### Table 7: Performance indices for the training and the test phase in example 5.2

"... In PAGE 18: ... Through a random sampling of the state space a data set with 7500 different example is generated, being NT = 5000 and NE = 2500. Table7 shows the performance indices obtained during the training and the test phase, together with the number of rules generated. The HC procedure trained for the operating system state y = 1 produces 21 minimal paths, ... ..."

### Table 4: System Function generated by HC for example 5.1: every logical product corresponds to a minimum path

### Table 1 Maximum errors and the estimated order of convergence rate for the fourth-order compact scheme Test problems Re

"... In PAGE 17: ... The accuracy data are given in Table 1 which also contains the estimated order of convergence as computed by ln je32j=je64j =ln 2; where je32j and je64j are the maximum errors associated with h 1=32 and h 1=64, respectively. It is clear from Table1 that our finite diC128erence scheme yields a fourth-order convergence rate for small to moderate Reynolds numbers though there is a slight degradation in the rates of con- vergence as Re is increased. We still obtain convergence rates of order O h3 or better and expect that fourth-order convergence would be present when the grid size h is further refined.... ..."

### Table 3: A set of 12 points whose convex hull is not castable.

"... In PAGE 31: ...Table 3: A set of 12 points whose convex hull is not castable. According to an exhaustive checking of all possible planes through three vertices, the convex hull of the set of points given in Table3 is not castable. The points were generated at random, near the surface of a sphere.... ..."

### Table 1: Summary of results for 1000 points 6 Analysis of Results on Matchings One of the most striking results in our experimental work is the fact that the maximum cardinality matching gave perfect, or near perfect, matchings in all the cases. While this is not surprising for serpentine triangulations (whose duals admit a hamiltonian path, as pointed our earlier), it is unexpected for the Delaunay and HVP-triangulations. However, we are able to explain this phenomenon. We show that the number of leftover triangles in a maximum cardinality matching of the dual graph of any triangulation of a point set depends only on the number of convex hull vertices. For randomly generated point sets in a disc or square, this number is relatively small [13]. In fact, the number of unmatched nodes in a maximum cardinality matching of the dual graph of a triangulation of a point set cannot exceed a third of the number of convex hull vertices. We prove this bound below.

"... In PAGE 14: ... The experiments conducted support this intuition. As the data in Table1 clearly shows, Delaunay triangulations consistently give the best results in terms of element quality. In particular, the maximum weighted matching algorithm run on the Delaunay triangulation dual has the best overall output with 99% of the triangles matched, 98% of the resulting quadrangles convex, mean maximum angle of 2.... ..."

### Table 1: Size of Maximum Maximum Range of

"... In PAGE 3: ...Maximum Maximum Range of Family n Family Correlation Linear Span Imbalance Gold 2m + 1 2n + 1 1 + 2n+12 2n [1; 2n+12 + 1] Gold 4m + 2 2n ? 1 1 + 2n+22 2n [1; 2n+22 + 1] Kasami 2m 2n2 1 + 2n2 3n 2 [1; 2n2 + 1] (Small Set) Kasami 4m + 2 2n2 (2n + 1) 1 + 2n+22 5n 2 [1; 2n+22 + 1] (Large Set) Bent 4m 2n2 1 + 2n2 n=2 n=4 2n4 1 No 2m 2n2 1 + 2n2 m(2m ? 1) [1; 2n2 + 1] TN 2km 2n2 1 + 2n2 gt; 3mk(3k ? 1)m?2 [1; 2n2 + 1] Table1 : Comparison of Properties of Families of Sequences of Period 2n ? 1 For simplicity we write q = 2m. By a d-form we mean a homogeneous function of degree d.... In PAGE 21: ... Table1 : Comparison of Properties of Families of Sequences of Period 2n ? 1... ..."

### Table 1: Initialization times and relevant plane set sizes, for di erent sized polyhedra. Our rst experiment was designed to analyze the per- formance characteristics of the algorithm presented in Sec- tion 3. The scene consists of two polyhedra of equal size generated by choosing points on the surface of a sphere of unit radius and computing the convex hull of these points. The observer moves in a circle of xed radius around the two polyhedra. Table 1 reports the number of relevant planes

### Table 3: HITEC + GA-COMPACT with Removal of Un- necessary Vectors

1996

"... In PAGE 6: ... Experiments were carried out to determine if remov- ing unnecessary vectors at the beginning and end of a partially-speci ed test sequence before the GA is in- voked is e ective in reducing the test set size. Results are shown in Table3 for a GA having a population size of 32 and 8 generations. Test set sizes are shown in bold if they are smaller than those for any of the previ- ous experiments and the fault coverage is at or near the maximum value obtained.... ..."

Cited by 12

### Table 5: The number of clusters and the maximum cluster size at di erent minimum support levels on four data sets

2005

"... In PAGE 10: ... Our rst step is to merge frequent itemsets into disjoint clusters. Table5 shows the number of frequent itemsets, the number of disjoint clusters, the average cluster size, and the maximum cluster size by varying support values on each data set. We observe that the items are grouped into a reasonable number of disjoint clusters for all four data sets.... ..."

Cited by 1

### Table 1: Grammar compaction statistics

2000

"... In PAGE 5: ...0 Table 2: Occurrences of tree sets in test sentences Before parsing, the trees in each tree set are stripped of their anchor, merged into a single automaton and minimized; at parse time the relevant automaton is retrieved and the appropriate anchoring lexical item inserted. Table1 shows what happens when the tree sets are converted into automata and minimized, giving figures for the distribution of tree sets, mean numbers of merged and minimized states in each tree set, and ratios of numbers of merged and minimized states. What is not clear from Table 1 is how often each of the a1 a7 a1 distinct tree sets occurred in the test sentences.... In PAGE 5: ... Table 1 shows what happens when the tree sets are converted into automata and minimized, giving figures for the distribution of tree sets, mean numbers of merged and minimized states in each tree set, and ratios of numbers of merged and minimized states. What is not clear from Table1 is how often each of the a1 a7 a1 distinct tree sets occurred in the test sentences. This is shown in Table 2 which gives the numbers and mean sizes of tree sets (number of trees and minimized states) relative to the number of times they occurred in the test suite sentences.... ..."

Cited by 4