### Table 2: Characteristic expressions for all possible types of color comparisons involv- ing vertices of weight at most 3 in the four-color plurality problem. The four colors are called cyan (C), magenta (M), yellow (Y), and black (K).

2006

"... In PAGE 16: ... We begin with a case by case examination of the characteristic expressions for color comparisons involving vertices with weights at most 3. These expressions are given in Table2 . Then, by counting the number of vertices of weights 0, 1, and 2 we obtain W0 = n 7 4N00 N01 N02 N03 W1 = 3 2N00 + 1 4N01 + 3 4N02 + 3 4N03 5 3N11 4 3N110 N12 1 2N120 N13 W2 = 1 2N01 1 4N02 + 4 3N11 + 10 9 N110 + 1 3N12 + 2 3N13 3 2N22 N220 N23: Using Theorem 1, W0, W1 and W2 are all O(pn).... ..."

### Table 3. Four-coloring the United States. In all trials, the maximum number of generations = 15.

2001

"... In PAGE 13: ...8, which implies that on average 116 partitions were encountered before chanc- ing upon a correct one. Table3 summarizes these results, and also the results when we reduced population size to a mere 10. Then a correct coloring was discovered on 25 of the 30 trials.... In PAGE 13: ... On 30 trials, each having an initial population of 1000 random permuta- tions, they report a correct coloring appearing already in the initial population! The greedy decoding of Jones and Beltramo has a similarity to our heuristic detailed above for distrib- uting no-show elements in the map coloring arena. Their result of finding a correct color- ing within 1000 individuals is not inconsistent with our results in Table3 , where for population size set at 20, we consistently find a correct coloring after encountering an average of 116 individuals. Table 3.... ..."

Cited by 4

### Table 4. Four-coloring the US with equi-sized color sets. In all trials, the maximum number of generations = 50.

2001

"... In PAGE 16: ... Figure 6 shows such a coloring. Also, Table4 summarizes the results just reported. That table also shows that decreasing the population size did not have disastrous Table 4.... ..."

Cited by 4

### Table IV . Spectral reconstruction of the targets with 55 patches using a Epson Photo Stylus 1200 printer with four colors (CMYK). The spectral reflectance of the patches were estimated using six channels of IBM PRO/3000 digital camera signals (obtained combined the trichromatic signal without filtering and with light-blue Kodak Wratten absorption filter). Six eigenvectors from the target were used in the spectral estimation. It corresponds to the diagram of Figure 8. Results

### Table 2 Relative error (Delta E CMC)over time for four colors.

### TABLE 5.5 Computational convergence factors, e, of one 3-D V(1,0)-cycle with (x,y)-plane zebra Gauss-Seidel (ZGS), and (x,y)-plane four-color Gauss-Seidel (4cGS).

Cited by 6

### Table 2 Basis for proof of Theorem 1.

in Logical

"... In PAGE 7: ... PH20850. Proof The proof of the theorem relies on the following reversible equivalent, inverse of every atomic statement, and constructor of pGCL; they are listed in Table2 , where v:D for some data type D, b:H11922 (H11922 :H11005 {F, T}) is a Boolean variable, and c is a predicate. The variable declaration var is not included because it does not contain any code.... ..."

### Table 1: Proof of Theorem 3.8.

1997

"... In PAGE 41: ... We make each group into a lemma, and we have to prove the lemmas in a certain order. Table1 describes the organization... ..."

Cited by 3

### Table 1: Proof of Theorem 3.8.

1997

"... In PAGE 25: ... We make each group into a lemma, and we have to prove the lemmas in a certain order. Table1 describes the organization... ..."

Cited by 1

### Table 1: Proof of Theorem 3.1.

"... In PAGE 4: ...onvergence #28Lemma 3.1#29. The middle steps of the proof use properties of the type of clustering computed. The sequence of steps is shown in Table1 . The rows of the table correspond to the sample and true cost and the columns correspond to the di#0Berent clusterings.... In PAGE 4: ... We apply uniform convergence #28Lemma 3.1#29 to the two clusterings ^ d s and d X to obtain that the values #281#29 and #282#29 as well as the values #285#29 and #286#29 in Table1 are close. Observe that the sample cost of ^ d S is within a factor of #0B of d s since we ran an #0B-approximation algorithm on the sample S, hence the inequalitybetween #282#29 and #283#29 in Table 1.... ..."