### Table 1 Properties and separation capabilities of several non-linearities

"... In PAGE 7: ... For example, in [2] the xed sigmoid pj(y(j)) quot;ds(y(j))/dy(j), s(r) quot;1/(1#e~r) is used, which corresponds to a posit- ive kurtosis 1.2 as shown in the second column of Table1 . It is reported in [2] that Eq.... In PAGE 7: ...hat it fails at sub-Gaussian sources (e.g., uniform density or gamma density). Stating another example, when we use the xed nonlinearity as shown in the rst column of Table1 with a positive standardized kurtosis 1.2216, the experiment in [5] has shown that Eq.... In PAGE 7: ...3) When the pre xed pj(y(j)) is sub-Gaussian, i.e., if its kurtosis is negative, Eq. (4) works for sources of sub-Gaussian, but fails for sources of super-Gaussian. When we use the xed nonlinearity as shown in the third column of Table1 with its kurtosis !0.8118, experiments have shown that Eq.... ..."

### Table 1. Evidence of non-linear relationships in length-affinity data for several MHC class II alleles

"... In PAGE 3: ... Parametric fits were then made based on polynomials with one, two, or three fitted parame- ters (linear, quadratic, and cubic, respectively). Analysis of vari- ance from these fits showed that for these MHC class II alleles the nature of the relationship was most likely nonlinear ( Table1 ). A quadratic or cubic fit resulted in a significant reduction in sum of squares in all three cases at the 0.... ..."

### Table 1: Nonlinear PBE methods.

1995

"... In PAGE 19: ... In addition, experiments indicate that the inexact Newton-multilevel approach is the most e cient and robust method for the test prob- lems, and in particular is both more e cient and more robust than the nonlinear multigrid method. Table1 provides a key to the plots and tables to follow. For reference, at times we also will refer to the linear methods in Table 2.... In PAGE 20: ... A more detailed performance analysis on several more sequential as well as some parallel machines can be found in references [5, 6]. Results for acetamide Figure 6 compares the methods in Table1 for the ac- etamide problem. For this problem, all of the methods converge, and the two multilevel-based algorithms are superior.... In PAGE 20: ... The method DINMH is extremely e cient, representing an improvement of more than a factor of fty over the non- linear SOR and nonlinear conjugate gradient methods, and a factor of ten over the nonlinear multigrid method NMH. Results for crambin Figure 5 compares the methods in Table1 for the cram- bin problem. Again, all of the methods converge, and the two multilevel-based algorithms are superior.... ..."

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### Table 1: Examples of data nonlinearities. Algorithm H(ui)

"... In PAGE 1: ... Usually, H(ui) is a multiple of the identity, say H(ui) = 1 g(ui)I for some function g( ). Table1 lists some common examples of data nonlinearities. There are several reasons for incorporating leakage into an adaptive lter update and special cases of (1){(2) have been studied before in the literature (see, e.... ..."

### Table 1: Results for nonlinear complementarity problems

"... In PAGE 12: ... If in the rst iteration the stepsize of one is accepted we use the nomonotone strategy of Algorithm B, otherwise we use algorithm A for the rst ve iterations and then switch to Algorithm B. In all the algorithms the following constants were used: quot; = 1; = 10?4; = 10?8; p = 2:1; = 0:9: We tried the algorithm on several test problems taken from the literature, we considered nonlinear ( Table1 ) but also linear problems (Table 2); the test set includes problems that are not P0 and problems that are not R-regular or b-regular at the solution. Some details on these problems, the starting points, and adequate references are reported in the appendix.... In PAGE 15: ... This problem has two solutions: x1 = (0:5p6; 0; 0; 0:5) and x2 = (1; 0; 3; 0); x1 fails to be R-regular and is degenerate. In the results of Table1 convergence always occurred to x1 except in the case indicated by an asterisk. The linearized complementarity problem at 0 has no solution.... ..."

### Table 4: Computation times for nonlinear cloth simulation

"... In PAGE 20: ... 7 Results and Applications We have performed several cloth simulations using the parameters computed from the KES curves of section 6. Table4 summarizes the performance of our algorithm on an Intel Pentium 4-2Ghz.... ..."

### Table 1. Impulsive noise models; envelope PDFs and LO nonlinear filters.

2002

"... In PAGE 13: ...onparametric filters. These require no explicit knowledge of the noise PDF. An example is the hardlimiter narrowband correlator (HNC) filter ([8, 10]) which is widely used in impulsive environments; y y g 1 ) ( = (4) The parametric version of the processor requires a choice of noise model, and estimation of the model parameters from the received data. The LO filters for several impulsive noise models are given in Table1 . To apply the processor, we read-in a segment of time-series data, estimate the model parameters from that segment of data,9 and then input these parameter estimates into the nonlinear filter to tune the processor.... ..."

### Table 6. Example Scoring Technique for Different Severity Levels

"... In PAGE 14: ... A single level 5 severity failure may be more important than a test case that produces multiple failures of lower severity. To handle this situation, a non-linear scoring method such as that shown in Table6 is recommended. Table 6.... In PAGE 18: ... The scoring system used is shown in Table 8. This is the same scoring technique proposed in Table6 . Multiple failures per test case were also simulated.... ..."

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### Table 10: Results for nonlinear wave equation (4.7) under (4.8)

2007

"... In PAGE 18: ...7) with additional condition (4.8) and objective function F1, another solution of the PDE problem is obtained, which is documented in Table10 and pictured in Figure 12. Thus several solutions of problem (4.... ..."

### Table 10: Results for nonlinear wave equation (4.7) under (4.8)

2007

"... In PAGE 18: ...7) with additional condition (4.8) and objective function F1, another solution of the PDE problem is obtained, which is documented in Table10 and pictured in Figure 12. Thus several solutions of problem (4.... ..."