### Table 1. pMSE and Bias of Power Estimates for Two-sample t-Statistic with Parametric Bootstrap Critical Values O = 1000, I = 59

2000

"... In PAGE 12: ... We look at two (O; I) combinations, (O = 1000; I = 59) and (O = 596; I = 99), that have about 59000 computations each. Table1 reports estimates of the root mean squared error (pMSE) and bias 1000 of the various power estimates. The standard errors of the estimates are in the range .... In PAGE 12: ...002 for pMSE and around 2 for the bias 1000. The rst and seventh rows (p1) of Table1 give results for power estimates based on the true known t percentiles appropriate for normal data. They are labeled p1 to re ect the fact that resampling with I approaching 1 would give this result.... In PAGE 12: ... They are labeled p1 to re ect the fact that resampling with I approaching 1 would give this result. These of course are unbiased (the nonzero bias results in Table1 just re ect Monte Carlo variation), and here pMSE could have been calculated simply by ppower(1-power)=O. For a given O, p1 represents the best power estimates possible.... In PAGE 12: ... For these raw estimates the (O = 596; I = 99) situation is more e cient in terms of pMSE than (O = 1000; I = 59) for all but = 0:5 because the bias is a large factor except at = 0:5. The other estimators in Table1 are 1. b plin: the simple linear extrapolation method using (5) for the (O = 1000; I = 59) case and (6) for the (O = 596; I = 99) case.... In PAGE 13: ...a;bb) distribution. From Table1 we see that the the linear extrapolation estimators, b plin and b pgls, perform the best and very similarly. Their similarity is likely due to the fact (not displayed) that the estimated covariance matrix of the b pI used as dependent variables in the regressions has nearly equal diagonal elements and nearly equal o -diagonal elements.... ..."

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### Table 1. Differences in performance from pretest to posttest

2003

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### Table 6: Lagrangean algorithm and CPLEX results - Instance set III

"... In PAGE 17: ... Actually, the largest instances of this set overestimate the size of real cellular networks. Table6 reports the results of the Lagrangean algorithm and CPLEX. The meaning of each column is the same previously defined for table 2.... ..."

### TABLE V: COMPARISON TO NUSMV BOUNDED MODEL CHECKING Seq-SAT NuSMV

### Tables I and III compare the execution time of the algorithm on the

1991

### Table 1: Node counts and time for instances of multi-commodity network ow problems CPLEX CPLEX + CUTS

2007

"... In PAGE 126: ... CPLEX branch-and-bound was used to solve the two mixed integer programming formulations. Table1 1: Comparison of two formulations: lower and upper bounds were returned at the end of 300s of computation time (P1) (P2) Prob LB UB LB UB E10 10 0.00 0.... In PAGE 127: ... This shows that as an integer programming formulation, with no additional cuts or heuristics added, formulation (P 2) performs better than formulation (P 1). Table1 2: Comparison of two formulations: Node counts and solve times (P1) (P2) Prob Node Count Time Node Count Time E10 10 240 1.5 56 0.... In PAGE 128: ... The time limit was 300s, so if optimal solution is not found in the allotted time for a problem the corresponding entry for solve time is 300s and node count entry is the number of nodes explored in 300s. Table1 3: Comparison of two formulations with cutting planes and heuristics: lower and upper Bounds after 300s of computation time (P1) (P2) Prob LB UB LB UB E10 10 0.00 0.... In PAGE 128: ...00 0.00 Entries in bold represent that optimal solution was found in 300 second Looking at the results from Table1 3, we can see that, with the help of cuts and heuristics, formulation (P 1) was able to provide better results than (P 2). More problems were solved to optimality and for except one, the bounds provided for the problems not solved to optimality in allotted time by formulation (P 1) were stronger than formulation (P 2).... In PAGE 129: ...Table1 4: Comparison of two formulations with cutting Planes and heuristics: node counts and computation times (P1) (P2) Prob Node Count Time Node Count Time E10 10 0 4.01 0 0.... ..."

### TABLE 4 MEANS OF PROBLEMS IN RESEARCH BY SECTOR d

2005

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### Table 4: Selected MINLP problems from [8]

2004

"... In PAGE 31: ...Table4 where, for each problem, we report the globally optimal objective function value, the number of problem constraints (m), the total number of problem variables (n), and the number of discrete variables (nd), in addition to CPU and node information. Problems nvs01 through nvs24 originate from [16] who used local solutions to noncon- vex nonlinear programs at each node and conducted branch-and-bound on the integer variables.... ..."

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### Table 29: Perceptions of the Youth Gang Problem in 1997, by Area Type*

"... In PAGE 50: ... Table29 illustrates the perceptions of the youth gang problem in 1997, by area type. The percentage of respondents who felt the youth gang problem was getting worse was highest in suburban and rural counties (43 percent) and lowest in small cities (25 percent).... ..."

### Table I. Pruning domains in a trivial problem.

2002

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