### Table 6 shows timings for the solution of the three-dimensional problem

"... In PAGE 22: ...6 14.3 Table6 : Solution times (in seconds) and speedups for the restricted weakly overlap- ping algorithm on the three-dimensional problem (58) (taken from [40]). equations based upon a geometric decomposition of the problem.... ..."

### Table 6 shows timings for the solution of the three-dimensional problem

"... In PAGE 22: ...6 14.3 Table6 : Solution times (in seconds) and speedups for the restricted weakly overlap- ping algorithm on the three-dimensional problem (58) (taken from [40]). equations based upon a geometric decomposition of the problem.... ..."

### Table 1: An example of a three-dimensional table.

1993

"... In PAGE 3: ...Table1 has three categories, D1, D2 and D3; thus, it is a three-dimensional table. The logical relationship among the data items of a table is the association between labels and entries.... In PAGE 3: ... Each entry is associated with one or more sets of labels of di erent categories simultaneously. For example, in Table1 , entry e1 is associated with a set of labels fd11; d21; d311g simultaneously; entry e7 is associated with both fd12; d21; d312g and fd12; d22; d312g simultaneously. The data items and the logical relationship among them provide the logical structure of the table, which is the primary information that a table conveys and which is independent of its format.... In PAGE 6: ... This function guarantees that every entry in E is mapped from at least one ff1; ; fng 2 D1 n. Using this model, Table1 can be abstracted by (3; fD1; D2; D3g; E; ), where D1 = fd11; d12g D2 = fd21; d22; d23g D3 = fd31; d32g d31 = fd311; d312g d11 = d12 = d21 = d22 = d23 = d32 = d311 = d312 = fg E = fe1; e2; e3; e4; e5; e6; e7; e8; e9g (fD1:d11; D2:d21; D3:d31:d311g) = e1; (fD1:d11; D2:d21; D3:d31:d312g) = e2; (fD1:d11; D2:d22; D3:d31:d311g) = e3; (fD1:d11; D2:d22; D3:d31:d312g) = e3; (fD1:d11; D2:d23; D3:d31:d311g) = e4; (fD1:d11; D2:d21; D3:d32g) = e5; (fD1:d11; D2:d22; D3:d32g) = e5; (fD1:d11; D2:d23; D3:d32g) = e5; (fD1:d12; D2:d21; D3:d31:d311g) = e6; (fD1:d12; D2:d21; D3:d31:d312g) = e7; (fD1:d12; D2:d22; D3:d31:d312g) = e7; (fD1:d12; D2:d23; D3:d31:d312g) = e8; (fD1:d12; D2:d21; D3:d32g) = e9; (fD1:d12; D2:d22; D3:d32g) = e9; (fD1:d12; D2:d23; D3:d32g) = e9; 4.2 Basic operators in the tabular model We rst describe the syntax of all basic operators in function form by giving the operator identi ers and the types of their operands and results.... ..."

Cited by 2

### Table 6 and Table 7 show how many test set instance mis-classifications fall into the various distance-to-cluster-center intervals. Figure 3 visualizes misclassifications for a Breast Cancer test data set using a recent visualization technique [10]. This technique places the cluster centers in three-dimensional space so that similar clusters are adjacent and different clusters far apart. This involves mapping the distances between the cluster centers that occur in the original higher-dimensional instance space into the lower three dimensional space. The instances are then placed amongst the cluster centers to reflect their distance to the cluster centers.

"... In PAGE 6: ...76-100% of Closest Observations 68 73 64 35 35 32 25 Table6 . The percentage of all instance misclassifications occurring in a distance-to-cluster-... In PAGE 8: ...table learners. Regardless of the stability of the learner, MSE is reduced. Finally, we investigated if misclassified instances more likely to be outliers with respect to the clustering scheme. Table6 and Table 7 shows that when the segmentation scheme yields a SEGMENTATION ACCURACY greater than the BASE ACCURACY, overwhelmingly the misclassifications are outliers. Figure 3 shows that the misclassified instances are located on the outer edges of the clusters.... ..."

