### Table 5. Euclidean Distance in 7-Dimensional Principal Component Space for 19 Isospectral Graph Pairs isospectral pairs isospectral pairs Euclidean

"... In PAGE 4: ...16-20 used the Euclidean distance (ED) in the n-dimensional PC-space in characterizing structural similarity/dissimilarity of molecules. In Table5 we give the ED between 19 isospectral pairs of graphs. For all pairs of graphs considered in this paper, the value of ED was nonzero which shows the discriminating ability of the six-dimensional PC-space generated out of the calculated PCs.... ..."

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### Table 1: Parameters and base values used in the experiments for evaluating the precision of embedding.

2000

"... In PAGE 9: ...nterval [MinDistance..MaxDistance], keeping only those objects that satisfied the triangle inequality as in [20]. Table1 summarizes the parameters and base values used in the experiments. In generating protein distances, we selected a set of 230 kinase sequences obtained from the protein database in the Cold Spring Harbor Laboratory.... In PAGE 11: ... Figure 3 graphs Errr as a function of the dimensionality of the target space, k, for the synthetic Euclidean data. The parameters have the values shown in Table1 . We see that for all the mappers, Errr drops as k increases.... In PAGE 12: ...Table1 . The LowBound in Figure 6 is fixed at 1.... ..."

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### Table 1: Parameters and base values used in the experiments for evaluating the precision of embedding.

"... In PAGE 9: ...nterval [MinDistance..MaxDistance], keeping only those objects that satis ed the triangle inequality as in [20]. Table1 summarizes the parameters and base values used in the experiments. In generating protein distances, we selected a set of 230 kinase sequences obtained from the protein database in the Cold Spring Harbor Laboratory.... In PAGE 11: ...Figure 3 graphs Errr as a function of the dimensionality of the target space, k, for the synthetic Euclidean data. The parameters have the values shown in Table1 . We see that for all the mappers, Errr drops as k increases.... In PAGE 12: ...Table1 . The LowBound in Figure 6 is xed at 1.... ..."

### Table 3: Modulo graph embedding results for the dedicated register file CGRA.

2006

"... In PAGE 9: ... This shows that the modulo graph embedding scheduler is able to achieve quality solutions for significantly lower cost CGRAs. The modulo scheduler runtimes (last column of Table3 ) are rea- sonably fast, as all benchmarks are scheduled within 5 seconds on a 3 GHz Pentium-4 machine with 1G of RAM. This is because the search space is limited to operations in the DFG with the same height; thus, fewer than 20 operations are generally considered at a time.... ..."

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### Table 1. The embedded graph invariant

"... In PAGE 2: ... In the process, simple formulae, such as the de nition (1), become apparent, and the properties and examples can be developed rapidly. Table1 gives some examples of the evaluation of the invariant for 4-valent graphs and links.... ..."

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### Table 2: Distance matrix between 5 major US cities.

2006

"... In PAGE 6: ... The goal is to map the high dimensional graph structure onto a lower dimensional euclidean space while approximately preserving distances.7 Figure 2 shows an embedding of the distances between 5 US cities (see Table2 ) in 2 dimensions. The euclidean coordinates resulting from an embedding can directly be used as the dis- tance labels for the respective nodes and outliers are likely to be a minor problem in this approach, since a large amount of other paths can compensate for a single short edge.... In PAGE 7: ...(1464/561) (-1227/1014) (-1199/-307) (1697/132) Chicago LosAngeles Miami NewYork SanFrancisco Figure 2: A 2-dimensional embedding of the (complete) graph resulting from the distance matrix given in Table2 . The embedding only defines the relative positions among the nodes but not the direction of the coordinate axes.... ..."

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### TABLE I DISTANCE ESTIMATION STEPS OF ISOMAP/C-ISOMAP ALGORITHMS TO RECONSTRUCT EUCLIDEAN DISTANCES BETWEEN a0a2a1 ON THE EMBEDDING PARAMETERIZATION SPACE FROM POINTS a3a4a1 OVER THE

2004

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### Table 1. Average interpixel distances within and between the different dyes calculated in the embedded space.

"... In PAGE 5: ... 1, respectively. In Table1 , the average interpixel distances in the embedded space were calculated between all combination of dyes and within the five dyes. The results show a low average interpixel distance within a dye while this distance increases significantly across the different dyes, suggesting that the constituents are well separated.... In PAGE 5: ... 2(b) shows the histogram of the interpixel distances within the Rhodamine dye and between the Rhodamine and the DASPI-II dyes. Although the average interpixel distance between the two dyes correspond to the lowest amongst all dyes combinations in Table1 , the graph shows that the two constituents are clearly separated by using the proposed FR-IsoMap method. Table 1.... ..."

### Table 2. Embedding public watermark to real life graph and randomized graph

2001

"... In PAGE 14: ...html) and the DIMACS on-line challenge graph. Table2 shows the number of vertices in each graph (vert. column), the opti- mal solutions (opt.... ..."

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