### Table 1: Incremental vs. Optimal Retiming.

in Theory

"... In PAGE 5: ... 4. RESULTS The rst question that needs to be answered is: How does the incremental algorithm compare to the optimal retiming algorithm? Table1 presents the relevant results. We applied optimal retiming and incremental retiming to a number of MCNC circuits and various free-IP cores that have been synthesized into netlists of 4-LUTs.... In PAGE 5: ... In this experiment a constant delay is assumed for every logic element and a sep- arate constant is used for each wire in the circuit. The 3rd, 4th and 5th columns of Table1 show the critical path de- lays for the incrementally retimined circuit, the optimally retimed circuit and the unretimed circuit, respectively. In each case, the incremental retiming algorihtm matches the performance of the optimal retiming algorithm or is very close.... In PAGE 6: ... These results show that the behavior of the retiming algorithm changes in the presence of user assigned constraints and that the behavior is to try to improve the part of the circuit with the tightest constraint. In Table1 (b), we show that circuit c2 achieves a 178% TMAX improvement, but with a 75% TSU degradation. This represents the realistic situation in which the required TSU = EASY can still be met, even when increased by a large amount.... ..."

### TABLE I OUTLINE FOR INCREMENTAL OPTIMIZATION TRANSFER ALGORITHMS.

2004

Cited by 8

### TABLE I OUTLINE FOR INCREMENTAL OPTIMIZATION TRANSFER ALGORITHMS.

2004

Cited by 8

### Table 2 Nonlinear models.

1998

"... In PAGE 16: ... Much of the emphasis will be on the choice of bandwidth and the new aspects brought in by using local polynomial approximation. A power experiment on a wide class of nonlinear models listed in Table2 has been conducted in Section 6.3.... In PAGE 18: ...Table2 , however, where M1(x) is approximately quadratic (see Figure 1), as can be expected the best result is achieved with T = 2 and h = 1. For the ^ L(V1)-tests the size tends to be too low.... In PAGE 18: ... If no corrections are made for this e ect, it will lead to conservative tests. Figure 5 shows the power of the ^ L(V )-tests for model la) of Table2 , and we see the same general trend as for the ^ L(M)-tests; the optimal h increases with T and the derivative. Here ^ L1(V1) also has some power for h = 1 because the variance is constant, not only linear, under the null hypothesis.... In PAGE 18: ... Here ^ L1(V1) also has some power for h = 1 because the variance is constant, not only linear, under the null hypothesis. ^ L0(V1) is much more robust than ^ L0(M1), and this is the case for the other models listed in Table2 as well. 6.... In PAGE 18: ... In particular when we have a nonlinear model, we do of course not want h = 1 to be chosen when T = 0 or T = 1, but with a small autocorrelation, this may well happen for T = 0. In fact h = 1 was chosen in 136 of 500 realizations of model lc) of Table2 which is clearly nonlinear (cf. Figure 1).... In PAGE 19: ... 6.3 A power experiment for a wide set of models We have performed a power experiment for the models listed in Table2 , where t N(0; 0:62) in model ld) - lf), t N(0; 0:72) in lg) - lj) and t N(0; 1) in the other models. Models la) - lj), aa) - ag) and Aa) - Ag) are discussed in Luukkonen et al.... In PAGE 36: ...Figure 1-2: Plots of ^ M1(x) (Figure 1) and ^ V1(e) (Figure 2) for the models listed in Table2 with n = 100 000. The kernel estimator with bandwidth h = 0:2 is used and each plot consists of two realizations.... In PAGE 36: ... The possible values for h is given at the vertical axes. Figure 7: The gure is based on 500 realizations of the models in Table2 . It shows the power of ^ LT (M1) with h cross-validated and n = 100, 250 and 204 for models la) - li), aa) - ag) and Aa) - Ag), respectively.... In PAGE 36: ...ower achieved in Hjellvik and Tj stheim (1995). The nominal size is 0.05. Figure 8: The gure is based on 500 realizations of the models in Table2 and shows the power of ^ LT (V1) with h cross-validated and n = 100, 250 and 204 for models la), aa) - ag) and Aa) - Ag), respectively.... In PAGE 37: ....05 for the standard normal distribution has been used. The model is Xt = t, the bandwidth is h = n?1=9 and the number of realizations are 500. Table2 : Various nonlinear models. Models la) - lj), aa) - ag) and Aa) - Ag) are discussed in Luukkonen et al.... ..."

