD BM (10) Trying to determine the optimal number of steps D1 opt using (10) leads to tran- scendental equations that cannot be solved.... ..."

### Table 6 Including macroeconomic predictors, RMSFE and average RMSFE ratios of direct multi-step forecast of annualised inflation in percentage points . horizon 1 6 12

2005

"... In PAGE 31: ... In this case estimation uncertainty of a high number of parameters increases the MSFE relatively more. Table6 displays the results for the factor model forecasts, again based on direct multi-step ahead forecasts of annualised inflation. Here the majority of the factor forecasts outperforms the ARSIC over all horizons.... ..."