### Table 2: Differential Upper Bounds

2004

"... In PAGE 11: ... Therefore, the upper bound on a differential for 7 rounds is a1 a9 a8a7 a3 and for 8 rounds is a1 a9 a25a24a25 a26 when the first swap step starts at the first bit in the left half. Table2 summarizes the bounds. 5 Key Dependent Permutation We discuss the benefit of adding a key dependent mixing step after the initial whitening and prior to the final whitening when creating an elastic block cipher.... ..."

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### Table 4. Improvement in classification accuracy using majority voting ensembles. Optimal unweighted majority-voting ensemble classifiers were formed by selecting classifiers from all 8 classifiers for each feature set listed and the average classification accuracy for 10-fold cross-validation was calculated. A paired-t test was performed for each ensemble classifier against the previous neural network classifier for each feature subset (SLF15 and SLF16 were compared against the previous classifier for SLF8 and SLF13, respectively). Each ensemble classifier was also compared against the optimal classifier for each feature set listed in Table 2 (SLF15 and SLF16 were compared with the individual optimal classifiers for SLF8 and SLF13, respectively).

"... In PAGE 10: ... Therefore, we constructed an unweighted majority-voting ensemble of all possible combinations of the 8 classifiers for each feature set. Table4 shows the optimal majority-voting classifiers found for each feature set. The accuracies on both SLF8 and SLF13 feature sets were improved by 1% by combining three classifiers for each: exponential-rbf-kernel SVM, AdaBoost, and Bagging for SLF8; rbf-kernel SVM, AdaBoost, and Mixtures-of-Experts for SLF13.... In PAGE 12: ...11 SVM, exponential-rbf-kernel SVM, polynomial-kernel SVM, and AdaBoost for SLF16, and rbf-kernel SVM, exponential-rbf-kernel SVM, and polynomial-kernel SVM for SLF15 ( Table4 ). We achieved a 92.... In PAGE 12: ... The benefits of including the new texture features can be represented by a 2% improvement on classifying 2D protein fluorescence microscope images both with and without DNA features. Table4 also showed that the accuracy upper bounds for SLF16 and SLF15 are higher than those of SLF13 and SLF8 feature sets respectively. To gain insight into the basis for the improvement, we compared the distributions in the two feature spaces of those images that were misclassified by the neural network classifier using SLF13 but were correctly classified by the ensemble classifier using SLF16.... In PAGE 13: ... Furthermore, the relatively independent errors (Table 3) among the classifiers of a majority-voting ensemble contribute to a more robust prediction. For instance, linear-kernel SVM, one of the five classifiers in the best performing ensemble classifier of SLF16 ( Table4 ), predicted the image of the transferrin receptor pattern in Figure 6 as tubulin, while all other classifiers in the ensemble made the accurate prediction. This error would not be avoided if the linear-kernel SVM was selected as the only classifier.... In PAGE 14: ... Firstly, different image set sizes were tested for the six feature sets. Figure 8A shows the average performance of the majority-voting classifier for each feature set ( Table4 ) over 1000 random trials of image sets drawn from each class in the test set. The dominant predicted class in an image set was taken as the output, while random choice was made if several classes tied.... ..."

### Table 2: Evaluation of an Upper Bound of 1094591

1994

"... In PAGE 4: ...nly 282 can abort 1224591, i.e. 904591 61 1022103. Table2 presents the value of the left and right sides of (1) by incrementing 109 from one by one. From this table, we can see that (1) is first met when 109 61 2.... ..."

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### Table 7. Impact of components of Balance heuristic in slowdown for nontrivial superblocks.

1999

"... In PAGE 11: ... Impact of components of Balance heuristic in slowdown for nontrivial superblocks. Lastly, in Table7 we investigate which components contribute most to the Balance heuristic. Entries (1) and (2) refer to the previously investigated Help and Balance heu- ristics, respectively.... In PAGE 11: ... Another variable is whether the updating of the bound information is done once per cycle or once per scheduled operation. By comparing the two rows of Table7 it can be seen that updating the bound information once per scheduled opera- tion has the largest effect on performance. This allows the... In PAGE 12: ... The third factor is that HlpDelay alone is only beneficial with the bounds, and in fact is best with both bounds and branch tradeoffs. Table7 also indicates that if the cost of computing the Pairwise bounds needed by the Tradeoff component is too large, the heuristic with Help and Bounds performs nearly as well as the full Balance heuristic. 7 Conclusion The first contribution of this paper is a set of tighter lower bounds on the execution times of superblocks that specifically accounts for the dependence and resource con- flicts between branch pairs and triples.... ..."