Cited by 1

### Table 1: Three-dimensional input data in which each sample vector x consists of the RGB (red-green-blue) values of the color shown in the rightmost column.

1997

"... In PAGE 15: ...ransformation (Kohonen et al., 1984; Kohonen, 1988). 2.1 The Self-Organizing Map algorithm Assume that some sample data sets (such as in Table1 4) have to be mapped onto the array depicted in Figure 1; the set of input samples is described by a real vector x(t) 2 Rn where t is the index of the sample, or the discrete-time coordinate. Each node i in the map contains a model vector mi(t) 2 Rn, which has the same number of elements as the input vector x(t).... In PAGE 17: ... Each map node, visualized as a circle on the grid, serves as a model, mi, or to use another term, a prototype of a class of similar inputs. The line diagrams inside the circles denote the three RGB values of Table1 . For instance, the nodes on the lower left corner correspond to colors which have high values of all the components, i.... In PAGE 18: ... Each circle corresponds to a map node. Inside the circle the model vector consisting of the three RGB values from Table1 is visualized. The initial value of the learning step size, alpha0, was 0:2 and the neighborhood width was initially 5.... In PAGE 20: ...green-yellow pale green pale- goldenrod antique-white papaya-whip linen old lacebeige floral white khaki light- goldenrod moccasinwheat mint creamalice blue ghost whitewhite dark- sea green dark khaki burlywoodtan light pinkpink thistle lavender dark salmon rosy brown plum light blue pale turquoisepowder blue dark orange goldenrod coral sandy brown light coral hot pink orchid violet sky blue salmon pale- violet red medium-orchid medium-purple chocolatedark- goldenrod indian red medium- violet red violet red dark orchiddark violet purple blue violet maroon slate blue olive drab sienna brown firebrick slate gray steel blue cornflower- blue royal blue dark olive-green dark slate-blue cadet blue medium sea-green forest greenlime green dark green black midnight-blue navy blue light sea-green medium- turquoise turquoisedark- turquoise Figure 3: A map of colors based on their RGB values. The color symbols in the rightmost column of Table1 as used in labeling the map. The best matching unit is searched for each input sample and that node is labeled accordingly.... In PAGE 25: ... When all di erent word forms in the input material are listed, a code vector can be de ned to have as many components as there are word forms in the list. As an example related to Table1 shown earlier, the color symbols of Table 2 are here replaced by binary numbers that encode them. One vector element (column in the table) corresponds to one unique color symbol.... ..."

Cited by 25

### Table 4: Three dimensional table of B4CPBN CQB5 for stripline structures.

"... In PAGE 12: ...2 Effective Coupling Model Based on those studies on micro-stripline and stripline structures, we proposed formula (2) to model the coupling coefficient CZCXCY between two wires CX and CY: CZCXCY BP CTA0CPD7CQ (2) where D7 is the pitch spacing between wire CX and wire CY, and CP and CQ are constants depending on the wire width2 and P/G plane distance BW. A two-dimension table for CP and CQ (see an example in Table 3) can be built for micro-stripline structure, and a three-dimension table for CP and CQ (see an example in Table4 ) can be built for stripline structure. We call (2) as CZCTCUCU model for micro-stripline and stripline structures.... ..."

### Table 4: Three dimensional table of B4CPBN CQB5 for stripline structures.

"... In PAGE 12: ...2 Effective Coupling Model Based on those studies on micro-stripline and stripline structures, we proposed formula (2) to model the coupling coefficient CZCXCY between two wires CX and CY: CZCXCY BP CTA0CPD7CQ (2) where D7 is the pitch spacing between wire CX and wire CY, and CP and CQ are constants depending on the wire width2 and P/G plane distance BW. A two-dimension table for CP and CQ (see an example in Table 3) can be built for micro-stripline structure, and a three-dimension table for CP and CQ (see an example in Table4 ) can be built for stripline structure. We call (2) as CZCTCUCU model for micro-stripline and stripline structures.... ..."

### Table 4.5 Average farthest distance of the neighbors of all the points, for three-dimensional curves.

### Table 6.2 Performance of Algencan, Ipopt and Lancelot in the three-dimensional Bratu-based optimization problem.

2005

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