### Table 2 Refinement statistics.

"... In PAGE 4: ... In addition, nine side chains were modelled with two alternate conformations (Table 4). The final model has good stereochemistry ( Table2 ). The Ramachandran plot (Ramak- rishnan amp; Ramachandran, 1965) calculated by the program PROCHECK (Morris et al.... ..."

### TABLE 2 Refinement statistics

2007

### Table 1. Test-analysis correlation of the LANL 8-DOF testbed for nonlinear vibrations. (The table shows the correlation between the nominal, undamaged system without impact between the masses and the corresponding linear model.) Mode

2001

"... In PAGE 7: ... Time-domain acceleration data are measured at each one of the eight masses and modal parameters are identified using a classical frequency-domain curve fitting algorithm. Table1 shows that the original, linear and undamped model is in good agreement with the identified modal parameters prior to any parametric adjustment. Nevertheless, an optimization is performed to resolve the more-or-less uniform shift in frequency seen in Table 1 for the first three modes.... In PAGE 7: ... Table 1 shows that the original, linear and undamped model is in good agreement with the identified modal parameters prior to any parametric adjustment. Nevertheless, an optimization is performed to resolve the more-or-less uniform shift in frequency seen in Table1 for the first three modes. The test discussed in this publication consists of identifying the damaged spring using a linear model that does not account for the friction nor the source of contact/impact.... In PAGE 14: ....3. VALIDATION OF MODAL-BASED METRICS To illustrate that modal parameters are unable to characterize nonlinear dynamics properly, the numerical model associated with the LANL 8-DOF system is refined using three different cost functions based on metrics (4-6). The objective of this test is to make the updated, linear model match the identified mode shapes and frequencies with a better degree of confidence than the one illustrated in Table1 . In doing so, the main modeling error (a 14% stiffness reduction located at the fifth spring) should be identified.... ..."

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### 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.... ..."

Cited by 8

### Table 1: Nonlinear materials

2000

"... In PAGE 12: ... The soft material is a large deformation (Neo-Hookean) hyperelastic material with a mixed formulation [26]. Table1 shows a summary of the constitution of our two material types.... ..."

Cited by 3

### Table 4: Nonlinear Adjustment

2000

Cited by 2

### Table 5. Nonlinear programming

### Table 2. ProB refinement checking and size of refinement relation

2005

"... In PAGE 9: ...ref is a refinement thereof. Refinement checking Table2 are the results of performing various refinement checks on these machines. Entries marked with an asterisk mean that no pre- vious consistency checking was performed, i.... ..."

Cited by 8

### Table 2. ProB refinement checking and size of refinement relation

2007

"... In PAGE 13: ...erver example, while ServerR.ref is a refinement thereof. 7.2 Refinement checking Table2 are the results of performing various refinement checks on these machines. Entries marked with an as- terisk mean that no previous consistency checking was performed, i.... ..."