### 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 5.5: Dense cubic graphs

### Table 5.5: Dense cubic graphs

### 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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### Table 2. Results of Our u(t) Derivation Method For Demonstrations 1 and 3 of the Spindle-Assembly Task

"... In PAGE 17: ... However, in this paper, we show only a subset of the results presented there. We show (in Table2 ) the results of deriving uij for the uij existing in demonstration1andsegmentsofdemonstrations2and5.Note that we have selected for presentation in Table 2 a subset of results from these experiments that will allow us to draw out, in a more compact discussion, all the important conclusions identified for the method in Chen (2001).... In PAGE 17: ... We show (in Table 2) the results of deriving uij for the uij existing in demonstration1andsegmentsofdemonstrations2and5.Note that we have selected for presentation in Table2 a subset of results from these experiments that will allow us to draw out, in a more compact discussion, all the important conclusions identified for the method in Chen (2001). Table 2 presents the experimental results in five columns.... In PAGE 17: ...Note that we have selected for presentation in Table 2 a subset of results from these experiments that will allow us to draw out, in a more compact discussion, all the important conclusions identified for the method in Chen (2001). Table2 presents the experimental results in five columns. Column 1 shows the uij for which the result was obtained.... In PAGE 18: ...aths in these states, i.e., u4,1, u7,1, u9,1, u1,2, etc., have each had noise successfully removed. In contrast, Table2 shows 5.... In PAGE 18: ... Otherwise, the method will revert to using the original demonstrated path, even if it contained noise. The second important question regarding each uij shown in Table2... In PAGE 19: ... Remember that our method derives uij that are likely obstacle- free. We show in column 6 of Table2 the result for each uij in this regard. A key finding in these experiments was that each uij did in fact define an obstacle-free path.... In PAGE 19: ... A key finding in these experiments was that each uij did in fact define an obstacle-free path. We have seen that three distinct types of uij exist in Table2 . First, uij derived where no noise existed.... In PAGE 19: ... Then for this type of uij, if the demonstrated path on which a uij is based does contain noise, the good coverage of points of the C-surface means that an alternate, noise-free path for uij will most likely be found. The third and final type of uij in Table2 is those where noise existed but was not removed. We noted how our method reverted to using the underlying demonstrated path for this type of uij.... ..."

### TABLE 4 Radius of connected cubic graphs on 14 vertices

### TABLE 1. Counts of cubic graphs with additional properties. The percentages show Kotzig graphs among the hamiltonian graphs.

### Table 1. Common graph embedding view for the most popular dimensionality reduction algorithms. Note that type D means direct graph embedding, while L and K mean the linearization and kernelization of the graph embedding, respectively.

2005

"... In PAGE 4: ... (2-4). Table1 lists the similarity and constraint matrices for all above mentioned methods. And their corresponding graph embedding types are also demonstrated.... In PAGE 4: ... From Eq. (6) and (7), we can easily have the listed formulations of the similarity matrix W and constraint matrix B for PCA/KPCA and LDA/KDA as listed in Table1 . Figure 2 plots the intrinsic graphs for PCA and LDA, respectively.... ..."

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### Table 2. Percentage of area where the 2D component is line- of-sight, obstructed line-of-sight and blocked for Bristol and Lillehammer

"... In PAGE 2: ... Surface map from the undulating rural terrain There are distinct differences in the terrain statistics between the two areas. Table2 shows the percentage of the coverage area where the 2D component is in line-of-sight, obstructed line-of-sight and blocked, respectively. Two base station antenna heights are used; 20 m (high) and 10 m (low).... ..."