### Table 2 compares the lowest-order case (p = 0) with the hp-FEM on the relative error level of approx. 0.15 %. One can see that the hp-FEM performed approx. 1 200 times faster compared to the lowest-order method. The memory requirements of the hp-FEM were about 1 000 times less. DOFs CPU time rel. error

### 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.... ..."

Cited by 4

### Table 2: Multi-level density analysis on results from existing fixed-dissection filling methods. Notation: T/W/r: Layout / window size / r-dissection; LP: linear programming method; Greedy: Greedy method; MC: Monte-Carlo method; IGreedy: iterated Greedy method; IMC: iterated Monte-Carlo method; OrgDen: density of original layout; FD: fixed-dissection density analysis; Multi-Level: multi-level density analysis; MaxD: maximum window density; MinD: minimum window density; DenV: density

in ABSTRACT

"... In PAGE 3: ...rom an industry standard-cell layout4 (Table 2.3). Benchmark L1 is the M2 layer from an 8,131-cell design and benchmark L2 is the M3 layer from a 20,577-cell layout. Table2 shows that underestimation of the window density varia- tion as well as violation of the maximum window density in fixed- 3 For the test cases used in this paper, the runtimes of the multi- level analysis with accuracy =1:5#25 appear reasonable. Our (un- optimized) implementation has the following runtimes for Min-Var LP solutions and the spatial density model: L1/32 (45 sec), L1/16 (183 sec), L2/28 (99 sec), L2/14 (390 sec), For the effective density model, the runtimes are: L1/32 (49 sec), L1/16 (194 sec), L2/28 (109 sec), L2/14 (416 sec).... ..."

### Table 2: Multi-level density analysis on results from existing fixed-dissection filling methods. Notation: T/W/r: Layout / window size / r-dissection; LP: linear programming method; Greedy: Greedy method; MC: Monte-Carlo method; IGreedy: iterated Greedy method; IMC: iterated Monte-Carlo method; OrgDen: density of original layout; FD: fixed-dissection density analysis; Multi-Level: multi-level density analysis; MaxD: maximum window density; MinD: minimum window density; DenV: density

in ABSTRACT

"... In PAGE 3: ...rom an industry standard-cell layout4 (Table 2.3). Benchmark L1 is the M2 layer from an 8,131-cell design and benchmark L2 is the M3 layer from a 20,577-cell layout. Table2 shows that underestimation of the window density varia- tion as well as violation of the maximum window density in fixed- 3 For the test cases used in this paper, the runtimes of the multi- level analysis with accuracy =1:5#25 appear reasonable. Our (un- optimized) implementation has the following runtimes for Min-Var LP solutions and the spatial density model: L1/32 (45 sec), L1/16 (183 sec), L2/28 (99 sec), L2/14 (390 sec), For the effective density model, the runtimes are: L1/32 (49 sec), L1/16 (194 sec), L2/28 (109 sec), L2/14 (416 sec).... ..."

### Table 4 Effect of nurse background on proportion of calls sent to self care (211 nurses taking 231,112 calls)

2007

"... In PAGE 12: ... The proportion of callssent to self care was16% overall, but varied three fold between the bottom and top decilesof nurse. Variability waspartly explained by the main type of experience of nurses ( Table4 ). Nurses with a background mainly in the community, for example aspractice nurses, district nurses or health visitors, were lesslikely to send patientsto self care than nursesmainly with acute hospital experience.... ..."

### Table 2 shows the performance improvement of the multi-level optimization over the usual optimization method.

"... In PAGE 10: ...5 W 0 0 100 200 300 400 CPU Time (msec) Figure 8: Convergence Curve for Bending Cow. Table2 : Performance Improvement by Multi-Level Optimization. 7, and lt; are the total CPU time (msec) without and with Multi Level Optimization respectively.... ..."

### Table 3: Preconditioned convergence factors for the multi-level method (accelerated by CGS) applied to the `staircase apos; problem.

1997

"... In PAGE 20: ...and, as discussed in [27], re ects the error better than that of the residual itself since the preconditioned system is better-conditioned than the original one.) The results in Table3 are as expected from Theorem 1 in the sense that the preconditioned convergence factor increases slowly with L so long as L 3. The deterioration of the convergence rate when L = 4 is used is due to the large p3 obtained in this case, which implies a large upper bound in (18).... ..."

Cited by 2

### Table I Total execution time and accuracy for LDM and Multi-level method on Calcium molecule and BPTI molecule

### Table 3: Preconditioned convergence factors for the multi-level method (accelerated by CGS) applied to the `staircase apos; problem.

"... In PAGE 27: ... This is an advantage of left preconditioning over right and symmetric ones. The results in Table3 are as expected from Theorem 1 in the sense that the preconditioned convergence factor increases slowly with L so long as L 3. The deterioration of the convergence rate when L = 4 is used is due to the large p3 obtained in this case, which implies a large upper bound in (21).... ..."

### Table 3. Multi-Level Models Including and Excluding the Main Effect Parameters

"... In PAGE 4: ... Data on job level were obtained from company administrative data. Table3 shows the multilevel model results including the regression coefficients, betas (H9252), and their standard errors. Model 2 shows the chair-with-training group ex- perienced a statistically significant reduction in symp- toms postintervention compared with the control group (H9252chair*intervention* time of day H11005 0.... In PAGE 4: ...f models 1 and 2 (13.46; P H11005 0.001) indicate the hy- pothesized intervention effects significantly improve model fit. The predicted intervention results based on estimates in Table3 are depicted in Figure 2. The chair- with-training group experiences a reduction in growth of symptoms over the day compared with either the control or the training only groups.... ..."