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### Table 7. Impact of components of Balance heuristic in slowdown for nontrivial superblocks.

1999

"... In PAGE 11: ... Impact of components of Balance heuristic in slowdown for nontrivial superblocks. Lastly, in Table7 we investigate which components contribute most to the Balance heuristic. Entries (1) and (2) refer to the previously investigated Help and Balance heu- ristics, respectively.... In PAGE 11: ... Another variable is whether the updating of the bound information is done once per cycle or once per scheduled operation. By comparing the two rows of Table7 it can be seen that updating the bound information once per scheduled opera- tion has the largest effect on performance. This allows the... In PAGE 12: ... The third factor is that HlpDelay alone is only beneficial with the bounds, and in fact is best with both bounds and branch tradeoffs. Table7 also indicates that if the cost of computing the Pairwise bounds needed by the Tradeoff component is too large, the heuristic with Help and Bounds performs nearly as well as the full Balance heuristic. 7 Conclusion The first contribution of this paper is a set of tighter lower bounds on the execution times of superblocks that specifically accounts for the dependence and resource con- flicts between branch pairs and triples.... ..."

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### Table 2: Comparison of the Upper Bounds on the Competitiveness

"... In PAGE 4: ... Table 1 summarizes the algorithms discussed above and compares the commonalities and differences of their basic aspects (c is the target competitiveness). Table2 presents the comparison of the results of the algorithms. Table 1: Comparison of the Algorithms Ba rta l Choose the shortest machine from the shorter machines or the shortest machine form the taller machines Keep the height of the machine assigned the new job less than c times the average height of the shorter machines before assigning the job Shorter machines consist of the first 44.... ..."

### Table 4. Average percentage of nontrivial superblocks op- timally scheduled.

1999

"... In PAGE 11: ... Average percentage of nontrivial superblocks op- timally scheduled. Table4 shows the percentage of optimally scheduled nontrivial superblocks. This data suggests that we can re- duce compilation time by first comparing the result of DHASY to a lower bound, and then only using a more ex- pensive heuristic when DHASY is not known to be optimal.... ..."

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### Table 4. Average percentage of nontrivial superblocks op- timally scheduled.

1999

"... In PAGE 11: ... Average percentage of nontrivial superblocks op- timally scheduled. Table4 shows the percentage of optimally scheduled nontrivial superblocks. This data suggests that we can re- duce compilation time by first comparing the result of DHASY to a lower bound, and then only using a more ex- pensive heuristic when DHASY is not known to be optimal.... ..."

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### Table 2. The upper bounds obtained from the upper bound heuristics introduced in Section 3.2

2006

"... In PAGE 18: ...Emgad Bachoore and Hans L. Bodlaender In Table2 , we show the results of implementing the upper bound heuristics, introduced in Section 3.2 on the same set of graphs.... In PAGE 18: ...ection 3.2 on the same set of graphs. We notice clearly from the results in these tables the following: First, the upper bounds of 5 instances, obtained from these heuristics, equal the exact weighted treewidths of these instances, where the best lower bounds of all these five instances equal their best upper bounds. Second, the upper bounds obtained from the three versions of WMFEO are better than or equal to those obtained from MMNWF as well as from MF W for all instances of Table2 . Third, the upper bounds of two instances, namely, Oesoca+ and Oow-solo, obtained from WMFEO, version 1 and 3 are better than the upper bounds obtained from all other upper bound heuristics for the same graphs.... In PAGE 18: ... Fourth, the upper bound of only one graph, namely, Oow-trad, obtained from Ratio1 is better than that obtained from all other upper bound heuristics for the same graph. Five, the upper bound obtained from Ratio2 heuristic are the worst amongst all other upper bound heuristic, for all graphs of Table2 . The running time of implementing the upper bound heuristics on this set of graphs are given in Table 3.... ..."

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