### Table 6. Three-dimensional compressible derivatives

1997

"... In PAGE 5: ... In this test, the cost function is a combination of the lift and drag coefficients so that only one adjoint solution is required. The derivatives of the cost with respect to the angle of attack and the Mach number as well as the derivatives with respect to four of the shape parameterization variables are shown in Table6 . As can be seen, the consistency between the derivatives obtained with the ad- joint formulation and finite differences is excellent.... ..."

Cited by 68

### Table 6. Three-dimensional compressible derivatives

1997

"... In PAGE 5: ... In this test, the cost function is a combination of the lift and drag coefficients so that only one adjoint solution is required. The derivatives of the cost with respect to the angle of attack and the Mach number as well as the derivatives with respect to four of the shape parameterization variables are shown in Table6 . As can be seen, the consistency between the derivatives obtained with the ad- joint formulation and finite differences is excellent.... ..."

Cited by 68

### Table 2. Two and Three Dimensional Results

in SUMMARY

"... In PAGE 8: ... Under these conditions the difference in the effectiveness of the learning algorithm with targetsfandf can be attributed directly to the additional input dimension. Table2 provides the results of approximatingAx,y) = (x+y)/2 and f(xy,z) = (x*)/2. For the 5/25 system cotiguration, the three-dimensional system generated with 50,000 training examples was less accurate than the two- dimensional approximation produced with 5000 examples.... In PAGE 9: ... As in the case of the propagation model, the localized FAMs may not require all of the dimensions of the input space to produce an appropriate response. In fact, the target function and experimental data shown in Table2 is an example of this type of behavior. The test for the contribution of the ith input dimension begins by constructing the n-dimensional FAM for the region.... ..."

### Table 1: Categorization of feature selection algorithms in a three-dimensional framework

2005

"... In PAGE 9: ...There exists a vast body of available feature selection algorithms. In order to better understand the inner instrument of each algorithm and the commonalities and differences among them, we develop a three-dimensional categorizing framework (shown in Table1 ) based on the previous dis- cussions. We understand that search strategies and evaluation criteria are two dominating factors in designing a feature selection algorithm, so they are chosen as two dimensions in the framework.... In PAGE 9: ... We understand that search strategies and evaluation criteria are two dominating factors in designing a feature selection algorithm, so they are chosen as two dimensions in the framework. In Table1 , under Search Strategies, algorithms are categorized into Complete, Sequential,andRan- dom. Under Evaluation Criteria, algorithms are categorized into Filter, Wrapper,andHybrid.... In PAGE 10: ... Within the Wrapper category, Predictive Accuracy is used for Classification,andCluster Goodness for Clustering. Many feature selection algorithms collected in Table1 can be grouped into distinct categories according to these characteristics. The categorizing framework serves three roles.... In PAGE 10: ...nd Random. Both groups have more than one algorithm available 1. Third, the framework also reveals what are missing in the current collection of feature selection algorithms. As we can see, there are many empty blocks in Table1 , indicating that no feature selection algorithm exists for these combinations which might be suitable for potential future work. In particular, for example, current feature selection algorithms for clustering are only limited to sequential search.... ..."

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### Table 6: Head-Driven Three-Dimensional Extensions: Ac- curacy results for parsing the devest (section 0)

"... In PAGE 9: ... We set our baseline at the (0, 0, 0) coordi- nate and evaluate models that combine one, two and three dimensions of parametrization. Table6 shows the accuracy results for parsing section 0 using the resulting models. The first outcome of these experiments is that our new baseline improves on the accuracy results of a simple treebank PCFG.... ..."

### Table 2: Results for two- and three-dimensional Rayleigh-Taylor simulation data sets Max. Max. Avg. Avg.

1999

"... In PAGE 7: ... To test the interactive performance of this system, we change the global insertion criterion and/or also specify a region of interest to be displayed at a higher resolution for each data set. The performance results for these experiments are given in Table2 . For each level of detail, we give the insertion criterion, a24a31a25a33a27a30a29a71a70a64a38a72a24a31a25a33a32a34a21a18a73 , the number of resulting leaf octants, a24 , and the percentage of the full data set to which a24 corresponds, a74 .... In PAGE 9: ...12 0.14 1000 10000 100000 1e+06 Normalized Error a92 N sigma max error Figure 4: The relationship between a24 and the error measures average a19a79a21 (sigma) and average a20a23a21 (max error) for the Rayleigh-Taylor data sets in both two and three dimensions In Figures 5 and 6, we show the reduced R-T data sets corresponding the cases discussed in Table2 . In each case we show the reduced data set image, the error plots associated with that level of detail, and the associated leaf octants.... ..."

Cited by 23

### Table 4 The 45 combinations of base pairing patterns found in the set of loop 785-797 three-dimensional structures gen- erated by the MC-SYM program.

"... In PAGE 7: ... The conformational search space size of the selected spanning tree is 1023 corresponding to 3375 different combinations of base pairing patterns. MC-SYM generated 33998 consistent three- dimensional structures, composed of 45 different combinations of base pairing patterns (see Table4 ). The RMS deviation among the 45 classes vary from 2.... ..."

### Table 7. Parameters used in implicit MOC3D simulation of transport from a continuous point source in a three-dimensional, uniform, steady- state flow system

### Table 1. Three-dimensional abscissa counts

"... In PAGE 10: ... The fth abscissa count Nprev is readily gleaned from the cited literature. The three-dimensional abscissa counts listed in Table1 are all precisely as de ned above. The four-dimensional abscissa counts listed in Table 2 are also precisely as de ned above for 13.... ..."

Cited by 2

### Table 1: The models in all the possible ways. Intuitively, the situation can be graphically repre- sented, as in the picture below, by a three-dimensional frame of reference whose coordinate axes represent the three parameters.

"... In PAGE 3: ...Our choices of models are summarized in Table1 . It is worth noticing that, with the exception of the new model of transition systems with independence, each model is well-known.... ..."