### Table 1: Performance of ^ v0 on 100 Monte-Carlo runs.

"... In PAGE 4: ... The AR part of the ARMA(4,4) model used for y[n] was estimated us- ing a modified Yule-Walker algorithm on length 4096 data frames with an overlap factor of 1/2. Table1 presents some typical results for the estimation of the speed v0 from 8 s samples of y(t). The best performance were obtained by using a set of weights f 1; 2g strongly in favor of the pole fit to the detriment of the power fit.... ..."

### Table 2. NP-hard problems

1998

"... In PAGE 3: ... Hence, only these two problems are proved to be ordinarily NP-hard. The other NP-hard problems in Table2 as well as the NP-hard J2jno wait; rj; pij = 1jCmax, which is equivalent to J2jno wait; pij = 1jLmax by symmetry, and J2jno wait; pij = 1j Tj are open for the ordinary or strong NP-hardness. The letter C in the machine environment eld denotes a cycle shop, a special case of a job shop, where all the jobs have the same route passing through the machines like in a ow shop but repetitions of machines in the route are allowed.... ..."

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### Table 1: Complexity status of some unrelated machine problems

2005

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### Table 2.1: Complexity status of some unrelated machine problems.

### Table 3: Monte Carlo means for rstab#28#29 routine

"... In PAGE 23: ...kewness = 0. This seems due to some problem in the actual implementation of the routine. We had to resort to approximating the true means via Monte Carlo simulations using very large sample sizes. Table3 presents the means whichwe obtained. When generating small samples for our #0Cnal simulation studies we subtracted the appropriate Monte Carlo means from the rstab#28#29 outputs.... ..."

### Table 1 Comparison of Direct Monte Carlo with Subset Simulation

"... In PAGE 17: ... The 2001 values of W (t) at each time instant tk represent the random variables in the problem which was solved using the Newmark scheme. Table1 summarizes the results obtained by averaging over 1000 independent runs, for = 2:0 and various levels b. Since in all simulation methods, the coe cient of variation decays as =pN with respect to the sample size N, we report herein only the values of the constant for the methods compared.... In PAGE 24: ... The following table (Table 2) contains convergence results obtained using Line Sampling for d = 2000 and various values of the parameter b. As in Table1 , the decay factor of the coe cient of variation is reported. 3.... ..."

### Table 4. Overcoming bias and Monte Carlo variation in conventional PEA( quot;)

1997

"... In PAGE 41: ...results are based on I = 50). These are reported in column 2 of Table4 (column 1 simply reproduces the results from Table 3 for convenience.) TO diagnose the reasons for the poor performance of conventional PEA for model (7), consider the results in Figure 4.... In PAGE 41: ... The poor performance of the PEA for financial rates of return reflects that it oversamples the high probability region of the capital stock. One way to see this is to examine the results for apos;Modified Conventional PEA apos; reported in columns 3 and 4 in Table4 . Those are based on a modified version of conventional PEA which samples relatively more heavily from the tails of [k, X].... In PAGE 42: ... The figures confirm that, by comparison with modified conventional PEA, conventional - 20 PEA emphasizes capital stocks that are relatively more concentrated in the interior of [b, k]. The results in columns 3 and 4 of Table4 are based on I = 50 repetitions of modified conventional PEA. Interestingly, the problems with st atistics associated with the rate of return on equity have been dramatically reduced.... In PAGE 43: ... To save space, we do not discuss these results and we instead focus on the analysis of model (7). The last two columns of Table4 report results using PEA collocation to approximate the function, e, for model (7). In these columns, we set N, M to 3 and 5, respectively.... In PAGE 43: ... When 6 = a the rule fails by only six, one-thousandths of a percent of current consumption. These are tiny numbers and yet the N = M = 3 rule does not produce acceptable accuracy (see Table4 .) To get the desired degree of accuracy, one has to go to N = M = 5.... In PAGE 47: ... Third, though it is not evident from Table 6, conventional PEA also fails to meet the accuracy test at least for model (7). Table4 shows that conventional PEA with N = 3, M = 10,000 and N = 5, M = 50,000 violates our accuracy criterion. In addition, in results not shown, we get a little closer to the accuracy target with N = 3, M = 50,000, but bias in the return on equity is still over 40 percent and the associated coefficient of variation is over 70 percent in this case.... In PAGE 47: ... In addition, in results not shown, we get a little closer to the accuracy target with N = 3, M = 50,000, but bias in the return on equity is still over 40 percent and the associated coefficient of variation is over 70 percent in this case.25 Although Table4 shows that modified conventional PEA improves on the accuracy of conventional PEA, when N = 5, M = 50,000 and N = 5, M = 10,000, it too fails to meet our accuracy criterion. 6.... ..."

### Table 1. 6-DOF Monte-Carlo variables.

1997

"... In PAGE 6: ...g., aerodynamics or winds), the uncertainty is es- timated using linear interpolation between the regions given in Table1 . Gaussian distributions are sampled for most parameters.... In PAGE 10: ...ion frequency is approximately 2.5 Hz. Monte-Carlo Simulation During ight of the Mars Microprobe space- craft, a combination of o -nominal e ects is likely to be encountered. Hence, it is impor- tant to statistically assess the e ect of combi- natorial variations in all of the EDI parame- ters listed in Table1 . To accomplish this, two- thousand o -nominal cases were randomly esti- mated and simulated in a Monte-Carlo fashion.... In PAGE 10: ... A 99.7% probability exists that each random pa- rameter will remain within the 3{ uncertainty bounds of Table1 . In addition to a detailed set of impact conditions, the total angle-of-attack was monitored at discrete points along the heat pulse.... ..."

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### Table 2. Monte Carlo Results

"... In PAGE 12: ... In case I, the nucleus can experience arbitrarily high electric elds, while in case II, the stronger elds do not contribute because they have smaller Boltzmann weights. Numerical results are shown in Table2 for di erent values, NMC, of Monte Carlo realizations of ion con gurations. The percent deviations shown are fractional di erences with respect to the mean eld theoretical result of 3.... In PAGE 14: ...alculations for the 7Be electron capture rate in the Sun (see, e.g., Iben, Kalata, amp; Schwartz 1967; Bahcall amp; Moeller 1969; Bahcall 1989). The results of numerical simulations (see Table2 ) show that the standard formula (Bahcall 1989) is accurate to better than 1% .We obtained similar results for R=R = 0:0, 0.... In PAGE 14: ... They conclude that Debye screening describes the electron capture rates to within 2% . Combining the results of Table2... ..."

### Table 1: Point estimates and variances for ordinary Monte Carlo (MC) and weighted Monte Carlo estimators using three objective functions for an Asian option with m =1,2,and4 controls.

2003

"... In PAGE 14: ... The same procedure can be used to compute confidence intervals. Results for m = 1, 2, and 4 controls are displayed in Table1 for the quadratic, log, and entropy objectives, along with results for ordinary (equally weighted) Monte Carlo (MC). The variances of the WMC estimators are indeed very close, in most cases for sample sizes as small... ..."

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