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### Table 7: Average Ratios of Tensor Method versus Gauss-Newton Method on All Sparse Nonlinear Least Squares

### Table 3 Solutions for the nonlinear formulation

2003

"... In PAGE 9: ... This is an example of the kind of information that a meta-model might store and use for model selection and system induced decision guidance. Table3 summarizes the results from applying a simple GA to the nonlinear formulation of the PMP. Fig.... In PAGE 9: ... Given that GA is a heuristic search and may not result in the optimal solution and that each run may be subject to randomness, we report the average solution and CPU time for the 10 problem instances. Table3 presents the best (column 3) and average (column 4) solutions as well as the average solution time (column 7) to find the best solution for each problem instance. The number of facilities and known optimal solutions are reported in columns 1 and 2, respectively, and standard deviations for the CPU times are reported in column 8.... In PAGE 9: ... The GA started with a random feasible initial solution. Table3 illustrates that the GA searching the solution nonlinear problems. space of the nonlinear formulation of the problem always found the optimal solution at least once for each problem instance, resulting in an average opti- mality gap of 0% (Best Solution, column 3).... ..."

### Table 4. Comparison between increment and mortality groups Mortality group Increment

1990

"... In PAGE 8: ... Table 3. Mortality pattern and size at maturity Number of species classified by size at maturity (Stocker 1983) Mortality group Small ( lt;40 cm dbh) Intermediate (40-100 cm dbh) Large ( gt;100 cm dbh) Total number of species 1 5 24 4 33 5 19 15 0 34 10 2 8 7 17 Others 11 15 0 26 Total species 37 62 11 110* * based on specific name, not common name, for species classified by Stocker (Appendix) Table4 illustrates the correspondence between the increment groups (Vanclay 1991) and the mortality groups. The 100 species employed in the preceeding analysis belong to 41 different increment groups, and were grouped into ten mortality groups.... In PAGE 8: ... The 100 species employed in the preceeding analysis belong to 41 different increment groups, and were grouped into ten mortality groups. If increment group provided a perfect indication of mortality pattern, Table4 would have only 41 entries. Conversely, the worst case would exhibit 100 entries, and random allocation would result in 83 entries (Table 5).... In PAGE 8: ... In fact, it contains 84 entries which suggests that increment pattern provides no indication of the appropriate mortality group. The standard v2 test cannot be applied to sparse data such as Table4 , but a comparison of the the observed and expected frequency of numbers of species per cell indicates that the difference is not significant and that the diameter increment group provides no guide to the relevant mortality group ... In PAGE 10: ... So the possibility of some correspondence will be further investigated. The mortality group indicated by the diameter increment pattern is given in Table4 , and has been calculated as the mortality group most frequently represented within each increment group. Since all species from increment groups 1, 2, 18 and 32 were found to quot;belong quot; to mortality group 1, it is reasonable to argue that any other species in these increment groups may also be best assigned to mortality group 1.... ..."

### Table 1: Search direction in nonlinear optimization meth- ods.

"... In PAGE 5: ... In the gradient algorithm, minimization of a179 a56a83a168a120a67 is performed by iteration of the following formula, a168a174a243a66a253 a91 a54a254a168a71a243 a92a94a255 a242a196a243a248a61 a255 a54 a1a0a3a2a5a4 a149a151a150a111a152 a6 a179 a56a83a168a174a243 a92a94a255 a242a236a243a104a67 where, search direction a242 a243 is calculated using gradient vec- tor a244 a243 a128 a54 a8a7 a179 a56a12a168a174a243a8a67 when a168 is estimated as a168a26a243 . Major algo- rithm for nonlinear optimization is shown in Table1 where a251 a252 a243 denotes approximated Hessian matrix, a247a18a243 denotes Jaco- bian matrix and a245 a243a130a61 a249 a243 are parameters. In the LM method, Hessian matrix is approximated by a56a14a247a181a69 a243 a247 a243 a89a132a249 a243 a250a60a67 where Jacobian a247 is defined as follows.... ..."

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